xref: /petsc/src/ts/impls/arkimex/arkimex.c (revision 3a2a065f407e7da3bb6fc7eaf619dbab56034fde)
18a381b04SJed Brown /*
2d27334e2SStefano Zampini   Code for timestepping with additive Runge-Kutta IMEX method or Diagonally Implicit Runge-Kutta methods.
38a381b04SJed Brown 
48a381b04SJed Brown   Notes:
5d27334e2SStefano Zampini   For ARK, the general system is written as
68a381b04SJed Brown 
7f9c1d6abSBarry Smith   F(t,U,Udot) = G(t,U)
88a381b04SJed Brown 
98a381b04SJed Brown   where F represents the stiff part of the physics and G represents the non-stiff part.
108a381b04SJed Brown 
118a381b04SJed Brown */
12af0996ceSBarry Smith #include <petsc/private/tsimpl.h> /*I   "petscts.h"   I*/
131e25c274SJed Brown #include <petscdm.h>
14*3a2a065fSHong Zhang #include <../src/ts/impls/arkimex/arkimex.h>
15*3a2a065fSHong Zhang #include <../src/ts/impls/arkimex/fsarkimex.h>
168a381b04SJed Brown 
17*3a2a065fSHong Zhang static ARKTableauLink ARKTableauList;
1819fd82e9SBarry Smith static TSARKIMEXType  TSARKIMEXDefault = TSARKIMEX3;
193405e92cSStefano Zampini static TSDIRKType     TSDIRKDefault    = TSDIRKES213SAL;
208a381b04SJed Brown static PetscBool      TSARKIMEXRegisterAllCalled;
218a381b04SJed Brown static PetscBool      TSARKIMEXPackageInitialized;
2256dcabbaSDebojyoti Ghosh static PetscErrorCode TSExtrapolate_ARKIMEX(TS, PetscReal, Vec);
238a381b04SJed Brown 
241f80e275SEmil Constantinescu /*MC
251d27aa22SBarry Smith      TSARKIMEXARS122 - Second order ARK IMEX scheme, {cite}`ascher_1997`
268a381b04SJed Brown 
271f80e275SEmil Constantinescu      This method has one explicit stage and one implicit stage.
281f80e275SEmil Constantinescu 
29bcf0153eSBarry Smith      Options Database Key:
3067b8a455SSatish Balay .      -ts_arkimex_type ars122 - set arkimex type to ars122
319bd3e852SBarry Smith 
32bcf0153eSBarry Smith      Level: advanced
33bcf0153eSBarry Smith 
341cc06b55SBarry Smith .seealso: [](ch_ts), `TSARKIMEX`, `TSARKIMEXType`, `TSARKIMEXSetType()`
351f80e275SEmil Constantinescu M*/
36d27334e2SStefano Zampini 
371f80e275SEmil Constantinescu /*MC
381f80e275SEmil Constantinescu      TSARKIMEXA2 - Second order ARK IMEX scheme with A-stable implicit part.
391f80e275SEmil Constantinescu 
401f80e275SEmil Constantinescu      This method has an explicit stage and one implicit stage, and has an A-stable implicit scheme. This method was provided by Emil Constantinescu.
411f80e275SEmil Constantinescu 
42bcf0153eSBarry Smith      Options Database Key:
4367b8a455SSatish Balay .      -ts_arkimex_type a2 - set arkimex type to a2
449bd3e852SBarry Smith 
451f80e275SEmil Constantinescu      Level: advanced
461f80e275SEmil Constantinescu 
471cc06b55SBarry Smith .seealso: [](ch_ts), `TSARKIMEX`, `TSARKIMEXType`, `TSARKIMEXSetType()`
481f80e275SEmil Constantinescu M*/
49d27334e2SStefano Zampini 
501f80e275SEmil Constantinescu /*MC
511d27aa22SBarry Smith      TSARKIMEXL2 - Second order ARK IMEX scheme with L-stable implicit part, {cite}`pareschi_2005`
521f80e275SEmil Constantinescu 
531f80e275SEmil Constantinescu      This method has two implicit stages, and L-stable implicit scheme.
541f80e275SEmil Constantinescu 
55bcf0153eSBarry Smith      Options Database Key:
5667b8a455SSatish Balay .      -ts_arkimex_type l2 - set arkimex type to l2
579bd3e852SBarry Smith 
58bcf0153eSBarry Smith      Level: advanced
59bcf0153eSBarry Smith 
601cc06b55SBarry Smith .seealso: [](ch_ts), `TSARKIMEX`, `TSARKIMEXType`, `TSARKIMEXSetType()`
611f80e275SEmil Constantinescu M*/
62d27334e2SStefano Zampini 
631f80e275SEmil Constantinescu /*MC
64c79dcfbdSBarry Smith      TSARKIMEX1BEE - First order backward Euler represented as an ARK IMEX scheme with extrapolation as error estimator. This is a 3-stage method.
65e817cc15SEmil Constantinescu 
66e817cc15SEmil Constantinescu      This method is aimed at starting the integration of implicit DAEs when explicit first-stage ARK methods are used.
67e817cc15SEmil Constantinescu 
68bcf0153eSBarry Smith      Options Database Key:
6967b8a455SSatish Balay .      -ts_arkimex_type 1bee - set arkimex type to 1bee
709bd3e852SBarry Smith 
71e817cc15SEmil Constantinescu      Level: advanced
72e817cc15SEmil Constantinescu 
731cc06b55SBarry Smith .seealso: [](ch_ts), `TSARKIMEX`, `TSARKIMEXType`, `TSARKIMEXSetType()`
74e817cc15SEmil Constantinescu M*/
75d27334e2SStefano Zampini 
76e817cc15SEmil Constantinescu /*MC
771f80e275SEmil Constantinescu      TSARKIMEX2C - Second order ARK IMEX scheme with L-stable implicit part.
781f80e275SEmil Constantinescu 
791f80e275SEmil Constantinescu      This method has one explicit stage and two implicit stages. The implicit part is the same as in TSARKIMEX2D and TSARKIMEX2E, but the explicit part has a larger stability region on the negative real axis. This method was provided by Emil Constantinescu.
801f80e275SEmil Constantinescu 
81bcf0153eSBarry Smith      Options Database Key:
8267b8a455SSatish Balay .      -ts_arkimex_type 2c - set arkimex type to 2c
839bd3e852SBarry Smith 
841f80e275SEmil Constantinescu      Level: advanced
851f80e275SEmil Constantinescu 
861cc06b55SBarry Smith .seealso: [](ch_ts), `TSARKIMEX`, `TSARKIMEXType`, `TSARKIMEXSetType()`
871f80e275SEmil Constantinescu M*/
88d27334e2SStefano Zampini 
8964f491ddSJed Brown /*MC
9064f491ddSJed Brown      TSARKIMEX2D - Second order ARK IMEX scheme with L-stable implicit part.
9164f491ddSJed Brown 
92da81f932SPierre Jolivet      This method has one explicit stage and two implicit stages. The stability function is independent of the explicit part in the infinity limit of the implicit component. This method was provided by Emil Constantinescu.
9364f491ddSJed Brown 
94bcf0153eSBarry Smith      Options Database Key:
9567b8a455SSatish Balay .      -ts_arkimex_type 2d - set arkimex type to 2d
969bd3e852SBarry Smith 
97b330ce4dSSatish Balay      Level: advanced
98b330ce4dSSatish Balay 
991cc06b55SBarry Smith .seealso: [](ch_ts), `TSARKIMEX`, `TSARKIMEXType`, `TSARKIMEXSetType()`
10064f491ddSJed Brown M*/
101d27334e2SStefano Zampini 
10264f491ddSJed Brown /*MC
10364f491ddSJed Brown      TSARKIMEX2E - Second order ARK IMEX scheme with L-stable implicit part.
10464f491ddSJed Brown 
10515229ffcSPierre Jolivet      This method has one explicit stage and two implicit stages. It is an optimal method developed by Emil Constantinescu.
10664f491ddSJed Brown 
107bcf0153eSBarry Smith      Options Database Key:
10867b8a455SSatish Balay .      -ts_arkimex_type 2e - set arkimex type to 2e
1099bd3e852SBarry Smith 
110b330ce4dSSatish Balay     Level: advanced
111b330ce4dSSatish Balay 
1121cc06b55SBarry Smith .seealso: [](ch_ts), `TSARKIMEX`, `TSARKIMEXType`, `TSARKIMEXSetType()`
11364f491ddSJed Brown M*/
114d27334e2SStefano Zampini 
11564f491ddSJed Brown /*MC
1161d27aa22SBarry Smith      TSARKIMEXPRSSP2 - Second order SSP ARK IMEX scheme, {cite}`pareschi_2005`
1176cf0794eSJed Brown 
1186cf0794eSJed Brown      This method has three implicit stages.
1196cf0794eSJed Brown 
1201d27aa22SBarry Smith      This method is referred to as SSP2-(3,3,2) in <https://arxiv.org/abs/1110.4375>
1216cf0794eSJed Brown 
122bcf0153eSBarry Smith      Options Database Key:
12367b8a455SSatish Balay .      -ts_arkimex_type prssp2 - set arkimex type to prssp2
1249bd3e852SBarry Smith 
1256cf0794eSJed Brown      Level: advanced
1266cf0794eSJed Brown 
1271cc06b55SBarry Smith .seealso: [](ch_ts), `TSARKIMEX`, `TSARKIMEXType`, `TSARKIMEXSetType()`
1286cf0794eSJed Brown M*/
129d27334e2SStefano Zampini 
1306cf0794eSJed Brown /*MC
1311d27aa22SBarry Smith      TSARKIMEX3 - Third order ARK IMEX scheme with L-stable implicit part, {cite}`kennedy_2003`
13264f491ddSJed Brown 
13364f491ddSJed Brown      This method has one explicit stage and three implicit stages.
13464f491ddSJed Brown 
135bcf0153eSBarry Smith      Options Database Key:
13667b8a455SSatish Balay .      -ts_arkimex_type 3 - set arkimex type to 3
1379bd3e852SBarry Smith 
138bcf0153eSBarry Smith      Level: advanced
139bcf0153eSBarry Smith 
1401cc06b55SBarry Smith .seealso: [](ch_ts), `TSARKIMEX`, `TSARKIMEXType`, `TSARKIMEXSetType()`
14164f491ddSJed Brown M*/
142d27334e2SStefano Zampini 
14364f491ddSJed Brown /*MC
1441d27aa22SBarry Smith      TSARKIMEXARS443 - Third order ARK IMEX scheme, {cite}`ascher_1997`
1456cf0794eSJed Brown 
1466cf0794eSJed Brown      This method has one explicit stage and four implicit stages.
1476cf0794eSJed Brown 
148bcf0153eSBarry Smith      Options Database Key:
14967b8a455SSatish Balay .      -ts_arkimex_type ars443 - set arkimex type to ars443
1509bd3e852SBarry Smith 
151bcf0153eSBarry Smith      Level: advanced
152bcf0153eSBarry Smith 
1531d27aa22SBarry Smith      Notes:
1541d27aa22SBarry Smith      This method is referred to as ARS(4,4,3) in <https://arxiv.org/abs/1110.4375>
1556cf0794eSJed Brown 
1561cc06b55SBarry Smith .seealso: [](ch_ts), `TSARKIMEX`, `TSARKIMEXType`, `TSARKIMEXSetType()`
1576cf0794eSJed Brown M*/
158d27334e2SStefano Zampini 
1596cf0794eSJed Brown /*MC
1601d27aa22SBarry Smith      TSARKIMEXBPR3 - Third order ARK IMEX scheme. Referred to as ARK3 in <https://arxiv.org/abs/1110.4375>
1616cf0794eSJed Brown 
1626cf0794eSJed Brown      This method has one explicit stage and four implicit stages.
1636cf0794eSJed Brown 
164bcf0153eSBarry Smith      Options Database Key:
16567b8a455SSatish Balay .      -ts_arkimex_type bpr3 - set arkimex type to bpr3
1669bd3e852SBarry Smith 
167bcf0153eSBarry Smith      Level: advanced
168bcf0153eSBarry Smith 
1691cc06b55SBarry Smith .seealso: [](ch_ts), `TSARKIMEX`, `TSARKIMEXType`, `TSARKIMEXSetType()`
1706cf0794eSJed Brown M*/
171d27334e2SStefano Zampini 
1726cf0794eSJed Brown /*MC
1731d27aa22SBarry Smith      TSARKIMEX4 - Fourth order ARK IMEX scheme with L-stable implicit part, {cite}`kennedy_2003`.
17464f491ddSJed Brown 
17564f491ddSJed Brown      This method has one explicit stage and four implicit stages.
17664f491ddSJed Brown 
177bcf0153eSBarry Smith      Options Database Key:
17867b8a455SSatish Balay .      -ts_arkimex_type 4 - set arkimex type to4
1799bd3e852SBarry Smith 
180bcf0153eSBarry Smith      Level: advanced
181bcf0153eSBarry Smith 
1821cc06b55SBarry Smith .seealso: [](ch_ts), `TSARKIMEX`, `TSARKIMEXType`, `TSARKIMEXSetType()`
18364f491ddSJed Brown M*/
184d27334e2SStefano Zampini 
18564f491ddSJed Brown /*MC
1861d27aa22SBarry Smith      TSARKIMEX5 - Fifth order ARK IMEX scheme with L-stable implicit part, {cite}`kennedy_2003`.
18764f491ddSJed Brown 
18864f491ddSJed Brown      This method has one explicit stage and five implicit stages.
18964f491ddSJed Brown 
190bcf0153eSBarry Smith      Options Database Key:
19167b8a455SSatish Balay .      -ts_arkimex_type 5 - set arkimex type to 5
1929bd3e852SBarry Smith 
193bcf0153eSBarry Smith      Level: advanced
194bcf0153eSBarry Smith 
1951cc06b55SBarry Smith .seealso: [](ch_ts), `TSARKIMEX`, `TSARKIMEXType`, `TSARKIMEXSetType()`
19664f491ddSJed Brown M*/
19764f491ddSJed Brown 
1983405e92cSStefano Zampini /*MC
1993405e92cSStefano Zampini      TSDIRKS212 - Second order DIRK scheme.
2003405e92cSStefano Zampini 
2013405e92cSStefano Zampini      This method has two implicit stages with an embedded method of other 1.
2023405e92cSStefano Zampini      See `TSDIRK` for additional details.
2033405e92cSStefano Zampini 
2043405e92cSStefano Zampini      Options Database Key:
2053405e92cSStefano Zampini .      -ts_dirk_type s212 - select this method.
2063405e92cSStefano Zampini 
2073405e92cSStefano Zampini      Level: advanced
2083405e92cSStefano Zampini 
2093405e92cSStefano Zampini      Note:
2103405e92cSStefano Zampini      This is the default DIRK scheme in SUNDIALS.
2113405e92cSStefano Zampini 
2123405e92cSStefano Zampini .seealso: [](ch_ts), `TSDIRK`, `TSDIRKType`, `TSDIRKSetType()`
2133405e92cSStefano Zampini M*/
2143405e92cSStefano Zampini 
2153405e92cSStefano Zampini /*MC
2161d27aa22SBarry Smith      TSDIRKES122SAL - First order DIRK scheme <https://arxiv.org/abs/1803.01613>
2173405e92cSStefano Zampini 
2183405e92cSStefano Zampini      Uses backward Euler as advancing method and trapezoidal rule as embedded method. See `TSDIRK` for additional details.
2193405e92cSStefano Zampini 
2203405e92cSStefano Zampini      Options Database Key:
2213405e92cSStefano Zampini .      -ts_dirk_type es122sal - select this method.
2223405e92cSStefano Zampini 
2233405e92cSStefano Zampini      Level: advanced
2243405e92cSStefano Zampini 
2253405e92cSStefano Zampini .seealso: [](ch_ts), `TSDIRK`, `TSDIRKType`, `TSDIRKSetType()`
2263405e92cSStefano Zampini M*/
2273405e92cSStefano Zampini 
2283405e92cSStefano Zampini /*MC
2291d27aa22SBarry Smith      TSDIRKES213SAL - Second order DIRK scheme {cite}`kennedy2019diagonally`. Also known as TR-BDF2, see{cite}`hosea1996analysis`
2303405e92cSStefano Zampini 
2313405e92cSStefano Zampini      See `TSDIRK` for additional details.
2323405e92cSStefano Zampini 
2333405e92cSStefano Zampini      Options Database Key:
2343405e92cSStefano Zampini .      -ts_dirk_type es213sal - select this method.
2353405e92cSStefano Zampini 
2363405e92cSStefano Zampini      Level: advanced
2373405e92cSStefano Zampini 
2383405e92cSStefano Zampini      Note:
2393405e92cSStefano Zampini      This is the default DIRK scheme used in PETSc.
2403405e92cSStefano Zampini 
2413405e92cSStefano Zampini .seealso: [](ch_ts), `TSDIRK`, `TSDIRKType`, `TSDIRKSetType()`
2423405e92cSStefano Zampini M*/
2433405e92cSStefano Zampini 
2443405e92cSStefano Zampini /*MC
2451d27aa22SBarry Smith      TSDIRKES324SAL - Third order DIRK scheme, {cite}`kennedy2019diagonally`
2463405e92cSStefano Zampini 
2473405e92cSStefano Zampini      See `TSDIRK` for additional details.
2483405e92cSStefano Zampini 
2493405e92cSStefano Zampini      Options Database Key:
2503405e92cSStefano Zampini .      -ts_dirk_type es324sal - select this method.
2513405e92cSStefano Zampini 
2523405e92cSStefano Zampini      Level: advanced
2533405e92cSStefano Zampini 
2543405e92cSStefano Zampini .seealso: [](ch_ts), `TSDIRK`, `TSDIRKType`, `TSDIRKSetType()`
2553405e92cSStefano Zampini M*/
2563405e92cSStefano Zampini 
2573405e92cSStefano Zampini /*MC
2581d27aa22SBarry Smith      TSDIRKES325SAL - Third order DIRK scheme {cite}`kennedy2019diagonally`.
2593405e92cSStefano Zampini 
2603405e92cSStefano Zampini      See `TSDIRK` for additional details.
2613405e92cSStefano Zampini 
2623405e92cSStefano Zampini      Options Database Key:
2633405e92cSStefano Zampini .      -ts_dirk_type es325sal - select this method.
2643405e92cSStefano Zampini 
2653405e92cSStefano Zampini      Level: advanced
2663405e92cSStefano Zampini 
2673405e92cSStefano Zampini .seealso: [](ch_ts), `TSDIRK`, `TSDIRKType`, `TSDIRKSetType()`
2683405e92cSStefano Zampini M*/
2693405e92cSStefano Zampini 
2703405e92cSStefano Zampini /*MC
2711d27aa22SBarry Smith      TSDIRK657A - Sixth order DIRK scheme <https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs>
2723405e92cSStefano Zampini 
2733405e92cSStefano Zampini      See `TSDIRK` for additional details.
2743405e92cSStefano Zampini 
2753405e92cSStefano Zampini      Options Database Key:
2763405e92cSStefano Zampini .      -ts_dirk_type 657a - select this method.
2773405e92cSStefano Zampini 
2783405e92cSStefano Zampini      Level: advanced
2793405e92cSStefano Zampini 
2803405e92cSStefano Zampini .seealso: [](ch_ts), `TSDIRK`, `TSDIRKType`, `TSDIRKSetType()`
2813405e92cSStefano Zampini M*/
2823405e92cSStefano Zampini 
2833405e92cSStefano Zampini /*MC
2841d27aa22SBarry Smith      TSDIRKES648SA - Sixth order DIRK scheme <https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs>
2853405e92cSStefano Zampini 
2863405e92cSStefano Zampini      See `TSDIRK` for additional details.
2873405e92cSStefano Zampini 
2883405e92cSStefano Zampini      Options Database Key:
2893405e92cSStefano Zampini .      -ts_dirk_type es648sa - select this method.
2903405e92cSStefano Zampini 
2913405e92cSStefano Zampini      Level: advanced
2923405e92cSStefano Zampini 
2933405e92cSStefano Zampini .seealso: [](ch_ts), `TSDIRK`, `TSDIRKType`, `TSDIRKSetType()`
2943405e92cSStefano Zampini M*/
2953405e92cSStefano Zampini 
2963405e92cSStefano Zampini /*MC
2971d27aa22SBarry Smith      TSDIRK658A - Sixth order DIRK scheme  <https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs>
2983405e92cSStefano Zampini 
2993405e92cSStefano Zampini      See `TSDIRK` for additional details.
3003405e92cSStefano Zampini 
3013405e92cSStefano Zampini      Options Database Key:
3023405e92cSStefano Zampini .      -ts_dirk_type 658a - select this method.
3033405e92cSStefano Zampini 
3043405e92cSStefano Zampini      Level: advanced
3053405e92cSStefano Zampini 
3063405e92cSStefano Zampini .seealso: [](ch_ts), `TSDIRK`, `TSDIRKType`, `TSDIRKSetType()`
3073405e92cSStefano Zampini M*/
3083405e92cSStefano Zampini 
3093405e92cSStefano Zampini /*MC
3101d27aa22SBarry Smith      TSDIRKS659A - Sixth order DIRK scheme  <https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs>
3113405e92cSStefano Zampini 
3123405e92cSStefano Zampini      See `TSDIRK` for additional details.
3133405e92cSStefano Zampini 
3143405e92cSStefano Zampini      Options Database Key:
3153405e92cSStefano Zampini .      -ts_dirk_type s659a - select this method.
3163405e92cSStefano Zampini 
3173405e92cSStefano Zampini      Level: advanced
3183405e92cSStefano Zampini 
3193405e92cSStefano Zampini .seealso: [](ch_ts), `TSDIRK`, `TSDIRKType`, `TSDIRKSetType()`
3203405e92cSStefano Zampini M*/
3213405e92cSStefano Zampini 
3223405e92cSStefano Zampini /*MC
3231d27aa22SBarry Smith      TSDIRK7510SAL - Seventh order DIRK scheme <https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs>
3243405e92cSStefano Zampini 
3253405e92cSStefano Zampini      See `TSDIRK` for additional details.
3263405e92cSStefano Zampini 
3273405e92cSStefano Zampini      Options Database Key:
3283405e92cSStefano Zampini .      -ts_dirk_type 7510sal - select this method.
3293405e92cSStefano Zampini 
3303405e92cSStefano Zampini      Level: advanced
3313405e92cSStefano Zampini 
3323405e92cSStefano Zampini .seealso: [](ch_ts), `TSDIRK`, `TSDIRKType`, `TSDIRKSetType()`
3333405e92cSStefano Zampini M*/
3343405e92cSStefano Zampini 
3353405e92cSStefano Zampini /*MC
3361d27aa22SBarry Smith      TSDIRKES7510SA - Seventh order DIRK scheme <https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs>
3373405e92cSStefano Zampini 
3383405e92cSStefano Zampini      See `TSDIRK` for additional details.
3393405e92cSStefano Zampini 
3403405e92cSStefano Zampini      Options Database Key:
3413405e92cSStefano Zampini .      -ts_dirk_type es7510sa - select this method.
3423405e92cSStefano Zampini 
3433405e92cSStefano Zampini      Level: advanced
3443405e92cSStefano Zampini 
3453405e92cSStefano Zampini .seealso: [](ch_ts), `TSDIRK`, `TSDIRKType`, `TSDIRKSetType()`
3463405e92cSStefano Zampini M*/
3473405e92cSStefano Zampini 
3483405e92cSStefano Zampini /*MC
3491d27aa22SBarry Smith      TSDIRK759A - Seventh order DIRK scheme <https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs>
3503405e92cSStefano Zampini 
3513405e92cSStefano Zampini      See `TSDIRK` for additional details.
3523405e92cSStefano Zampini 
3533405e92cSStefano Zampini      Options Database Key:
3543405e92cSStefano Zampini .      -ts_dirk_type 759a - select this method.
3553405e92cSStefano Zampini 
3563405e92cSStefano Zampini      Level: advanced
3573405e92cSStefano Zampini 
3583405e92cSStefano Zampini .seealso: [](ch_ts), `TSDIRK`, `TSDIRKType`, `TSDIRKSetType()`
3593405e92cSStefano Zampini M*/
3603405e92cSStefano Zampini 
3613405e92cSStefano Zampini /*MC
3621d27aa22SBarry Smith      TSDIRKS7511SAL - Seventh order DIRK scheme <https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs>
3633405e92cSStefano Zampini 
3643405e92cSStefano Zampini      See `TSDIRK` for additional details.
3653405e92cSStefano Zampini 
3663405e92cSStefano Zampini      Options Database Key:
3673405e92cSStefano Zampini .      -ts_dirk_type s7511sal - select this method.
3683405e92cSStefano Zampini 
3693405e92cSStefano Zampini      Level: advanced
3703405e92cSStefano Zampini 
3713405e92cSStefano Zampini .seealso: [](ch_ts), `TSDIRK`, `TSDIRKType`, `TSDIRKSetType()`
3723405e92cSStefano Zampini M*/
3733405e92cSStefano Zampini 
3743405e92cSStefano Zampini /*MC
3751d27aa22SBarry Smith      TSDIRK8614A - Eighth order DIRK scheme <https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs>
3763405e92cSStefano Zampini 
3773405e92cSStefano Zampini      See `TSDIRK` for additional details.
3783405e92cSStefano Zampini 
3793405e92cSStefano Zampini      Options Database Key:
3803405e92cSStefano Zampini .      -ts_dirk_type 8614a - select this method.
3813405e92cSStefano Zampini 
3823405e92cSStefano Zampini      Level: advanced
3833405e92cSStefano Zampini 
3843405e92cSStefano Zampini .seealso: [](ch_ts), `TSDIRK`, `TSDIRKType`, `TSDIRKSetType()`
3853405e92cSStefano Zampini M*/
3863405e92cSStefano Zampini 
3873405e92cSStefano Zampini /*MC
3881d27aa22SBarry Smith      TSDIRK8616SAL - Eighth order DIRK scheme <https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs>
3893405e92cSStefano Zampini 
3903405e92cSStefano Zampini      See `TSDIRK` for additional details.
3913405e92cSStefano Zampini 
3923405e92cSStefano Zampini      Options Database Key:
3933405e92cSStefano Zampini .      -ts_dirk_type 8616sal - select this method.
3943405e92cSStefano Zampini 
3953405e92cSStefano Zampini      Level: advanced
3963405e92cSStefano Zampini 
3973405e92cSStefano Zampini .seealso: [](ch_ts), `TSDIRK`, `TSDIRKType`, `TSDIRKSetType()`
3983405e92cSStefano Zampini M*/
3993405e92cSStefano Zampini 
4003405e92cSStefano Zampini /*MC
4011d27aa22SBarry Smith      TSDIRKES8516SAL - Eighth order DIRK scheme <https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs>
4023405e92cSStefano Zampini 
4033405e92cSStefano Zampini      See `TSDIRK` for additional details.
4043405e92cSStefano Zampini 
4053405e92cSStefano Zampini      Options Database Key:
4063405e92cSStefano Zampini .      -ts_dirk_type es8516sal - select this method.
4073405e92cSStefano Zampini 
4083405e92cSStefano Zampini      Level: advanced
4093405e92cSStefano Zampini 
4103405e92cSStefano Zampini .seealso: [](ch_ts), `TSDIRK`, `TSDIRKType`, `TSDIRKSetType()`
4113405e92cSStefano Zampini M*/
4123405e92cSStefano Zampini 
413*3a2a065fSHong Zhang PetscErrorCode TSHasRHSFunction(TS ts, PetscBool *has)
414d27334e2SStefano Zampini {
4158434afd1SBarry Smith   TSRHSFunctionFn *func;
416d27334e2SStefano Zampini 
417d27334e2SStefano Zampini   PetscFunctionBegin;
418d27334e2SStefano Zampini   *has = PETSC_FALSE;
419d27334e2SStefano Zampini   PetscCall(DMTSGetRHSFunction(ts->dm, &func, NULL));
420d27334e2SStefano Zampini   if (func) *has = PETSC_TRUE;
421d27334e2SStefano Zampini   PetscFunctionReturn(PETSC_SUCCESS);
422d27334e2SStefano Zampini }
423d27334e2SStefano Zampini 
4248a381b04SJed Brown /*@C
425bcf0153eSBarry Smith   TSARKIMEXRegisterAll - Registers all of the additive Runge-Kutta implicit-explicit methods in `TSARKIMEX`
4268a381b04SJed Brown 
427fca742c7SJed Brown   Not Collective, but should be called by all processes which will need the schemes to be registered
4288a381b04SJed Brown 
4298a381b04SJed Brown   Level: advanced
4308a381b04SJed Brown 
4311cc06b55SBarry Smith .seealso: [](ch_ts), `TS`, `TSARKIMEX`, `TSARKIMEXRegisterDestroy()`
4328a381b04SJed Brown @*/
433d71ae5a4SJacob Faibussowitsch PetscErrorCode TSARKIMEXRegisterAll(void)
434d71ae5a4SJacob Faibussowitsch {
4358a381b04SJed Brown   PetscFunctionBegin;
4363ba16761SJacob Faibussowitsch   if (TSARKIMEXRegisterAllCalled) PetscFunctionReturn(PETSC_SUCCESS);
4378a381b04SJed Brown   TSARKIMEXRegisterAllCalled = PETSC_TRUE;
438e817cc15SEmil Constantinescu 
439d27334e2SStefano Zampini #define RC  PetscRealConstant
440d27334e2SStefano Zampini #define s2  RC(1.414213562373095048802)  /* PetscSqrtReal((PetscReal)2.0) */
441d27334e2SStefano Zampini #define us2 RC(0.2928932188134524755992) /* 1.0-1.0/PetscSqrtReal((PetscReal)2.0); */
442d27334e2SStefano Zampini 
443d27334e2SStefano Zampini   /* Diagonally implicit methods */
444e817cc15SEmil Constantinescu   {
445d27334e2SStefano Zampini     /* DIRK212, default of SUNDIALS */
446d27334e2SStefano Zampini     const PetscReal A[2][2] = {
447d27334e2SStefano Zampini       {RC(1.0),  RC(0.0)},
448d27334e2SStefano Zampini       {RC(-1.0), RC(1.0)}
449d27334e2SStefano Zampini     };
450d27334e2SStefano Zampini     const PetscReal b[2]      = {RC(0.5), RC(0.5)};
451d27334e2SStefano Zampini     const PetscReal bembed[2] = {RC(1.0), RC(0.0)};
452d27334e2SStefano Zampini     PetscCall(TSDIRKRegister(TSDIRKS212, 2, 2, &A[0][0], b, NULL, bembed, 1, b));
453d27334e2SStefano Zampini   }
454d27334e2SStefano Zampini 
4559371c9d4SSatish Balay   {
456d27334e2SStefano Zampini     /* ESDIRK12 from https://arxiv.org/pdf/1803.01613.pdf */
457d27334e2SStefano Zampini     const PetscReal A[2][2] = {
458d27334e2SStefano Zampini       {RC(0.0), RC(0.0)},
459d27334e2SStefano Zampini       {RC(0.0), RC(1.0)}
460d27334e2SStefano Zampini     };
461d27334e2SStefano Zampini     const PetscReal b[2]      = {RC(0.0), RC(1.0)};
462d27334e2SStefano Zampini     const PetscReal bembed[2] = {RC(0.5), RC(0.5)};
4633405e92cSStefano Zampini     PetscCall(TSDIRKRegister(TSDIRKES122SAL, 1, 2, &A[0][0], b, NULL, bembed, 1, b));
464d27334e2SStefano Zampini   }
465d27334e2SStefano Zampini 
466d27334e2SStefano Zampini   {
467d27334e2SStefano Zampini     /* ESDIRK213L[2]SA from KC16.
