/* Code for time stepping with the Runge-Kutta method Notes: The general system is written as Udot = F(t,U) */ #include /*I "petscts.h" I*/ #include #include <../src/ts/impls/explicit/rk/rk.h> #include <../src/ts/impls/explicit/rk/mrk.h> static TSRKType TSRKDefault = TSRK3BS; static PetscBool TSRKRegisterAllCalled; static PetscBool TSRKPackageInitialized; static RKTableauLink RKTableauList; /*MC TSRK1FE - First order forward Euler scheme. This method has one stage. Options database: . -ts_rk_type 1fe Level: advanced .seealso: TSRK, TSRKType, TSRKSetType() M*/ /*MC TSRK2A - Second order RK scheme. This method has two stages. Options database: . -ts_rk_type 2a Level: advanced .seealso: TSRK, TSRKType, TSRKSetType() M*/ /*MC TSRK3 - Third order RK scheme. This method has three stages. Options database: . -ts_rk_type 3 Level: advanced .seealso: TSRK, TSRKType, TSRKSetType() M*/ /*MC TSRK3BS - Third order RK scheme of Bogacki-Shampine with 2nd order embedded method. This method has four stages with the First Same As Last (FSAL) property. Options database: . -ts_rk_type 3bs Level: advanced References: https://doi.org/10.1016/0893-9659(89)90079-7 .seealso: TSRK, TSRKType, TSRKSetType() M*/ /*MC TSRK4 - Fourth order RK scheme. This is the classical Runge-Kutta method with four stages. Options database: . -ts_rk_type 4 Level: advanced .seealso: TSRK, TSRKType, TSRKSetType() M*/ /*MC TSRK5F - Fifth order Fehlberg RK scheme with a 4th order embedded method. This method has six stages. Options database: . -ts_rk_type 5f Level: advanced .seealso: TSRK, TSRKType, TSRKSetType() M*/ /*MC TSRK5DP - Fifth order Dormand-Prince RK scheme with the 4th order embedded method. This method has seven stages with the First Same As Last (FSAL) property. Options database: . -ts_rk_type 5dp Level: advanced References: https://doi.org/10.1016/0771-050X(80)90013-3 .seealso: TSRK, TSRKType, TSRKSetType() M*/ /*MC TSRK5BS - Fifth order Bogacki-Shampine RK scheme with 4th order embedded method. This method has eight stages with the First Same As Last (FSAL) property. Options database: . -ts_rk_type 5bs Level: advanced References: https://doi.org/10.1016/0898-1221(96)00141-1 .seealso: TSRK, TSRKType, TSRKSetType() M*/ /*MC TSRK6VR - Sixth order robust Verner RK scheme with fifth order embedded method. This method has nine stages with the First Same As Last (FSAL) property. Options database: . -ts_rk_type 6vr Level: advanced References: http://people.math.sfu.ca/~jverner/RKV65.IIIXb.Robust.00010102836.081204.CoeffsOnlyRAT .seealso: TSRK, TSRKType, TSRKSetType() M*/ /*MC TSRK7VR - Seventh order robust Verner RK scheme with sixth order embedded method. This method has ten stages. Options database: . -ts_rk_type 7vr Level: advanced References: http://people.math.sfu.ca/~jverner/RKV76.IIa.Robust.000027015646.081206.CoeffsOnlyRAT .seealso: TSRK, TSRKType, TSRKSetType() M*/ /*MC TSRK8VR - Eigth order robust Verner RK scheme with seventh order embedded method. This method has thirteen stages. Options database: . -ts_rk_type 8vr Level: advanced References: http://people.math.sfu.ca/~jverner/RKV87.IIa.Robust.00000754677.081208.CoeffsOnlyRATandFLOAT .seealso: TSRK, TSRKType, TSRKSetType() M*/ /*@C TSRKRegisterAll - Registers all of the Runge-Kutta explicit methods in TSRK Not Collective, but should be called by all processes which will need the schemes to be registered Level: advanced .seealso: TSRKRegisterDestroy() @*/ PetscErrorCode TSRKRegisterAll(void) { PetscErrorCode ierr; PetscFunctionBegin; if (TSRKRegisterAllCalled) PetscFunctionReturn(0); TSRKRegisterAllCalled = PETSC_TRUE; #define RC PetscRealConstant { const