4683405e92cSStefano Zampini        TR-BDF2 from Hosea and Shampine
4693405e92cSStefano Zampini        ESDIRK23 in https://arxiv.org/pdf/1803.01613.pdf */
470d27334e2SStefano Zampini     const PetscReal A[3][3] = {
471d27334e2SStefano Zampini       {RC(0.0),      RC(0.0),      RC(0.0)},
472d27334e2SStefano Zampini       {us2,          us2,          RC(0.0)},
473d27334e2SStefano Zampini       {s2 / RC(4.0), s2 / RC(4.0), us2    },
474d27334e2SStefano Zampini     };
475d27334e2SStefano Zampini     const PetscReal b[3]      = {s2 / RC(4.0), s2 / RC(4.0), us2};
476d27334e2SStefano Zampini     const PetscReal bembed[3] = {(RC(1.0) - s2 / RC(4.0)) / RC(3.0), (RC(3.0) * s2 / RC(4.0) + RC(1.0)) / RC(3.0), us2 / RC(3.0)};
477d27334e2SStefano Zampini     PetscCall(TSDIRKRegister(TSDIRKES213SAL, 2, 3, &A[0][0], b, NULL, bembed, 1, b));
478d27334e2SStefano Zampini   }
479d27334e2SStefano Zampini 
480d27334e2SStefano Zampini   {
481d27334e2SStefano Zampini #define g   RC(0.43586652150845899941601945)
482d27334e2SStefano Zampini #define g2  PetscSqr(g)
483d27334e2SStefano Zampini #define g3  g *g2
484d27334e2SStefano Zampini #define g4  PetscSqr(g2)
485d27334e2SStefano Zampini #define g5  g *g4
486d27334e2SStefano Zampini #define c3  RC(1.0)
487d27334e2SStefano Zampini #define a32 c3 *(c3 - RC(2.0) * g) / (RC(4.0) * g)
488d27334e2SStefano Zampini #define b2  (-RC(2.0) + RC(3.0) * c3 + RC(6.0) * g * (RC(1.0) - c3)) / (RC(12.0) * g * (c3 - RC(2.0) * g))
489d27334e2SStefano Zampini #define b3  (RC(1.0) - RC(6.0) * g + RC(6.0) * g2) / (RC(3.0) * c3 * (c3 - RC(2.0) * g))
490d27334e2SStefano Zampini #if 0
491d27334e2SStefano Zampini /* This is for c3 = 3/5 */
492d27334e2SStefano Zampini   #define bh2 \
493d27334e2SStefano Zampini     c3 * (-RC(1.0) + RC(6.0) * g - RC(23.0) * g3 + RC(12.0) * g4 - RC(6.0) * g5) / (RC(4.0) * (RC(2.0) * g - c3) * (RC(1.0) - RC(6.0) * g + RC(6.0) * g2)) + (RC(3.0) - RC(27.0) * g + RC(68.0) * g2 - RC(55.0) * g3 + RC(21.0) * g4 - RC(6.0) * g5) / (RC(2.0) * (RC(2.0) * g - c3) * (RC(1.0) - RC(6.0) * g + RC(6.0) * g2))
494d27334e2SStefano Zampini   #define bh3 -g * (-RC(2.0) + RC(21.0) * g - RC(68.0) * g2 + RC(79.0) * g3 - RC(33.0) * g4 + RC(12.0) * g5) / (RC(2.0) * (RC(2.0) * g - c3) * (RC(1.0) - RC(6.0) * g + RC(6.0) * g2))
495d27334e2SStefano Zampini   #define bh4 -RC(3.0) * g2 * (-RC(1.0) + RC(4.0) * g - RC(2.0) * g2 + g3) / (RC(1.0) - RC(6.0) * g + RC(6.0) * g2)
496d27334e2SStefano Zampini #else
497d27334e2SStefano Zampini   /* This is for c3 = 1.0 */
498d27334e2SStefano Zampini   #define bh2 a32
499d27334e2SStefano Zampini   #define bh3 g
500d27334e2SStefano Zampini   #define bh4 RC(0.0)
501d27334e2SStefano Zampini #endif
502d27334e2SStefano Zampini     /* ESDIRK3(2I)4L[2]SA from KC16 with c3 = 1.0 */
503d27334e2SStefano Zampini     /* Given by Kvaerno https://link.springer.com/article/10.1023/b:bitn.0000046811.70614.38 */
504d27334e2SStefano Zampini     const PetscReal A[4][4] = {
505d27334e2SStefano Zampini       {RC(0.0),               RC(0.0), RC(0.0), RC(0.0)},
506d27334e2SStefano Zampini       {g,                     g,       RC(0.0), RC(0.0)},
507d27334e2SStefano Zampini       {c3 - a32 - g,          a32,     g,       RC(0.0)},
508d27334e2SStefano Zampini       {RC(1.0) - b2 - b3 - g, b2,      b3,      g      },
509d27334e2SStefano Zampini     };
510d27334e2SStefano Zampini     const PetscReal b[4]      = {RC(1.0) - b2 - b3 - g, b2, b3, g};
511d27334e2SStefano Zampini     const PetscReal bembed[4] = {RC(1.0) - bh2 - bh3 - bh4, bh2, bh3, bh4};
512d27334e2SStefano Zampini     PetscCall(TSDIRKRegister(TSDIRKES324SAL, 3, 4, &A[0][0], b, NULL, bembed, 1, b));
513d27334e2SStefano Zampini #undef g
514d27334e2SStefano Zampini #undef g2
515d27334e2SStefano Zampini #undef g3
516d27334e2SStefano Zampini #undef c3
517d27334e2SStefano Zampini #undef a32
518d27334e2SStefano Zampini #undef b2
519d27334e2SStefano Zampini #undef b3
520d27334e2SStefano Zampini #undef bh2
521d27334e2SStefano Zampini #undef bh3
522d27334e2SStefano Zampini #undef bh4
523d27334e2SStefano Zampini   }
524d27334e2SStefano Zampini 
525d27334e2SStefano Zampini   {
526d27334e2SStefano Zampini     /* ESDIRK3(2I)5L[2]SA from KC16 */
527d27334e2SStefano Zampini     const PetscReal A[5][5] = {
528d27334e2SStefano Zampini       {RC(0.0),                  RC(0.0),                  RC(0.0),                 RC(0.0),                   RC(0.0)           },
529d27334e2SStefano Zampini       {RC(9.0) / RC(40.0),       RC(9.0) / RC(40.0),       RC(0.0),                 RC(0.0),                   RC(0.0)           },
530d27334e2SStefano Zampini       {RC(19.0) / RC(72.0),      RC(14.0) / RC(45.0),      RC(9.0) / RC(40.0),      RC(0.0),                   RC(0.0)           },
531d27334e2SStefano Zampini       {RC(3337.0) / RC(11520.0), RC(233.0) / RC(720.0),    RC(207.0) / RC(1280.0),  RC(9.0) / RC(40.0),        RC(0.0)           },
532d27334e2SStefano Zampini       {RC(7415.0) / RC(34776.0), RC(9920.0) / RC(30429.0), RC(4845.0) / RC(9016.0), -RC(5827.0) / RC(19320.0), RC(9.0) / RC(40.0)},
533d27334e2SStefano Zampini     };
534d27334e2SStefano Zampini     const PetscReal b[5]      = {RC(7415.0) / RC(34776.0), RC(9920.0) / RC(30429.0), RC(4845.0) / RC(9016.0), -RC(5827.0) / RC(19320.0), RC(9.0) / RC(40.0)};
535d27334e2SStefano Zampini     const PetscReal bembed[5] = {RC(23705.0) / RC(104328.0), RC(29720.0) / RC(91287.0), RC(4225.0) / RC(9016.0), -RC(69304987.0) / RC(337732920.0), RC(42843.0) / RC(233080.0)};
536d27334e2SStefano Zampini     PetscCall(TSDIRKRegister(TSDIRKES325SAL, 3, 5, &A[0][0], b, NULL, bembed, 1, b));
537d27334e2SStefano Zampini   }
538d27334e2SStefano Zampini 
539d27334e2SStefano Zampini   {
540d27334e2SStefano Zampini     // DIRK(6,6)[1]A[(7,5)A] from https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs
541d27334e2SStefano Zampini     const PetscReal A[7][7] = {
542d27334e2SStefano Zampini       {RC(0.303487844706747),    RC(0.0),                RC(0.0),                   RC(0.0),                   RC(0.0),                 RC(0.0),                RC(0.0)              },
543d27334e2SStefano Zampini       {RC(-0.279756492709814),   RC(0.500032236020747),  RC(0.0),                   RC(0.0),                   RC(0.0),                 RC(0.0),                RC(0.0)              },
544d27334e2SStefano Zampini       {RC(0.280583215743895),    RC(-0.438560061586751), RC(0.217250734515736),     RC(0.0),                   RC(0.0),                 RC(0.0),                RC(0.0)              },
545d27334e2SStefano Zampini       {RC(-0.0677678738539846),  RC(0.984312781232293),  RC(-0.266720192540149),    RC(0.2476680834526),       RC(0.0),                 RC(0.0),                RC(0.0)              },
546d27334e2SStefano Zampini       {RC(0.125671616147993),    RC(-0.995401751002415), RC(0.761333109549059),     RC(-0.210281837202208),    RC(0.866743712636936),   RC(0.0),                RC(0.0)              },
547d27334e2SStefano Zampini       {RC(-0.368056238801488),   RC(-0.999928082701516), RC(0.534734253232519),     RC(-0.174856916279082),    RC(0.615007160285509),   RC(0.696549912132029),  RC(0.0)              },
548d27334e2SStefano Zampini       {RC(-0.00570546839653984), RC(-0.113110431835656), RC(-0.000965563207671587), RC(-0.000130490084629567), RC(0.00111737736895673), RC(-0.279385587378871), RC(0.618455906845342)}
549d27334e2SStefano Zampini     };
550d27334e2SStefano Zampini     const PetscReal b[7]      = {RC(0.257561510484877), RC(0.234281287047716), RC(0.126658904241469), RC(0.252363215441784), RC(0.396701083526306), RC(-0.267566000742152), RC(0.0)};
551d27334e2SStefano Zampini     const PetscReal bembed[7] = {RC(0.257561510484945), RC(0.387312822934391), RC(0.126658904241468), RC(0.252363215441784), RC(0.396701083526306), RC(-0.267566000742225), RC(-0.153031535886669)};
552d27334e2SStefano Zampini     PetscCall(TSDIRKRegister(TSDIRK657A, 6, 7, &A[0][0], b, NULL, bembed, 1, b));
553d27334e2SStefano Zampini   }
554d27334e2SStefano Zampini   {
555d27334e2SStefano Zampini     // ESDIRK(8,6)[2]SA[(8,4)] from https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs
556d27334e2SStefano Zampini     const PetscReal A[8][8] = {
557d27334e2SStefano Zampini       {RC(0.0),                RC(0.0),                 RC(0.0),                 RC(0.0),               RC(0.0),                RC(0.0),                RC(0.0),               RC(0.0)              },
558d27334e2SStefano Zampini       {RC(0.333222149217725),  RC(0.333222149217725),   RC(0.0),                 RC(0.0),               RC(0.0),                RC(0.0),                RC(0.0),               RC(0.0)              },
559d27334e2SStefano Zampini       {RC(0.0639743773182214), RC(-0.0830330224410214), RC(0.333222149217725),   RC(0.0),               RC(0.0),                RC(0.0),                RC(0.0),               RC(0.0)              },
560d27334e2SStefano Zampini       {RC(-0.728522201369326), RC(-0.210414479522485),  RC(0.532519916559342),   RC(0.333222149217725), RC(0.0),                RC(0.0),                RC(0.0),               RC(0.0)              },
561d27334e2SStefano Zampini       {RC(-0.175135269272067), RC(0.666675582067552),   RC(-0.304400907370867),  RC(0.656797712445756), RC(0.333222149217725),  RC(0.0),                RC(0.0),               RC(0.0)              },
562d27334e2SStefano Zampini       {RC(0.222695802705462),  RC(-0.0948971794681061), RC(-0.0234336346686545), RC(-0.45385925012042), RC(0.0283910313826958), RC(0.333222149217725),  RC(0.0),               RC(0.0)              },
563d27334e2SStefano Zampini       {RC(-0.132534078051299), RC(0.702597935004879),   RC(-0.433316453128078),  RC(0.893717488547587), RC(0.057381454791406),  RC(-0.207798411552402), RC(0.333222149217725), RC(0.0)              },
564d27334e2SStefano Zampini       {RC(0.0802253121418085), RC(0.281196044671022),   RC(0.406758926172157),   RC(-0.01945708512416), RC(-0.41785600088526),  RC(0.0545342658870322), RC(0.281376387919675), RC(0.333222149217725)}
565d27334e2SStefano Zampini     };
566d27334e2SStefano Zampini     const PetscReal b[8]      = {RC(0.0802253121418085), RC(0.281196044671022), RC(0.406758926172157), RC(-0.01945708512416), RC(-0.41785600088526), RC(0.0545342658870322), RC(0.281376387919675), RC(0.333222149217725)};
567d27334e2SStefano Zampini     const PetscReal bembed[8] = {RC(0.0), RC(0.292331064554014), RC(0.409676102283681), RC(-0.002094718084982), RC(-0.282771520835975), RC(0.113862336644901), RC(0.181973572260693), RC(0.287023163177669)};
568d27334e2SStefano Zampini     PetscCall(TSDIRKRegister(TSDIRKES648SA, 6, 8, &A[0][0], b, NULL, bembed, 1, b));
569d27334e2SStefano Zampini   }
570d27334e2SStefano Zampini   {
571d27334e2SStefano Zampini     // DIRK(8,6)[1]SAL[(8,5)A] from https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs
572d27334e2SStefano Zampini     const PetscReal A[8][8] = {
573d27334e2SStefano Zampini       {RC(0.477264457385826),    RC(0.0),                RC(0.0),                   RC(0.0),                 RC(0.0),                RC(0.0),                RC(0.0),                 RC(0.0)              },
574d27334e2SStefano Zampini       {RC(-0.197052588415002),   RC(0.476363428459584),  RC(0.0),                   RC(0.0),                 RC(0.0),                RC(0.0),                RC(0.0),                 RC(0.0)              },
575d27334e2SStefano Zampini       {RC(-0.0347674430372966),  RC(0.633051807335483),  RC(0.193634310075028),     RC(0.0),                 RC(0.0),                RC(0.0),                RC(0.0),                 RC(0.0)              },
576d27334e2SStefano Zampini       {RC(0.0967797668578702),   RC(-0.193533526466535), RC(-0.000207622945800473), RC(0.159572204849431),   RC(0.0),                RC(0.0),                RC(0.0),                 RC(0.0)              },
577d27334e2SStefano Zampini       {RC(0.162527231819875),    RC(-0.249672513547382), RC(-0.0459079972041795),   RC(0.36579476400859),    RC(0.255752838307699),  RC(0.0),                RC(0.0),                 RC(0.0)              },
578d27334e2SStefano Zampini       {RC(-0.00707603197171262), RC(0.846299854860295),  RC(0.344020016925018),     RC(-0.0720926054548865), RC(-0.215492331980875), RC(0.104341097622161),  RC(0.0),                 RC(0.0)              },
579d27334e2SStefano Zampini       {RC(0.00176857935179744),  RC(0.0779960013127515), RC(0.303333277564557),     RC(0.213160806732836),   RC(0.351769320319038),  RC(-0.381545894386538), RC(0.433517909105558),   RC(0.0)              },
580d27334e2SStefano Zampini       {RC(0.0),                  RC(0.22732353410559),   RC(0.308415837980118),     RC(0.157263419573007),   RC(0.243551137152275),  RC(-0.120953626732831), RC(-0.0802678473399899), RC(0.264667545261832)}
581d27334e2SStefano Zampini     };
582d27334e2SStefano Zampini     const PetscReal b[8]      = {RC(0.0), RC(0.22732353410559), RC(0.308415837980118), RC(0.157263419573007), RC(0.243551137152275), RC(-0.120953626732831), RC(-0.0802678473399899), RC(0.264667545261832)};
583d27334e2SStefano Zampini     const PetscReal bembed[8] = {RC(0.0), RC(0.22732353410559), RC(0.308415837980118), RC(0.157263419573007), RC(0.243551137152275), RC(-0.103483943222765), RC(-0.0103721771642262), RC(0.177302191576001)};
584d27334e2SStefano Zampini     PetscCall(TSDIRKRegister(TSDIRK658A, 6, 8, &A[0][0], b, NULL, bembed, 1, b));
585d27334e2SStefano Zampini   }
586d27334e2SStefano Zampini   {
587d27334e2SStefano Zampini     // SDIRK(9,6)[1]SAL[(9,5)A] from https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs
588d27334e2SStefano Zampini     const PetscReal A[9][9] = {
589d27334e2SStefano Zampini       {RC(0.218127781944908),   RC(0.0),                RC(0.0),                 RC(0.0),                 RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)              },
590d27334e2SStefano Zampini       {RC(-0.0903514856119419), RC(0.218127781944908),  RC(0.0),                 RC(0.0),                 RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)              },
591d27334e2SStefano Zampini       {RC(0.172952039138937),   RC(-0.35365501036282),  RC(0.218127781944908),   RC(0.0),                 RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)              },
592d27334e2SStefano Zampini       {RC(0.511999875919193),   RC(0.0289640332201925), RC(-0.0144030945657094), RC(0.218127781944908),   RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)              },
593d27334e2SStefano Zampini       {RC(0.00465303495506782), RC(-0.075635818766597), RC(0.217273030786712),   RC(-0.0206519428725472), RC(0.218127781944908),  RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)              },
594d27334e2SStefano Zampini       {RC(0.896145501762472),   RC(0.139267327700498),  RC(-0.186920979752805),  RC(0.0672971012371723),  RC(-0.350891963442176), RC(0.218127781944908),  RC(0.0),                RC(0.0),                RC(0.0)              },
595d27334e2SStefano Zampini       {RC(0.552959701885751),   RC(-0.439360579793662), RC(0.333704002325091),   RC(-0.0339426520778416), RC(-0.151947445912595), RC(0.0213825661026943), RC(0.218127781944908),  RC(0.0),                RC(0.0)              },
596d27334e2SStefano Zampini       {RC(0.631360374036476),   RC(0.724733619641466),  RC(-0.432170625425258),  RC(0.598611382182477),   RC(-0.709087197034345), RC(-0.483986685696934), RC(0.378391562905131),  RC(0.218127781944908),  RC(0.0)              },
597d27334e2SStefano Zampini       {RC(0.0),                 RC(-0.15504452530869),  RC(0.194518478660789),   RC(0.63515640279203),    RC(0.81172278664173),   RC(0.110736108691585),  RC(-0.495304692414479), RC(-0.319912341007872), RC(0.218127781944908)}
598d27334e2SStefano Zampini     };
599d27334e2SStefano Zampini     const PetscReal b[9]      = {RC(0.0), RC(-0.15504452530869), RC(0.194518478660789), RC(0.63515640279203), RC(0.81172278664173), RC(0.110736108691585), RC(-0.495304692414479), RC(-0.319912341007872), RC(0.218127781944908)};
600d27334e2SStefano Zampini     const PetscReal bembed[9] = {RC(3.62671059311602e-16), RC(0.0736615558278942), RC(0.103527397262229), RC(1.00247481935499), RC(0.361377289250057), RC(-0.785425929961365), RC(-0.0170499047960784), RC(0.296321252214769), RC(-0.0348864791524953)};
601d27334e2SStefano Zampini     PetscCall(TSDIRKRegister(TSDIRKS659A, 6, 9, &A[0][0], b, NULL, bembed, 1, b));
602d27334e2SStefano Zampini   }
603d27334e2SStefano Zampini   {
604d27334e2SStefano Zampini     // DIRK(10,7)[1]SAL[(10,5)A] from https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs
605d27334e2SStefano Zampini     const PetscReal A[10][10] = {
606d27334e2SStefano Zampini       {RC(0.233704632125264),   RC(0.0),                RC(0.0),                  RC(0.0),                  RC(0.0),                   RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),               RC(0.0)              },
607d27334e2SStefano Zampini       {RC(-0.0739324813149407), RC(0.200056838146104),  RC(0.0),                  RC(0.0),                  RC(0.0),                   RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),               RC(0.0)              },
608d27334e2SStefano Zampini       {RC(0.0943790344044812),  RC(0.264056067701605),  RC(0.133245202456465),    RC(0.0),                  RC(0.0),                   RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),               RC(0.0)              },
609d27334e2SStefano Zampini       {RC(0.269084810601201),   RC(-0.503479002548384), RC(-0.00486736469695022), RC(0.251518716213569),    RC(0.0),                   RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),               RC(0.0)              },
610d27334e2SStefano Zampini       {RC(0.145665801918423),   RC(0.204983170463176),  RC(0.407154634069484),    RC(-0.0121039135200389),  RC(0.190243622486334),     RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),               RC(0.0)              },
611d27334e2SStefano Zampini       {RC(0.985450198547345),   RC(0.806942652811456),  RC(-0.808130934167263),   RC(-0.669035819439391),   RC(0.0269384406756128),    RC(0.462144080607327),    RC(0.0),                RC(0.0),                 RC(0.0),               RC(0.0)              },
612d27334e2SStefano Zampini       {RC(0.163902957809563),   RC(0.228315094960095),  RC(0.0745971021260249),   RC(0.000509793400156559), RC(0.0166533681378294),    RC(-0.0229383879045797),  RC(0.103505486637336),  RC(0.0),                 RC(0.0),               RC(0.0)              },
613d27334e2SStefano Zampini       {RC(-0.162694156858437),  RC(0.0453478837428434), RC(0.997443481211424),    RC(0.200251514941093),    RC(-0.000161755458839048), RC(-0.0848134335980281),  RC(-0.36438666566666),  RC(0.158604420136055),   RC(0.0),               RC(0.0)              },
614d27334e2SStefano Zampini       {RC(0.200733156477425),   RC(0.239686443444433),  RC(0.303837014418929),    RC(-0.0534390596279896),  RC(0.0314067599640569),    RC(-0.00764032790448536), RC(0.0609191260198661), RC(-0.0736319201590642), RC(0.204602530607021), RC(0.0)              },
615d27334e2SStefano Zampini       {RC(0.0),                 RC(0.235563761744267),  RC(0.658651488684319),    RC(0.0308877804992098),   RC(-0.906514945595336),    RC(-0.0248488551739974),  RC(-0.309967582365257), RC(0.191663316925525),   RC(0.923933712199542), RC(0.200631323081727)}
616d27334e2SStefano Zampini     };
617d27334e2SStefano Zampini     const PetscReal b[10] = {RC(0.0), RC(0.235563761744267), RC(0.658651488684319), RC(0.0308877804992098), RC(-0.906514945595336), RC(-0.0248488551739974), RC(-0.309967582365257), RC(0.191663316925525), RC(0.923933712199542), RC(0.200631323081727)};
618d27334e2SStefano Zampini     const PetscReal bembed[10] =
619d27334e2SStefano Zampini       {RC(0.0), RC(0.222929376486581), RC(0.950668440138169), RC(0.0342694607044032), RC(0.362875840545746), RC(0.223572979288581), RC(-0.764361723526727), RC(0.563476909230026), RC(-0.690896961894185), RC(0.0974656790270323)};
620d27334e2SStefano Zampini     PetscCall(TSDIRKRegister(TSDIRK7510SAL, 7, 10, &A[0][0], b, NULL, bembed, 1, b));
621d27334e2SStefano Zampini   }
622d27334e2SStefano Zampini   {
623d27334e2SStefano Zampini     // ESDIRK(10,7)[2]SA[(10,5)] from https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs
624d27334e2SStefano Zampini     const PetscReal A[10][10] = {
625d27334e2SStefano Zampini       {RC(0.0),                 RC(0.0),                 RC(0.0),                 RC(0.0),                  RC(0.0),                  RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),               RC(0.0)              },
626d27334e2SStefano Zampini       {RC(0.210055790203419),   RC(0.210055790203419),   RC(0.0),                 RC(0.0),                  RC(0.0),                  RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),               RC(0.0)              },
627d27334e2SStefano Zampini       {RC(0.255781739921086),   RC(0.239850916980976),   RC(0.210055790203419),   RC(0.0),                  RC(0.0),                  RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),               RC(0.0)              },
628d27334e2SStefano Zampini       {RC(0.286789624880437),   RC(0.230494748834778),   RC(0.263925149885491),   RC(0.210055790203419),    RC(0.0),                  RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),               RC(0.0)              },
629d27334e2SStefano Zampini       {RC(-0.0219118128774335), RC(0.897684380345907),   RC(-0.657954605498907),  RC(0.124962304722633),    RC(0.210055790203419),    RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),               RC(0.0)              },
630d27334e2SStefano Zampini       {RC(-0.065614879584776),  RC(-0.0565630711859497), RC(0.0254881105065311),  RC(-0.00368981790650006), RC(-0.0115178258446329),  RC(0.210055790203419),    RC(0.0),                RC(0.0),                 RC(0.0),               RC(0.0)              },
631d27334e2SStefano Zampini       {RC(0.399860851232098),   RC(0.915588469718705),   RC(-0.0758429094934412), RC(-0.263369154872759),   RC(0.719687583564526),    RC(-0.787410407015369),   RC(0.210055790203419),  RC(0.0),                 RC(0.0),               RC(0.0)              },
632d27334e2SStefano Zampini       {RC(0.51693616104628),    RC(1.00000540846973),    RC(-0.0485110663289207), RC(-0.315208041581942),   RC(0.749742806451587),    RC(-0.990975090921248),   RC(0.0159279583407308), RC(0.210055790203419),   RC(0.0),               RC(0.0)              },
633d27334e2SStefano Zampini       {RC(-0.0303062129076945), RC(-0.297035174659034),  RC(0.184724697462164),   RC(-0.0351876079516183),  RC(-0.00324668230690761), RC(0.216151004053531),    RC(-0.126676252098317), RC(0.114040254365262),   RC(0.210055790203419), RC(0.0)              },
634d27334e2SStefano Zampini       {RC(0.0705997961586714),  RC(-0.0281516061956374), RC(0.314600470734633),   RC(-0.0907057557963371),  RC(0.168078953957742),    RC(-0.00655694984590575), RC(0.0505384497804303), RC(-0.0569572058725042), RC(0.368498056875488), RC(0.210055790203419)}
635d27334e2SStefano Zampini     };
636d27334e2SStefano Zampini     const PetscReal b[10]      = {RC(0.0705997961586714),   RC(-0.0281516061956374), RC(0.314600470734633),   RC(-0.0907057557963371), RC(0.168078953957742),
637d27334e2SStefano Zampini                                   RC(-0.00655694984590575), RC(0.0505384497804303),  RC(-0.0569572058725042), RC(0.368498056875488),   RC(0.210055790203419)};
638d27334e2SStefano Zampini     const PetscReal bembed[10] = {RC(-0.015494246543626), RC(0.167657963820093), RC(0.269858958144236),  RC(-0.0443258997755156), RC(0.150049236875266),
639d27334e2SStefano Zampini                                   RC(0.259452082755846),  RC(0.244624573502521), RC(-0.215528446920284), RC(0.0487601760292619),  RC(0.134945602112201)};
640d27334e2SStefano Zampini     PetscCall(TSDIRKRegister(TSDIRKES7510SA, 7, 10, &A[0][0], b, NULL, bembed, 1, b));
641d27334e2SStefano Zampini   }
642d27334e2SStefano Zampini   {
643d27334e2SStefano Zampini     // DIRK(9,7)[1]A[(9,5)A] from https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs
644d27334e2SStefano Zampini     const PetscReal A[9][9] = {
645d27334e2SStefano Zampini       {RC(0.179877789855839),   RC(0.0),                 RC(0.0),                RC(0.0),                  RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)               },
646d27334e2SStefano Zampini       {RC(-0.100405844885157),  RC(0.214948590644819),   RC(0.0),                RC(0.0),                  RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)               },
647d27334e2SStefano Zampini       {RC(0.112251360198995),   RC(-0.206162139150298),  RC(0.125159642941958),  RC(0.0),                  RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)               },
648d27334e2SStefano Zampini       {RC(-0.0335164000768257), RC(0.999942349946143),   RC(-0.491470853833294), RC(0.19820086325566),     RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)               },
649d27334e2SStefano Zampini       {RC(-0.0417345265478321), RC(0.187864510308215),   RC(0.0533789224305102), RC(-0.00822060284862916), RC(0.127670843671646),  RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)               },
650d27334e2SStefano Zampini       {RC(-0.0278257925239257), RC(0.600979340683382),   RC(-0.242632273241134), RC(-0.11318753652081),    RC(0.164326917632931),  RC(0.284116597781395),  RC(0.0),                RC(0.0),                RC(0.0)               },
651d27334e2SStefano Zampini       {RC(0.041465583858922),   RC(0.429657872601836),   RC(-0.381323410582524), RC(0.391934277498434),    RC(-0.245918275501241), RC(-0.35960669741231),  RC(0.184000022289158),  RC(0.0),                RC(0.0)               },
652d27334e2SStefano Zampini       {RC(-0.105565651574538),  RC(-0.0557833155018609), RC(0.358967568942643),  RC(-0.13489263413921),    RC(0.129553247260677),  RC(0.0992493795371489), RC(-0.15716610563461),  RC(0.17918862279814),   RC(0.0)               },
653d27334e2SStefano Zampini       {RC(0.00439696079965225), RC(0.960250486570491),   RC(0.143558372286706),  RC(0.0819015241056593),   RC(0.999562318563625),  RC(0.325203439314358),  RC(-0.679013149331228), RC(-0.990589559837246), RC(0.0773648037639896)}
654d27334e2SStefano Zampini     };
655d27334e2SStefano Zampini 
656d27334e2SStefano Zampini     const PetscReal b[9]      = {RC(0.0), RC(0.179291520437966), RC(0.115310295273026), RC(-0.857943261453138), RC(0.654911318641998), RC(1.18713633508094), RC(-0.0949482361570542), RC(-0.37661430946407), RC(0.19285633764033)};
657d27334e2SStefano Zampini     const PetscReal bembed[9] = {RC(0.0), RC(0.1897135479408), RC(0.127461414808862), RC(-0.835810807663404), RC(0.665114177777166), RC(1.16481046518346), RC(-0.11661858889792), RC(-0.387303251022099), RC(0.192633041873135)};
658d27334e2SStefano Zampini     PetscCall(TSDIRKRegister(TSDIRK759A, 7, 9, &A[0][0], b, NULL, bembed, 1, b));
659d27334e2SStefano Zampini   }
660d27334e2SStefano Zampini   {
661d27334e2SStefano Zampini     // SDIRK(11,7)[1]SAL[(11,5)A] from https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs
662d27334e2SStefano Zampini     const PetscReal A[11][11] = {
663d27334e2SStefano Zampini       {RC(0.200252661187742),  RC(0.0),                 RC(0.0),                  RC(0.0),                 RC(0.0),                 RC(0.0),                 RC(0.0),                 RC(0.0),                 RC(0.0),               RC(0.0),               RC(0.0)              },
664d27334e2SStefano Zampini       {RC(-0.082947368165267), RC(0.200252661187742),   RC(0.0),                  RC(0.0),                 RC(0.0),                 RC(0.0),                 RC(0.0),                 RC(0.0),                 RC(0.0),               RC(0.0),               RC(0.0)              },
665d27334e2SStefano Zampini       {RC(0.483452690540751),  RC(0.0),                 RC(0.200252661187742),    RC(0.0),                 RC(0.0),                 RC(0.0),                 RC(0.0),                 RC(0.0),                 RC(0.0),               RC(0.0),               RC(0.0)              },
666d27334e2SStefano Zampini       {RC(0.771076453481321),  RC(-0.22936926341842),   RC(0.289733373208823),    RC(0.200252661187742),   RC(0.0),                 RC(0.0),                 RC(0.0),                 RC(0.0),                 RC(0.0),               RC(0.0),               RC(0.0)              },
667d27334e2SStefano Zampini       {RC(0.0329683054968892), RC(-0.162397421903366),  RC(0.000951777538562805), RC(0.0),                 RC(0.200252661187742),   RC(0.0),                 RC(0.0),                 RC(0.0),                 RC(0.0),               RC(0.0),               RC(0.0)              },
668d27334e2SStefano Zampini       {RC(0.265888743485945),  RC(0.606743151103931),   RC(0.173443800537369),    RC(-0.0433968261546912), RC(-0.385211017224481),  RC(0.200252661187742),   RC(0.0),                 RC(0.0),                 RC(0.0),               RC(0.0),               RC(0.0)              },
669d27334e2SStefano Zampini       {RC(0.220662294551146),  RC(-0.0465078507657608), RC(-0.0333111995282464),  RC(0.011801580836998),   RC(0.169480801030105),   RC(-0.0167974432139385), RC(0.200252661187742),   RC(0.0),                 RC(0.0),               RC(0.0),               RC(0.0)              },