PetscReal A[1][1] = {{0}}, b[1] = {RC(1.0)}; ierr = TSRKRegister(TSRK1FE,1,1,&A[0][0],b,NULL,NULL,0,NULL);CHKERRQ(ierr); } { const PetscReal A[2][2] = {{0,0}, {RC(1.0),0}}, b[2] = {RC(0.5),RC(0.5)}, bembed[2] = {RC(1.0),0}; ierr = TSRKRegister(TSRK2A,2,2,&A[0][0],b,NULL,bembed,0,NULL);CHKERRQ(ierr); } { const PetscReal A[3][3] = {{0,0,0}, {RC(2.0)/RC(3.0),0,0}, {RC(-1.0)/RC(3.0),RC(1.0),0}}, b[3] = {RC(0.25),RC(0.5),RC(0.25)}; ierr = TSRKRegister(TSRK3,3,3,&A[0][0],b,NULL,NULL,0,NULL);CHKERRQ(ierr); } { const PetscReal A[4][4] = {{0,0,0,0}, {RC(1.0)/RC(2.0),0,0,0}, {0,RC(3.0)/RC(4.0),0,0}, {RC(2.0)/RC(9.0),RC(1.0)/RC(3.0),RC(4.0)/RC(9.0),0}}, b[4] = {RC(2.0)/RC(9.0),RC(1.0)/RC(3.0),RC(4.0)/RC(9.0),0}, bembed[4] = {RC(7.0)/RC(24.0),RC(1.0)/RC(4.0),RC(1.0)/RC(3.0),RC(1.0)/RC(8.0)}; ierr = TSRKRegister(TSRK3BS,3,4,&A[0][0],b,NULL,bembed,0,NULL);CHKERRQ(ierr); } { const PetscReal A[4][4] = {{0,0,0,0}, {RC(0.5),0,0,0}, {0,RC(0.5),0,0}, {0,0,RC(1.0),0}}, b[4] = {RC(1.0)/RC(6.0),RC(1.0)/RC(3.0),RC(1.0)/RC(3.0),RC(1.0)/RC(6.0)}; ierr = TSRKRegister(TSRK4,4,4,&A[0][0],b,NULL,NULL,0,NULL);CHKERRQ(ierr); } { const PetscReal A[6][6] = {{0,0,0,0,0,0}, {RC(0.25),0,0,0,0,0}, {RC(3.0)/RC(32.0),RC(9.0)/RC(32.0),0,0,0,0}, {RC(1932.0)/RC(2197.0),RC(-7200.0)/RC(2197.0),RC(7296.0)/RC(2197.0),0,0,0}, {RC(439.0)/RC(216.0),RC(-8.0),RC(3680.0)/RC(513.0),RC(-845.0)/RC(4104.0),0,0}, {RC(-8.0)/RC(27.0),RC(2.0),RC(-3544.0)/RC(2565.0),RC(1859.0)/RC(4104.0),RC(-11.0)/RC(40.0),0}}, b[6] = {RC(16.0)/RC(135.0),0,RC(6656.0)/RC(12825.0),RC(28561.0)/RC(56430.0),RC(-9.0)/RC(50.0),RC(2.0)/RC(55.0)}, bembed[6] = {RC(25.0)/RC(216.0),0,RC(1408.0)/RC(2565.0),RC(2197.0)/RC(4104.0),RC(-1.0)/RC(5.0),0}; ierr = TSRKRegister(TSRK5F,5,6,&A[0][0],b,NULL,bembed,0,NULL);CHKERRQ(ierr); } { const PetscReal A[7][7] = {{0,0,0,0,0,0,0}, {RC(1.0)/RC(5.0),0,0,0,0,0,0}, {RC(3.0)/RC(40.0),RC(9.0)/RC(40.0),0,0,0,0,0}, {RC(44.0)/RC(45.0),RC(-56.0)/RC(15.0),RC(32.0)/RC(9.0),0,0,0,0}, {RC(19372.0)/RC(6561.0),RC(-25360.0)/RC(2187.0),RC(64448.0)/RC(6561.0),RC(-212.0)/RC(729.0),0,0,0}, {RC(9017.0)/RC(3168.0),RC(-355.0)/RC(33.0),RC(46732.0)/RC(5247.0),RC(49.0)/RC(176.0),RC(-5103.0)/RC(18656.0),0,0}, {RC(35.0)/RC(384.0),0,RC(500.0)/RC(1113.0),RC(125.0)/RC(192.0),RC(-2187.0)/RC(6784.0),RC(11.0)/RC(84.0),0}}, b[7] = {RC(35.0)/RC(384.0),0,RC(500.0)/RC(1113.0),RC(125.0)/RC(192.0),RC(-2187.0)/RC(6784.0),RC(11.0)/RC(84.0),0}, bembed[7] = {RC(5179.0)/RC(57600.0),0,RC(7571.0)/RC(16695.0),RC(393.0)/RC(640.0),RC(-92097.0)/RC(339200.0),RC(187.0)/RC(2100.0),RC(1.0)/RC(40.0)}, binterp[7][5] = {{RC(1.0),RC(-4034104133.0)/RC(1410260304.0),RC(105330401.0)/RC(33982176.0),RC(-13107642775.0)/RC(11282082432.0),RC(6542295.0)/RC(470086768.0)}, {0,0,0,0,0}, {0,RC(132343189600.0)/RC(32700410799.0),RC(-833316000.0)/RC(131326951.0),RC(91412856700.0)/RC(32700410799.0),RC(-523383600.0)/RC(10900136933.0)}, {0,RC(-115792950.0)/RC(29380423.0),RC(185270875.0)/RC(16991088.0),RC(-12653452475.0)/RC(1880347072.0),RC(98134425.0)/RC(235043384.0)}, {0,RC(70805911779.0)/RC(24914598704.0),RC(-4531260609.0)/RC(600351776.0),RC(988140236175.0)/RC(199316789632.0),RC(-14307999165.0)/RC(24914598704.0)}, {0,RC(-331320693.0)/RC(205662961.0),RC(31361737.0)/RC(7433601.0),RC(-2426908385.0)/RC(822651844.0),RC(97305120.0)/RC(205662961.0)}, {0,RC(44764047.0)/RC(29380423.0),RC(-1532549.0)/RC(353981.0),RC(90730570.0)/RC(29380423.0),RC(-8293050.0)/RC(29380423.0)}}; ierr = TSRKRegister(TSRK5DP,5,7,&A[0][0],b,NULL,bembed,5,binterp[0]);CHKERRQ(ierr); } { const PetscReal