670d27334e2SStefano Zampini       {RC(0.323099728365267),  RC(0.0288371831672575),  RC(-0.0543404318773196),  RC(0.0137765831431662),  RC(0.0516799019060702),  RC(-0.0421359763835713), RC(0.181297932037826),   RC(0.200252661187742),   RC(0.0),               RC(0.0),               RC(0.0)              },
671d27334e2SStefano Zampini       {RC(-0.164226696476538), RC(0.187552004946792),   RC(0.0628674420973025),   RC(-0.0108886582703428), RC(-0.0117628641717889), RC(0.0432176880867965),  RC(-0.0315206836275473), RC(-0.0846007021638797), RC(0.200252661187742), RC(0.0),               RC(0.0)              },
672d27334e2SStefano Zampini       {RC(0.651428598623771),  RC(-0.10208078475356),   RC(0.198305701801888),    RC(-0.0117354096673789), RC(-0.0440385966743686), RC(-0.0358364455795087), RC(-0.0075408087654097), RC(0.160320941654639),   RC(0.017940248694499), RC(0.200252661187742), RC(0.0)              },
673d27334e2SStefano Zampini       {RC(0.0),                RC(-0.266259448580236),  RC(-0.615982357748271),   RC(0.561474126687165),   RC(0.266911112787025),   RC(0.219775952207137),   RC(0.387847665451514),   RC(0.612483137773236),   RC(0.330027015806089), RC(-0.6965298655714),  RC(0.200252661187742)}
674d27334e2SStefano Zampini     };
675d27334e2SStefano Zampini     const PetscReal b[11] =
676d27334e2SStefano Zampini       {RC(0.0), RC(-0.266259448580236), RC(-0.615982357748271), RC(0.561474126687165), RC(0.266911112787025), RC(0.219775952207137), RC(0.387847665451514), RC(0.612483137773236), RC(0.330027015806089), RC(-0.6965298655714), RC(0.200252661187742)};
677d27334e2SStefano Zampini     const PetscReal bembed[11] =
678d27334e2SStefano Zampini       {RC(0.0), RC(0.180185524442613), RC(-0.628869710835338), RC(0.186185675988647), RC(0.0484716652630425), RC(0.203927720607141), RC(0.44041662512573), RC(0.615710527731245), RC(0.0689648839032607), RC(-0.253599870605903), RC(0.138606958379488)};
679d27334e2SStefano Zampini     PetscCall(TSDIRKRegister(TSDIRKS7511SAL, 7, 11, &A[0][0], b, NULL, bembed, 1, b));
680d27334e2SStefano Zampini   }
681d27334e2SStefano Zampini   {
682d27334e2SStefano Zampini     // DIRK(13,8)[1]A[(14,6)A] from https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs
683d27334e2SStefano Zampini     const PetscReal A[14][14] = {
684d27334e2SStefano Zampini       {RC(0.421050745442291),   RC(0.0),                RC(0.0),                 RC(0.0),                  RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)               },
685d27334e2SStefano Zampini       {RC(-0.0761079419591268), RC(0.264353986580857),  RC(0.0),                 RC(0.0),                  RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)               },
686d27334e2SStefano Zampini       {RC(0.0727106904170694),  RC(-0.204265976977285), RC(0.181608196544136),   RC(0.0),                  RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)               },
687d27334e2SStefano Zampini       {RC(0.55763054816611),    RC(-0.409773579543499), RC(0.510926516886944),   RC(0.259892204518476),    RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)               },
688d27334e2SStefano Zampini       {RC(0.0228083864844437),  RC(-0.445569051836454), RC(-0.0915242778636248), RC(0.00450055909321655),  RC(0.6397807199983),      RC(0.0),                RC(0.0),                 RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)               },
689d27334e2SStefano Zampini       {RC(-0.135945849505152),  RC(0.0946509646963754), RC(-0.236110197279175),  RC(0.00318944206456517),  RC(0.255453021028118),    RC(0.174805219173446),  RC(0.0),                 RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)               },
690d27334e2SStefano Zampini       {RC(-0.147960260670772),  RC(-0.402188192230535), RC(-0.703014530043888),  RC(0.00941974677418186),  RC(0.885747111289207),    RC(0.261314066449028),  RC(0.16307697503668),    RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)               },
691d27334e2SStefano Zampini       {RC(0.165597241042244),   RC(0.824182962188923),  RC(-0.0280136160783609), RC(0.282372386631758),    RC(-0.957721354131182),   RC(0.489439550159977),  RC(0.170094415598103),   RC(0.0522519785718563),   RC(0.0),                RC(0.0),                 RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)               },
692d27334e2SStefano Zampini       {RC(0.0335292011495618),  RC(0.575750388029166),  RC(0.223289855356637),   RC(-0.00317458833242804), RC(-0.112890382135193),   RC(-0.419809267954284), RC(0.0466136902102104),  RC(-0.00115413813041085), RC(0.109685363692383),  RC(0.0),                 RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)               },
693d27334e2SStefano Zampini       {RC(-0.0512616878252355), RC(0.699261265830807),  RC(-0.117939611738769),  RC(0.0021745241931243),   RC(-0.00932826702640947), RC(-0.267575057469428), RC(0.126949139814065),   RC(0.00330353204502163),  RC(0.185949445053766),  RC(0.0938215615963721),  RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)               },
694d27334e2SStefano Zampini       {RC(-0.106521517960343),  RC(0.41835889096168),   RC(0.353585905881916),   RC(-0.0746474161579599),  RC(-0.015450626460289),   RC(-0.46224659192275),  RC(-0.0576406327329181), RC(-0.00712066942504018), RC(0.377776558014452),  RC(0.36890054338294),    RC(0.0618488746331837), RC(0.0),                RC(0.0),                RC(0.0)               },
695d27334e2SStefano Zampini       {RC(-0.163079104890997),  RC(0.644561721693806),  RC(0.636968661639572),   RC(-0.122346720085377),   RC(-0.333062564990312),   RC(-0.3054226490478),   RC(-0.357820712828352),  RC(-0.0125510510334706),  RC(0.371263681186311),  RC(0.371979640363694),   RC(0.0531090658708968), RC(0.0518279459132049), RC(0.0),                RC(0.0)               },
696d27334e2SStefano Zampini       {RC(0.579993784455521),   RC(-0.188833728676494), RC(0.999975696843775),   RC(0.0572810855901161),   RC(-0.264374735003671),   RC(0.165091739976854),  RC(-0.546675809010452),  RC(-0.0283821822291982),  RC(-0.102639860418374), RC(-0.0343251040446405), RC(0.4762598462591),    RC(-0.304153104931261), RC(0.0953911855943621), RC(0.0)               },
697d27334e2SStefano Zampini       {RC(0.0848552694007844),  RC(0.287193912340074),  RC(0.543683503004232),   RC(-0.081311059300692),   RC(-0.0328661289388557),  RC(-0.323456834372922), RC(-0.240378871658975),  RC(-0.0189913019930369),  RC(0.220663114082036),  RC(0.253029984360864),   RC(0.252011799370563),  RC(-0.154882222605423), RC(0.0315202264687415), RC(0.0514095812104714)}
698d27334e2SStefano Zampini     };
699d27334e2SStefano Zampini     const PetscReal b[14] = {RC(0.0), RC(0.516650324205117), RC(0.0773227217357826), RC(-0.12474204666975), RC(-0.0241052115180679), RC(-0.325821145180359), RC(0.0907237460123951), RC(0.0459271880596652), RC(0.221012259404702), RC(0.235510906761942), RC(0.491109674204385), RC(-0.323506525837343), RC(0.119918108821531), RC(0.0)};
700d27334e2SStefano Zampini     const PetscReal bembed[14] = {RC(2.32345691433618e-16), RC(0.499150900944401), RC(0.080991997189243), RC(-0.0359440417166322), RC(-0.0258910397441454), RC(-0.304540350278636),  RC(0.0836627473632563),
701d27334e2SStefano Zampini                                   RC(0.0417664613347638),   RC(0.223636394275293), RC(0.231569156867596), RC(0.240526201277663),   RC(-0.222933582911926),  RC(-0.0111479879597561), RC(0.19915314335888)};
702d27334e2SStefano Zampini     PetscCall(TSDIRKRegister(TSDIRK8614A, 8, 14, &A[0][0], b, NULL, bembed, 1, b));
703d27334e2SStefano Zampini   }
704d27334e2SStefano Zampini   {
705d27334e2SStefano Zampini     // DIRK(15,8)[1]SAL[(16,6)A] from https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs
706d27334e2SStefano Zampini     const PetscReal A[16][16] = {
707d27334e2SStefano Zampini       {RC(0.498904981271193),   RC(0.0),                  RC(0.0),                 RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                RC(0.0),                 RC(0.0),                   RC(0.0),                 RC(0.0),                  RC(0.0),                 RC(0.0),               RC(0.0),                 RC(0.0),                 RC(0.0)              },
708d27334e2SStefano Zampini       {RC(-0.303806037341816),  RC(0.886299445992379),    RC(0.0),                 RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                RC(0.0),                 RC(0.0),                   RC(0.0),                 RC(0.0),                  RC(0.0),                 RC(0.0),               RC(0.0),                 RC(0.0),                 RC(0.0)              },
709d27334e2SStefano Zampini       {RC(-0.581440223471476),  RC(0.371003719460259),    RC(0.43844717752802),    RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                RC(0.0),                 RC(0.0),                   RC(0.0),                 RC(0.0),                  RC(0.0),                 RC(0.0),               RC(0.0),                 RC(0.0),                 RC(0.0)              },
710d27334e2SStefano Zampini       {RC(0.531852638870051),   RC(-0.339363014907108),   RC(0.422373239795441),   RC(0.223854203543397),    RC(0.0),                RC(0.0),                 RC(0.0),                RC(0.0),                 RC(0.0),                   RC(0.0),                 RC(0.0),                  RC(0.0),                 RC(0.0),               RC(0.0),                 RC(0.0),                 RC(0.0)              },
711d27334e2SStefano Zampini       {RC(0.118517891868867),   RC(-0.0756235584174296),  RC(-0.0864284870668712), RC(0.000536692838658312), RC(0.10101418329932),   RC(0.0),                 RC(0.0),                RC(0.0),                 RC(0.0),                   RC(0.0),                 RC(0.0),                  RC(0.0),                 RC(0.0),               RC(0.0),                 RC(0.0),                 RC(0.0)              },
712d27334e2SStefano Zampini       {RC(0.218733626116401),   RC(-0.139568928299635),   RC(0.30473612813488),    RC(0.00354038623073564),  RC(0.0932085751160559), RC(0.140161806097591),   RC(0.0),                RC(0.0),                 RC(0.0),                   RC(0.0),                 RC(0.0),                  RC(0.0),                 RC(0.0),               RC(0.0),                 RC(0.0),                 RC(0.0)              },
713d27334e2SStefano Zampini       {RC(0.0692944686081835),  RC(-0.0442152168939502),  RC(-0.0903375348855603), RC(0.00259030241156141),  RC(0.204514233679515),  RC(-0.0245383758960002), RC(0.199289437094059),  RC(0.0),                 RC(0.0),                   RC(0.0),                 RC(0.0),                  RC(0.0),                 RC(0.0),               RC(0.0),                 RC(0.0),                 RC(0.0)              },
714d27334e2SStefano Zampini       {RC(0.990640016505571),   RC(-0.632104756315967),   RC(0.856971425234221),   RC(0.174494099232246),    RC(-0.113715829680145), RC(-0.151494045307366),  RC(-0.438268629569005), RC(0.120578398912139),   RC(0.0),                   RC(0.0),                 RC(0.0),                  RC(0.0),                 RC(0.0),               RC(0.0),                 RC(0.0),                 RC(0.0)              },
715d27334e2SStefano Zampini       {RC(-0.099415677713136),  RC(0.211832014309207),    RC(-0.245998265866888),  RC(-0.182249672235861),   RC(0.167897635713799),  RC(0.212850335030069),   RC(-0.391739299440123), RC(-0.0118718506876767), RC(0.526293701659093),     RC(0.0),                 RC(0.0),                  RC(0.0),                 RC(0.0),               RC(0.0),                 RC(0.0),                 RC(0.0)              },
716d27334e2SStefano Zampini       {RC(0.383983914845461),   RC(-0.245011361219604),   RC(0.46717278554955),    RC(-0.0361272447593202),  RC(0.0742234660511333), RC(-0.0474816271948766), RC(-0.229859978525756), RC(0.0516283729206322),  RC(0.0),                   RC(0.193823890777594),   RC(0.0),                  RC(0.0),                 RC(0.0),               RC(0.0),                 RC(0.0),                 RC(0.0)              },
717d27334e2SStefano Zampini       {RC(0.0967855003180134),  RC(-0.0481037037916184),  RC(0.191268138832434),   RC(0.234977164564126),    RC(0.0620265921753097), RC(0.403432826534738),   RC(0.152403846687238),  RC(-0.118420429237746),  RC(0.0582141598685892),    RC(-0.13924540906863),   RC(0.106661313117545),    RC(0.0),                 RC(0.0),               RC(0.0),                 RC(0.0),                 RC(0.0)              },
718d27334e2SStefano Zampini       {RC(0.133941307432055),   RC(-0.0722076602896254),  RC(0.217086297689275),   RC(0.00495499602192887),  RC(0.0306090174933995), RC(0.26483526755746),    RC(0.204442440745605),  RC(0.196883395136708),   RC(0.056527012583996),     RC(-0.150216381356784),  RC(-0.217209415757333),   RC(0.330353722743315),   RC(0.0),               RC(0.0),                 RC(0.0),                 RC(0.0)              },
719d27334e2SStefano Zampini       {RC(0.157014274561299),   RC(-0.0883810256381874),  RC(0.117193033885034),   RC(-0.0362304243769466),  RC(0.0169030211466111), RC(-0.169835753576141),  RC(0.399749979234113),  RC(0.31806704093008),    RC(0.050340008347693),     RC(0.120284837472214),   RC(-0.235313193645423),   RC(0.232488522208926),   RC(0.117719679450729), RC(0.0),                 RC(0.0),                 RC(0.0)              },
720d27334e2SStefano Zampini       {RC(0.00276453816875833), RC(-0.00366028255231782), RC(-0.331078914515559),  RC(0.623377549031949),    RC(0.167618142989491),  RC(0.0748467945312516),  RC(0.797629286699677),  RC(-0.390714256799583),  RC(-0.00808553925131555),  RC(0.014840324980952),   RC(-0.0856180410248133),  RC(0.602943304937827),   RC(-0.5771359338496),  RC(0.112273026653282),   RC(0.0),                 RC(0.0)              },
721d27334e2SStefano Zampini       {RC(0.0),                 RC(0.0),                  RC(0.085283971980307),   RC(0.51334393454179),     RC(0.144355978013514),  RC(0.255379109487853),   RC(0.225075750790524),  RC(-0.343241323394982),  RC(0.0),                   RC(0.0798250392218852),  RC(0.0528824734082655),   RC(-0.0830350888900362), RC(0.022567388707279), RC(-0.0592631119040204), RC(0.106825878037621),   RC(0.0)              },
722d27334e2SStefano Zampini       {RC(0.173784481207652),   RC(-0.110887906116241),   RC(0.190052513365204),   RC(-0.0688345422674029),  RC(0.10326505079603),   RC(0.267127097115219),   RC(0.141703423176897),  RC(0.0117966866651728),  RC(-6.65650091812762e-15), RC(-0.0213725083662519), RC(-0.00931148598712566), RC(-0.10007679077114),   RC(0.123471797451553), RC(0.00203684241073055), RC(-0.0294320891781173), RC(0.195746619921528)}
723d27334e2SStefano Zampini     };
724d27334e2SStefano Zampini     const PetscReal b[16] = {RC(0.0), RC(0.0), RC(0.085283971980307), RC(0.51334393454179), RC(0.144355978013514), RC(0.255379109487853), RC(0.225075750790524), RC(-0.343241323394982), RC(0.0), RC(0.0798250392218852), RC(0.0528824734082655), RC(-0.0830350888900362), RC(0.022567388707279), RC(-0.0592631119040204), RC(0.106825878037621), RC(0.0)};
725d27334e2SStefano Zampini     const PetscReal bembed[16] = {RC(-1.31988512519898e-15), RC(7.53606601764004e-16), RC(0.0886789133915965),   RC(0.0968726531622137),  RC(0.143815375874267),     RC(0.335214773313601),  RC(0.221862366978063),  RC(-0.147408947987273),
726d27334e2SStefano Zampini                                   RC(4.16297599203445e-16),  RC(0.000727276166520566), RC(-0.00284892677941246), RC(0.00512492274297611), RC(-0.000275595071215218), RC(0.0136014719350733), RC(0.0165190013607726), RC(0.228116714912817)};
727d27334e2SStefano Zampini     PetscCall(TSDIRKRegister(TSDIRK8616SAL, 8, 16, &A[0][0], b, NULL, bembed, 1, b));
728d27334e2SStefano Zampini   }
729d27334e2SStefano Zampini   {
730d27334e2SStefano Zampini     // ESDIRK(16,8)[2]SAL[(16,5)] from https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs
731d27334e2SStefano Zampini     const PetscReal A[16][16] = {
732d27334e2SStefano Zampini       {RC(0.0),                  RC(0.0),                 RC(0.0),                  RC(0.0),                   RC(0.0),                  RC(0.0),                  RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                 RC(0.0),                RC(0.0),                 RC(0.0),                 RC(0.0),                  RC(0.0),               RC(0.0)              },
733d27334e2SStefano Zampini       {RC(0.117318819358521),    RC(0.117318819358521),   RC(0.0),                  RC(0.0),                   RC(0.0),                  RC(0.0),                  RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                 RC(0.0),                RC(0.0),                 RC(0.0),                 RC(0.0),                  RC(0.0),               RC(0.0)              },
734d27334e2SStefano Zampini       {RC(0.0557014605974616),   RC(0.385525646638742),   RC(0.117318819358521),    RC(0.0),                   RC(0.0),                  RC(0.0),                  RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                 RC(0.0),                RC(0.0),                 RC(0.0),                 RC(0.0),                  RC(0.0),               RC(0.0)              },
735d27334e2SStefano Zampini       {RC(0.063493276428895),    RC(0.373556126263681),   RC(0.0082994166438953),   RC(0.117318819358521),     RC(0.0),                  RC(0.0),                  RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                 RC(0.0),                RC(0.0),                 RC(0.0),                 RC(0.0),                  RC(0.0),               RC(0.0)              },
736d27334e2SStefano Zampini       {RC(0.0961351856230088),   RC(0.335558324517178),   RC(0.207077765910132),    RC(-0.0581917140797146),   RC(0.117318819358521),    RC(0.0),                  RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                 RC(0.0),                RC(0.0),                 RC(0.0),                 RC(0.0),                  RC(0.0),               RC(0.0)              },
737d27334e2SStefano Zampini       {RC(0.0497669214238319),   RC(0.384288616546039),   RC(0.0821728117583936),   RC(0.120337007107103),     RC(0.202262782645888),    RC(0.117318819358521),    RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                 RC(0.0),                RC(0.0),                 RC(0.0),                 RC(0.0),                  RC(0.0),               RC(0.0)              },
738d27334e2SStefano Zampini       {RC(0.00626710666809847),  RC(0.496491452640725),   RC(-0.111303249827358),   RC(0.170478821683603),     RC(0.166517073971103),    RC(-0.0328669811542241),  RC(0.117318819358521),    RC(0.0),                RC(0.0),                 RC(0.0),                 RC(0.0),                RC(0.0),                 RC(0.0),                 RC(0.0),                  RC(0.0),               RC(0.0)              },
739d27334e2SStefano Zampini       {RC(0.0463439767281591),   RC(0.00306724391019652), RC(-0.00816305222386205), RC(-0.0353302599538294),   RC(0.0139313601702569),   RC(-0.00992014507967429), RC(0.0210087909090165),   RC(0.117318819358521),  RC(0.0),                 RC(0.0),                 RC(0.0),                RC(0.0),                 RC(0.0),                 RC(0.0),                  RC(0.0),               RC(0.0)              },
740d27334e2SStefano Zampini       {RC(0.111574049232048),    RC(0.467639166482209),   RC(0.237773114804619),    RC(0.0798895699267508),    RC(0.109580615914593),    RC(0.0307353103825936),   RC(-0.0404391509541147),  RC(-0.16942110744293),  RC(0.117318819358521),   RC(0.0),                 RC(0.0),                RC(0.0),                 RC(0.0),                 RC(0.0),                  RC(0.0),               RC(0.0)              },
741d27334e2SStefano Zampini       {RC(-0.0107072484863877),  RC(-0.231376703354252),  RC(0.017541113036611),    RC(0.144871527682418),     RC(-0.041855459769806),   RC(0.0841832168332261),   RC(-0.0850020937282192),  RC(0.486170343825899),  RC(-0.0526717116822739), RC(0.117318819358521),   RC(0.0),                RC(0.0),                 RC(0.0),                 RC(0.0),                  RC(0.0),               RC(0.0)              },
742d27334e2SStefano Zampini       {RC(-0.0142238262314935),  RC(0.14752923682514),    RC(0.238235830732566),    RC(0.037950291904103),     RC(0.252075123381518),    RC(0.0474266904224567),   RC(-0.00363139069342027), RC(0.274081442388563),  RC(-0.0599166970745255), RC(-0.0527138812389185), RC(0.117318819358521),  RC(0.0),                 RC(0.0),                 RC(0.0),                  RC(0.0),               RC(0.0)              },
743d27334e2SStefano Zampini       {RC(-0.11837020183211),    RC(-0.635712481821264),  RC(0.239738832602538),    RC(0.330058936651707),     RC(-0.325784087988237),   RC(-0.0506514314589253),  RC(-0.281914404487009),   RC(0.852596345144291),  RC(0.651444614298805),   RC(-0.103476387303591),  RC(-0.354835880209975), RC(0.117318819358521),   RC(0.0),                 RC(0.0),                  RC(0.0),               RC(0.0)              },
744d27334e2SStefano Zampini       {RC(-0.00458164025442349), RC(0.296219694015248),   RC(0.322146049419995),    RC(0.15917778285238),      RC(0.284864871688843),    RC(0.185509526463076),    RC(-0.0784621067883274),  RC(0.166312223692047),  RC(-0.284152486083397),  RC(-0.357125104338944),  RC(0.078437074055306),  RC(0.0884129667114481),  RC(0.117318819358521),   RC(0.0),                  RC(0.0),               RC(0.0)              },
745d27334e2SStefano Zampini       {RC(-0.0545561913848106),  RC(0.675785423442753),   RC(0.423066443201941),    RC(-0.000165300126841193), RC(0.104252994793763),    RC(-0.105763019303021),   RC(-0.15988308809318),    RC(0.0515050001032011), RC(0.56013979290924),    RC(-0.45781539708603),   RC(-0.255870699752664), RC(0.026960254296416),   RC(-0.0721245985053681), RC(0.117318819358521),    RC(0.0),               RC(0.0)              },
746d27334e2SStefano Zampini       {RC(0.0649253995775223),   RC(-0.0216056457922249), RC(-0.073738139377975),   RC(0.0931033310077225),    RC(-0.0194339577299149),  RC(-0.0879623837313009),  RC(0.057125517179467),    RC(0.205120850488097),  RC(0.132576503537441),   RC(0.489416890627328),   RC(-0.1106765720501),   RC(-0.081038793996096),  RC(0.0606031613503788),  RC(-0.00241467937442272), RC(0.117318819358521), RC(0.0)              },
747d27334e2SStefano Zampini       {RC(0.0459979286336779),   RC(0.0780075394482806),  RC(0.015021874148058),    RC(0.195180277284195),     RC(-0.00246643310153235), RC(0.0473977117068314),   RC(-0.0682773558610363),  RC(0.19568019123878),   RC(-0.0876765449323747), RC(0.177874852409192),   RC(-0.337519251582222), RC(-0.0123255553640736), RC(0.311573291192553),   RC(0.0458604327754991),   RC(0.278352222645651), RC(0.117318819358521)}
748d27334e2SStefano Zampini     };
749d27334e2SStefano Zampini     const PetscReal b[16]      = {RC(0.0459979286336779),  RC(0.0780075394482806), RC(0.015021874148058),  RC(0.195180277284195),   RC(-0.00246643310153235), RC(0.0473977117068314), RC(-0.0682773558610363), RC(0.19568019123878),
750d27334e2SStefano Zampini                                   RC(-0.0876765449323747), RC(0.177874852409192),  RC(-0.337519251582222), RC(-0.0123255553640736), RC(0.311573291192553),    RC(0.0458604327754991), RC(0.278352222645651),   RC(0.117318819358521)};
751d27334e2SStefano Zampini     const PetscReal bembed[16] = {RC(0.0603373529853206),   RC(0.175453809423998),  RC(0.0537707777611352), RC(0.195309248607308),  RC(0.0135893741970232), RC(-0.0221160259296707), RC(-0.00726526156430691), RC(0.102961059369124),
752d27334e2SStefano Zampini                                   RC(0.000900215457460583), RC(0.0547959465692338), RC(-0.334995726863153), RC(0.0464409662093384), RC(0.301388101652194),  RC(0.00524851570622031), RC(0.229538601845236),    RC(0.124643044573514)};
753d27334e2SStefano Zampini     PetscCall(TSDIRKRegister(TSDIRKES8516SAL, 8, 16, &A[0][0], b, NULL, bembed, 1, b));
754d27334e2SStefano Zampini   }
755d27334e2SStefano Zampini 
756d27334e2SStefano Zampini   /* Additive methods */
757d27334e2SStefano Zampini   {
758d27334e2SStefano Zampini     const PetscReal A[3][3] = {
759e817cc15SEmil Constantinescu       {0.0, 0.0, 0.0},
7609371c9d4SSatish Balay       {0.0, 0.0, 0.0},
7619371c9d4SSatish Balay       {0.0, 0.5, 0.0}
762d27334e2SStefano Zampini     };
763d27334e2SStefano Zampini     const PetscReal At[3][3] = {
764d27334e2SStefano Zampini       {1.0, 0.0, 0.0},
765d27334e2SStefano Zampini       {0.0, 0.5, 0.0},
766d27334e2SStefano Zampini       {0.0, 0.5, 0.5}
767d27334e2SStefano Zampini     };
768d27334e2SStefano Zampini     const PetscReal b[3]       = {0.0, 0.5, 0.5};
769d27334e2SStefano Zampini     const PetscReal bembedt[3] = {1.0, 0.0, 0.0};
7709566063dSJacob Faibussowitsch     PetscCall(TSARKIMEXRegister(TSARKIMEX1BEE, 2, 3, &At[0][0], b, NULL, &A[0][0], b, NULL, bembedt, bembedt, 1, b, NULL));
771e817cc15SEmil Constantinescu   }
7728a381b04SJed Brown   {
773d27334e2SStefano Zampini     const PetscReal A[2][2] = {
7749371c9d4SSatish Balay       {0.0, 0.0},
7759371c9d4SSatish Balay       {0.5, 0.0}
776d27334e2SStefano Zampini     };
777d27334e2SStefano Zampini     const PetscReal At[2][2] = {
778d27334e2SStefano Zampini       {0.0, 0.0},
779d27334e2SStefano Zampini       {0.0, 0.5}
780d27334e2SStefano Zampini     };
781d27334e2SStefano Zampini     const PetscReal b[2]       = {0.0, 1.0};
782d27334e2SStefano Zampini     const PetscReal bembedt[2] = {0.5, 0.5};
7831f80e275SEmil Constantinescu     /* binterpt[2][2] = {{1.0,-1.0},{0.0,1.0}};  second order dense output has poor stability properties and hence it is not currently in use */
7849566063dSJacob Faibussowitsch     PetscCall(TSARKIMEXRegister(TSARKIMEXARS122, 2, 2, &At[0][0], b, NULL, &A[0][0], b, NULL, bembedt, bembedt, 1, b, NULL));
7851f80e275SEmil Constantinescu   }
7861f80e275SEmil Constantinescu   {
787d27334e2SStefano Zampini     const PetscReal A[2][2] = {
7889371c9d4SSatish Balay       {0.0, 0.0},
7899371c9d4SSatish Balay       {1.0, 0.0}
790d27334e2SStefano Zampini     };
791d27334e2SStefano Zampini     const PetscReal At[2][2] = {
792d27334e2SStefano Zampini       {0.0, 0.0},
793d27334e2SStefano Zampini       {0.5, 0.5}
794d27334e2SStefano Zampini     };
795d27334e2SStefano Zampini     const PetscReal b[2]       = {0.5, 0.5};
796d27334e2SStefano Zampini     const PetscReal bembedt[2] = {0.0, 1.0};
7971f80e275SEmil Constantinescu     /* binterpt[2][2] = {{1.0,-0.5},{0.0,0.5}}  second order dense output has poor stability properties and hence it is not currently in use */
7989566063dSJacob Faibussowitsch     PetscCall(TSARKIMEXRegister(TSARKIMEXA2, 2, 2, &At[0][0], b, NULL, &A[0][0], b, NULL, bembedt, bembedt, 1, b, NULL));
7991f80e275SEmil Constantinescu   }
8001f80e275SEmil Constantinescu   {
801d27334e2SStefano Zampini     const PetscReal A[2][2] = {
8029371c9d4SSatish Balay       {0.0, 0.0},
8039371c9d4SSatish Balay       {1.0, 0.0}
804d27334e2SStefano Zampini     };
805d27334e2SStefano Zampini     const PetscReal At[2][2] = {
806d27334e2SStefano Zampini       {us2,             0.0},
807d27334e2SStefano Zampini       {1.0 - 2.0 * us2, us2}
808d27334e2SStefano Zampini     };
809d27334e2SStefano Zampini     const PetscReal b[2]           = {0.5, 0.5};
810d27334e2SStefano Zampini     const PetscReal bembedt[2]     = {0.0, 1.0};
811d27334e2SStefano Zampini     const PetscReal binterpt[2][2] = {
812d27334e2SStefano Zampini       {(us2 - 1.0) / (2.0 * us2 - 1.0),     -1 / (2.0 * (1.0 - 2.0 * us2))},
813d27334e2SStefano Zampini       {1 - (us2 - 1.0) / (2.0 * us2 - 1.0), -1 / (2.0 * (1.0 - 2.0 * us2))}
814d27334e2SStefano Zampini     };
815d27334e2SStefano Zampini     const PetscReal binterp[2][2] = {
816d27334e2SStefano Zampini       {1.0, -0.5},
817d27334e2SStefano Zampini       {0.0, 0.5 }
818d27334e2SStefano Zampini     };
8199566063dSJacob Faibussowitsch     PetscCall(TSARKIMEXRegister(TSARKIMEXL2, 2, 2, &At[0][0], b, NULL, &A[0][0], b, NULL, bembedt, bembedt, 2, binterpt[0], binterp[0]));
8201f80e275SEmil Constantinescu   }
8211f80e275SEmil Constantinescu   {
822d27334e2SStefano Zampini     const PetscReal A[3][3] = {
8239371c9d4SSatish Balay       {0,      0,   0},
824d27334e2SStefano Zampini       {2 - s2, 0,   0},
8259371c9d4SSatish Balay       {0.5,    0.5, 0}
826d27334e2SStefano Zampini     };
827d27334e2SStefano Zampini     const PetscReal At[3][3] = {
828d27334e2SStefano Zampini       {0,            0,            0         },
829d27334e2SStefano Zampini       {1 - 1 / s2,   1 - 1 / s2,   0         },
830d27334e2SStefano Zampini       {1 / (2 * s2), 1 / (2 * s2), 1 - 1 / s2}
831d27334e2SStefano Zampini     };
832d27334e2SStefano Zampini     const PetscReal bembedt[3]     = {(4. - s2) / 8., (4. - s2) / 8., 1 / (2. * s2)};
833d27334e2SStefano Zampini     const PetscReal binterpt[3][2] = {
834d27334e2SStefano Zampini       {1.0 / s2, -1.0 / (2.0 * s2)},
835d27334e2SStefano Zampini       {1.0 / s2, -1.0 / (2.0 * s2)},
836d27334e2SStefano Zampini       {1.0 - s2, 1.0 / s2         }
837d27334e2SStefano Zampini     };