A[8][8] = {{0,0,0,0,0,0,0,0}, {RC(1.0)/RC(6.0),0,0,0,0,0,0,0}, {RC(2.0)/RC(27.0),RC(4.0)/RC(27.0),0,0,0,0,0,0}, {RC(183.0)/RC(1372.0),RC(-162.0)/RC(343.0),RC(1053.0)/RC(1372.0),0,0,0,0,0}, {RC(68.0)/RC(297.0),RC(-4.0)/RC(11.0),RC(42.0)/RC(143.0),RC(1960.0)/RC(3861.0),0,0,0,0}, {RC(597.0)/RC(22528.0),RC(81.0)/RC(352.0),RC(63099.0)/RC(585728.0),RC(58653.0)/RC(366080.0),RC(4617.0)/RC(20480.0),0,0,0}, {RC(174197.0)/RC(959244.0),RC(-30942.0)/RC(79937.0),RC(8152137.0)/RC(19744439.0),RC(666106.0)/RC(1039181.0),RC(-29421.0)/RC(29068.0),RC(482048.0)/RC(414219.0),0,0}, {RC(587.0)/RC(8064.0),0,RC(4440339.0)/RC(15491840.0),RC(24353.0)/RC(124800.0),RC(387.0)/RC(44800.0),RC(2152.0)/RC(5985.0),RC(7267.0)/RC(94080.0),0}}, b[8] = {RC(587.0)/RC(8064.0),0,RC(4440339.0)/RC(15491840.0),RC(24353.0)/RC(124800.0),RC(387.0)/RC(44800.0),RC(2152.0)/RC(5985.0),RC(7267.0)/RC(94080.0),0}, bembed[8] = {RC(2479.0)/RC(34992.0),0,RC(123.0)/RC(416.0),RC(612941.0)/RC(3411720.0),RC(43.0)/RC(1440.0),RC(2272.0)/RC(6561.0),RC(79937.0)/RC(1113912.0),RC(3293.0)/RC(556956.0)}; ierr = TSRKRegister(TSRK5BS,5,8,&A[0][0],b,NULL,bembed,0,NULL);CHKERRQ(ierr); } { const PetscReal A[9][9] = {{0,0,0,0,0,0,0,0,0}, {RC(1.8000000000000000000000000000000000000000e-01),0,0,0,0,0,0,0,0}, {RC(8.9506172839506172839506172839506172839506e-02),RC(7.7160493827160493827160493827160493827160e-02),0,0,0,0,0,0,0}, {RC(6.2500000000000000000000000000000000000000e-02),0,RC(1.8750000000000000000000000000000000000000e-01),0,0,0,0,0,0}, {RC(3.1651600000000000000000000000000000000000e-01),0,RC(-1.0449480000000000000000000000000000000000e+00),RC(1.2584320000000000000000000000000000000000e+00),0,0,0,0,0}, {RC(2.7232612736485626257225065566674305502508e-01),0,RC(-8.2513360323886639676113360323886639676113e-01),RC(1.0480917678812415654520917678812415654521e+00),RC(1.0471570799276856873679117969088177628396e-01),0,0,0,0}, {RC(-1.6699418599716514314329607278961797333198e-01),0,RC(6.3170850202429149797570850202429149797571e-01),RC(1.7461044552773876082146758838488161796432e-01),RC(-1.0665356459086066122525194734018680677781e+00),RC(1.2272108843537414965986394557823129251701e+00),0,0,0}, {RC(3.6423751686909581646423751686909581646424e-01),0,RC(-2.0404858299595141700404858299595141700405e-01),RC(-3.4883737816068643136312309244640071707741e-01),RC(3.2619323032856867443333608747142581729048e+00),RC(-2.7551020408163265306122448979591836734694e+00),RC(6.8181818181818181818181818181818181818182e-01),0,0}, {RC(7.6388888888888888888888888888888888888889e-02),0,0,RC(3.6940836940836940836940836940836940836941e-01),0,RC(2.4801587301587301587301587301587301587302e-01),RC(2.3674242424242424242424242424242424242424e-01),RC(6.9444444444444444444444444444444444444444e-02),0}}, b[9] = {RC(7.6388888888888888888888888888888888888889e-02),0,0,RC(3.6940836940836940836940836940836940836941e-01),0,RC(2.4801587301587301587301587301587301587302e-01),RC(2.3674242424242424242424242424242424242424e-01),RC(6.9444444444444444444444444444444444444444e-02),0}, bembed[9] = {RC(5.8700209643605870020964360587002096436059e-02),0,0,RC(4.8072562358276643990929705215419501133787e-01),RC(-8.5341242076919085578832094861228313083563e-01),RC(1.2046485260770975056689342403628117913832e+00),0,RC(-5.9242373072160306202859394348756050883710e-02),RC(1.6858043453788134639198468985703028256220e-01)}; ierr = TSRKRegister(TSRK6VR,6,9,&A[0][0],b,NULL,bembed,0,NULL);CHKERRQ(ierr); } { const PetscReal