8389566063dSJacob Faibussowitsch     PetscCall(TSARKIMEXRegister(TSARKIMEX2C, 2, 3, &At[0][0], NULL, NULL, &A[0][0], NULL, NULL, bembedt, bembedt, 2, binterpt[0], NULL));
8391f80e275SEmil Constantinescu   }
8401f80e275SEmil Constantinescu   {
841d27334e2SStefano Zampini     const PetscReal A[3][3] = {
8429371c9d4SSatish Balay       {0,      0,    0},
843d27334e2SStefano Zampini       {2 - s2, 0,    0},
8449371c9d4SSatish Balay       {0.75,   0.25, 0}
845d27334e2SStefano Zampini     };
846d27334e2SStefano Zampini     const PetscReal At[3][3] = {
847d27334e2SStefano Zampini       {0,            0,            0         },
848d27334e2SStefano Zampini       {1 - 1 / s2,   1 - 1 / s2,   0         },
849d27334e2SStefano Zampini       {1 / (2 * s2), 1 / (2 * s2), 1 - 1 / s2}
850d27334e2SStefano Zampini     };
851d27334e2SStefano Zampini     const PetscReal bembedt[3]     = {(4. - s2) / 8., (4. - s2) / 8., 1 / (2. * s2)};
852d27334e2SStefano Zampini     const PetscReal binterpt[3][2] = {
853d27334e2SStefano Zampini       {1.0 / s2, -1.0 / (2.0 * s2)},
854d27334e2SStefano Zampini       {1.0 / s2, -1.0 / (2.0 * s2)},
855d27334e2SStefano Zampini       {1.0 - s2, 1.0 / s2         }
856d27334e2SStefano Zampini     };
8579566063dSJacob Faibussowitsch     PetscCall(TSARKIMEXRegister(TSARKIMEX2D, 2, 3, &At[0][0], NULL, NULL, &A[0][0], NULL, NULL, bembedt, bembedt, 2, binterpt[0], NULL));
8588a381b04SJed Brown   }
85906db7b1cSJed Brown   { /* Optimal for linear implicit part */
860d27334e2SStefano Zampini     const PetscReal A[3][3] = {
8619371c9d4SSatish Balay       {0,                0,                0},
862d27334e2SStefano Zampini       {2 - s2,           0,                0},
863d27334e2SStefano Zampini       {(3 - 2 * s2) / 6, (3 + 2 * s2) / 6, 0}
864d27334e2SStefano Zampini     };
865d27334e2SStefano Zampini     const PetscReal At[3][3] = {
866d27334e2SStefano Zampini       {0,            0,            0         },
867d27334e2SStefano Zampini       {1 - 1 / s2,   1 - 1 / s2,   0         },
868d27334e2SStefano Zampini       {1 / (2 * s2), 1 / (2 * s2), 1 - 1 / s2}
869d27334e2SStefano Zampini     };
870d27334e2SStefano Zampini     const PetscReal bembedt[3]     = {(4. - s2) / 8., (4. - s2) / 8., 1 / (2. * s2)};
871d27334e2SStefano Zampini     const PetscReal binterpt[3][2] = {
872d27334e2SStefano Zampini       {1.0 / s2, -1.0 / (2.0 * s2)},
873d27334e2SStefano Zampini       {1.0 / s2, -1.0 / (2.0 * s2)},
874d27334e2SStefano Zampini       {1.0 - s2, 1.0 / s2         }
875d27334e2SStefano Zampini     };
8769566063dSJacob Faibussowitsch     PetscCall(TSARKIMEXRegister(TSARKIMEX2E, 2, 3, &At[0][0], NULL, NULL, &A[0][0], NULL, NULL, bembedt, bembedt, 2, binterpt[0], NULL));
877a3a57f36SJed Brown   }
8786cf0794eSJed Brown   { /* Optimal for linear implicit part */
879d27334e2SStefano Zampini     const PetscReal A[3][3] = {
8809371c9d4SSatish Balay       {0,   0,   0},
8816cf0794eSJed Brown       {0.5, 0,   0},
8829371c9d4SSatish Balay       {0.5, 0.5, 0}
883d27334e2SStefano Zampini     };
884d27334e2SStefano Zampini     const PetscReal At[3][3] = {
885d27334e2SStefano Zampini       {0.25,   0,      0     },
886d27334e2SStefano Zampini       {0,      0.25,   0     },
887d27334e2SStefano Zampini       {1. / 3, 1. / 3, 1. / 3}
888d27334e2SStefano Zampini     };
8899566063dSJacob Faibussowitsch     PetscCall(TSARKIMEXRegister(TSARKIMEXPRSSP2, 2, 3, &At[0][0], NULL, NULL, &A[0][0], NULL, NULL, NULL, NULL, 0, NULL, NULL));
8906cf0794eSJed Brown   }
891a3a57f36SJed Brown   {
892d27334e2SStefano Zampini     const PetscReal A[4][4] = {
8939371c9d4SSatish Balay       {0,                                0,                                0,                                 0},
8944040e9f2SJed Brown       {1767732205903. / 2027836641118.,  0,                                0,                                 0},
8954040e9f2SJed Brown       {5535828885825. / 10492691773637., 788022342437. / 10882634858940.,  0,                                 0},
8969371c9d4SSatish Balay       {6485989280629. / 16251701735622., -4246266847089. / 9704473918619., 10755448449292. / 10357097424841., 0}
897d27334e2SStefano Zampini     };
898d27334e2SStefano Zampini     const PetscReal At[4][4] = {
899d27334e2SStefano Zampini       {0,                                0,                                0,                                 0                              },
900d27334e2SStefano Zampini       {1767732205903. / 4055673282236.,  1767732205903. / 4055673282236.,  0,                                 0                              },
901d27334e2SStefano Zampini       {2746238789719. / 10658868560708., -640167445237. / 6845629431997.,  1767732205903. / 4055673282236.,   0                              },
902d27334e2SStefano Zampini       {1471266399579. / 7840856788654.,  -4482444167858. / 7529755066697., 11266239266428. / 11593286722821., 1767732205903. / 4055673282236.}
903d27334e2SStefano Zampini     };
904d27334e2SStefano Zampini     const PetscReal bembedt[4]     = {2756255671327. / 12835298489170., -10771552573575. / 22201958757719., 9247589265047. / 10645013368117., 2193209047091. / 5459859503100.};
905d27334e2SStefano Zampini     const PetscReal binterpt[4][2] = {
906d27334e2SStefano Zampini       {4655552711362. / 22874653954995.,  -215264564351. / 13552729205753.  },
907d27334e2SStefano Zampini       {-18682724506714. / 9892148508045., 17870216137069. / 13817060693119. },
908d27334e2SStefano Zampini       {34259539580243. / 13192909600954., -28141676662227. / 17317692491321.},
909d27334e2SStefano Zampini       {584795268549. / 6622622206610.,    2508943948391. / 7218656332882.   }
910d27334e2SStefano Zampini     };
9119566063dSJacob Faibussowitsch     PetscCall(TSARKIMEXRegister(TSARKIMEX3, 3, 4, &At[0][0], NULL, NULL, &A[0][0], NULL, NULL, bembedt, bembedt, 2, binterpt[0], NULL));
912a3a57f36SJed Brown   }
913a3a57f36SJed Brown   {
914d27334e2SStefano Zampini     const PetscReal A[5][5] = {
9159371c9d4SSatish Balay       {0,        0,       0,      0,       0},
9166cf0794eSJed Brown       {1. / 2,   0,       0,      0,       0},
9176cf0794eSJed Brown       {11. / 18, 1. / 18, 0,      0,       0},
9186cf0794eSJed Brown       {5. / 6,   -5. / 6, .5,     0,       0},
9199371c9d4SSatish Balay       {1. / 4,   7. / 4,  3. / 4, -7. / 4, 0}
920d27334e2SStefano Zampini     };
921d27334e2SStefano Zampini     const PetscReal At[5][5] = {
922d27334e2SStefano Zampini       {0, 0,       0,       0,      0     },
923d27334e2SStefano Zampini       {0, 1. / 2,  0,       0,      0     },
924d27334e2SStefano Zampini       {0, 1. / 6,  1. / 2,  0,      0     },
925d27334e2SStefano Zampini       {0, -1. / 2, 1. / 2,  1. / 2, 0     },
926d27334e2SStefano Zampini       {0, 3. / 2,  -3. / 2, 1. / 2, 1. / 2}
927d27334e2SStefano Zampini     };
928d27334e2SStefano Zampini     PetscCall(TSARKIMEXRegister(TSARKIMEXARS443, 3, 5, &At[0][0], NULL, NULL, &A[0][0], NULL, NULL, NULL, NULL, 0, NULL, NULL));
9296cf0794eSJed Brown   }
9306cf0794eSJed Brown   {
931d27334e2SStefano Zampini     const PetscReal A[5][5] = {
9329371c9d4SSatish Balay       {0,      0,      0,      0, 0},
9336cf0794eSJed Brown       {1,      0,      0,      0, 0},
9346cf0794eSJed Brown       {4. / 9, 2. / 9, 0,      0, 0},
9356cf0794eSJed Brown       {1. / 4, 0,      3. / 4, 0, 0},
9369371c9d4SSatish Balay       {1. / 4, 0,      3. / 5, 0, 0}
937d27334e2SStefano Zampini     };
938d27334e2SStefano Zampini     const PetscReal At[5][5] = {
939d27334e2SStefano Zampini       {0,       0,       0,   0,   0 },
940d27334e2SStefano Zampini       {.5,      .5,      0,   0,   0 },
941d27334e2SStefano Zampini       {5. / 18, -1. / 9, .5,  0,   0 },
942d27334e2SStefano Zampini       {.5,      0,       0,   .5,  0 },
943d27334e2SStefano Zampini       {.25,     0,       .75, -.5, .5}
944d27334e2SStefano Zampini     };
945d27334e2SStefano Zampini     PetscCall(TSARKIMEXRegister(TSARKIMEXBPR3, 3, 5, &At[0][0], NULL, NULL, &A[0][0], NULL, NULL, NULL, NULL, 0, NULL, NULL));
9466cf0794eSJed Brown   }
9476cf0794eSJed Brown   {
948d27334e2SStefano Zampini     const PetscReal A[6][6] = {
9499371c9d4SSatish Balay       {0,                               0,                                 0,                                 0,                                0,              0},
950a3a57f36SJed Brown       {1. / 2,                          0,                                 0,                                 0,                                0,              0},
9514040e9f2SJed Brown       {13861. / 62500.,                 6889. / 62500.,                    0,                                 0,                                0,              0},
9524040e9f2SJed Brown       {-116923316275. / 2393684061468., -2731218467317. / 15368042101831., 9408046702089. / 11113171139209.,  0,                                0,              0},
9534040e9f2SJed Brown       {-451086348788. / 2902428689909., -2682348792572. / 7519795681897.,  12662868775082. / 11960479115383., 3355817975965. / 11060851509271., 0,              0},
9549371c9d4SSatish Balay       {647845179188. / 3216320057751.,  73281519250. / 8382639484533.,     552539513391. / 3454668386233.,    3354512671639. / 8306763924573.,  4040. / 17871., 0}
955d27334e2SStefano Zampini     };
956d27334e2SStefano Zampini     const PetscReal At[6][6] = {
957d27334e2SStefano Zampini       {0,                            0,                       0,                       0,                   0,             0     },
958d27334e2SStefano Zampini       {1. / 4,                       1. / 4,                  0,                       0,                   0,             0     },
959d27334e2SStefano Zampini       {8611. / 62500.,               -1743. / 31250.,         1. / 4,                  0,                   0,             0     },
960d27334e2SStefano Zampini       {5012029. / 34652500.,         -654441. / 2922500.,     174375. / 388108.,       1. / 4,              0,             0     },
961d27334e2SStefano Zampini       {15267082809. / 155376265600., -71443401. / 120774400., 730878875. / 902184768., 2285395. / 8070912., 1. / 4,        0     },
962d27334e2SStefano Zampini       {82889. / 524892.,             0,                       15625. / 83664.,         69875. / 102672.,    -2260. / 8211, 1. / 4}
963d27334e2SStefano Zampini     };
964d27334e2SStefano Zampini     const PetscReal bembedt[6]     = {4586570599. / 29645900160., 0, 178811875. / 945068544., 814220225. / 1159782912., -3700637. / 11593932., 61727. / 225920.};
965d27334e2SStefano Zampini     const PetscReal binterpt[6][3] = {
966d27334e2SStefano Zampini       {6943876665148. / 7220017795957.,   -54480133. / 30881146., 6818779379841. / 7100303317025.  },
967d27334e2SStefano Zampini       {0,                                 0,                      0                                },
968d27334e2SStefano Zampini       {7640104374378. / 9702883013639.,   -11436875. / 14766696., 2173542590792. / 12501825683035. },
969d27334e2SStefano Zampini       {-20649996744609. / 7521556579894., 174696575. / 18121608., -31592104683404. / 5083833661969.},
970d27334e2SStefano Zampini       {8854892464581. / 2390941311638.,   -12120380. / 966161.,   61146701046299. / 7138195549469. },
971d27334e2SStefano Zampini       {-11397109935349. / 6675773540249., 3843. / 706.,           -17219254887155. / 4939391667607.}
972d27334e2SStefano Zampini     };
9739566063dSJacob Faibussowitsch     PetscCall(TSARKIMEXRegister(TSARKIMEX4, 4, 6, &At[0][0], NULL, NULL, &A[0][0], NULL, NULL, bembedt, bembedt, 3, binterpt[0], NULL));
974a3a57f36SJed Brown   }
975a3a57f36SJed Brown   {
976d27334e2SStefano Zampini     const PetscReal A[8][8] = {
9779371c9d4SSatish Balay       {0,                                  0,                              0,                                 0,                                  0,                               0,                                 0,                               0},
978a3a57f36SJed Brown       {41. / 100,                          0,                              0,                                 0,                                  0,                               0,                                 0,                               0},
9794040e9f2SJed Brown       {367902744464. / 2072280473677.,     677623207551. / 8224143866563., 0,                                 0,                                  0,                               0,                                 0,                               0},
9804040e9f2SJed Brown       {1268023523408. / 10340822734521.,   0,                              1029933939417. / 13636558850479.,  0,                                  0,                               0,                                 0,                               0},
9814040e9f2SJed Brown       {14463281900351. / 6315353703477.,   0,                              66114435211212. / 5879490589093.,  -54053170152839. / 4284798021562.,  0,                               0,                                 0,                               0},
9824040e9f2SJed Brown       {14090043504691. / 34967701212078.,  0,                              15191511035443. / 11219624916014., -18461159152457. / 12425892160975., -281667163811. / 9011619295870., 0,                                 0,                               0},
9834040e9f2SJed Brown       {19230459214898. / 13134317526959.,  0,                              21275331358303. / 2942455364971.,  -38145345988419. / 4862620318723.,  -1. / 8,                         -1. / 8,                           0,                               0},
9849371c9d4SSatish Balay       {-19977161125411. / 11928030595625., 0,                              -40795976796054. / 6384907823539., 177454434618887. / 12078138498510., 782672205425. / 8267701900261.,  -69563011059811. / 9646580694205., 7356628210526. / 4942186776405., 0}
985d27334e2SStefano Zampini     };
986d27334e2SStefano Zampini     const PetscReal At[8][8] = {
987d27334e2SStefano Zampini       {0,                                0,                                0,                                 0,                                  0,                                0,                                  0,                                 0         },
988d27334e2SStefano Zampini       {41. / 200.,                       41. / 200.,                       0,                                 0,                                  0,                                0,                                  0,                                 0         },
989d27334e2SStefano Zampini       {41. / 400.,                       -567603406766. / 11931857230679., 41. / 200.,                        0,                                  0,                                0,                                  0,                                 0         },
990d27334e2SStefano Zampini       {683785636431. / 9252920307686.,   0,                                -110385047103. / 1367015193373.,   41. / 200.,                         0,                                0,                                  0,                                 0         },
991d27334e2SStefano Zampini       {3016520224154. / 10081342136671., 0,                                30586259806659. / 12414158314087., -22760509404356. / 11113319521817., 41. / 200.,                       0,                                  0,                                 0         },
992d27334e2SStefano Zampini       {218866479029. / 1489978393911.,   0,                                638256894668. / 5436446318841.,    -1179710474555. / 5321154724896.,   -60928119172. / 8023461067671.,   41. / 200.,                         0,                                 0         },
993d27334e2SStefano Zampini       {1020004230633. / 5715676835656.,  0,                                25762820946817. / 25263940353407., -2161375909145. / 9755907335909.,   -211217309593. / 5846859502534.,  -4269925059573. / 7827059040749.,   41. / 200,                         0         },
994d27334e2SStefano Zampini       {-872700587467. / 9133579230613.,  0,                                0,                                 22348218063261. / 9555858737531.,   -1143369518992. / 8141816002931., -39379526789629. / 19018526304540., 32727382324388. / 42900044865799., 41. / 200.}
995d27334e2SStefano Zampini     };
996d27334e2SStefano Zampini     const PetscReal bembedt[8]     = {-975461918565. / 9796059967033., 0, 0, 78070527104295. / 32432590147079., -548382580838. / 3424219808633., -33438840321285. / 15594753105479., 3629800801594. / 4656183773603., 4035322873751. / 18575991585200.};
997d27334e2SStefano Zampini     const PetscReal binterpt[8][3] = {
998d27334e2SStefano Zampini       {-17674230611817. / 10670229744614., 43486358583215. / 12773830924787.,  -9257016797708. / 5021505065439. },
999d27334e2SStefano Zampini       {0,                                  0,                                  0                                },
1000d27334e2SStefano Zampini       {0,                                  0,                                  0                                },
1001d27334e2SStefano Zampini       {65168852399939. / 7868540260826.,   -91478233927265. / 11067650958493., 26096422576131. / 11239449250142.},
1002d27334e2SStefano Zampini       {15494834004392. / 5936557850923.,   -79368583304911. / 10890268929626., 92396832856987. / 20362823103730.},
1003d27334e2SStefano Zampini       {-99329723586156. / 26959484932159., -12239297817655. / 9152339842473.,  30029262896817. / 10175596800299.},
1004d27334e2SStefano Zampini       {-19024464361622. / 5461577185407.,  115839755401235. / 10719374521269., -26136350496073. / 3983972220547.},
1005d27334e2SStefano Zampini       {-6511271360970. / 6095937251113.,   5843115559534. / 2180450260947.,    -5289405421727. / 3760307252460. }
1006d27334e2SStefano Zampini     };
10079566063dSJacob Faibussowitsch     PetscCall(TSARKIMEXRegister(TSARKIMEX5, 5, 8, &At[0][0], NULL, NULL, &A[0][0], NULL, NULL, bembedt, bembedt, 3, binterpt[0], NULL));
1008a3a57f36SJed Brown   }
1009d27334e2SStefano Zampini #undef RC
1010d27334e2SStefano Zampini #undef us2
1011d27334e2SStefano Zampini #undef s2
10123ba16761SJacob Faibussowitsch   PetscFunctionReturn(PETSC_SUCCESS);
10138a381b04SJed Brown }
10148a381b04SJed Brown 
10158a381b04SJed Brown /*@C
1016bcf0153eSBarry Smith   TSARKIMEXRegisterDestroy - Frees the list of schemes that were registered by `TSARKIMEXRegister()`.
10178a381b04SJed Brown 
10188a381b04SJed Brown   Not Collective
10198a381b04SJed Brown 
10208a381b04SJed Brown   Level: advanced
10218a381b04SJed Brown 
10221cc06b55SBarry Smith .seealso: [](ch_ts), `TSARKIMEX`, `TSARKIMEXRegister()`, `TSARKIMEXRegisterAll()`
10238a381b04SJed Brown @*/
1024d71ae5a4SJacob Faibussowitsch PetscErrorCode TSARKIMEXRegisterDestroy(void)
1025d71ae5a4SJacob Faibussowitsch {
10268a381b04SJed Brown   ARKTableauLink link;
10278a381b04SJed Brown 
10288a381b04SJed Brown   PetscFunctionBegin;
10298a381b04SJed Brown   while ((link = ARKTableauList)) {
10308a381b04SJed Brown     ARKTableau t   = &link->tab;
10318a381b04SJed Brown     ARKTableauList = link->next;
10329566063dSJacob Faibussowitsch     PetscCall(PetscFree6(t->At, t->bt, t->ct, t->A, t->b, t->c));
10339566063dSJacob Faibussowitsch     PetscCall(PetscFree2(t->bembedt, t->bembed));
10349566063dSJacob Faibussowitsch     PetscCall(PetscFree2(t->binterpt, t->binterp));
10359566063dSJacob Faibussowitsch     PetscCall(PetscFree(t->name));
10369566063dSJacob Faibussowitsch     PetscCall(PetscFree(link));
10378a381b04SJed Brown   }
10388a381b04SJed Brown   TSARKIMEXRegisterAllCalled = PETSC_FALSE;
10393ba16761SJacob Faibussowitsch   PetscFunctionReturn(PETSC_SUCCESS);
10408a381b04SJed Brown }
10418a381b04SJed Brown 
10428a381b04SJed Brown /*@C
1043bcf0153eSBarry Smith   TSARKIMEXInitializePackage - This function initializes everything in the `TSARKIMEX` package. It is called
1044bcf0153eSBarry Smith   from `TSInitializePackage()`.
10458a381b04SJed Brown 
10468a381b04SJed Brown   Level: developer
10478a381b04SJed Brown 
10481cc06b55SBarry Smith .seealso: [](ch_ts), `PetscInitialize()`, `TSARKIMEXFinalizePackage()`
10498a381b04SJed Brown @*/
1050d71ae5a4SJacob Faibussowitsch PetscErrorCode TSARKIMEXInitializePackage(void)
1051d71ae5a4SJacob Faibussowitsch {
10528a381b04SJed Brown   PetscFunctionBegin;
10533ba16761SJacob Faibussowitsch   if (TSARKIMEXPackageInitialized) PetscFunctionReturn(PETSC_SUCCESS);
10548a381b04SJed Brown   TSARKIMEXPackageInitialized = PETSC_TRUE;
10559566063dSJacob Faibussowitsch   PetscCall(TSARKIMEXRegisterAll());
10569566063dSJacob Faibussowitsch   PetscCall(PetscRegisterFinalize(TSARKIMEXFinalizePackage));
10573ba16761SJacob Faibussowitsch   PetscFunctionReturn(PETSC_SUCCESS);
10588a381b04SJed Brown }
10598a381b04SJed Brown 
10608a381b04SJed Brown /*@C
1061bcf0153eSBarry Smith   TSARKIMEXFinalizePackage - This function destroys everything in the `TSARKIMEX` package. It is
1062bcf0153eSBarry Smith   called from `PetscFinalize()`.
10638a381b04SJed Brown 
10648a381b04SJed Brown   Level: developer
10658a381b04SJed Brown 
10661cc06b55SBarry Smith .seealso: [](ch_ts), `PetscFinalize()`, `TSARKIMEXInitializePackage()`
10678a381b04SJed Brown @*/
1068d71ae5a4SJacob Faibussowitsch PetscErrorCode TSARKIMEXFinalizePackage(void)
1069d71ae5a4SJacob Faibussowitsch {
10708a381b04SJed Brown   PetscFunctionBegin;
10718a381b04SJed Brown   TSARKIMEXPackageInitialized = PETSC_FALSE;
10729566063dSJacob Faibussowitsch   PetscCall(TSARKIMEXRegisterDestroy());
10733ba16761SJacob Faibussowitsch   PetscFunctionReturn(PETSC_SUCCESS);
10748a381b04SJed Brown }
10758a381b04SJed Brown 
1076cd652676SJed Brown /*@C
1077bcf0153eSBarry Smith   TSARKIMEXRegister - register a `TSARKIMEX` scheme by providing the entries in the Butcher tableau and optionally embedded approximations and interpolation
1078cd652676SJed Brown 
1079cc4c1da9SBarry Smith   Logically Collective
1080cd652676SJed Brown 
1081cd652676SJed Brown   Input Parameters:
1082cd652676SJed Brown + name     - identifier for method
1083cd652676SJed Brown . order    - approximation order of method
1084cd652676SJed Brown . s        - number of stages, this is the dimension of the matrices below
1085cd652676SJed Brown . At       - Butcher table of stage coefficients for stiff part (dimension s*s, row-major)
10860298fd71SBarry Smith . bt       - Butcher table for completing the stiff part of the step (dimension s; NULL to use the last row of At)
10870298fd71SBarry Smith . ct       - Abscissa of each stiff stage (dimension s, NULL to use row sums of At)
1088cd652676SJed Brown . A        - Non-stiff stage coefficients (dimension s*s, row-major)
10890298fd71SBarry Smith . b        - Non-stiff step completion table (dimension s; NULL to use last row of At)
10900298fd71SBarry Smith . c        - Non-stiff abscissa (dimension s; NULL to use row sums of A)
10910298fd71SBarry Smith . bembedt  - Stiff part of completion table for embedded method (dimension s; NULL if not available)
10920298fd71SBarry Smith . bembed   - Non-stiff part of completion table for embedded method (dimension s; NULL to use bembedt if provided)
1093cd652676SJed Brown . pinterp  - Order of the interpolation scheme, equal to the number of columns of binterpt and binterp
1094cd652676SJed Brown . binterpt - Coefficients of the interpolation formula for the stiff part (dimension s*pinterp)
10950298fd71SBarry Smith - binterp  - Coefficients of the interpolation formula for the non-stiff part (dimension s*pinterp; NULL to reuse binterpt)
1096cd652676SJed Brown 
1097cd652676SJed Brown   Level: advanced
1098cd652676SJed Brown 
1099bcf0153eSBarry Smith   Note:
1100bcf0153eSBarry Smith   Several `TSARKIMEX` methods are provided, this function is only needed to create new methods.
1101bcf0153eSBarry Smith 
11021cc06b55SBarry Smith .seealso: [](ch_ts), `TSARKIMEX`, `TSType`, `TS`
1103cd652676SJed Brown @*/
1104d71ae5a4SJacob Faibussowitsch PetscErrorCode TSARKIMEXRegister(TSARKIMEXType name, PetscInt order, PetscInt s, const PetscReal At[], const PetscReal bt[], const PetscReal ct[], const PetscReal A[], const PetscReal b[], const PetscReal c[], const PetscReal bembedt[], const PetscReal bembed[], PetscInt pinterp, const PetscReal binterpt[], const PetscReal binterp[])
1105d71ae5a4SJacob Faibussowitsch {
11068a381b04SJed Brown   ARKTableauLink link;
11078a381b04SJed Brown   ARKTableau     t;
11088a381b04SJed Brown   PetscInt       i, j;
11098a381b04SJed Brown 
11108a381b04SJed Brown   PetscFunctionBegin;
1111a748edf9SJed Brown   PetscCheck(s > 0, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Expected number of stages s %" PetscInt_FMT " > 0", s);
11129566063dSJacob Faibussowitsch   PetscCall(TSARKIMEXInitializePackage());
1113d27334e2SStefano Zampini   for (link = ARKTableauList; link; link = link->next) {
1114d27334e2SStefano Zampini     PetscBool match;
1115d27334e2SStefano Zampini 
1116d27334e2SStefano Zampini     PetscCall(PetscStrcmp(link->tab.name, name, &match));
1117d27334e2SStefano Zampini     PetscCheck(!match, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Method with name \"%s\" already registered", name);
1118d27334e2SStefano Zampini   }
11199566063dSJacob Faibussowitsch   PetscCall(PetscNew(&link));
11208a381b04SJed Brown   t = &link->tab;
11219566063dSJacob Faibussowitsch   PetscCall(PetscStrallocpy(name, &t->name));
11228a381b04SJed Brown   t->order = order;
11238a381b04SJed Brown   t->s     = s;
11249566063dSJacob Faibussowitsch   PetscCall(PetscMalloc6(s * s, &t->At, s, &t->bt, s, &t->ct, s * s, &t->A, s, &t->b, s, &t->c));
11259566063dSJacob Faibussowitsch   PetscCall(PetscArraycpy(t->At, At, s * s));
1126d27334e2SStefano Zampini   if (A) {
11279566063dSJacob Faibussowitsch     PetscCall(PetscArraycpy(t->A, A, s * s));
1128d27334e2SStefano Zampini     t->additive = PETSC_TRUE;
1129d27334e2SStefano Zampini   }
1130d27334e2SStefano Zampini 
11319566063dSJacob Faibussowitsch   if (bt) PetscCall(PetscArraycpy(t->bt, bt, s));
11329371c9d4SSatish Balay   else
11339371c9d4SSatish Balay     for (i = 0; i < s; i++) t->bt[i] = At[(s - 1) * s + i];
1134d27334e2SStefano Zampini 
1135d27334e2SStefano Zampini   if (t->additive) {
11369566063dSJacob Faibussowitsch     if (b) PetscCall(PetscArraycpy(t->b, b, s));
11379371c9d4SSatish Balay     else
11389371c9d4SSatish Balay       for (i = 0; i < s; i++) t->b[i] = t->bt[i];
1139d27334e2SStefano Zampini   } else PetscCall(PetscArrayzero(t->b, s));
1140d27334e2SStefano Zampini 
11419566063dSJacob Faibussowitsch   if (ct) PetscCall(PetscArraycpy(t->ct, ct, s));
11429371c9d4SSatish Balay   else
11439371c9d4SSatish Balay     for (i = 0; i < s; i++)
11449371c9d4SSatish Balay       for (j = 0, t->ct[i] = 0; j < s; j++) t->ct[i] += At[i * s + j];
1145d27334e2SStefano Zampini 
1146d27334e2SStefano Zampini   if (t->additive) {
11479566063dSJacob Faibussowitsch     if (c) PetscCall(PetscArraycpy(t->c, c, s));
11489371c9d4SSatish Balay     else
11499371c9d4SSatish Balay       for (i = 0; i < s; i++)
11509371c9d4SSatish Balay         for (j = 0, t->c[i] = 0; j < s; j++) t->c[i] += A[i * s + j];
1151d27334e2SStefano Zampini   } else PetscCall(PetscArrayzero(t->c, s));
1152d27334e2SStefano Zampini 
1153e817cc15SEmil Constantinescu   t->stiffly_accurate = PETSC_TRUE;
11549371c9d4SSatish Balay   for (i = 0; i < s; i++)
11559371c9d4SSatish Balay     if (t->At[(s - 1) * s + i] != t->bt[i]) t->stiffly_accurate = PETSC_FALSE;
1156d27334e2SStefano Zampini 
1157e817cc15SEmil Constantinescu   t->explicit_first_stage = PETSC_TRUE;
11589371c9d4SSatish Balay   for (i = 0; i < s; i++)
11599371c9d4SSatish Balay     if (t->At[i] != 0.0) t->explicit_first_stage = PETSC_FALSE;
1160d27334e2SStefano Zampini 
1161e817cc15SEmil Constantinescu   /* def of FSAL can be made more precise */
11624e9d4bf5SJed Brown   t->FSAL_implicit = (PetscBool)(t->explicit_first_stage && t->stiffly_accurate);
1163d27334e2SStefano Zampini 
1164108c343cSJed Brown   if (bembedt) {
11659566063dSJacob Faibussowitsch     PetscCall(PetscMalloc2(s, &t->bembedt, s, &t->bembed));
11669566063dSJacob Faibussowitsch     PetscCall(PetscArraycpy(t->bembedt, bembedt, s));
11679566063dSJacob Faibussowitsch     PetscCall(PetscArraycpy(t->bembed, bembed ? bembed : bembedt, s));
1168108c343cSJed Brown   }
1169108c343cSJed Brown 
11704f385281SJed Brown   t->pinterp = pinterp;
11719566063dSJacob Faibussowitsch   PetscCall(PetscMalloc2(s * pinterp, &t->binterpt, s * pinterp, &t->binterp));
11729566063dSJacob Faibussowitsch   PetscCall(PetscArraycpy(t->binterpt, binterpt, s * pinterp));
11739566063dSJacob Faibussowitsch   PetscCall(PetscArraycpy(t->binterp, binterp ? binterp : binterpt, s * pinterp));
1174d27334e2SStefano Zampini 
11758a381b04SJed Brown   link->next     = ARKTableauList;
11768a381b04SJed Brown   ARKTableauList = link;
11773ba16761SJacob Faibussowitsch   PetscFunctionReturn(PETSC_SUCCESS);
11788a381b04SJed Brown }
11798a381b04SJed Brown 
1180d27334e2SStefano Zampini /*@C
1181d27334e2SStefano Zampini   TSDIRKRegister - register a `TSDIRK` scheme by providing the entries in its Butcher tableau and, optionally, embedded approximations and interpolation
1182d27334e2SStefano Zampini 
1183d27334e2SStefano Zampini   Logically Collective.
1184d27334e2SStefano Zampini 
1185d27334e2SStefano Zampini   Input Parameters:
1186d27334e2SStefano Zampini + name     - identifier for method
1187d27334e2SStefano Zampini . order    - approximation order of method
1188d27334e2SStefano Zampini . s        - number of stages, this is the dimension of the matrices below
1189d27334e2SStefano Zampini . At       - Butcher table of stage coefficients (dimension `s`*`s`, row-major order)
1190d27334e2SStefano Zampini . bt       - Butcher table for completing the step (dimension `s`; pass `NULL` to use the last row of `At`)
1191d27334e2SStefano Zampini . ct       - Abscissa of each stage (dimension s, NULL to use row sums of At)
1192d27334e2SStefano Zampini . bembedt  - Stiff part of completion table for embedded method (dimension s; `NULL` if not available)
1193d27334e2SStefano Zampini . pinterp  - Order of the interpolation scheme, equal to the number of columns of `binterpt` and `binterp`
1194d27334e2SStefano Zampini - binterpt - Coefficients of the interpolation formula (dimension s*pinterp)
1195d27334e2SStefano Zampini 
1196d27334e2SStefano Zampini   Level: advanced
1197d27334e2SStefano Zampini 
1198d27334e2SStefano Zampini   Note:
1199d27334e2SStefano Zampini   Several `TSDIRK` methods are provided, the use of this function is only needed to create new methods.
1200d27334e2SStefano Zampini 
1201d27334e2SStefano Zampini .seealso: [](ch_ts), `TSDIRK`, `TSType`, `TS`
1202d27334e2SStefano Zampini @*/
1203d27334e2SStefano Zampini PetscErrorCode TSDIRKRegister(TSDIRKType name, PetscInt order, PetscInt s, const PetscReal At[], const PetscReal bt[], const PetscReal ct[], const PetscReal bembedt[], PetscInt pinterp, const PetscReal binterpt[])
1204d27334e2SStefano Zampini {
1205d27334e2SStefano Zampini   PetscFunctionBegin;
1206d27334e2SStefano Zampini   PetscCall(TSARKIMEXRegister(name, order, s, At, bt, ct, NULL, NULL, NULL, bembedt, NULL, pinterp, binterpt, NULL));
1207d27334e2SStefano Zampini   PetscFunctionReturn(PETSC_SUCCESS);
1208d27334e2SStefano Zampini }
1209d27334e2SStefano Zampini 
1210108c343cSJed Brown /*
1211108c343cSJed Brown  The step completion formula is
1212108c343cSJed Brown 
1213108c343cSJed Brown  x1 = x0 - h bt^T YdotI + h b^T YdotRHS
1214108c343cSJed Brown 
1215108c343cSJed Brown  This function can be called before or after ts->vec_sol has been updated.
1216108c343cSJed Brown  Suppose we have a completion formula (bt,b) and an embedded formula (bet,be) of different order.
1217108c343cSJed Brown  We can write
1218108c343cSJed Brown 
1219108c343cSJed Brown  x1e = x0 - h bet^T YdotI + h be^T YdotRHS
1220108c343cSJed Brown      = x1 + h bt^T YdotI - h b^T YdotRHS - h bet^T YdotI + h be^T YdotRHS
1221108c343cSJed Brown      = x1 - h (bet - bt)^T YdotI + h (be - b)^T YdotRHS
1222108c343cSJed Brown 
1223108c343cSJed Brown  so we can evaluate the method with different order even after the step has been optimistically completed.
1224108c343cSJed Brown */
1225d71ae5a4SJacob Faibussowitsch static PetscErrorCode TSEvaluateStep_ARKIMEX(TS ts, PetscInt order, Vec X, PetscBool *done)
1226d71ae5a4SJacob Faibussowitsch {
1227108c343cSJed Brown   TS_ARKIMEX  *ark = (TS_ARKIMEX *)ts->data;
1228108c343cSJed Brown   ARKTableau   tab = ark->tableau;
1229108c343cSJed Brown   PetscScalar *w   = ark->work;
1230108c343cSJed Brown   PetscReal    h;
1231108c343cSJed Brown   PetscInt     s = tab->s, j;
1232d27334e2SStefano Zampini   PetscBool    hasE;
1233108c343cSJed Brown 
1234108c343cSJed Brown   PetscFunctionBegin;
1235108c343cSJed Brown   switch (ark->status) {
1236108c343cSJed Brown   case TS_STEP_INCOMPLETE:
1237d71ae5a4SJacob Faibussowitsch   case TS_STEP_PENDING:
1238d71ae5a4SJacob Faibussowitsch     h = ts->time_step;
1239d71ae5a4SJacob Faibussowitsch     break;
1240d71ae5a4SJacob Faibussowitsch   case TS_STEP_COMPLETE:
1241d71ae5a4SJacob Faibussowitsch     h = ts->ptime - ts->ptime_prev;
1242d71ae5a4SJacob Faibussowitsch     break;
1243d71ae5a4SJacob Faibussowitsch   default:
1244d71ae5a4SJacob Faibussowitsch     SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_PLIB, "Invalid TSStepStatus");
1245108c343cSJed Brown   }
1246108c343cSJed Brown   if (order == tab->order) {
1247e817cc15SEmil Constantinescu     if (ark->status == TS_STEP_INCOMPLETE) {
1248740132f1SEmil Constantinescu       if (!ark->imex && tab->stiffly_accurate) { /* Only the stiffly accurate implicit formula is used */
12499566063dSJacob Faibussowitsch         PetscCall(VecCopy(ark->Y[s - 1], X));
1250e817cc15SEmil Constantinescu       } else { /* Use the standard completion formula (bt,b) */
12519566063dSJacob Faibussowitsch         PetscCall(VecCopy(ts->vec_sol, X));
1252e817cc15SEmil Constantinescu         for (j = 0; j < s; j++) w[j] = h * tab->bt[j];
12539566063dSJacob Faibussowitsch         PetscCall(VecMAXPY(X, s, w, ark->YdotI));
1254d27334e2SStefano Zampini         if (tab->additive && ark->imex) { /* Method is IMEX, complete the explicit formula */
1255d27334e2SStefano Zampini           PetscCall(TSHasRHSFunction(ts, &hasE));
1256d27334e2SStefano Zampini           if (hasE) {
1257108c343cSJed Brown             for (j = 0; j < s; j++) w[j] = h * tab->b[j];
12589566063dSJacob Faibussowitsch             PetscCall(VecMAXPY(X, s, w, ark->YdotRHS));
1259e817cc15SEmil Constantinescu           }
1260e817cc15SEmil Constantinescu         }
1261d27334e2SStefano Zampini       }
12629566063dSJacob Faibussowitsch     } else PetscCall(VecCopy(ts->vec_sol, X));
1263108c343cSJed Brown     if (done) *done = PETSC_TRUE;
12643ba16761SJacob Faibussowitsch     PetscFunctionReturn(PETSC_SUCCESS);
1265108c343cSJed Brown   } else if (order == tab->order - 1) {
1266108c343cSJed Brown     if (!tab->bembedt) goto unavailable;
1267108c343cSJed Brown     if (ark->status == TS_STEP_INCOMPLETE) { /* Complete with the embedded method (bet,be) */
12689566063dSJacob Faibussowitsch       PetscCall(VecCopy(ts->vec_sol, X));
1269e817cc15SEmil Constantinescu       for (j = 0; j < s; j++) w[j] = h * tab->bembedt[j];
12709566063dSJacob Faibussowitsch       PetscCall(VecMAXPY(X, s, w, ark->YdotI));
1271d27334e2SStefano Zampini       if (tab->additive) {
1272d27334e2SStefano Zampini         PetscCall(TSHasRHSFunction(ts, &hasE));
1273d27334e2SStefano Zampini         if (hasE) {
1274108c343cSJed Brown           for (j = 0; j < s; j++) w[j] = h * tab->bembed[j];
12759566063dSJacob Faibussowitsch           PetscCall(VecMAXPY(X, s, w, ark->YdotRHS));
1276d27334e2SStefano Zampini         }
1277d27334e2SStefano Zampini       }
1278108c343cSJed Brown     } else { /* Rollback and re-complete using (bet-be,be-b) */
12799566063dSJacob Faibussowitsch       PetscCall(VecCopy(ts->vec_sol, X));
1280e817cc15SEmil Constantinescu       for (j = 0; j < s; j++) w[j] = h * (tab->bembedt[j] - tab->bt[j]);
12819566063dSJacob Faibussowitsch       PetscCall(VecMAXPY(X, tab->s, w, ark->YdotI));
1282d27334e2SStefano Zampini       if (tab->additive) {
1283d27334e2SStefano Zampini         PetscCall(TSHasRHSFunction(ts, &hasE));
1284d27334e2SStefano Zampini         if (hasE) {
1285108c343cSJed Brown           for (j = 0; j < s; j++) w[j] = h * (tab->bembed[j] - tab->b[j]);
12869566063dSJacob Faibussowitsch           PetscCall(VecMAXPY(X, s, w, ark->YdotRHS));
1287108c343cSJed Brown         }
1288d27334e2SStefano Zampini       }
1289d27334e2SStefano Zampini     }
1290108c343cSJed Brown     if (done) *done = PETSC_TRUE;
12913ba16761SJacob Faibussowitsch     PetscFunctionReturn(PETSC_SUCCESS);
1292108c343cSJed Brown   }
1293108c343cSJed Brown unavailable:
1294108c343cSJed Brown   if (done) *done = PETSC_FALSE;
12959371c9d4SSatish Balay   else
12969371c9d4SSatish Balay     SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_SUP, "ARKIMEX '%s' of order %" PetscInt_FMT " cannot evaluate step at order %" PetscInt_FMT ". Consider using -ts_adapt_type none or a different method that has an embedded estimate.", tab->name,
12979371c9d4SSatish Balay             tab->order, order);
12983ba16761SJacob Faibussowitsch   PetscFunctionReturn(PETSC_SUCCESS);
1299108c343cSJed Brown }
1300108c343cSJed Brown 
1301d71ae5a4SJacob Faibussowitsch static PetscErrorCode TSARKIMEXTestMassIdentity(TS ts, PetscBool *id)
1302d71ae5a4SJacob Faibussowitsch {
1303c79dcfbdSBarry Smith   Vec         Udot, Y1, Y2;
1304c79dcfbdSBarry Smith   TS_ARKIMEX *ark = (TS_ARKIMEX *)ts->data;
1305c79dcfbdSBarry Smith   PetscReal   norm;
1306c79dcfbdSBarry Smith 
1307c79dcfbdSBarry Smith   PetscFunctionBegin;
13089566063dSJacob Faibussowitsch   PetscCall(VecDuplicate(ts->vec_sol, &Udot));
13099566063dSJacob Faibussowitsch   PetscCall(VecDuplicate(ts->vec_sol, &Y1));
13109566063dSJacob Faibussowitsch   PetscCall(VecDuplicate(ts->vec_sol, &Y2));
13119566063dSJacob Faibussowitsch   PetscCall(TSComputeIFunction(ts, ts->ptime, ts->vec_sol, Udot, Y1, ark->imex));
13129566063dSJacob Faibussowitsch   PetscCall(VecSetRandom(Udot, NULL));
13139566063dSJacob Faibussowitsch   PetscCall(TSComputeIFunction(ts, ts->ptime, ts->vec_sol, Udot, Y2, ark->imex));
13149566063dSJacob Faibussowitsch   PetscCall(VecAXPY(Y2, -1.0, Y1));
13159566063dSJacob Faibussowitsch   PetscCall(VecAXPY(Y2, -1.0, Udot));
13169566063dSJacob Faibussowitsch   PetscCall(VecNorm(Y2, NORM_2, &norm));
1317c79dcfbdSBarry Smith   if (norm < 100.0 * PETSC_MACHINE_EPSILON) {
1318c79dcfbdSBarry Smith     *id = PETSC_TRUE;
1319c79dcfbdSBarry Smith   } else {
1320c79dcfbdSBarry Smith     *id = PETSC_FALSE;
13219566063dSJacob Faibussowitsch     PetscCall(PetscInfo((PetscObject)ts, "IFunction(Udot = random) - IFunction(Udot = 0) is not near Udot, %g, suspect mass matrix implied in IFunction() is not the identity as required\n", (double)norm));
1322c79dcfbdSBarry Smith   }
13239566063dSJacob Faibussowitsch   PetscCall(VecDestroy(&Udot));
13249566063dSJacob Faibussowitsch   PetscCall(VecDestroy(&Y1));
13259566063dSJacob Faibussowitsch   PetscCall(VecDestroy(&Y2));
13263ba16761SJacob Faibussowitsch   PetscFunctionReturn(PETSC_SUCCESS);
1327c79dcfbdSBarry Smith }
1328c79dcfbdSBarry Smith 
13290467964bSStefano Zampini static PetscErrorCode TSARKIMEXComputeAlgebraicIS(TS, PetscReal, Vec, IS *);
13300467964bSStefano Zampini 
1331d71ae5a4SJacob Faibussowitsch static PetscErrorCode TSStep_ARKIMEX(TS ts)
1332d71ae5a4SJacob Faibussowitsch {
13338a381b04SJed Brown   TS_ARKIMEX      *ark = (TS_ARKIMEX *)ts->data;
13348a381b04SJed Brown   ARKTableau       tab = ark->tableau;
13358a381b04SJed Brown   const PetscInt   s   = tab->s;
133624655328SShri   const PetscReal *At = tab->At, *A = tab->A, *ct = tab->ct, *c = tab->c;
1337406d0ec2SJed Brown   PetscScalar     *w = ark->work;
13381297b224SEmil Constantinescu   Vec             *Y = ark->Y, *YdotI = ark->YdotI, *YdotRHS = ark->YdotRHS, Ydot = ark->Ydot, Ydot0 = ark->Ydot0, Z = ark->Z;
133996400bd6SLisandro Dalcin   PetscBool        extrapolate = ark->extrapolate;
1340108c343cSJed Brown   TSAdapt          adapt;
13418a381b04SJed Brown   SNES             snes;
1342fecfb714SLisandro Dalcin   PetscInt         i, j, its, lits;
1343be5899b3SLisandro Dalcin   PetscInt         rejections = 0;
1344d27334e2SStefano Zampini   PetscBool        hasE = PETSC_FALSE, dirk = (PetscBool)(!tab->additive), stageok, accept = PETSC_TRUE;
134596400bd6SLisandro Dalcin   PetscReal        next_time_step = ts->time_step;
13468a381b04SJed Brown 
13478a381b04SJed Brown   PetscFunctionBegin;
134896400bd6SLisandro Dalcin   if (ark->extrapolate && !ark->Y_prev) {
13499566063dSJacob Faibussowitsch     PetscCall(VecDuplicateVecs(ts->vec_sol, tab->s, &ark->Y_prev));
13509566063dSJacob Faibussowitsch     PetscCall(VecDuplicateVecs(ts->vec_sol, tab->s, &ark->YdotI_prev));
1351d27334e2SStefano Zampini     if (tab->additive) PetscCall(VecDuplicateVecs(ts->vec_sol, tab->s, &ark->YdotRHS_prev));
135296400bd6SLisandro Dalcin   }
135396400bd6SLisandro Dalcin 
1354d27334e2SStefano Zampini   if (!dirk) PetscCall(TSHasRHSFunction(ts, &hasE));
1355d27334e2SStefano Zampini   if (!hasE) dirk = PETSC_TRUE;
1356d27334e2SStefano Zampini 
135796400bd6SLisandro Dalcin   if (!ts->steprollback) {
1358d27334e2SStefano Zampini     if (dirk || ts->equation_type >= TS_EQ_IMPLICIT) { /* Save the initial slope for the next step */
13599566063dSJacob Faibussowitsch       PetscCall(VecCopy(YdotI[s - 1], Ydot0));
136096400bd6SLisandro Dalcin     }
1361fecfb714SLisandro Dalcin     if (ark->extrapolate && !ts->steprestart) { /* Save the Y, YdotI, YdotRHS for extrapolation initial guess */
136296400bd6SLisandro Dalcin       for (i = 0; i < s; i++) {
13639566063dSJacob Faibussowitsch         PetscCall(VecCopy(Y[i], ark->Y_prev[i]));
13649566063dSJacob Faibussowitsch         PetscCall(VecCopy(YdotI[i], ark->YdotI_prev[i]));
1365d27334e2SStefano Zampini         if (tab->additive && hasE) PetscCall(VecCopy(YdotRHS[i], ark->YdotRHS_prev[i]));
136696400bd6SLisandro Dalcin       }
136796400bd6SLisandro Dalcin     }
136896400bd6SLisandro Dalcin   }
136996400bd6SLisandro Dalcin 
13703b98415fSStefano Zampini   /*
13713b98415fSStefano Zampini      For fully implicit formulations we must solve the equations
13723b98415fSStefano Zampini 
13733b98415fSStefano Zampini        F(t_n,x_n,xdot) = 0
13743b98415fSStefano Zampini 
13753b98415fSStefano Zampini      for the explicit first stage.
13763b98415fSStefano Zampini      Here we call SNESSolve using PETSC_MAX_REAL as shift to flag it.
13773b98415fSStefano Zampini      Special handling is inside SNESTSFormFunction_ARKIMEX and SNESTSFormJacobian_ARKIMEX
1378c6bf8827SStefano Zampini      We compute Ydot0 if we restart the step or if we resized the problem after remeshing
13793b98415fSStefano Zampini   */
1380c6bf8827SStefano Zampini   if (dirk && tab->explicit_first_stage && (ts->steprestart || ts->stepresize)) {
138198940a98SHong Zhang     ark->scoeff = PETSC_MAX_REAL;
1382d27334e2SStefano Zampini     PetscCall(VecCopy(ts->vec_sol, Z));
13830467964bSStefano Zampini     if (!ark->alg_is) {
13840467964bSStefano Zampini       PetscCall(TSARKIMEXComputeAlgebraicIS(ts, ts->ptime, Z, &ark->alg_is));
13850467964bSStefano Zampini       PetscCall(ISViewFromOptions(ark->alg_is, (PetscObject)ts, "-ts_arkimex_algebraic_is_view"));
13860467964bSStefano Zampini     }
1387d27334e2SStefano Zampini     PetscCall(TSGetSNES(ts, &snes));
13880467964bSStefano Zampini     PetscCall(PetscObjectIncrementTabLevel((PetscObject)snes, (PetscObject)snes, 1));
1389d27334e2SStefano Zampini     PetscCall(SNESSolve(snes, NULL, Ydot0));
1390c6bf8827SStefano Zampini     if (ark->alg_is) PetscCall(VecISSet(Ydot0, ark->alg_is, 0.0));
13910467964bSStefano Zampini     PetscCall(PetscObjectIncrementTabLevel((PetscObject)snes, (PetscObject)snes, -1));
1392d27334e2SStefano Zampini   }
1393d27334e2SStefano Zampini 
1394d27334e2SStefano Zampini   /* For IMEX we compute a step */
1395d27334e2SStefano Zampini   if (!dirk && ts->equation_type >= TS_EQ_IMPLICIT && tab->explicit_first_stage && ts->steprestart) {
139696400bd6SLisandro Dalcin     TS ts_start;
1397d27334e2SStefano Zampini     if (PetscDefined(USE_DEBUG) && hasE) {
1398c79dcfbdSBarry Smith       PetscBool id = PETSC_FALSE;
13999566063dSJacob Faibussowitsch       PetscCall(TSARKIMEXTestMassIdentity(ts, &id));
14008434afd1SBarry Smith       PetscCheck(id, PetscObjectComm((PetscObject)ts), PETSC_ERR_ARG_INCOMP, "This scheme requires an identity mass matrix, however the TSIFunctionFn you provided does not utilize an identity mass matrix");
1401c79dcfbdSBarry Smith     }
14029566063dSJacob Faibussowitsch     PetscCall(TSClone(ts, &ts_start));
14039566063dSJacob Faibussowitsch     PetscCall(TSSetSolution(ts_start, ts->vec_sol));
14049566063dSJacob Faibussowitsch     PetscCall(TSSetTime(ts_start, ts->ptime));
14059566063dSJacob Faibussowitsch     PetscCall(TSSetMaxSteps(ts_start, ts->steps + 1));
14069566063dSJacob Faibussowitsch     PetscCall(TSSetMaxTime(ts_start, ts->ptime + ts->time_step));
14079566063dSJacob Faibussowitsch     PetscCall(TSSetExactFinalTime(ts_start, TS_EXACTFINALTIME_STEPOVER));
14089566063dSJacob Faibussowitsch     PetscCall(TSSetTimeStep(ts_start, ts->time_step));
14099566063dSJacob Faibussowitsch     PetscCall(TSSetType(ts_start, TSARKIMEX));
14109566063dSJacob Faibussowitsch     PetscCall(TSARKIMEXSetFullyImplicit(ts_start, PETSC_TRUE));
14119566063dSJacob Faibussowitsch     PetscCall(TSARKIMEXSetType(ts_start, TSARKIMEX1BEE));
141234561852SEmil Constantinescu 
14139566063dSJacob Faibussowitsch     PetscCall(TSRestartStep(ts_start));
14149566063dSJacob Faibussowitsch     PetscCall(TSSolve(ts_start, ts->vec_sol));
14159566063dSJacob Faibussowitsch     PetscCall(TSGetTime(ts_start, &ts->ptime));
14169566063dSJacob Faibussowitsch     PetscCall(TSGetTimeStep(ts_start, &ts->time_step));
1417bbd56ea5SKarl Rupp 
141885fc7851SLisandro Dalcin     { /* Save the initial slope for the next step */
141985fc7851SLisandro Dalcin       TS_ARKIMEX *ark_start = (TS_ARKIMEX *)ts_start->data;
14209566063dSJacob Faibussowitsch       PetscCall(VecCopy(ark_start->YdotI[ark_start->tableau->s - 1], Ydot0));
142185fc7851SLisandro Dalcin     }
142296400bd6SLisandro Dalcin     ts->steps++;
142334561852SEmil Constantinescu 
1424d15a3a53SEmil Constantinescu     /* Set the correct TS in SNES */
1425d15a3a53SEmil Constantinescu     /* We'll try to bypass this by changing the method on the fly */
142696400bd6SLisandro Dalcin     {
14279566063dSJacob Faibussowitsch       PetscCall(TSGetSNES(ts, &snes));
14289566063dSJacob Faibussowitsch       PetscCall(TSSetSNES(ts, snes));
142996400bd6SLisandro Dalcin     }
14309566063dSJacob Faibussowitsch     PetscCall(TSDestroy(&ts_start));
1431e817cc15SEmil Constantinescu   }
1432e817cc15SEmil Constantinescu 
1433108c343cSJed Brown   ark->status = TS_STEP_INCOMPLETE;
143496400bd6SLisandro Dalcin   while (!ts->reason && ark->status != TS_STEP_COMPLETE) {
143596400bd6SLisandro Dalcin     PetscReal t = ts->ptime;
1436108c343cSJed Brown     PetscReal h = ts->time_step;
14378a381b04SJed Brown     for (i = 0; i < s; i++) {
14389be3e283SDebojyoti Ghosh       ark->stage_time = t + h * ct[i];
14399566063dSJacob Faibussowitsch       PetscCall(TSPreStage(ts, ark->stage_time));
14408a381b04SJed Brown       if (At[i * s + i] == 0) { /* This stage is explicit */
14413c633725SBarry Smith         PetscCheck(i == 0 || ts->equation_type < TS_EQ_IMPLICIT, PetscObjectComm((PetscObject)ts), PETSC_ERR_SUP, "Explicit stages other than the first one are not supported for implicit problems");
14429566063dSJacob Faibussowitsch         PetscCall(VecCopy(ts->vec_sol, Y[i]));
1443e817cc15SEmil Constantinescu         for (j = 0; j < i; j++) w[j] = h * At[i * s + j];
14449566063dSJacob Faibussowitsch         PetscCall(VecMAXPY(Y[i], i, w, YdotI));
1445d27334e2SStefano Zampini         if (tab->additive && hasE) {
14468a381b04SJed Brown           for (j = 0; j < i; j++) w[j] = h * A[i * s + j];
14479566063dSJacob Faibussowitsch           PetscCall(VecMAXPY(Y[i], i, w, YdotRHS));
1448d27334e2SStefano Zampini         }
144912b1dd1aSStefano Zampini         PetscCall(TSGetSNES(ts, &snes));
145012b1dd1aSStefano Zampini         PetscCall(SNESResetCounters(snes));
14518a381b04SJed Brown       } else {
1452b296d7d5SJed Brown         ark->scoeff = 1. / At[i * s + i];
14538a381b04SJed Brown         /* Ydot = shift*(Y-Z) */
14549566063dSJacob Faibussowitsch         PetscCall(VecCopy(ts->vec_sol, Z));
1455e817cc15SEmil Constantinescu         for (j = 0; j < i; j++) w[j] = h * At[i * s + j];
14569566063dSJacob Faibussowitsch         PetscCall(VecMAXPY(Z, i, w, YdotI));
1457d27334e2SStefano Zampini         if (tab->additive && hasE) {
1458c58d1302SEmil Constantinescu           for (j = 0; j < i; j++) w[j] = h * A[i * s + j];
14599566063dSJacob Faibussowitsch           PetscCall(VecMAXPY(Z, i, w, YdotRHS));
1460d27334e2SStefano Zampini         }
1461fecfb714SLisandro Dalcin         if (extrapolate && !ts->steprestart) {
146256dcabbaSDebojyoti Ghosh           /* Initial guess extrapolated from previous time step stage values */
14639566063dSJacob Faibussowitsch           PetscCall(TSExtrapolate_ARKIMEX(ts, c[i], Y[i]));
146456dcabbaSDebojyoti Ghosh         } else {
14658a381b04SJed Brown           /* Initial guess taken from last stage */
14669566063dSJacob Faibussowitsch           PetscCall(VecCopy(i > 0 ? Y[i - 1] : ts->vec_sol, Y[i]));
146756dcabbaSDebojyoti Ghosh         }
14689566063dSJacob Faibussowitsch         PetscCall(TSGetSNES(ts, &snes));
14699566063dSJacob Faibussowitsch         PetscCall(SNESSolve(snes, NULL, Y[i]));
14709566063dSJacob Faibussowitsch         PetscCall(SNESGetIterationNumber(snes, &its));
14719566063dSJacob Faibussowitsch         PetscCall(SNESGetLinearSolveIterations(snes, &lits));
14729371c9d4SSatish Balay         ts->snes_its += its;
14739371c9d4SSatish Balay         ts->ksp_its += lits;
14749566063dSJacob Faibussowitsch         PetscCall(TSGetAdapt(ts, &adapt));
14759566063dSJacob Faibussowitsch         PetscCall(TSAdaptCheckStage(adapt, ts, ark->stage_time, Y[i], &stageok));
147696400bd6SLisandro Dalcin         if (!stageok) {
14771be93e3eSJed Brown           /* We are likely rejecting the step because of solver or function domain problems so we should not attempt to
14781be93e3eSJed Brown            * use extrapolation to initialize the solves on the next attempt. */
147996400bd6SLisandro Dalcin           extrapolate = PETSC_FALSE;
14801be93e3eSJed Brown           goto reject_step;
14811be93e3eSJed Brown         }
14828a381b04SJed Brown       }
1483d27334e2SStefano Zampini       if (dirk || ts->equation_type >= TS_EQ_IMPLICIT) {
1484e817cc15SEmil Constantinescu         if (i == 0 && tab->explicit_first_stage) {
1485d27334e2SStefano Zampini           PetscCheck(tab->stiffly_accurate, PetscObjectComm((PetscObject)ts), PETSC_ERR_SUP, "%s %s is not stiffly accurate and therefore explicit-first stage methods cannot be used if the equation is implicit because the slope cannot be evaluated",
1486d27334e2SStefano Zampini                      ((PetscObject)ts)->type_name, ark->tableau->name);
14879566063dSJacob Faibussowitsch           PetscCall(VecCopy(Ydot0, YdotI[0])); /* YdotI = YdotI(tn-1) */
1488e817cc15SEmil Constantinescu         } else {
14899566063dSJacob Faibussowitsch           PetscCall(VecAXPBYPCZ(YdotI[i], -ark->scoeff / h, ark->scoeff / h, 0, Z, Y[i])); /* YdotI = shift*(X-Z) */
1490e817cc15SEmil Constantinescu         }
1491e817cc15SEmil Constantinescu       } else {
14925eca1a21SEmil Constantinescu         if (i == 0 && tab->explicit_first_stage) {
14939566063dSJacob Faibussowitsch           PetscCall(VecZeroEntries(Ydot));
14949566063dSJacob Faibussowitsch           PetscCall(TSComputeIFunction(ts, t + h * ct[i], Y[i], Ydot, YdotI[i], ark->imex)); /* YdotI = -G(t,Y,0)   */
14959566063dSJacob Faibussowitsch           PetscCall(VecScale(YdotI[i], -1.0));
14965eca1a21SEmil Constantinescu         } else {
14979566063dSJacob Faibussowitsch           PetscCall(VecAXPBYPCZ(YdotI[i], -ark->scoeff / h, ark->scoeff / h, 0, Z, Y[i])); /* YdotI = shift*(X-Z) */
14985eca1a21SEmil Constantinescu         }
1499d27334e2SStefano Zampini         if (hasE) {
15004cc180ffSJed Brown           if (ark->imex) {
15019566063dSJacob Faibussowitsch             PetscCall(TSComputeRHSFunction(ts, t + h * c[i], Y[i], YdotRHS[i]));
15024cc180ffSJed Brown           } else {
15039566063dSJacob Faibussowitsch             PetscCall(VecZeroEntries(YdotRHS[i]));
15044cc180ffSJed Brown           }
15058a381b04SJed Brown         }
1506d27334e2SStefano Zampini       }
15079566063dSJacob Faibussowitsch       PetscCall(TSPostStage(ts, ark->stage_time, i, Y));
1508e817cc15SEmil Constantinescu     }
150996400bd6SLisandro Dalcin 
1510be5899b3SLisandro Dalcin     ark->status = TS_STEP_INCOMPLETE;
15119566063dSJacob Faibussowitsch     PetscCall(TSEvaluateStep_ARKIMEX(ts, tab->order, ts->vec_sol, NULL));
1512108c343cSJed Brown     ark->status = TS_STEP_PENDING;
15139566063dSJacob Faibussowitsch     PetscCall(TSGetAdapt(ts, &adapt));
15149566063dSJacob Faibussowitsch     PetscCall(TSAdaptCandidatesClear(adapt));
15159566063dSJacob Faibussowitsch     PetscCall(TSAdaptCandidateAdd(adapt, tab->name, tab->order, 1, tab->ccfl, (PetscReal)tab->s, PETSC_TRUE));
15169566063dSJacob Faibussowitsch     PetscCall(TSAdaptChoose(adapt, ts, ts->time_step, NULL, &next_time_step, &accept));
151796400bd6SLisandro Dalcin     ark->status = accept ? TS_STEP_COMPLETE : TS_STEP_INCOMPLETE;
151896400bd6SLisandro Dalcin     if (!accept) { /* Roll back the current step */
1519c61711c8SStefano Zampini       PetscCall(VecCopy(ts->vec_sol0, ts->vec_sol));
1520be5899b3SLisandro Dalcin       ts->time_step = next_time_step;
1521be5899b3SLisandro Dalcin       goto reject_step;
152296400bd6SLisandro Dalcin     }
152396400bd6SLisandro Dalcin 
15248a381b04SJed Brown     ts->ptime += ts->time_step;
1525cdbf8f93SLisandro Dalcin     ts->time_step = next_time_step;
1526108c343cSJed Brown     break;
152796400bd6SLisandro Dalcin 
152896400bd6SLisandro Dalcin   reject_step:
15299371c9d4SSatish Balay     ts->reject++;
15309371c9d4SSatish Balay     accept = PETSC_FALSE;
1531be5899b3SLisandro Dalcin     if (!ts->reason && ++rejections > ts->max_reject && ts->max_reject >= 0) {
153296400bd6SLisandro Dalcin       ts->reason = TS_DIVERGED_STEP_REJECTED;
153363a3b9bcSJacob Faibussowitsch       PetscCall(PetscInfo(ts, "Step=%" PetscInt_FMT ", step rejections %" PetscInt_FMT " greater than current TS allowed, stopping solve\n", ts->steps, rejections));
1534108c343cSJed Brown     }
1535f85781f1SEmil Constantinescu   }
15363ba16761SJacob Faibussowitsch   PetscFunctionReturn(PETSC_SUCCESS);
15378a381b04SJed Brown }
1538d27334e2SStefano Zampini 
153980ab5e31SHong Zhang /*
154080ab5e31SHong Zhang   This adjoint step function assumes the partitioned ODE system has an identity mass matrix and thus can be represented in the form
154180ab5e31SHong Zhang   Udot = H(t,U) + G(t,U)
154280ab5e31SHong Zhang   This corresponds to F(t,U,Udot) = Udot-H(t,U).