A[10][10] = {{0,0,0,0,0,0,0,0,0,0}, {RC(5.0000000000000000000000000000000000000000e-03),0,0,0,0,0,0,0,0,0}, {RC(-1.0767901234567901234567901234567901234568e+00),RC(1.1856790123456790123456790123456790123457e+00),0,0,0,0,0,0,0,0}, {RC(4.0833333333333333333333333333333333333333e-02),0,RC(1.2250000000000000000000000000000000000000e-01),0,0,0,0,0,0,0}, {RC(6.3607142857142857142857142857142857142857e-01),0,RC(-2.4444642857142857142857142857142857142857e+00),RC(2.2633928571428571428571428571428571428571e+00),0,0,0,0,0,0}, {RC(-2.5351211079349245229256383554660215487207e+00),0,RC(1.0299374654449267920438514460756024913612e+01),RC(-7.9513032885990579949493217458266876536482e+00),RC(7.9301148923100592201226014271115261823800e-01),0,0,0,0,0}, {RC(1.0018765812524632961969196583094999808207e+00),0,RC(-4.1665712824423798331313938005470971453189e+00),RC(3.8343432929128642412552665218251378665197e+00),RC(-5.0233333560710847547464330228611765612403e-01),RC(6.6768474388416077115385092269857695410259e-01),0,0,0,0}, {RC(2.7255018354630767130333963819175005717348e+01),0,RC(-4.2004617278410638355318645443909295369611e+01),RC(-1.0535713126619489917921081600546526103722e+01),RC(8.0495536711411937147983652158926826634202e+01),RC(-6.7343882271790513468549075963212975640927e+01),RC(1.3048657610777937463471187029566964762710e+01),0,0,0}, {RC(-3.0397378057114965146943658658755763226883e+00),0,RC(1.0138161410329801111857946190709700150441e+01),RC(-6.4293056748647215721462825629555298064437e+00),RC(-1.5864371483408276587115312853798610579467e+00),RC(1.8921781841968424410864308909131353365021e+00),RC(1.9699335407608869061292360163336442838006e-02),RC(5.4416989827933235465102724247952572977903e-03),0,0}, {RC(-1.4449518916777735137351003179355712360517e+00),0,RC(8.0318913859955919224117033223019560435041e+00),RC(-7.5831741663401346820798883023671588604984e+00),RC(3.5816169353190074211247685442452878696855e+00),RC(-2.4369722632199529411183809065693752383733e+00),RC(8.5158999992326179339689766032486142173390e-01),0,0,0}}, b[10] = {RC(4.7425837833706756083569172717574534698932e-02),0,0,RC(2.5622361659370562659961727458274623448160e-01),RC(2.6951376833074206619473817258075952886764e-01),RC(1.2686622409092782845989138364739173247882e-01),RC(2.4887225942060071622046449427647492767292e-01),RC(3.0744837408200631335304388479099184768645e-03),RC(4.8023809989496943308189063347143123323209e-02),0}, bembed[10] = {RC(4.7485247699299631037531273805727961552268e-02),0,0,RC(2.5599412588690633297154918245905393870497e-01),RC(2.7058478081067688722530891099268135732387e-01),RC(1.2505618684425992913638822323746917920448e-01),RC(2.5204468723743860507184043820197442562182e-01),0,0,RC(4.8834971521418614557381971303093137592592e-02)}; ierr = TSRKRegister(TSRK7VR,7,10,&A[0][0],b,NULL,bembed,0,NULL);CHKERRQ(ierr); } { const PetscReal A[13][13] = {{0,0,0,0,0,0,0,0,0,0,0,0,0}, {RC(2.5000000000000000000000000000000000000000e-01),0,0,0,0,0,0,0,0,0,0,0,0}, {RC(8.7400846504915232052686327594877411977046e-02),RC(2.5487604938654321753087950620345685135815e-02),0,0,0,0,0,0,0,0,0,0,0}, {RC(4.2333169291338582677165354330708661417323e-02),0,RC(1.2699950787401574803149606299212598425197e-01),0,0,0,0,0,0,0,0,0,0}, {RC(4.2609505888742261494881445237572274090942e-01),0,RC(-1.5987952846591523265427733230657181117089e+00),RC(1.5967002257717297115939588706899953707994e+00),0,0,0,0,0,0,0,0,0}, {RC(5.0719337296713929515090618138513639239329e-02),0,0,RC(2.5433377264600407582754714408877778031369e-01),RC(2.0394689005728199465736223777270858044698e-01),0,0,0,0,0,0,0,0}, {RC(-2.9000374717523110970388379285425896124091e-01),0,0,RC(1.3441873910260789889438681109414337003184e+00),RC(-2.8647779433614427309611103827036562829470e+00),RC(2.6775942995105948517211260646164815438695e+00),0,0,0,0,0,0,0}, {RC(9.8535011337993546469740402980727014284756e-02),0,0,0,RC(2.2192680630751384842024036498197387903583e-01),RC(-1.8140622911806994312690338288073952457474e-01),RC(1.0944411472562548236922614918038631254153e-02),0,0,0,0,0,0}, {RC(3.8711052545731144679444618165166373405645e-01),0,0,RC(-1.4424454974855277571256745553077927767173e+00),RC(2.9053981890699509317691346449233848441744e+00),RC(-1.8537710696301059290843332675811978025183e+00),RC(1.4003648098728154269497325109771241479223e-01),RC(5.7273940811495816575746774624447706488753e-01),0,0,0,0,0}, {RC(-1.6124403444439308100630016197913480595436e-01),0,0,RC(-1.7339602957358984083578404473962567894901e-01),RC(-1.3012892814065147406016812745172492529744e+00),RC(1.1379503751738617308558792131431003472124e+00),RC(-3.1747649663966880106923521138043024698980e-02),RC(9.3351293824933666439811064486056884856590e-01),RC(-8.3786318334733852703300855629616433201504e-02),0,0,0,0}, {RC(-1.9199444881589533281510804651483576073142e-02),0,0,RC(2.7330857265264284907942326254016124275617e-01),RC(-6.7534973206944372919691611210942380856240e-01),RC(3.4151849813846016071738489974728382711981e-01),RC(-6.7950064803375772478920516198524629391910e-02),RC(9.6591752247623878884265586491216376509746e-02),RC(1.3253082511182101180721038466545389951226e-01),RC(3.6854959360386113446906329951531666812946e-01),0,0,0}, {RC(6.0918774036452898676888412111588817784584e-01),0,0,RC(-2.2725690858980016768999800931413088399719e+00),RC(4.7578983426940290068155255881914785497547e+00),RC(-5.5161067066927584824294689667844248244842e+00),RC(2.9005963696801192709095818565946174378180e-01),RC(5.6914239633590368229109858454801849145630e-01),RC(7.9267957603321670271339916205893327579951e-01),RC(1.5473720453288822894126190771849898232047e-01),RC(1.6149708956621816247083215106334544434974e+00),0,0}, {RC(8.8735762208534719663211694051981022704884e-01),0,0,RC(-2.9754597821085367558513632804709301581977e+00),RC(5.6007170094881630597990392548350098923829e+00),RC(-5.9156074505366744680014930189941657351840e+00),RC(2.2029689156134927016879142540807638331238e-01),RC(1.0155097824462216666143271340902996997549e-01),RC(1.1514345647386055909780397752125850553556e+00),RC(1.9297101665271239396134361900805843653065e+00),0,0,0}}, b[13] = {RC(4.4729564666695714203015840429049382466467e-02),0,0,0,0,RC(1.5691033527708199813368698010726645409175e-01),RC(1.8460973408151637740702451873526277892035e-01),RC(2.2516380602086991042479419400350721970920e-01),RC(1.4794615651970234687005179885449141753736e-01),RC(7.6055542444955825269798361910336491012732e-02),RC(1.2277290235018619610824346315921437388535e-01),RC(4.1811958638991631583384842800871882376786e-02),0}, bembed[13] = {RC(4.5847111400495925878664730122010282095875e-02),0,0,0,0,RC(2.6231891404152387437443356584845803392392e-01),RC(1.9169372337852611904485738635688429008025e-01),RC(2.1709172327902618330978407422906448568196e-01),RC(1.2738189624833706796803169450656737867900e-01),RC(1.1510530385365326258240515750043192148894e-01),0,0,RC(4.0561327798437566841823391436583608050053e-02)}; ierr = TSRKRegister(TSRK8VR,8,13,&A[0][0],b,NULL,bembed,0,NULL);CHKERRQ(ierr); } #undef RC PetscFunctionReturn(0); } /*@C TSRKRegisterDestroy - Frees the list of schemes that were registered by TSRKRegister(). Not Collective Level: advanced .seealso: TSRKRegister(), TSRKRegisterAll() @*/ PetscErrorCode TSRKRegisterDestroy(void) { PetscErrorCode ierr; RKTableauLink link; PetscFunctionBegin; while ((link = RKTableauList)) { RKTableau t = &link->tab; RKTableauList = link->next; ierr = PetscFree3(t->A,t->b,t->c);CHKERRQ(ierr); ierr = PetscFree(t->bembed);CHKERRQ(ierr); ierr = PetscFree(t->binterp);CHKERRQ(ierr); ierr = PetscFree(t->name);CHKERRQ(ierr); ierr = PetscFree(link);CHKERRQ(ierr); } TSRKRegisterAllCalled = PETSC_FALSE; PetscFunctionReturn(0); } /*@C TSRKInitializePackage - This function initializes everything in the TSRK package. It is called from TSInitializePackage(). Level: developer .seealso: PetscInitialize() @*/ PetscErrorCode TSRKInitializePackage(void) { PetscErrorCode ierr; PetscFunctionBegin; if (TSRKPackageInitialized) PetscFunctionReturn(0); TSRKPackageInitialized = PETSC_TRUE; ierr = TSRKRegisterAll();CHKERRQ(ierr); ierr = PetscRegisterFinalize(TSRKFinalizePackage);CHKERRQ(ierr); PetscFunctionReturn(0); } /*@C TSRKFinalizePackage - This function destroys everything in the TSRK package. It is called from PetscFinalize(). Level: developer .seealso: PetscFinalize() @*/ PetscErrorCode TSRKFinalizePackage(void) { PetscErrorCode ierr; PetscFunctionBegin; TSRKPackageInitialized = PETSC_FALSE; ierr = TSRKRegisterDestroy();CHKERRQ(ierr); PetscFunctionReturn(0); } /*@C TSRKRegister - register an RK scheme by providing the entries in the Butcher tableau and optionally embedded approximations and interpolation Not Collective, but the same schemes should be registered on all processes on which they will be used Input Parameters: + name - identifier for method . order - approximation order of method . s - number of stages, this is the dimension of the matrices below . A - stage coefficients (dimension s*s, row-major) . b - step completion table (dimension s; NULL to use last row of A) . c - abscissa (dimension s; NULL to use row sums of A) . bembed - completion table for embedded method (dimension s; NULL if not available) . p - Order of the interpolation scheme, equal to the number of columns of binterp - binterp - Coefficients of the interpolation formula (dimension s*p; NULL to reuse b with p=1) Notes: Several RK methods are provided, this function is only needed to create new methods. Level: advanced .seealso: TSRK @*/ PetscErrorCode TSRKRegister(TSRKType name,PetscInt order,PetscInt s, const PetscReal A[],const PetscReal b[],const PetscReal c[], const PetscReal bembed[],PetscInt p,const PetscReal binterp[]) { PetscErrorCode ierr; RKTableauLink link; RKTableau t; PetscInt i,j; PetscFunctionBegin; PetscValidCharPointer(name,1); PetscValidRealPointer(A,4); if (b) PetscValidRealPointer(b,5); if (c) PetscValidRealPointer(c,6); if (bembed) PetscValidRealPointer(bembed,7); if (binterp || p > 1) PetscValidRealPointer(binterp,9); ierr = TSRKInitializePackage();CHKERRQ(ierr); ierr = PetscNew(&link);CHKERRQ(ierr); t = &link->tab; ierr = PetscStrallocpy(name,&t->name);CHKERRQ(ierr); t->order = order; t->s = s; ierr = PetscMalloc3(s*s,&t->A,s,&t->b,s,&t->c);CHKERRQ(ierr); ierr = PetscArraycpy(t->A,A,s*s);CHKERRQ(ierr); if (b) { ierr = PetscArraycpy(t->b,b,s);CHKERRQ(ierr); } else for (i=0; ib[i] = A[(s-1)*s+i]; if (c) { ierr = PetscArraycpy(t->c,c,s);CHKERRQ(ierr); } else for (i=0; ic[i]=0; jc[i] += A[i*s+j]; t->FSAL = PETSC_TRUE; for (i=0; iA[(s-1)*s+i] != t->b[i]) t->FSAL = PETSC_FALSE; if (bembed) { ierr = PetscMalloc1(s,&t->bembed);CHKERRQ(ierr); ierr = PetscArraycpy(t->bembed,bembed,s);CHKERRQ(ierr); } if (!binterp) { p = 1; binterp = t->b; } t->p = p; ierr = PetscMalloc1(s*p,&t->binterp);CHKERRQ(ierr); ierr = PetscArraycpy(t->binterp,binterp,s*p);CHKERRQ(ierr); link->next = RKTableauList; RKTableauList = link; PetscFunctionReturn(0); } PetscErrorCode TSRKGetTableau_RK(TS ts, PetscInt *s, const PetscReal **A, const PetscReal **b, const PetscReal **c, const PetscReal **bembed, PetscInt *p, const PetscReal **binterp, PetscBool *FSAL) { TS_RK *rk = (TS_RK*)ts->data; RKTableau tab = rk->tableau; PetscFunctionBegin; if (s) *s = tab->s; if (A) *A = tab->A; if (b) *b = tab->b; if (c) *c = tab->c; if (bembed) *bembed = tab->bembed; if (p) *p = tab->p; if (binterp) *binterp = tab->binterp; if (FSAL) *FSAL = tab->FSAL; PetscFunctionReturn(0); } /*@C TSRKGetTableau - Get info on the RK tableau Not Collective Input Parameter: . ts - timestepping context Output Parameters: + s - number of stages, this is the dimension of the matrices below . A - stage coefficients (dimension s*s, row-major) . b - step completion table (dimension s) . c - abscissa (dimension s) . bembed - completion table for embedded method (dimension s; NULL if not available) . p - Order of the interpolation scheme, equal to the number of columns of binterp . binterp - Coefficients of the interpolation formula (dimension s*p) - FSAL - wheather or not the scheme has the First Same As Last property Level: developer .seealso: TSRK @*/ PetscErrorCode TSRKGetTableau(TS ts, PetscInt *s, const PetscReal **A, const PetscReal **b, const PetscReal **c, const PetscReal **bembed, PetscInt *p, const PetscReal **binterp, PetscBool *FSAL) { PetscErrorCode ierr; PetscFunctionBegin; PetscValidHeaderSpecific(ts,TS_CLASSID,1); ierr = PetscUseMethod(ts,"TSRKGetTableau_C",(TS,PetscInt*,const PetscReal**,const PetscReal**,const PetscReal**,const PetscReal**, PetscInt*,const PetscReal**,PetscBool*),(ts,s,A,b,c,bembed,p,binterp,FSAL));CHKERRQ(ierr); PetscFunctionReturn(0); } /* This is for single-step RK method The step completion formula is x1 = x0 + h b^T YdotRHS This function can be called before or after ts->vec_sol has been updated. Suppose we have a completion formula (b) and an embedded formula (be) of different order. We can write x1e = x0 + h be^T YdotRHS = x1 - h b^T YdotRHS + h be^T YdotRHS = x1 + h (be - b)^T YdotRHS so we can evaluate the method with different order even after the step has been optimistically completed. */ static PetscErrorCode TSEvaluateStep_RK(TS ts,PetscInt order,Vec X,PetscBool *done) { TS_RK *rk = (TS_RK*)ts->data; RKTableau tab = rk->tableau; PetscScalar *w = rk->work; PetscReal h; PetscInt s = tab->s,j; PetscErrorCode ierr; PetscFunctionBegin; switch (rk->status) { case TS_STEP_INCOMPLETE: case TS_STEP_PENDING: h = ts->time_step; break; case TS_STEP_COMPLETE: h = ts->ptime - ts->ptime_prev; break; default: SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_PLIB,"Invalid TSStepStatus"); } if (order == tab->order) { if (rk->status == TS_STEP_INCOMPLETE) { ierr = VecCopy(ts->vec_sol,X);CHKERRQ(ierr); for (j=0; jb[j]/rk->dtratio; ierr = VecMAXPY(X,s,w,rk->YdotRHS);CHKERRQ(ierr); } else {ierr = VecCopy(ts->vec_sol,X);CHKERRQ(ierr);} PetscFunctionReturn(0); } else if (order == tab->order-1) { if (!tab->bembed) goto unavailable; if (rk->status == TS_STEP_INCOMPLETE) { /*Complete with the embedded method (be)*/ ierr = VecCopy(ts->vec_sol,X);CHKERRQ(ierr); for (j=0; jbembed[j]; ierr = VecMAXPY(X,s,w,rk->YdotRHS);CHKERRQ(ierr); } else { /*Rollback and re-complete using (be-b) */ ierr = VecCopy(ts->vec_sol,X);CHKERRQ(ierr); for (j=0; jbembed[j] - tab->b[j]); ierr = VecMAXPY(X,s,w,rk->YdotRHS);CHKERRQ(ierr); } if (done) *done = PETSC_TRUE; PetscFunctionReturn(0); } unavailable: if (done) *done = PETSC_FALSE; else SETERRQ3(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"RK '%s' of order %D cannot evaluate step at order %D. Consider using -ts_adapt_type none or a different method that has an embedded estimate.",tab->name,tab->order,order); PetscFunctionReturn(0); } static PetscErrorCode TSForwardCostIntegral_RK(TS ts) { TS_RK *rk = (TS_RK*)ts->data; TS quadts = ts->quadraturets; RKTableau tab = rk->tableau; const PetscInt s = tab->s; const PetscReal *b = tab->b,*c = tab->c; Vec *Y = rk->Y; PetscInt i; PetscErrorCode ierr; PetscFunctionBegin; /* No need