154380ab5e31SHong Zhang 
154480ab5e31SHong Zhang   The complete adjoint equations are
154580ab5e31SHong Zhang   (shift*I - dHdu) lambda_s[i]   = 1/at[i][i] (
15465d7a6ebeSHong Zhang     dGdU (b_i lambda_{n+1} + \sum_{j=i+1}^s a[j][i] lambda_s[j])
15475d7a6ebeSHong Zhang     + dHdU (bt[i] lambda_{n+1} +  \sum_{j=i+1}^s at[j][i] lambda_s[j])), i = s-1,...,0
154880ab5e31SHong Zhang   lambda_n = lambda_{n+1} + \sum_{j=1}^s lambda_s[j]
154980ab5e31SHong Zhang   mu_{n+1}[i]   = h (at[i][i] dHdP lambda_s[i]
15505d7a6ebeSHong Zhang     + dGdP (b_i lambda_{n+1} + \sum_{j=i+1}^s a[j][i] lambda_s[j])
15515d7a6ebeSHong Zhang     + dHdP (bt[i] lambda_{n+1} + \sum_{j=i+1}^s at[j][i] lambda_s[j])), i = s-1,...,0
155280ab5e31SHong Zhang   mu_n = mu_{n+1} + \sum_{j=1}^s mu_{n+1}[j]
155380ab5e31SHong Zhang   where shift = 1/(at[i][i]*h)
155480ab5e31SHong Zhang 
155580ab5e31SHong Zhang   If at[i][i] is 0, the first equation falls back to
155680ab5e31SHong Zhang   lambda_s[i] = h (
155780ab5e31SHong Zhang     (b_i dGdU + bt[i] dHdU) lambda_{n+1} + dGdU \sum_{j=i+1}^s a[j][i] lambda_s[j]
155880ab5e31SHong Zhang     + dHdU \sum_{j=i+1}^s at[j][i] lambda_s[j])
155980ab5e31SHong Zhang 
156080ab5e31SHong Zhang */
156180ab5e31SHong Zhang static PetscErrorCode TSAdjointStep_ARKIMEX(TS ts)
156280ab5e31SHong Zhang {
156380ab5e31SHong Zhang   TS_ARKIMEX      *ark = (TS_ARKIMEX *)ts->data;
156480ab5e31SHong Zhang   ARKTableau       tab = ark->tableau;
156580ab5e31SHong Zhang   const PetscInt   s   = tab->s;
156680ab5e31SHong Zhang   const PetscReal *At = tab->At, *A = tab->A, *ct = tab->ct, *c = tab->c, *b = tab->b, *bt = tab->bt;
156780ab5e31SHong Zhang   PetscScalar     *w = ark->work;
156880ab5e31SHong Zhang   Vec             *Y = ark->Y, Ydot = ark->Ydot, *VecsDeltaLam = ark->VecsDeltaLam, *VecsSensiTemp = ark->VecsSensiTemp, *VecsSensiPTemp = ark->VecsSensiPTemp;
156980ab5e31SHong Zhang   Mat              Jex, Jim, Jimpre;
157080ab5e31SHong Zhang   PetscInt         i, j, nadj;
157180ab5e31SHong Zhang   PetscReal        t                 = ts->ptime, stage_time_ex;
157280ab5e31SHong Zhang   PetscReal        adjoint_time_step = -ts->time_step; /* always positive since ts->time_step is negative */
157380ab5e31SHong Zhang   KSP              ksp;
157480ab5e31SHong Zhang 
157580ab5e31SHong Zhang   PetscFunctionBegin;
157680ab5e31SHong Zhang   ark->status = TS_STEP_INCOMPLETE;
157780ab5e31SHong Zhang   PetscCall(SNESGetKSP(ts->snes, &ksp));
157880ab5e31SHong Zhang   PetscCall(TSGetRHSMats_Private(ts, &Jex, NULL));
157980ab5e31SHong Zhang   PetscCall(TSGetIJacobian(ts, &Jim, &Jimpre, NULL, NULL));
158080ab5e31SHong Zhang 
158180ab5e31SHong Zhang   for (i = s - 1; i >= 0; i--) {
158280ab5e31SHong Zhang     ark->stage_time = t - adjoint_time_step * (1.0 - ct[i]);
158380ab5e31SHong Zhang     stage_time_ex   = t - adjoint_time_step * (1.0 - c[i]);
158480ab5e31SHong Zhang     if (At[i * s + i] == 0) { // This stage is explicit
158580ab5e31SHong Zhang       ark->scoeff = 0.;
158680ab5e31SHong Zhang     } else {
158780ab5e31SHong Zhang       ark->scoeff = -1. / At[i * s + i]; // this makes shift=ark->scoeff/ts->time_step positive since ts->time_step is negative
158880ab5e31SHong Zhang     }
158980ab5e31SHong Zhang     PetscCall(TSComputeSNESJacobian(ts, Y[i], Jim, Jimpre));
159080ab5e31SHong Zhang     PetscCall(TSComputeRHSJacobian(ts, stage_time_ex, Y[i], Jex, Jex));
159180ab5e31SHong Zhang     if (ts->vecs_sensip) {
159280ab5e31SHong Zhang       PetscCall(TSComputeIJacobianP(ts, ark->stage_time, Y[i], Ydot, ark->scoeff / adjoint_time_step, ts->Jacp, PETSC_TRUE)); // get dFdP (-dHdP), Ydot not really used since mass matrix is identity
159380ab5e31SHong Zhang       PetscCall(TSComputeRHSJacobianP(ts, stage_time_ex, Y[i], ts->Jacprhs));                                                 // get dGdP
159480ab5e31SHong Zhang     }
159580ab5e31SHong Zhang     /* Build RHS (stored in VecsDeltaLam) for first-order adjoint */
15965d7a6ebeSHong Zhang     for (nadj = 0; nadj < ts->numcost; nadj++) {
15975d7a6ebeSHong Zhang       /* build implicit part */
15985d7a6ebeSHong Zhang       PetscCall(VecSet(VecsSensiTemp[nadj], 0));
159980ab5e31SHong Zhang       if (s - i - 1 > 0) {
160080ab5e31SHong Zhang         /* Temp = -\sum_{j=i+1}^s at[j][i] lambda_s[j] */
160180ab5e31SHong Zhang         for (j = i + 1; j < s; j++) w[j - i - 1] = -At[j * s + i];
160280ab5e31SHong Zhang         PetscCall(VecMAXPY(VecsSensiTemp[nadj], s - i - 1, w, &VecsDeltaLam[nadj * s + i + 1]));
16035d7a6ebeSHong Zhang       }
16045d7a6ebeSHong Zhang       /* Temp = Temp - bt[i] lambda_{n+1} */
16055d7a6ebeSHong Zhang       PetscCall(VecAXPY(VecsSensiTemp[nadj], -bt[i], ts->vecs_sensi[nadj]));
16065d7a6ebeSHong Zhang       if (bt[i] || s - i - 1 > 0) {
160780ab5e31SHong Zhang         /* (shift I - dHdU) Temp */
160880ab5e31SHong Zhang         PetscCall(MatMultTranspose(Jim, VecsSensiTemp[nadj], VecsDeltaLam[nadj * s + i]));
160980ab5e31SHong Zhang         /* cancel out shift Temp where shift=-scoeff/h */
161080ab5e31SHong Zhang         PetscCall(VecAXPY(VecsDeltaLam[nadj * s + i], ark->scoeff / adjoint_time_step, VecsSensiTemp[nadj]));
161180ab5e31SHong Zhang         if (ts->vecs_sensip) {
161280ab5e31SHong Zhang           /* - dHdP Temp */
161380ab5e31SHong Zhang           PetscCall(MatMultTranspose(ts->Jacp, VecsSensiTemp[nadj], VecsSensiPTemp[nadj]));
16145d7a6ebeSHong Zhang           /* mu_n += -h dHdP Temp */
16155d7a6ebeSHong Zhang           PetscCall(VecAXPY(ts->vecs_sensip[nadj], adjoint_time_step, VecsSensiPTemp[nadj]));
161680ab5e31SHong Zhang         }
16175d7a6ebeSHong Zhang       } else {
16185d7a6ebeSHong Zhang         PetscCall(VecSet(VecsDeltaLam[nadj * s + i], 0)); // make sure it is initialized
16195d7a6ebeSHong Zhang       }
16205d7a6ebeSHong Zhang       /* build explicit part */
16215d7a6ebeSHong Zhang       PetscCall(VecSet(VecsSensiTemp[nadj], 0));
16225d7a6ebeSHong Zhang       if (s - i - 1 > 0) {
162380ab5e31SHong Zhang         /* Temp = \sum_{j=i+1}^s a[j][i] lambda_s[j] */
162480ab5e31SHong Zhang         for (j = i + 1; j < s; j++) w[j - i - 1] = A[j * s + i];
162580ab5e31SHong Zhang         PetscCall(VecMAXPY(VecsSensiTemp[nadj], s - i - 1, w, &VecsDeltaLam[nadj * s + i + 1]));
16265d7a6ebeSHong Zhang       }
16275d7a6ebeSHong Zhang       /* Temp = Temp + b[i] lambda_{n+1} */
16285d7a6ebeSHong Zhang       PetscCall(VecAXPY(VecsSensiTemp[nadj], b[i], ts->vecs_sensi[nadj]));
16295d7a6ebeSHong Zhang       if (b[i] || s - i - 1 > 0) {
163080ab5e31SHong Zhang         /* dGdU Temp */
163180ab5e31SHong Zhang         PetscCall(MatMultTransposeAdd(Jex, VecsSensiTemp[nadj], VecsDeltaLam[nadj * s + i], VecsDeltaLam[nadj * s + i]));
163280ab5e31SHong Zhang         if (ts->vecs_sensip) {
163380ab5e31SHong Zhang           /* dGdP Temp */
163480ab5e31SHong Zhang           PetscCall(MatMultTranspose(ts->Jacprhs, VecsSensiTemp[nadj], VecsSensiPTemp[nadj]));
163580ab5e31SHong Zhang           /* mu_n += h dGdP Temp */
163680ab5e31SHong Zhang           PetscCall(VecAXPY(ts->vecs_sensip[nadj], adjoint_time_step, VecsSensiPTemp[nadj]));
163780ab5e31SHong Zhang         }
163880ab5e31SHong Zhang       }
163980ab5e31SHong Zhang       /* Build LHS for first-order adjoint */
164080ab5e31SHong Zhang       if (At[i * s + i] == 0) { // This stage is explicit
164180ab5e31SHong Zhang         PetscCall(VecScale(VecsDeltaLam[nadj * s + i], adjoint_time_step));
164280ab5e31SHong Zhang       } else {
164380ab5e31SHong Zhang         KSP                ksp;
164480ab5e31SHong Zhang         KSPConvergedReason kspreason;
164580ab5e31SHong Zhang         PetscCall(SNESGetKSP(ts->snes, &ksp));
164680ab5e31SHong Zhang         PetscCall(KSPSetOperators(ksp, Jim, Jimpre));
164780ab5e31SHong Zhang         PetscCall(VecScale(VecsDeltaLam[nadj * s + i], 1. / At[i * s + i]));
164880ab5e31SHong Zhang         PetscCall(KSPSolveTranspose(ksp, VecsDeltaLam[nadj * s + i], VecsDeltaLam[nadj * s + i]));
164980ab5e31SHong Zhang         PetscCall(KSPGetConvergedReason(ksp, &kspreason));
165080ab5e31SHong Zhang         if (kspreason < 0) {
165180ab5e31SHong Zhang           ts->reason = TSADJOINT_DIVERGED_LINEAR_SOLVE;
165280ab5e31SHong Zhang           PetscCall(PetscInfo(ts, "Step=%" PetscInt_FMT ", %" PetscInt_FMT "th cost function, transposed linear solve fails, stopping 1st-order adjoint solve\n", ts->steps, nadj));
165380ab5e31SHong Zhang         }
165480ab5e31SHong Zhang         if (ts->vecs_sensip) {
165580ab5e31SHong Zhang           /* -dHdP lambda_s[i] */
165680ab5e31SHong Zhang           PetscCall(MatMultTranspose(ts->Jacp, VecsDeltaLam[nadj * s + i], VecsSensiPTemp[nadj]));
165780ab5e31SHong Zhang           /* mu_n += h at[i][i] dHdP lambda_s[i] */
165880ab5e31SHong Zhang           PetscCall(VecAXPY(ts->vecs_sensip[nadj], -At[i * s + i] * adjoint_time_step, VecsSensiPTemp[nadj]));
165980ab5e31SHong Zhang         }
166080ab5e31SHong Zhang       }
166180ab5e31SHong Zhang     }
166280ab5e31SHong Zhang   }
166380ab5e31SHong Zhang   for (j = 0; j < s; j++) w[j] = 1.0;
166480ab5e31SHong Zhang   for (nadj = 0; nadj < ts->numcost; nadj++) // no need to do this for mu's
166580ab5e31SHong Zhang     PetscCall(VecMAXPY(ts->vecs_sensi[nadj], s, w, &VecsDeltaLam[nadj * s]));
166680ab5e31SHong Zhang   ark->status = TS_STEP_COMPLETE;
166780ab5e31SHong Zhang   PetscFunctionReturn(PETSC_SUCCESS);
166880ab5e31SHong Zhang }
16698a381b04SJed Brown 
1670d71ae5a4SJacob Faibussowitsch static PetscErrorCode TSInterpolate_ARKIMEX(TS ts, PetscReal itime, Vec X)
1671d71ae5a4SJacob Faibussowitsch {
1672cd652676SJed Brown   TS_ARKIMEX      *ark = (TS_ARKIMEX *)ts->data;
1673d27334e2SStefano Zampini   ARKTableau       tab = ark->tableau;
1674d27334e2SStefano Zampini   PetscInt         s = tab->s, pinterp = tab->pinterp, i, j;
1675108c343cSJed Brown   PetscReal        h;
1676108c343cSJed Brown   PetscReal        tt, t;
1677d27334e2SStefano Zampini   PetscScalar     *bt = ark->work, *b = ark->work + s;
1678d27334e2SStefano Zampini   const PetscReal *Bt = tab->binterpt, *B = tab->binterp;
1679cd652676SJed Brown 
1680cd652676SJed Brown   PetscFunctionBegin;
1681d27334e2SStefano Zampini   PetscCheck(Bt && B, PetscObjectComm((PetscObject)ts), PETSC_ERR_SUP, "%s %s does not have an interpolation formula", ((PetscObject)ts)->type_name, ark->tableau->name);
1682108c343cSJed Brown   switch (ark->status) {
1683108c343cSJed Brown   case TS_STEP_INCOMPLETE:
1684108c343cSJed Brown   case TS_STEP_PENDING:
1685108c343cSJed Brown     h = ts->time_step;
1686108c343cSJed Brown     t = (itime - ts->ptime) / h;
1687108c343cSJed Brown     break;
1688108c343cSJed Brown   case TS_STEP_COMPLETE:
1689be5899b3SLisandro Dalcin     h = ts->ptime - ts->ptime_prev;
1690108c343cSJed Brown     t = (itime - ts->ptime) / h + 1; /* In the interval [0,1] */
1691108c343cSJed Brown     break;
1692d71ae5a4SJacob Faibussowitsch   default:
1693d71ae5a4SJacob Faibussowitsch     SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_PLIB, "Invalid TSStepStatus");
1694108c343cSJed Brown   }
1695cd652676SJed Brown   for (i = 0; i < s; i++) bt[i] = b[i] = 0;
16964f385281SJed Brown   for (j = 0, tt = t; j < pinterp; j++, tt *= t) {
1697cd652676SJed Brown     for (i = 0; i < s; i++) {
1698c1758d98SDebojyoti Ghosh       bt[i] += h * Bt[i * pinterp + j] * tt;
1699108c343cSJed Brown       b[i] += h * B[i * pinterp + j] * tt;
1700cd652676SJed Brown     }
1701cd652676SJed Brown   }
17029566063dSJacob Faibussowitsch   PetscCall(VecCopy(ark->Y[0], X));
17039566063dSJacob Faibussowitsch   PetscCall(VecMAXPY(X, s, bt, ark->YdotI));
1704d27334e2SStefano Zampini   if (tab->additive) {
1705d27334e2SStefano Zampini     PetscBool hasE;
1706d27334e2SStefano Zampini     PetscCall(TSHasRHSFunction(ts, &hasE));
1707d27334e2SStefano Zampini     if (hasE) PetscCall(VecMAXPY(X, s, b, ark->YdotRHS));
1708d27334e2SStefano Zampini   }
17093ba16761SJacob Faibussowitsch   PetscFunctionReturn(PETSC_SUCCESS);
1710cd652676SJed Brown }
1711cd652676SJed Brown 
1712d71ae5a4SJacob Faibussowitsch static PetscErrorCode TSExtrapolate_ARKIMEX(TS ts, PetscReal c, Vec X)
1713d71ae5a4SJacob Faibussowitsch {
171456dcabbaSDebojyoti Ghosh   TS_ARKIMEX      *ark = (TS_ARKIMEX *)ts->data;
1715d27334e2SStefano Zampini   ARKTableau       tab = ark->tableau;
1716d27334e2SStefano Zampini   PetscInt         s = tab->s, pinterp = tab->pinterp, i, j;
1717be5899b3SLisandro Dalcin   PetscReal        h, h_prev, t, tt;
1718d27334e2SStefano Zampini   PetscScalar     *bt = ark->work, *b = ark->work + s;
1719d27334e2SStefano Zampini   const PetscReal *Bt = tab->binterpt, *B = tab->binterp;
172056dcabbaSDebojyoti Ghosh 
172156dcabbaSDebojyoti Ghosh   PetscFunctionBegin;
17223c633725SBarry Smith   PetscCheck(Bt && B, PetscObjectComm((PetscObject)ts), PETSC_ERR_SUP, "TSARKIMEX %s does not have an interpolation formula", ark->tableau->name);
172381d12688SDebojyoti Ghosh   h      = ts->time_step;
1724be5899b3SLisandro Dalcin   h_prev = ts->ptime - ts->ptime_prev;
1725be5899b3SLisandro Dalcin   t      = 1 + h / h_prev * c;
1726d27334e2SStefano Zampini   for (i = 0; i < s; i++) bt[i] = b[i] = 0;
172756dcabbaSDebojyoti Ghosh   for (j = 0, tt = t; j < pinterp; j++, tt *= t) {
172856dcabbaSDebojyoti Ghosh     for (i = 0; i < s; i++) {
172981d12688SDebojyoti Ghosh       bt[i] += h * Bt[i * pinterp + j] * tt;
173056dcabbaSDebojyoti Ghosh       b[i] += h * B[i * pinterp + j] * tt;
173156dcabbaSDebojyoti Ghosh     }
173256dcabbaSDebojyoti Ghosh   }
17333c633725SBarry Smith   PetscCheck(ark->Y_prev, PetscObjectComm((PetscObject)ts), PETSC_ERR_SUP, "Stages from previous step have not been stored");
17349566063dSJacob Faibussowitsch   PetscCall(VecCopy(ark->Y_prev[0], X));
17359566063dSJacob Faibussowitsch   PetscCall(VecMAXPY(X, s, bt, ark->YdotI_prev));
1736d27334e2SStefano Zampini   if (tab->additive) {
1737d27334e2SStefano Zampini     PetscBool hasE;
1738d27334e2SStefano Zampini     PetscCall(TSHasRHSFunction(ts, &hasE));
1739d27334e2SStefano Zampini     if (hasE) PetscCall(VecMAXPY(X, s, b, ark->YdotRHS_prev));
1740d27334e2SStefano Zampini   }
17413ba16761SJacob Faibussowitsch   PetscFunctionReturn(PETSC_SUCCESS);
174256dcabbaSDebojyoti Ghosh }
174356dcabbaSDebojyoti Ghosh 
1744d71ae5a4SJacob Faibussowitsch static PetscErrorCode TSARKIMEXTableauReset(TS ts)
1745d71ae5a4SJacob Faibussowitsch {
174696400bd6SLisandro Dalcin   TS_ARKIMEX *ark = (TS_ARKIMEX *)ts->data;
174796400bd6SLisandro Dalcin   ARKTableau  tab = ark->tableau;
174896400bd6SLisandro Dalcin 
174996400bd6SLisandro Dalcin   PetscFunctionBegin;
17503ba16761SJacob Faibussowitsch   if (!tab) PetscFunctionReturn(PETSC_SUCCESS);
17519566063dSJacob Faibussowitsch   PetscCall(PetscFree(ark->work));
17529566063dSJacob Faibussowitsch   PetscCall(VecDestroyVecs(tab->s, &ark->Y));
17539566063dSJacob Faibussowitsch   PetscCall(VecDestroyVecs(tab->s, &ark->YdotI));
17549566063dSJacob Faibussowitsch   PetscCall(VecDestroyVecs(tab->s, &ark->YdotRHS));
17559566063dSJacob Faibussowitsch   PetscCall(VecDestroyVecs(tab->s, &ark->Y_prev));
17569566063dSJacob Faibussowitsch   PetscCall(VecDestroyVecs(tab->s, &ark->YdotI_prev));
17579566063dSJacob Faibussowitsch   PetscCall(VecDestroyVecs(tab->s, &ark->YdotRHS_prev));
17583ba16761SJacob Faibussowitsch   PetscFunctionReturn(PETSC_SUCCESS);
175996400bd6SLisandro Dalcin }
176096400bd6SLisandro Dalcin 
1761d71ae5a4SJacob Faibussowitsch static PetscErrorCode TSReset_ARKIMEX(TS ts)
1762d71ae5a4SJacob Faibussowitsch {
17638a381b04SJed Brown   TS_ARKIMEX *ark = (TS_ARKIMEX *)ts->data;
17648a381b04SJed Brown 
17658a381b04SJed Brown   PetscFunctionBegin;
1766*3a2a065fSHong Zhang   if (ark->fastslowsplit) {
1767*3a2a065fSHong Zhang     PetscTryMethod(ts, "TSReset_ARKIMEX_FastSlowSplit_C", (TS), (ts));
1768*3a2a065fSHong Zhang   } else {
17699566063dSJacob Faibussowitsch     PetscCall(TSARKIMEXTableauReset(ts));
17709566063dSJacob Faibussowitsch     PetscCall(VecDestroy(&ark->Ydot));
17719566063dSJacob Faibussowitsch     PetscCall(VecDestroy(&ark->Ydot0));
17729566063dSJacob Faibussowitsch     PetscCall(VecDestroy(&ark->Z));
17730467964bSStefano Zampini     PetscCall(ISDestroy(&ark->alg_is));
1774*3a2a065fSHong Zhang   }
17753ba16761SJacob Faibussowitsch   PetscFunctionReturn(PETSC_SUCCESS);
17768a381b04SJed Brown }
17778a381b04SJed Brown 
177880ab5e31SHong Zhang static PetscErrorCode TSAdjointReset_ARKIMEX(TS ts)
177980ab5e31SHong Zhang {
178080ab5e31SHong Zhang   TS_ARKIMEX *ark = (TS_ARKIMEX *)ts->data;
178180ab5e31SHong Zhang   ARKTableau  tab = ark->tableau;
178280ab5e31SHong Zhang 
178380ab5e31SHong Zhang   PetscFunctionBegin;
178480ab5e31SHong Zhang   PetscCall(VecDestroyVecs(tab->s * ts->numcost, &ark->VecsDeltaLam));
178580ab5e31SHong Zhang   PetscCall(VecDestroyVecs(ts->numcost, &ark->VecsSensiTemp));
178680ab5e31SHong Zhang   PetscCall(VecDestroyVecs(ts->numcost, &ark->VecsSensiPTemp));
178780ab5e31SHong Zhang   PetscFunctionReturn(PETSC_SUCCESS);
178880ab5e31SHong Zhang }
178980ab5e31SHong Zhang 
1790d71ae5a4SJacob Faibussowitsch static PetscErrorCode TSARKIMEXGetVecs(TS ts, DM dm, Vec *Z, Vec *Ydot)
1791d71ae5a4SJacob Faibussowitsch {
1792d5e6173cSPeter Brune   TS_ARKIMEX *ax = (TS_ARKIMEX *)ts->data;
1793d5e6173cSPeter Brune 
1794d5e6173cSPeter Brune   PetscFunctionBegin;
1795d5e6173cSPeter Brune   if (Z) {
1796*3a2a065fSHong Zhang     if (dm && dm != ts->dm && !ax->fastslowsplit) {
17979566063dSJacob Faibussowitsch       PetscCall(DMGetNamedGlobalVector(dm, "TSARKIMEX_Z", Z));
1798d5e6173cSPeter Brune     } else *Z = ax->Z;
1799d5e6173cSPeter Brune   }
1800d5e6173cSPeter Brune   if (Ydot) {
1801*3a2a065fSHong Zhang     if (dm && dm != ts->dm && !ax->fastslowsplit) {
18029566063dSJacob Faibussowitsch       PetscCall(DMGetNamedGlobalVector(dm, "TSARKIMEX_Ydot", Ydot));
1803d5e6173cSPeter Brune     } else *Ydot = ax->Ydot;
1804d5e6173cSPeter Brune   }
18053ba16761SJacob Faibussowitsch   PetscFunctionReturn(PETSC_SUCCESS);
1806d5e6173cSPeter Brune }
1807d5e6173cSPeter Brune 
1808d71ae5a4SJacob Faibussowitsch static PetscErrorCode TSARKIMEXRestoreVecs(TS ts, DM dm, Vec *Z, Vec *Ydot)
1809d71ae5a4SJacob Faibussowitsch {
1810*3a2a065fSHong Zhang   TS_ARKIMEX *ax = (TS_ARKIMEX *)ts->data;
1811*3a2a065fSHong Zhang 
1812d5e6173cSPeter Brune   PetscFunctionBegin;
1813d5e6173cSPeter Brune   if (Z) {
1814*3a2a065fSHong Zhang     if (dm && dm != ts->dm && !ax->fastslowsplit) PetscCall(DMRestoreNamedGlobalVector(dm, "TSARKIMEX_Z", Z));
1815d5e6173cSPeter Brune   }
1816d5e6173cSPeter Brune   if (Ydot) {
1817*3a2a065fSHong Zhang     if (dm && dm != ts->dm && !ax->fastslowsplit) PetscCall(DMRestoreNamedGlobalVector(dm, "TSARKIMEX_Ydot", Ydot));
1818d5e6173cSPeter Brune   }
18193ba16761SJacob Faibussowitsch   PetscFunctionReturn(PETSC_SUCCESS);
1820d5e6173cSPeter Brune }
1821d5e6173cSPeter Brune 
18220467964bSStefano Zampini /*
18230467964bSStefano Zampini   DAEs need special handling for algebraic variables when restarting DIRK methods with explicit
18240467964bSStefano Zampini   first stage. In particular, we need:
18250467964bSStefano Zampini      - to zero the nonlinear function (in case the dual variables are not consistent in the first step)
18260467964bSStefano Zampini      - to modify the preconditioning matrix by calling MatZeroRows with identity on these variables.
18270467964bSStefano Zampini */
18280467964bSStefano Zampini static PetscErrorCode TSARKIMEXComputeAlgebraicIS(TS ts, PetscReal time, Vec X, IS *alg_is)
18290467964bSStefano Zampini {
18300467964bSStefano Zampini   TS_ARKIMEX        *ark = (TS_ARKIMEX *)ts->data;
18310467964bSStefano Zampini   DM                 dm;
18320467964bSStefano Zampini   Vec                F, W, Xdot;
18330467964bSStefano Zampini   const PetscScalar *w;
18340467964bSStefano Zampini   PetscInt           nz = 0, n, st;
18350467964bSStefano Zampini   PetscInt          *nzr;
18360467964bSStefano Zampini 
18370467964bSStefano Zampini   PetscFunctionBegin;
18380467964bSStefano Zampini   PetscCall(TSGetDM(ts, &dm)); /* may be already from SNES */
18390467964bSStefano Zampini   PetscCall(DMGetGlobalVector(dm, &Xdot));
18400467964bSStefano Zampini   PetscCall(DMGetGlobalVector(dm, &F));
18410467964bSStefano Zampini   PetscCall(DMGetGlobalVector(dm, &W));
18420467964bSStefano Zampini   PetscCall(VecSet(Xdot, 0.0));
18430467964bSStefano Zampini   PetscCall(TSComputeIFunction(ts, time, X, Xdot, F, ark->imex));
18440467964bSStefano Zampini   PetscCall(VecSetRandom(Xdot, NULL));
18450467964bSStefano Zampini   PetscCall(TSComputeIFunction(ts, time, X, Xdot, W, ark->imex));
18460467964bSStefano Zampini   PetscCall(VecAXPY(W, -1.0, F));
18470467964bSStefano Zampini   PetscCall(VecGetOwnershipRange(W, &st, NULL));
18480467964bSStefano Zampini   PetscCall(VecGetLocalSize(W, &n));
18490467964bSStefano Zampini   PetscCall(VecGetArrayRead(W, &w));
18500467964bSStefano Zampini   for (PetscInt i = 0; i < n; i++)
18510467964bSStefano Zampini     if (w[i] == 0.0) nz++;
18520467964bSStefano Zampini   PetscCall(PetscMalloc1(nz, &nzr));
18530467964bSStefano Zampini   nz = 0;
18540467964bSStefano Zampini   for (PetscInt i = 0; i < n; i++)
18550467964bSStefano Zampini     if (w[i] == 0.0) nzr[nz++] = i + st;
18560467964bSStefano Zampini   PetscCall(VecRestoreArrayRead(W, &w));
18570467964bSStefano Zampini   PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)dm), nz, nzr, PETSC_OWN_POINTER, alg_is));
18580467964bSStefano Zampini   PetscCall(DMRestoreGlobalVector(dm, &Xdot));
18590467964bSStefano Zampini   PetscCall(DMRestoreGlobalVector(dm, &F));
18600467964bSStefano Zampini   PetscCall(DMRestoreGlobalVector(dm, &W));
18610467964bSStefano Zampini   PetscFunctionReturn(PETSC_SUCCESS);
18620467964bSStefano Zampini }
18630467964bSStefano Zampini 
18640467964bSStefano Zampini /* As for the method specific Z and Ydot, we store the algebraic IS in the ARKIMEX data structure
18650467964bSStefano Zampini    at the finest level, in the DM for coarser solves. */
18660467964bSStefano Zampini static PetscErrorCode TSARKIMEXGetAlgebraicIS(TS ts, DM dm, IS *alg_is)
18670467964bSStefano Zampini {
18680467964bSStefano Zampini   TS_ARKIMEX *ax = (TS_ARKIMEX *)ts->data;
18690467964bSStefano Zampini 
18700467964bSStefano Zampini   PetscFunctionBegin;
18710467964bSStefano Zampini   if (dm && dm != ts->dm) {
18720467964bSStefano Zampini     PetscCall(PetscObjectQuery((PetscObject)dm, "TSARKIMEX_ALG_IS", (PetscObject *)alg_is));
18730467964bSStefano Zampini   } else *alg_is = ax->alg_is;
18740467964bSStefano Zampini   PetscFunctionReturn(PETSC_SUCCESS);
18750467964bSStefano Zampini }
18763b98415fSStefano Zampini 
18773b98415fSStefano Zampini /* This defines the nonlinear equation that is to be solved with SNES */
1878d71ae5a4SJacob Faibussowitsch static PetscErrorCode SNESTSFormFunction_ARKIMEX(SNES snes, Vec X, Vec F, TS ts)
1879d71ae5a4SJacob Faibussowitsch {
18808a381b04SJed Brown   TS_ARKIMEX *ark = (TS_ARKIMEX *)ts->data;
1881d5e6173cSPeter Brune   DM          dm, dmsave;
1882*3a2a065fSHong Zhang   Vec         Z, Ydot, Y = ark->Y_snes;
18830467964bSStefano Zampini   IS          alg_is;
1884*3a2a065fSHong Zhang   TS          subts = ark->subts_fast ? ark->subts_fast : ts;
18858a381b04SJed Brown 
18868a381b04SJed Brown   PetscFunctionBegin;
18879566063dSJacob Faibussowitsch   PetscCall(SNESGetDM(snes, &dm));
18889566063dSJacob Faibussowitsch   PetscCall(TSARKIMEXGetVecs(ts, dm, &Z, &Ydot));
18890467964bSStefano Zampini   if (ark->scoeff == PETSC_MAX_REAL) PetscCall(TSARKIMEXGetAlgebraicIS(ts, dm, &alg_is));
18900467964bSStefano Zampini 
1891d5e6173cSPeter Brune   dmsave = ts->dm;
1892d5e6173cSPeter Brune   ts->dm = dm;
1893740132f1SEmil Constantinescu 
189498940a98SHong Zhang   if (ark->scoeff == PETSC_MAX_REAL) {
18953b98415fSStefano Zampini     /* We are solving F(t_n,x_n,xdot) = 0 to start the method */
18960467964bSStefano Zampini     if (!alg_is) {
18970467964bSStefano Zampini       PetscCheck(dmsave != ts->dm, PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Missing algebraic IS");
18980467964bSStefano Zampini       PetscCall(TSARKIMEXComputeAlgebraicIS(ts, ark->stage_time, Z, &alg_is));
18990467964bSStefano Zampini       PetscCall(PetscObjectCompose((PetscObject)dm, "TSARKIMEX_ALG_IS", (PetscObject)alg_is));
19000467964bSStefano Zampini       PetscCall(PetscObjectDereference((PetscObject)alg_is));
19010467964bSStefano Zampini       PetscCall(ISViewFromOptions(alg_is, (PetscObject)snes, "-ts_arkimex_algebraic_is_view"));
19020467964bSStefano Zampini     }
1903*3a2a065fSHong Zhang     if (ark->fastslowsplit && ark->is_slow) PetscCall(VecISCopy(Y, ark->is_fast, SCATTER_FORWARD, Z));
1904*3a2a065fSHong Zhang     else Y = Z;
1905*3a2a065fSHong Zhang     PetscCall(TSComputeIFunction(subts, ark->stage_time, Y, X, F, ark->imex));
19060467964bSStefano Zampini     PetscCall(VecISSet(F, alg_is, 0.0));
1907d27334e2SStefano Zampini   } else {
190898940a98SHong Zhang     PetscReal shift = ark->scoeff / ts->time_step;
1909d27334e2SStefano Zampini     PetscCall(VecAXPBYPCZ(Ydot, -shift, shift, 0, Z, X)); /* Ydot = shift*(X-Z) */
1910*3a2a065fSHong Zhang     if (ark->fastslowsplit && ark->is_slow) PetscCall(VecISCopy(Y, ark->is_fast, SCATTER_FORWARD, X));
1911*3a2a065fSHong Zhang     else Y = X;
1912*3a2a065fSHong Zhang     PetscCall(TSComputeIFunction(subts, ark->stage_time, Y, Ydot, F, ark->imex));
1913d27334e2SStefano Zampini   }
1914e817cc15SEmil Constantinescu 
1915d5e6173cSPeter Brune   ts->dm = dmsave;
19169566063dSJacob Faibussowitsch   PetscCall(TSARKIMEXRestoreVecs(ts, dm, &Z, &Ydot));
19173ba16761SJacob Faibussowitsch   PetscFunctionReturn(PETSC_SUCCESS);
19188a381b04SJed Brown }
19198a381b04SJed Brown 
1920d71ae5a4SJacob Faibussowitsch static PetscErrorCode SNESTSFormJacobian_ARKIMEX(SNES snes, Vec X, Mat A, Mat B, TS ts)
1921d71ae5a4SJacob Faibussowitsch {
19228a381b04SJed Brown   TS_ARKIMEX *ark = (TS_ARKIMEX *)ts->data;
1923d5e6173cSPeter Brune   DM          dm, dmsave;
1924*3a2a065fSHong Zhang   Vec         Ydot, Z, Y = ark->Y_snes;
192598940a98SHong Zhang   PetscReal   shift;
19260467964bSStefano Zampini   IS          alg_is;
1927*3a2a065fSHong Zhang   TS          subts = ark->subts_fast ? ark->subts_fast : ts;
19288a381b04SJed Brown 
19298a381b04SJed Brown   PetscFunctionBegin;
19309566063dSJacob Faibussowitsch   PetscCall(SNESGetDM(snes, &dm));
19318a381b04SJed Brown   /* ark->Ydot has already been computed in SNESTSFormFunction_ARKIMEX (SNES guarantees this) */
19320467964bSStefano Zampini   PetscCall(TSARKIMEXGetVecs(ts, dm, &Z, &Ydot));
19330467964bSStefano Zampini   /* alg_is has been computed in SNESTSFormFunction_ARKIMEX */
19340467964bSStefano Zampini   if (ark->scoeff == PETSC_MAX_REAL) PetscCall(TSARKIMEXGetAlgebraicIS(ts, dm, &alg_is));
19350467964bSStefano Zampini 
1936d5e6173cSPeter Brune   dmsave = ts->dm;
1937d5e6173cSPeter Brune   ts->dm = dm;
1938740132f1SEmil Constantinescu 
193998940a98SHong Zhang   if (ark->scoeff == PETSC_MAX_REAL) {
19403b98415fSStefano Zampini     PetscBool hasZeroRows;
19413b98415fSStefano Zampini 
19423b98415fSStefano Zampini     /* We are solving F(t_n,x_n,xdot) = 0 to start the method
19430467964bSStefano Zampini        We compute with a very large shift and then scale back the matrix */
1944d27334e2SStefano Zampini     shift = 1.0 / PETSC_MACHINE_EPSILON;
1945*3a2a065fSHong Zhang     if (ark->fastslowsplit && ark->is_slow) PetscCall(VecISCopy(Y, ark->is_fast, SCATTER_FORWARD, Z));
1946*3a2a065fSHong Zhang     else Y = Z;
1947*3a2a065fSHong Zhang     PetscCall(TSComputeIJacobian(subts, ark->stage_time, Y, X, shift, A, B, ark->imex));
1948d27334e2SStefano Zampini     PetscCall(MatScale(B, PETSC_MACHINE_EPSILON));
19493b98415fSStefano Zampini     PetscCall(MatHasOperation(B, MATOP_ZERO_ROWS, &hasZeroRows));
19503b98415fSStefano Zampini     if (hasZeroRows) {
19510467964bSStefano Zampini       PetscCheck(alg_is, PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Missing algebraic IS");
19523b98415fSStefano Zampini       /* the default of AIJ is to not keep the pattern! We should probably change it someday */
19533b98415fSStefano Zampini       PetscCall(MatSetOption(B, MAT_KEEP_NONZERO_PATTERN, PETSC_TRUE));
19543b98415fSStefano Zampini       PetscCall(MatZeroRowsIS(B, alg_is, 1.0, NULL, NULL));
19553b98415fSStefano Zampini     }
19563b98415fSStefano Zampini     PetscCall(MatViewFromOptions(B, (PetscObject)snes, "-ts_arkimex_alg_mat_view"));
1957d27334e2SStefano Zampini     if (A != B) PetscCall(MatScale(A, PETSC_MACHINE_EPSILON));
1958d27334e2SStefano Zampini   } else {
195998940a98SHong Zhang     shift = ark->scoeff / ts->time_step;
1960*3a2a065fSHong Zhang     if (ark->fastslowsplit && ark->is_slow) PetscCall(VecISCopy(Y, ark->is_fast, SCATTER_FORWARD, X));
1961*3a2a065fSHong Zhang     else Y = X;
1962*3a2a065fSHong Zhang     PetscCall(TSComputeIJacobian(subts, ark->stage_time, Y, Ydot, shift, A, B, ark->imex));
1963d27334e2SStefano Zampini   }
1964d5e6173cSPeter Brune   ts->dm = dmsave;
1965d27334e2SStefano Zampini   PetscCall(TSARKIMEXRestoreVecs(ts, dm, &Z, &Ydot));
19663ba16761SJacob Faibussowitsch   PetscFunctionReturn(PETSC_SUCCESS);
1967d5e6173cSPeter Brune }
1968d5e6173cSPeter Brune 
196980ab5e31SHong Zhang static PetscErrorCode TSGetStages_ARKIMEX(TS ts, PetscInt *ns, Vec *Y[])
197080ab5e31SHong Zhang {
197180ab5e31SHong Zhang   TS_ARKIMEX *ark = (TS_ARKIMEX *)ts->data;
197280ab5e31SHong Zhang 
197380ab5e31SHong Zhang   PetscFunctionBegin;
197480ab5e31SHong Zhang   if (ns) *ns = ark->tableau->s;
197580ab5e31SHong Zhang   if (Y) *Y = ark->Y;
197680ab5e31SHong Zhang   PetscFunctionReturn(PETSC_SUCCESS);
197780ab5e31SHong Zhang }
197880ab5e31SHong Zhang 
1979d71ae5a4SJacob Faibussowitsch static PetscErrorCode DMCoarsenHook_TSARKIMEX(DM fine, DM coarse, void *ctx)
1980d71ae5a4SJacob Faibussowitsch {
1981d5e6173cSPeter Brune   PetscFunctionBegin;
19823ba16761SJacob Faibussowitsch   PetscFunctionReturn(PETSC_SUCCESS);
1983d5e6173cSPeter Brune }
1984d5e6173cSPeter Brune 
1985d71ae5a4SJacob Faibussowitsch static PetscErrorCode DMRestrictHook_TSARKIMEX(DM fine, Mat restrct, Vec rscale, Mat inject, DM coarse, void *ctx)
1986d71ae5a4SJacob Faibussowitsch {
1987d5e6173cSPeter Brune   TS  ts = (TS)ctx;
1988d5e6173cSPeter Brune   Vec Z, Z_c;
1989d5e6173cSPeter Brune 
1990d5e6173cSPeter Brune   PetscFunctionBegin;
19919566063dSJacob Faibussowitsch   PetscCall(TSARKIMEXGetVecs(ts, fine, &Z, NULL));
19929566063dSJacob Faibussowitsch   PetscCall(TSARKIMEXGetVecs(ts, coarse, &Z_c, NULL));
19939566063dSJacob Faibussowitsch   PetscCall(MatRestrict(restrct, Z, Z_c));
19949566063dSJacob Faibussowitsch   PetscCall(VecPointwiseMult(Z_c, rscale, Z_c));
19959566063dSJacob Faibussowitsch   PetscCall(TSARKIMEXRestoreVecs(ts, fine, &Z, NULL));
19969566063dSJacob Faibussowitsch   PetscCall(TSARKIMEXRestoreVecs(ts, coarse, &Z_c, NULL));
19973ba16761SJacob Faibussowitsch   PetscFunctionReturn(PETSC_SUCCESS);
19988a381b04SJed Brown }
19998a381b04SJed Brown 
2000d71ae5a4SJacob Faibussowitsch static PetscErrorCode DMSubDomainHook_TSARKIMEX(DM dm, DM subdm, void *ctx)
2001d71ae5a4SJacob Faibussowitsch {
2002cdb298fcSPeter Brune   PetscFunctionBegin;
20033ba16761SJacob Faibussowitsch   PetscFunctionReturn(PETSC_SUCCESS);
2004cdb298fcSPeter Brune }
2005cdb298fcSPeter Brune 
2006d71ae5a4SJacob Faibussowitsch static PetscErrorCode DMSubDomainRestrictHook_TSARKIMEX(DM dm, VecScatter gscat, VecScatter lscat, DM subdm, void *ctx)
2007d71ae5a4SJacob Faibussowitsch {
2008cdb298fcSPeter Brune   TS  ts = (TS)ctx;
2009cdb298fcSPeter Brune   Vec Z, Z_c;
2010cdb298fcSPeter Brune 
2011cdb298fcSPeter Brune   PetscFunctionBegin;
20129566063dSJacob Faibussowitsch   PetscCall(TSARKIMEXGetVecs(ts, dm, &Z, NULL));
20139566063dSJacob Faibussowitsch   PetscCall(TSARKIMEXGetVecs(ts, subdm, &Z_c, NULL));
2014cdb298fcSPeter Brune 
20159566063dSJacob Faibussowitsch   PetscCall(VecScatterBegin(gscat, Z, Z_c, INSERT_VALUES, SCATTER_FORWARD));
20169566063dSJacob Faibussowitsch   PetscCall(VecScatterEnd(gscat, Z, Z_c, INSERT_VALUES, SCATTER_FORWARD));
2017cdb298fcSPeter Brune 
20189566063dSJacob Faibussowitsch   PetscCall(TSARKIMEXRestoreVecs(ts, dm, &Z, NULL));
20199566063dSJacob Faibussowitsch   PetscCall(TSARKIMEXRestoreVecs(ts, subdm, &Z_c, NULL));
20203ba16761SJacob Faibussowitsch   PetscFunctionReturn(PETSC_SUCCESS);
2021cdb298fcSPeter Brune }
2022cdb298fcSPeter Brune 
2023d71ae5a4SJacob Faibussowitsch static PetscErrorCode TSARKIMEXTableauSetUp(TS ts)
2024d71ae5a4SJacob Faibussowitsch {
202596400bd6SLisandro Dalcin   TS_ARKIMEX *ark = (TS_ARKIMEX *)ts->data;
202696400bd6SLisandro Dalcin   ARKTableau  tab = ark->tableau;
202796400bd6SLisandro Dalcin 
202896400bd6SLisandro Dalcin   PetscFunctionBegin;
2029d27334e2SStefano Zampini   PetscCall(PetscMalloc1(2 * tab->s, &ark->work));
20309566063dSJacob Faibussowitsch   PetscCall(VecDuplicateVecs(ts->vec_sol, tab->s, &ark->Y));
20319566063dSJacob Faibussowitsch   PetscCall(VecDuplicateVecs(ts->vec_sol, tab->s, &ark->YdotI));
2032d27334e2SStefano Zampini   if (tab->additive) PetscCall(VecDuplicateVecs(ts->vec_sol, tab->s, &ark->YdotRHS));
203396400bd6SLisandro Dalcin   if (ark->extrapolate) {
20349566063dSJacob Faibussowitsch     PetscCall(VecDuplicateVecs(ts->vec_sol, tab->s, &ark->Y_prev));
20359566063dSJacob Faibussowitsch     PetscCall(VecDuplicateVecs(ts->vec_sol, tab->s, &ark->YdotI_prev));
2036d27334e2SStefano Zampini     if (tab->additive) PetscCall(VecDuplicateVecs(ts->vec_sol, tab->s, &ark->YdotRHS_prev));
203796400bd6SLisandro Dalcin   }
20383ba16761SJacob Faibussowitsch   PetscFunctionReturn(PETSC_SUCCESS);
203996400bd6SLisandro Dalcin }
204096400bd6SLisandro Dalcin 
2041d71ae5a4SJacob Faibussowitsch static PetscErrorCode TSSetUp_ARKIMEX(TS ts)
2042d71ae5a4SJacob Faibussowitsch {
20438a381b04SJed Brown   TS_ARKIMEX *ark = (TS_ARKIMEX *)ts->data;
2044d5e6173cSPeter Brune   DM          dm;
204596400bd6SLisandro Dalcin   SNES        snes;
2046f9c1d6abSBarry Smith 
20478a381b04SJed Brown   PetscFunctionBegin;
2048*3a2a065fSHong Zhang   if (ark->fastslowsplit) {
2049*3a2a065fSHong Zhang     PetscTryMethod(ts, "TSSetUp_ARKIMEX_FastSlowSplit_C", (TS), (ts));
2050*3a2a065fSHong Zhang   } else {
20519566063dSJacob Faibussowitsch     PetscCall(TSARKIMEXTableauSetUp(ts));
20529566063dSJacob Faibussowitsch     PetscCall(VecDuplicate(ts->vec_sol, &ark->Ydot));
20539566063dSJacob Faibussowitsch     PetscCall(VecDuplicate(ts->vec_sol, &ark->Ydot0));
20549566063dSJacob Faibussowitsch     PetscCall(VecDuplicate(ts->vec_sol, &ark->Z));
20559566063dSJacob Faibussowitsch     PetscCall(TSGetDM(ts, &dm));
20569566063dSJacob Faibussowitsch     PetscCall(DMCoarsenHookAdd(dm, DMCoarsenHook_TSARKIMEX, DMRestrictHook_TSARKIMEX, ts));
20579566063dSJacob Faibussowitsch     PetscCall(DMSubDomainHookAdd(dm, DMSubDomainHook_TSARKIMEX, DMSubDomainRestrictHook_TSARKIMEX, ts));
20589566063dSJacob Faibussowitsch     PetscCall(TSGetSNES(ts, &snes));
2059*3a2a065fSHong Zhang     PetscCall(SNESSetDM(snes, dm));
2060*3a2a065fSHong Zhang   }
20613ba16761SJacob Faibussowitsch   PetscFunctionReturn(PETSC_SUCCESS);
20628a381b04SJed Brown }
20638a381b04SJed Brown 
206480ab5e31SHong Zhang static PetscErrorCode TSAdjointSetUp_ARKIMEX(TS ts)
206580ab5e31SHong Zhang {
206680ab5e31SHong Zhang   TS_ARKIMEX *ark = (TS_ARKIMEX *)ts->data;
206780ab5e31SHong Zhang   ARKTableau  tab = ark->tableau;
206880ab5e31SHong Zhang 
206980ab5e31SHong Zhang   PetscFunctionBegin;
207080ab5e31SHong Zhang   PetscCall(VecDuplicateVecs(ts->vecs_sensi[0], tab->s * ts->numcost, &ark->VecsDeltaLam));
207180ab5e31SHong Zhang   PetscCall(VecDuplicateVecs(ts->vecs_sensi[0], ts->numcost, &ark->VecsSensiTemp));
207280ab5e31SHong Zhang   if (ts->vecs_sensip) { PetscCall(VecDuplicateVecs(ts->vecs_sensip[0], ts->numcost, &ark->VecsSensiPTemp)); }
207380ab5e31SHong Zhang   if (PetscDefined(USE_DEBUG)) {
207480ab5e31SHong Zhang     PetscBool id = PETSC_FALSE;
207580ab5e31SHong Zhang     PetscCall(TSARKIMEXTestMassIdentity(ts, &id));
20768434afd1SBarry Smith     PetscCheck(id, PetscObjectComm((PetscObject)ts), PETSC_ERR_ARG_INCOMP, "Adjoint ARKIMEX requires an identity mass matrix, however the TSIFunctionFn you provided does not utilize an identity mass matrix");
207780ab5e31SHong Zhang   }
207880ab5e31SHong Zhang   PetscFunctionReturn(PETSC_SUCCESS);
207980ab5e31SHong Zhang }
208080ab5e31SHong Zhang 
2081d71ae5a4SJacob Faibussowitsch static PetscErrorCode TSSetFromOptions_ARKIMEX(TS ts, PetscOptionItems *PetscOptionsObject)
2082d71ae5a4SJacob Faibussowitsch {
20834cc180ffSJed Brown   TS_ARKIMEX *ark = (TS_ARKIMEX *)ts->data;
2084d27334e2SStefano Zampini   PetscBool   dirk;
20858a381b04SJed Brown 
20868a381b04SJed Brown   PetscFunctionBegin;
2087d27334e2SStefano Zampini   PetscCall(PetscObjectTypeCompare((PetscObject)ts, TSDIRK, &dirk));
2088d27334e2SStefano Zampini   PetscOptionsHeadBegin(PetscOptionsObject, dirk ? "DIRK ODE solver options" : "ARKIMEX ODE solver options");
20898a381b04SJed Brown   {
20908a381b04SJed Brown     ARKTableauLink link;
20918a381b04SJed Brown     PetscInt       count, choice;
20928a381b04SJed Brown     PetscBool      flg;
20938a381b04SJed Brown     const char   **namelist;
2094d27334e2SStefano Zampini     for (link = ARKTableauList, count = 0; link; link = link->next) {
2095d27334e2SStefano Zampini       if (!dirk && link->tab.additive) count++;
2096d27334e2SStefano Zampini       if (dirk && !link->tab.additive) count++;
2097d27334e2SStefano Zampini     }
20989566063dSJacob Faibussowitsch     PetscCall(PetscMalloc1(count, (char ***)&namelist));
2099d27334e2SStefano Zampini     for (link = ARKTableauList, count = 0; link; link = link->next) {
2100d27334e2SStefano Zampini       if (!dirk && link->tab.additive) namelist[count++] = link->tab.name;
2101d27334e2SStefano Zampini       if (dirk && !link->tab.additive) namelist[count++] = link->tab.name;
2102d27334e2SStefano Zampini     }
2103d27334e2SStefano Zampini     if (dirk) {
2104d27334e2SStefano Zampini       PetscCall(PetscOptionsEList("-ts_dirk_type", "Family of DIRK method", "TSDIRKSetType", (const char *const *)namelist, count, ark->tableau->name, &choice, &flg));
2105d27334e2SStefano Zampini       if (flg) PetscCall(TSDIRKSetType(ts, namelist[choice]));
2106d27334e2SStefano Zampini     } else {
2107*3a2a065fSHong Zhang       PetscBool fastslowsplit;
21089566063dSJacob Faibussowitsch       PetscCall(PetscOptionsEList("-ts_arkimex_type", "Family of ARK IMEX method", "TSARKIMEXSetType", (const char *const *)namelist, count, ark->tableau->name, &choice, &flg));
21099566063dSJacob Faibussowitsch       if (flg) PetscCall(TSARKIMEXSetType(ts, namelist[choice]));
21104cc180ffSJed Brown       flg = (PetscBool)!ark->imex;
21119566063dSJacob Faibussowitsch       PetscCall(PetscOptionsBool("-ts_arkimex_fully_implicit", "Solve the problem fully implicitly", "TSARKIMEXSetFullyImplicit", flg, &flg, NULL));
21124cc180ffSJed Brown       ark->imex = (PetscBool)!flg;
2113*3a2a065fSHong Zhang       PetscCall(PetscOptionsBool("-ts_arkimex_fastslowsplit", "Use ARK IMEX for fast-slow systems", "TSARKIMEXSetFastSlowSplit", ark->fastslowsplit, &fastslowsplit, &flg));
2114*3a2a065fSHong Zhang       if (flg) PetscCall(TSARKIMEXSetFastSlowSplit(ts, fastslowsplit));
2115d27334e2SStefano Zampini     }
2116d27334e2SStefano Zampini     PetscCall(PetscFree(namelist));
21179566063dSJacob Faibussowitsch     PetscCall(PetscOptionsBool("-ts_arkimex_initial_guess_extrapolate", "Extrapolate the initial guess for the stage solution from stage values of the previous time step", "", ark->extrapolate, &ark->extrapolate, NULL));
21188a381b04SJed Brown   }
2119d0609cedSBarry Smith   PetscOptionsHeadEnd();
21203ba16761SJacob Faibussowitsch   PetscFunctionReturn(PETSC_SUCCESS);
21218a381b04SJed Brown }
21228a381b04SJed Brown 
2123d71ae5a4SJacob Faibussowitsch static PetscErrorCode TSView_ARKIMEX(TS ts, PetscViewer viewer)
2124d71ae5a4SJacob Faibussowitsch {
21258a381b04SJed Brown   TS_ARKIMEX *ark = (TS_ARKIMEX *)ts->data;
2126d27334e2SStefano Zampini   PetscBool   iascii, dirk;
21278a381b04SJed Brown 
21288a381b04SJed Brown   PetscFunctionBegin;
2129d27334e2SStefano Zampini   PetscCall(PetscObjectTypeCompare((PetscObject)ts, TSDIRK, &dirk));
21309566063dSJacob Faibussowitsch   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
21318a381b04SJed Brown   if (iascii) {
2132d27334e2SStefano Zampini     PetscViewerFormat format;
21339c334d8fSLisandro Dalcin     ARKTableau        tab = ark->tableau;
213419fd82e9SBarry Smith     TSARKIMEXType     arktype;
2135d27334e2SStefano Zampini     char              buf[2048];
21363a28c0e5SStefano Zampini     PetscBool         flg;
21373a28c0e5SStefano Zampini 
21389566063dSJacob Faibussowitsch     PetscCall(TSARKIMEXGetType(ts, &arktype));
21399566063dSJacob Faibussowitsch     PetscCall(TSARKIMEXGetFullyImplicit(ts, &flg));
2140d27334e2SStefano Zampini     PetscCall(PetscViewerASCIIPrintf(viewer, "  %s %s\n", dirk ? "DIRK" : "ARK IMEX", arktype));
21419566063dSJacob Faibussowitsch     PetscCall(PetscFormatRealArray(buf, sizeof(buf), "% 8.6f", tab->s, tab->ct));
2142d27334e2SStefano Zampini     PetscCall(PetscViewerASCIIPrintf(viewer, "  %sabscissa       ct = %s\n", dirk ? "" : "Stiff ", buf));
2143d27334e2SStefano Zampini     PetscCall(PetscViewerGetFormat(viewer, &format));
2144d27334e2SStefano Zampini     if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
2145d27334e2SStefano Zampini       PetscCall(PetscViewerASCIIPrintf(viewer, "  %sAt =\n", dirk ? "" : "Stiff "));
2146d27334e2SStefano Zampini       for (PetscInt i = 0; i < tab->s; i++) {
2147d27334e2SStefano Zampini         PetscCall(PetscFormatRealArray(buf, sizeof(buf), "% 8.6f", tab->s, tab->At + i * tab->s));
2148d27334e2SStefano Zampini         PetscCall(PetscViewerASCIIPrintf(viewer, "    %s\n", buf));
2149d27334e2SStefano Zampini       }
2150d27334e2SStefano Zampini       PetscCall(PetscFormatRealArray(buf, sizeof(buf), "% 8.6f", tab->s, tab->bt));
2151d27334e2SStefano Zampini       PetscCall(PetscViewerASCIIPrintf(viewer, "  %sbt = %s\n", dirk ? "" : "Stiff ", buf));
2152d27334e2SStefano Zampini       PetscCall(PetscFormatRealArray(buf, sizeof(buf), "% 8.6f", tab->s, tab->bembedt));
2153d27334e2SStefano Zampini       PetscCall(PetscViewerASCIIPrintf(viewer, "  %sbet = %s\n", dirk ? "" : "Stiff ", buf));
2154d27334e2SStefano Zampini     }
21559566063dSJacob Faibussowitsch     PetscCall(PetscViewerASCIIPrintf(viewer, "Fully implicit: %s\n", flg ? "yes" : "no"));
21569566063dSJacob Faibussowitsch     PetscCall(PetscViewerASCIIPrintf(viewer, "Stiffly accurate: %s\n", tab->stiffly_accurate ? "yes" : "no"));
21579566063dSJacob Faibussowitsch     PetscCall(PetscViewerASCIIPrintf(viewer, "Explicit first stage: %s\n", tab->explicit_first_stage ? "yes" : "no"));
21589566063dSJacob Faibussowitsch     PetscCall(PetscViewerASCIIPrintf(viewer, "FSAL property: %s\n", tab->FSAL_implicit ? "yes" : "no"));
2159d27334e2SStefano Zampini     if (!dirk) {
2160d27334e2SStefano Zampini       PetscCall(PetscFormatRealArray(buf, sizeof(buf), "% 8.6f", tab->s, tab->c));
21619566063dSJacob Faibussowitsch       PetscCall(PetscViewerASCIIPrintf(viewer, "  Nonstiff abscissa     c = %s\n", buf));
21628a381b04SJed Brown     }
2163d27334e2SStefano Zampini   }
21643ba16761SJacob Faibussowitsch   PetscFunctionReturn(PETSC_SUCCESS);
21658a381b04SJed Brown }
21668a381b04SJed Brown 
2167d71ae5a4SJacob Faibussowitsch static PetscErrorCode TSLoad_ARKIMEX(TS ts, PetscViewer viewer)
2168d71ae5a4SJacob Faibussowitsch {
2169f2c2a1b9SBarry Smith   SNES    snes;
21709c334d8fSLisandro Dalcin   TSAdapt adapt;
2171f2c2a1b9SBarry Smith 
2172f2c2a1b9SBarry Smith   PetscFunctionBegin;
21739566063dSJacob Faibussowitsch   PetscCall(TSGetAdapt(ts, &adapt));
21749566063dSJacob Faibussowitsch   PetscCall(TSAdaptLoad(adapt, viewer));
21759566063dSJacob Faibussowitsch   PetscCall(TSGetSNES(ts, &snes));
21769566063dSJacob Faibussowitsch   PetscCall(SNESLoad(snes, viewer));
2177ad6bc421SBarry Smith   /* function and Jacobian context for SNES when used with TS is always ts object */
21789566063dSJacob Faibussowitsch   PetscCall(SNESSetFunction(snes, NULL, NULL, ts));
21799566063dSJacob Faibussowitsch   PetscCall(SNESSetJacobian(snes, NULL, NULL, NULL, ts));
21803ba16761SJacob Faibussowitsch   PetscFunctionReturn(PETSC_SUCCESS);
2181f2c2a1b9SBarry Smith }
2182f2c2a1b9SBarry Smith 
2183cc4c1da9SBarry Smith /*@
2184bcf0153eSBarry Smith   TSARKIMEXSetType - Set the type of `TSARKIMEX` scheme
21858a381b04SJed Brown 
218620f4b53cSBarry Smith   Logically Collective
21878a381b04SJed Brown 
2188d8d19677SJose E. Roman   Input Parameters:
21898a381b04SJed Brown + ts      - timestepping context
2190bcf0153eSBarry Smith - arktype - type of `TSARKIMEX` scheme
21918a381b04SJed Brown 
2192bcf0153eSBarry Smith   Options Database Key:
2193bcf0153eSBarry Smith . -ts_arkimex_type <1bee,a2,l2,ars122,2c,2d,2e,prssp2,3,bpr3,ars443,4,5> - set `TSARKIMEX` scheme type
21949bd3e852SBarry Smith 
21958a381b04SJed Brown   Level: intermediate
21968a381b04SJed Brown 
21971cc06b55SBarry Smith .seealso: [](ch_ts), `TSARKIMEXGetType()`, `TSARKIMEX`, `TSARKIMEXType`, `TSARKIMEX1BEE`, `TSARKIMEXA2`, `TSARKIMEXL2`, `TSARKIMEXARS122`, `TSARKIMEX2C`, `TSARKIMEX2D`, `TSARKIMEX2E`, `TSARKIMEXPRSSP2`,
2198db781477SPatrick Sanan           `TSARKIMEX3`, `TSARKIMEXBPR3`, `TSARKIMEXARS443`, `TSARKIMEX4`, `TSARKIMEX5`
21998a381b04SJed Brown @*/
2200d71ae5a4SJacob Faibussowitsch PetscErrorCode TSARKIMEXSetType(TS ts, TSARKIMEXType arktype)
2201d71ae5a4SJacob Faibussowitsch {
22028a381b04SJed Brown   PetscFunctionBegin;
22038a381b04SJed Brown   PetscValidHeaderSpecific(ts, TS_CLASSID, 1);
22044f572ea9SToby Isaac   PetscAssertPointer(arktype, 2);
2205cac4c232SBarry Smith   PetscTryMethod(ts, "TSARKIMEXSetType_C", (TS, TSARKIMEXType), (ts, arktype));
22063ba16761SJacob Faibussowitsch   PetscFunctionReturn(PETSC_SUCCESS);
22078a381b04SJed Brown }
22088a381b04SJed Brown 
2209cc4c1da9SBarry Smith /*@
2210bcf0153eSBarry Smith   TSARKIMEXGetType - Get the type of `TSARKIMEX` scheme
22118a381b04SJed Brown 
221220f4b53cSBarry Smith   Logically Collective
22138a381b04SJed Brown 
22148a381b04SJed Brown   Input Parameter:
22158a381b04SJed Brown . ts - timestepping context
22168a381b04SJed Brown 
22178a381b04SJed Brown   Output Parameter:
2218bcf0153eSBarry Smith . arktype - type of `TSARKIMEX` scheme
22198a381b04SJed Brown 
22208a381b04SJed Brown   Level: intermediate
22218a381b04SJed Brown 
222242747ad1SJacob Faibussowitsch .seealso: [](ch_ts), `TSARKIMEXc`
22238a381b04SJed Brown @*/
2224d71ae5a4SJacob Faibussowitsch PetscErrorCode TSARKIMEXGetType(TS ts, TSARKIMEXType *arktype)
2225d71ae5a4SJacob Faibussowitsch {
22268a381b04SJed Brown   PetscFunctionBegin;
22278a381b04SJed Brown   PetscValidHeaderSpecific(ts, TS_CLASSID, 1);
2228cac4c232SBarry Smith   PetscUseMethod(ts, "TSARKIMEXGetType_C", (TS, TSARKIMEXType *), (ts, arktype));
22293ba16761SJacob Faibussowitsch   PetscFunctionReturn(PETSC_SUCCESS);
22308a381b04SJed Brown }
22318a381b04SJed Brown 
223216353aafSBarry Smith /*@
2233bcf0153eSBarry Smith   TSARKIMEXSetFullyImplicit - Solve both parts of the equation implicitly, including the part that is normally solved explicitly
22344cc180ffSJed Brown 
223520f4b53cSBarry Smith   Logically Collective
22364cc180ffSJed Brown 
2237d8d19677SJose E. Roman   Input Parameters:
22384cc180ffSJed Brown + ts  - timestepping context
2239bcf0153eSBarry Smith - flg - `PETSC_TRUE` for fully implicit
22404cc180ffSJed Brown 
22414cc180ffSJed Brown   Level: intermediate
22424cc180ffSJed Brown 
22431cc06b55SBarry Smith .seealso: [](ch_ts), `TSARKIMEX`, `TSARKIMEXGetType()`, `TSARKIMEXGetFullyImplicit()`
22444cc180ffSJed Brown @*/
2245d71ae5a4SJacob Faibussowitsch PetscErrorCode TSARKIMEXSetFullyImplicit(TS ts, PetscBool flg)
2246d71ae5a4SJacob Faibussowitsch {
22474cc180ffSJed Brown   PetscFunctionBegin;
22484cc180ffSJed Brown   PetscValidHeaderSpecific(ts, TS_CLASSID, 1);
22493a28c0e5SStefano Zampini   PetscValidLogicalCollectiveBool(ts, flg, 2);
2250cac4c232SBarry Smith   PetscTryMethod(ts, "TSARKIMEXSetFullyImplicit_C", (TS, PetscBool), (ts, flg));
22513ba16761SJacob Faibussowitsch   PetscFunctionReturn(PETSC_SUCCESS);
22524cc180ffSJed Brown }
22534cc180ffSJed Brown 
22543a28c0e5SStefano Zampini /*@
22553a28c0e5SStefano Zampini   TSARKIMEXGetFullyImplicit - Inquires if both parts of the equation are solved implicitly
22563a28c0e5SStefano Zampini 
225720f4b53cSBarry Smith   Logically Collective
22583a28c0e5SStefano Zampini 
22593a28c0e5SStefano Zampini   Input Parameter:
22603a28c0e5SStefano Zampini . ts - timestepping context
22613a28c0e5SStefano Zampini 
22627a7aea1fSJed Brown   Output Parameter:
2263bcf0153eSBarry Smith . flg - `PETSC_TRUE` for fully implicit
22643a28c0e5SStefano Zampini 
22653a28c0e5SStefano Zampini   Level: intermediate
22663a28c0e5SStefano Zampini 
22671cc06b55SBarry Smith .seealso: [](ch_ts), `TSARKIMEXGetType()`, `TSARKIMEXSetFullyImplicit()`
22683a28c0e5SStefano Zampini @*/
2269d71ae5a4SJacob Faibussowitsch PetscErrorCode TSARKIMEXGetFullyImplicit(TS ts, PetscBool *flg)
2270d71ae5a4SJacob Faibussowitsch {
22713a28c0e5SStefano Zampini   PetscFunctionBegin;
22723a28c0e5SStefano Zampini   PetscValidHeaderSpecific(ts, TS_CLASSID, 1);
22734f572ea9SToby Isaac   PetscAssertPointer(flg, 2);
2274cac4c232SBarry Smith   PetscUseMethod(ts, "TSARKIMEXGetFullyImplicit_C", (TS, PetscBool *), (ts, flg));
22753ba16761SJacob Faibussowitsch   PetscFunctionReturn(PETSC_SUCCESS);
22763a28c0e5SStefano Zampini }
22773a28c0e5SStefano Zampini 
2278d71ae5a4SJacob Faibussowitsch static PetscErrorCode TSARKIMEXGetType_ARKIMEX(TS ts, TSARKIMEXType *arktype)
2279d71ae5a4SJacob Faibussowitsch {
22808a381b04SJed Brown   TS_ARKIMEX *ark = (TS_ARKIMEX *)ts->data;
22818a381b04SJed Brown 
22828a381b04SJed Brown   PetscFunctionBegin;
22838a381b04SJed Brown   *arktype = ark->tableau->name;
22843ba16761SJacob Faibussowitsch   PetscFunctionReturn(PETSC_SUCCESS);
22858a381b04SJed Brown }
2286d27334e2SStefano Zampini 
2287d71ae5a4SJacob Faibussowitsch static PetscErrorCode TSARKIMEXSetType_ARKIMEX(TS ts, TSARKIMEXType arktype)
2288d71ae5a4SJacob Faibussowitsch {
22898a381b04SJed Brown   TS_ARKIMEX    *ark = (TS_ARKIMEX *)ts->data;
22908a381b04SJed Brown   PetscBool      match;
22918a381b04SJed Brown   ARKTableauLink link;
22928a381b04SJed Brown 
22938a381b04SJed Brown   PetscFunctionBegin;
22948a381b04SJed Brown   if (ark->tableau) {
22959566063dSJacob Faibussowitsch     PetscCall(PetscStrcmp(ark->tableau->name, arktype, &match));
22963ba16761SJacob Faibussowitsch     if (match) PetscFunctionReturn(PETSC_SUCCESS);
22978a381b04SJed Brown   }
22988a381b04SJed Brown   for (link = ARKTableauList; link; link = link->next) {
22999566063dSJacob Faibussowitsch     PetscCall(PetscStrcmp(link->tab.name, arktype, &match));
23008a381b04SJed Brown     if (match) {
23019566063dSJacob Faibussowitsch       if (ts->setupcalled) PetscCall(TSARKIMEXTableauReset(ts));
23028a381b04SJed Brown       ark->tableau = &link->tab;
23039566063dSJacob Faibussowitsch       if (ts->setupcalled) PetscCall(TSARKIMEXTableauSetUp(ts));
23042ffb9264SLisandro Dalcin       ts->default_adapt_type = ark->tableau->bembed ? TSADAPTBASIC : TSADAPTNONE;
23053ba16761SJacob Faibussowitsch       PetscFunctionReturn(PETSC_SUCCESS);
23068a381b04SJed Brown     }
23078a381b04SJed Brown   }
230898921bdaSJacob Faibussowitsch   SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_ARG_UNKNOWN_TYPE, "Could not find '%s'", arktype);
23098a381b04SJed Brown }
2310e0877f53SBarry Smith 
2311d71ae5a4SJacob Faibussowitsch static PetscErrorCode TSARKIMEXSetFullyImplicit_ARKIMEX(TS ts, PetscBool flg)
2312d71ae5a4SJacob Faibussowitsch {
23134cc180ffSJed Brown   TS_ARKIMEX *ark = (TS_ARKIMEX *)ts->data;
23144cc180ffSJed Brown 
23154cc180ffSJed Brown   PetscFunctionBegin;
23164cc180ffSJed Brown   ark->imex = (PetscBool)!flg;
23173ba16761SJacob Faibussowitsch   PetscFunctionReturn(PETSC_SUCCESS);
23184cc180ffSJed Brown }
23198a381b04SJed Brown 
2320d71ae5a4SJacob Faibussowitsch static PetscErrorCode TSARKIMEXGetFullyImplicit_ARKIMEX(TS ts, PetscBool *flg)
2321d71ae5a4SJacob Faibussowitsch {
23223a28c0e5SStefano Zampini   TS_ARKIMEX *ark = (TS_ARKIMEX *)ts->data;
23233a28c0e5SStefano Zampini 
23243a28c0e5SStefano Zampini   PetscFunctionBegin;
23253a28c0e5SStefano Zampini   *flg = (PetscBool)!ark->imex;
23263ba16761SJacob Faibussowitsch   PetscFunctionReturn(PETSC_SUCCESS);
23273a28c0e5SStefano Zampini }
23283a28c0e5SStefano Zampini 
2329d71ae5a4SJacob Faibussowitsch static PetscErrorCode TSDestroy_ARKIMEX(TS ts)
2330d71ae5a4SJacob Faibussowitsch {
2331b3a6b972SJed Brown   PetscFunctionBegin;
23329566063dSJacob Faibussowitsch   PetscCall(TSReset_ARKIMEX(ts));
2333b3a6b972SJed Brown   if (ts->dm) {
23349566063dSJacob Faibussowitsch     PetscCall(DMCoarsenHookRemove(ts->dm, DMCoarsenHook_TSARKIMEX, DMRestrictHook_TSARKIMEX, ts));
23359566063dSJacob Faibussowitsch     PetscCall(DMSubDomainHookRemove(ts->dm, DMSubDomainHook_TSARKIMEX, DMSubDomainRestrictHook_TSARKIMEX, ts));
2336b3a6b972SJed Brown   }
23379566063dSJacob Faibussowitsch   PetscCall(PetscFree(ts->data));
2338d27334e2SStefano Zampini   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSDIRKGetType_C", NULL));
2339d27334e2SStefano Zampini   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSDIRKSetType_C", NULL));
23409566063dSJacob Faibussowitsch   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSARKIMEXGetType_C", NULL));
23419566063dSJacob Faibussowitsch   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSARKIMEXSetType_C", NULL));
23429566063dSJacob Faibussowitsch   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSARKIMEXSetFullyImplicit_C", NULL));
23432e956fe4SStefano Zampini   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSARKIMEXGetFullyImplicit_C", NULL));
2344*3a2a065fSHong Zhang   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSARKIMEXSetFastSlowSplit_C", NULL));
2345*3a2a065fSHong Zhang   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSARKIMEXGetFastSlowSplit_C", NULL));
2346*3a2a065fSHong Zhang   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSSetUp_ARKIMEX_FastSlowSplit_C", NULL));
2347*3a2a065fSHong Zhang   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSReset_ARKIMEX_FastSlowSplit_C", NULL));
23483ba16761SJacob Faibussowitsch   PetscFunctionReturn(PETSC_SUCCESS);
2349b3a6b972SJed Brown }
2350b3a6b972SJed Brown 
23518a381b04SJed Brown /* ------------------------------------------------------------ */
23528a381b04SJed Brown /*MC
2353c79dcfbdSBarry Smith       TSARKIMEX - ODE and DAE solver using additive Runge-Kutta IMEX schemes
23548a381b04SJed Brown 
2355fca742c7SJed Brown   These methods are intended for problems with well-separated time scales, especially when a slow scale is strongly
2356fca742c7SJed Brown   nonlinear such that it is expensive to solve with a fully implicit method. The user should provide the stiff part
2357bcf0153eSBarry Smith   of the equation using `TSSetIFunction()` and the non-stiff part with `TSSetRHSFunction()`.
2358d0685a90SJed Brown 
23598a381b04SJed Brown   Level: beginner
23608a381b04SJed Brown 
2361bcf0153eSBarry Smith   Notes:
2362bcf0153eSBarry Smith   The default is `TSARKIMEX3`, it can be changed with `TSARKIMEXSetType()` or -ts_arkimex_type
23638a381b04SJed Brown 
2364bcf0153eSBarry Smith   If the equation is implicit or a DAE, then `TSSetEquationType()` needs to be set accordingly. Refer to the manual for further information.
2365bcf0153eSBarry Smith 
2366bcf0153eSBarry Smith   Methods with an explicit stage can only be used with ODE in which the stiff part G(t,X,Xdot) has the form Xdot + Ghat(t,X).
2367bcf0153eSBarry Smith 
2368bcf0153eSBarry Smith   Consider trying `TSROSW` if the stiff part is linear or weakly nonlinear.
2369bcf0153eSBarry Smith 
23701cc06b55SBarry Smith .seealso: [](ch_ts), `TSCreate()`, `TS`, `TSSetType()`, `TSARKIMEXSetType()`, `TSARKIMEXGetType()`, `TSARKIMEXSetFullyImplicit()`, `TSARKIMEXGetFullyImplicit()`,
2371bcf0153eSBarry Smith           `TSARKIMEX1BEE`, `TSARKIMEX2C`, `TSARKIMEX2D`, `TSARKIMEX2E`, `TSARKIMEX3`, `TSARKIMEXL2`, `TSARKIMEXA2`, `TSARKIMEXARS122`,
2372bcf0153eSBarry Smith           `TSARKIMEX4`, `TSARKIMEX5`, `TSARKIMEXPRSSP2`, `TSARKIMEXARS443`, `TSARKIMEXBPR3`, `TSARKIMEXType`, `TSARKIMEXRegister()`, `TSType`
23738a381b04SJed Brown M*/
2374d71ae5a4SJacob Faibussowitsch PETSC_EXTERN PetscErrorCode TSCreate_ARKIMEX(TS ts)
2375d71ae5a4SJacob Faibussowitsch {
237680ab5e31SHong Zhang   TS_ARKIMEX *ark;
2377d27334e2SStefano Zampini   PetscBool   dirk;
23788a381b04SJed Brown 
23798a381b04SJed Brown   PetscFunctionBegin;
23809566063dSJacob Faibussowitsch   PetscCall(TSARKIMEXInitializePackage());
2381d27334e2SStefano Zampini   PetscCall(PetscObjectTypeCompare((PetscObject)ts, TSDIRK, &dirk));
23828a381b04SJed Brown 
23838a381b04SJed Brown   ts->ops->reset          = TSReset_ARKIMEX;
238480ab5e31SHong Zhang   ts->ops->adjointreset   = TSAdjointReset_ARKIMEX;
23858a381b04SJed Brown   ts->ops->destroy        = TSDestroy_ARKIMEX;
23868a381b04SJed Brown   ts->ops->view           = TSView_ARKIMEX;
2387f2c2a1b9SBarry Smith   ts->ops->load           = TSLoad_ARKIMEX;
23888a381b04SJed Brown   ts->ops->setup          = TSSetUp_ARKIMEX;
238980ab5e31SHong Zhang   ts->ops->adjointsetup   = TSAdjointSetUp_ARKIMEX;
23908a381b04SJed Brown   ts->ops->step           = TSStep_ARKIMEX;
2391cd652676SJed Brown   ts->ops->interpolate    = TSInterpolate_ARKIMEX;
2392108c343cSJed Brown   ts->ops->evaluatestep   = TSEvaluateStep_ARKIMEX;
23938a381b04SJed Brown   ts->ops->setfromoptions = TSSetFromOptions_ARKIMEX;
23948a381b04SJed Brown   ts->ops->snesfunction   = SNESTSFormFunction_ARKIMEX;
23958a381b04SJed Brown   ts->ops->snesjacobian   = SNESTSFormJacobian_ARKIMEX;
239680ab5e31SHong Zhang   ts->ops->getstages      = TSGetStages_ARKIMEX;
239780ab5e31SHong Zhang   ts->ops->adjointstep    = TSAdjointStep_ARKIMEX;
23988a381b04SJed Brown 
2399efd4aadfSBarry Smith   ts->usessnes = PETSC_TRUE;
2400efd4aadfSBarry Smith 
240180ab5e31SHong Zhang   PetscCall(PetscNew(&ark));
240280ab5e31SHong Zhang   ts->data  = (void *)ark;
2403d27334e2SStefano Zampini   ark->imex = dirk ? PETSC_FALSE : PETSC_TRUE;
240480ab5e31SHong Zhang 
240580ab5e31SHong Zhang   ark->VecsDeltaLam   = NULL;
240680ab5e31SHong Zhang   ark->VecsSensiTemp  = NULL;
240780ab5e31SHong Zhang   ark->VecsSensiPTemp = NULL;
24088a381b04SJed Brown 
24099566063dSJacob Faibussowitsch   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSARKIMEXGetType_C", TSARKIMEXGetType_ARKIMEX));
2410d27334e2SStefano Zampini   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSARKIMEXGetFullyImplicit_C", TSARKIMEXGetFullyImplicit_ARKIMEX));
2411d27334e2SStefano Zampini   if (!dirk) {
24129566063dSJacob Faibussowitsch     PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSARKIMEXSetType_C", TSARKIMEXSetType_ARKIMEX));
24139566063dSJacob Faibussowitsch     PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSARKIMEXSetFullyImplicit_C", TSARKIMEXSetFullyImplicit_ARKIMEX));
2414*3a2a065fSHong Zhang     PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSARKIMEXSetFastSlowSplit_C", TSARKIMEXSetFastSlowSplit_ARKIMEX));
2415*3a2a065fSHong Zhang     PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSARKIMEXGetFastSlowSplit_C", TSARKIMEXGetFastSlowSplit_ARKIMEX));
24169566063dSJacob Faibussowitsch     PetscCall(TSARKIMEXSetType(ts, TSARKIMEXDefault));
2417d27334e2SStefano Zampini   }
2418d27334e2SStefano Zampini   PetscFunctionReturn(PETSC_SUCCESS);
2419d27334e2SStefano Zampini }
2420d27334e2SStefano Zampini 
2421d27334e2SStefano Zampini /* ------------------------------------------------------------ */
2422d27334e2SStefano Zampini 
2423d27334e2SStefano Zampini static PetscErrorCode TSDIRKSetType_DIRK(TS ts, TSDIRKType dirktype)
2424d27334e2SStefano Zampini {
2425d27334e2SStefano Zampini   TS_ARKIMEX *ark = (TS_ARKIMEX *)ts->data;
2426d27334e2SStefano Zampini 
2427d27334e2SStefano Zampini   PetscFunctionBegin;
2428d27334e2SStefano Zampini   PetscCall(TSARKIMEXSetType_ARKIMEX(ts, dirktype));
2429d27334e2SStefano Zampini   PetscCheck(!ark->tableau->additive, PetscObjectComm((PetscObject)ts), PETSC_ERR_ARG_WRONG, "Method \"%s\" is not DIRK", dirktype);
2430d27334e2SStefano Zampini   PetscFunctionReturn(PETSC_SUCCESS);
2431d27334e2SStefano Zampini }
2432d27334e2SStefano Zampini 
2433cc4c1da9SBarry Smith /*@
2434d27334e2SStefano Zampini   TSDIRKSetType - Set the type of `TSDIRK` scheme
2435d27334e2SStefano Zampini 
2436d27334e2SStefano Zampini   Logically Collective
2437d27334e2SStefano Zampini 
2438d27334e2SStefano Zampini   Input Parameters:
2439d27334e2SStefano Zampini + ts       - timestepping context
2440d27334e2SStefano Zampini - dirktype - type of `TSDIRK` scheme
2441d27334e2SStefano Zampini 
2442d27334e2SStefano Zampini   Options Database Key:
2443d27334e2SStefano Zampini . -ts_dirkimex_type - set `TSDIRK` scheme type
2444d27334e2SStefano Zampini 
2445d27334e2SStefano Zampini   Level: intermediate
2446d27334e2SStefano Zampini 
2447d27334e2SStefano Zampini .seealso: [](ch_ts), `TSDIRKGetType()`, `TSDIRK`, `TSDIRKType`
2448d27334e2SStefano Zampini @*/
2449d27334e2SStefano Zampini PetscErrorCode TSDIRKSetType(TS ts, TSDIRKType dirktype)
2450d27334e2SStefano Zampini {
2451d27334e2SStefano Zampini   PetscFunctionBegin;
2452d27334e2SStefano Zampini   PetscValidHeaderSpecific(ts, TS_CLASSID, 1);
2453d27334e2SStefano Zampini   PetscAssertPointer(dirktype, 2);
2454d27334e2SStefano Zampini   PetscTryMethod(ts, "TSDIRKSetType_C", (TS, TSDIRKType), (ts, dirktype));
2455d27334e2SStefano Zampini   PetscFunctionReturn(PETSC_SUCCESS);
2456d27334e2SStefano Zampini }
2457d27334e2SStefano Zampini 
2458cc4c1da9SBarry Smith /*@
2459d27334e2SStefano Zampini   TSDIRKGetType - Get the type of `TSDIRK` scheme
2460d27334e2SStefano Zampini 
2461d27334e2SStefano Zampini   Logically Collective
2462d27334e2SStefano Zampini 
2463d27334e2SStefano Zampini   Input Parameter:
2464d27334e2SStefano Zampini . ts - timestepping context
2465d27334e2SStefano Zampini 
2466d27334e2SStefano Zampini   Output Parameter:
2467d27334e2SStefano Zampini . dirktype - type of `TSDIRK` scheme
2468d27334e2SStefano Zampini 
2469d27334e2SStefano Zampini   Level: intermediate
2470d27334e2SStefano Zampini 
2471d27334e2SStefano Zampini .seealso: [](ch_ts), `TSDIRKSetType()`
2472d27334e2SStefano Zampini @*/
2473d27334e2SStefano Zampini PetscErrorCode TSDIRKGetType(TS ts, TSDIRKType *dirktype)
2474d27334e2SStefano Zampini {
2475d27334e2SStefano Zampini   PetscFunctionBegin;
2476d27334e2SStefano Zampini   PetscValidHeaderSpecific(ts, TS_CLASSID, 1);
2477d27334e2SStefano Zampini   PetscUseMethod(ts, "TSDIRKGetType_C", (TS, TSDIRKType *), (ts, dirktype));
2478d27334e2SStefano Zampini   PetscFunctionReturn(PETSC_SUCCESS);
2479d27334e2SStefano Zampini }
2480d27334e2SStefano Zampini 
2481d27334e2SStefano Zampini /*MC
24823405e92cSStefano Zampini       TSDIRK - ODE and DAE solver using Diagonally implicit Runge-Kutta schemes.
2483d27334e2SStefano Zampini 
2484d27334e2SStefano Zampini   Level: beginner
2485d27334e2SStefano Zampini 
2486d27334e2SStefano Zampini   Notes:
24873405e92cSStefano Zampini   The default is `TSDIRKES213SAL`, it can be changed with `TSDIRKSetType()` or -ts_dirk_type.
24883405e92cSStefano Zampini   The convention used in PETSc to name the DIRK methods is TSDIRK[E][S]PQS[SA][L][A] with:
24893405e92cSStefano Zampini + E - whether the method has an explicit first stage
24903405e92cSStefano Zampini . S - whether the method is single diagonal
24913405e92cSStefano Zampini . P - order of the advancing method
24923405e92cSStefano Zampini . Q - order of the embedded method
24933405e92cSStefano Zampini . S - number of stages
24943405e92cSStefano Zampini . SA - whether the method is stiffly accurate
24953405e92cSStefano Zampini . L - whether the method is L-stable
24963405e92cSStefano Zampini - A - whether the method is A-stable
2497d27334e2SStefano Zampini 
2498d27334e2SStefano Zampini .seealso: [](ch_ts), `TSCreate()`, `TS`, `TSSetType()`, `TSDIRKSetType()`, `TSDIRKGetType()`, `TSDIRKRegister()`.
2499d27334e2SStefano Zampini M*/
2500d27334e2SStefano Zampini PETSC_EXTERN PetscErrorCode TSCreate_DIRK(TS ts)
2501d27334e2SStefano Zampini {
2502d27334e2SStefano Zampini   PetscFunctionBegin;
2503d27334e2SStefano Zampini   PetscCall(TSCreate_ARKIMEX(ts));
2504d27334e2SStefano Zampini   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSDIRKGetType_C", TSARKIMEXGetType_ARKIMEX));
2505d27334e2SStefano Zampini   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSDIRKSetType_C", TSDIRKSetType_DIRK));
2506d27334e2SStefano Zampini   PetscCall(TSDIRKSetType(ts, TSDIRKDefault));
25073ba16761SJacob Faibussowitsch   PetscFunctionReturn(PETSC_SUCCESS);
25088a381b04SJed Brown }
2509*3a2a065fSHong Zhang 
2510*3a2a065fSHong Zhang /*@
2511*3a2a065fSHong Zhang   TSARKIMEXSetFastSlowSplit - Use `TSARKIMEX` for solving a fast-slow system
2512*3a2a065fSHong Zhang 
2513*3a2a065fSHong Zhang   Logically Collective
2514*3a2a065fSHong Zhang 
2515*3a2a065fSHong Zhang   Input Parameters:
2516*3a2a065fSHong Zhang + ts       - timestepping context
2517*3a2a065fSHong Zhang - fastslow - `PETSC_TRUE` enables the `TSARKIMEX` solver for a fast-slow system where the RHS is split component-wise.
2518*3a2a065fSHong Zhang 
2519*3a2a065fSHong Zhang   Options Database Key:
2520*3a2a065fSHong Zhang . -ts_arkimex_fastslowsplit - <true,false>
2521*3a2a065fSHong Zhang 
2522*3a2a065fSHong Zhang   Level: intermediate
2523*3a2a065fSHong Zhang 
2524*3a2a065fSHong Zhang .seealso: [](ch_ts), `TSARKIMEX`, `TSARKIMEXGetFastSlowSplit()`
2525*3a2a065fSHong Zhang @*/
2526*3a2a065fSHong Zhang PetscErrorCode TSARKIMEXSetFastSlowSplit(TS ts, PetscBool fastslow)
2527*3a2a065fSHong Zhang {
2528*3a2a065fSHong Zhang   PetscFunctionBegin;
2529*3a2a065fSHong Zhang   PetscTryMethod(ts, "TSARKIMEXSetFastSlowSplit_C", (TS, PetscBool), (ts, fastslow));
2530*3a2a065fSHong Zhang   PetscFunctionReturn(PETSC_SUCCESS);
2531*3a2a065fSHong Zhang }
2532*3a2a065fSHong Zhang 
2533*3a2a065fSHong Zhang /*@
2534*3a2a065fSHong Zhang   TSARKIMEXGetFastSlowSplit - Gets whether to use `TSARKIMEX` for a fast-slow system
2535*3a2a065fSHong Zhang 
2536*3a2a065fSHong Zhang   Not Collective
2537*3a2a065fSHong Zhang 
2538*3a2a065fSHong Zhang   Input Parameter:
2539*3a2a065fSHong Zhang . ts - timestepping context
2540*3a2a065fSHong Zhang 
2541*3a2a065fSHong Zhang   Output Parameter:
2542*3a2a065fSHong Zhang . fastslow - `PETSC_TRUE` if `TSARKIMEX` will be used for solving a fast-slow system, `PETSC_FALSE` otherwise
2543*3a2a065fSHong Zhang 
2544*3a2a065fSHong Zhang   Level: intermediate
2545*3a2a065fSHong Zhang 
2546*3a2a065fSHong Zhang .seealso: [](ch_ts), `TSARKIMEX`, `TSARKIMEXSetFastSlowSplit()`
2547*3a2a065fSHong Zhang @*/
2548*3a2a065fSHong Zhang PetscErrorCode TSARKIMEXGetFastSlowSplit(TS ts, PetscBool *fastslow)
2549*3a2a065fSHong Zhang {
2550*3a2a065fSHong Zhang   PetscFunctionBegin;
2551*3a2a065fSHong Zhang   PetscUseMethod(ts, "TSARKIMEXGetFastSlowSplit_C", (TS, PetscBool *), (ts, fastslow));
2552*3a2a065fSHong Zhang   PetscFunctionReturn(PETSC_SUCCESS);
2553*3a2a065fSHong Zhang }
2554