to backup quadts->vec_sol since it can be reverted in TSRollBack_RK */ for (i=s-1; i>=0; i--) { /* Evolve quadrature TS solution to compute integrals */ ierr = TSComputeRHSFunction(quadts,rk->ptime+rk->time_step*c[i],Y[i],ts->vec_costintegrand);CHKERRQ(ierr); ierr = VecAXPY(quadts->vec_sol,rk->time_step*b[i],ts->vec_costintegrand);CHKERRQ(ierr); } PetscFunctionReturn(0); } static PetscErrorCode TSAdjointCostIntegral_RK(TS ts) { TS_RK *rk = (TS_RK*)ts->data; RKTableau tab = rk->tableau; TS quadts = ts->quadraturets; const PetscInt s = tab->s; const PetscReal *b = tab->b,*c = tab->c; Vec *Y = rk->Y; PetscInt i; PetscErrorCode ierr; PetscFunctionBegin; for (i=s-1; i>=0; i--) { /* Evolve quadrature TS solution to compute integrals */ ierr = TSComputeRHSFunction(quadts,ts->ptime+ts->time_step*(1.0-c[i]),Y[i],ts->vec_costintegrand);CHKERRQ(ierr); ierr = VecAXPY(quadts->vec_sol,-ts->time_step*b[i],ts->vec_costintegrand);CHKERRQ(ierr); } PetscFunctionReturn(0); } static PetscErrorCode TSRollBack_RK(TS ts) { TS_RK *rk = (TS_RK*)ts->data; TS quadts = ts->quadraturets; RKTableau tab = rk->tableau; const PetscInt s = tab->s; const PetscReal *b = tab->b,*c = tab->c; PetscScalar *w = rk->work; Vec *Y = rk->Y,*YdotRHS = rk->YdotRHS; PetscInt j; PetscReal h; PetscErrorCode ierr; PetscFunctionBegin; switch (rk->status) { case TS_STEP_INCOMPLETE: case TS_STEP_PENDING: h = ts->time_step; break; case TS_STEP_COMPLETE: h = ts->ptime - ts->ptime_prev; break; default: SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_PLIB,"Invalid TSStepStatus"); } for (j=0; jvec_sol,s,w,YdotRHS);CHKERRQ(ierr); if (quadts && ts->costintegralfwd) { for (j=0; jptime+h*c[j],Y[j],ts->vec_costintegrand);CHKERRQ(ierr); ierr = VecAXPY(quadts->vec_sol,-h*b[j],ts->vec_costintegrand);CHKERRQ(ierr); } } PetscFunctionReturn(0); } static PetscErrorCode TSForwardStep_RK(TS ts) { TS_RK *rk = (TS_RK*)ts->data; RKTableau tab = rk->tableau; Mat J,*MatsFwdSensipTemp = rk->MatsFwdSensipTemp; const PetscInt s = tab->s; const PetscReal *A = tab->A,*c = tab->c,*b = tab->b; Vec *Y = rk->Y; PetscInt i,j; PetscReal stage_time,h = ts->time_step; PetscBool zero; PetscErrorCode ierr; PetscFunctionBegin; ierr = MatCopy(ts->mat_sensip,rk->MatFwdSensip0,SAME_NONZERO_PATTERN);CHKERRQ(ierr); ierr = TSGetRHSJacobian(ts,&J,NULL,NULL,NULL);CHKERRQ(ierr); for (i=0; iptime + h*c[i]; zero = PETSC_FALSE; if (b[i] == 0 && i == s-1) zero = PETSC_TRUE; /* TLM Stage values */ if (!i) { ierr = MatCopy(ts->mat_sensip,rk->MatsFwdStageSensip[i],SAME_NONZERO_PATTERN);CHKERRQ(ierr); } else if (!zero) { ierr = MatZeroEntries(rk->MatsFwdStageSensip[i]);CHKERRQ(ierr); for (j=0; jMatsFwdStageSensip[i],h*A[i*s+j],MatsFwdSensipTemp[j],SAME_NONZERO_PATTERN);CHKERRQ(ierr); } ierr = MatAXPY(rk->MatsFwdStageSensip[i],1.,ts->mat_sensip,SAME_NONZERO_PATTERN);CHKERRQ(ierr); } else { ierr = MatZeroEntries(rk->MatsFwdStageSensip[i]);CHKERRQ(ierr); } ierr = TSComputeRHSJacobian(ts,stage_time,Y[i],J,J);CHKERRQ(ierr); ierr = MatMatMult(J,rk->MatsFwdStageSensip[i],MAT_REUSE_MATRIX,PETSC_DEFAULT,&MatsFwdSensipTemp[i]);CHKERRQ(ierr); if (ts->Jacprhs) { ierr = TSComputeRHSJacobianP(ts,stage_time,Y[i],ts->Jacprhs);CHKERRQ(ierr); /* get f_p */ if (ts->vecs_sensi2p) { /* TLM used for 2nd-order adjoint */ PetscScalar *xarr; ierr = MatDenseGetColumn(MatsFwdSensipTemp[i],0,&xarr);CHKERRQ(ierr); ierr = VecPlaceArray(rk->VecDeltaFwdSensipCol,xarr);CHKERRQ(ierr); ierr = MatMultAdd(ts->Jacprhs,ts->vec_dir,rk->VecDeltaFwdSensipCol,rk->VecDeltaFwdSensipCol);CHKERRQ(ierr); ierr = VecResetArray(rk->VecDeltaFwdSensipCol);CHKERRQ(ierr); ierr = MatDenseRestoreColumn(MatsFwdSensipTemp[i],&xarr);CHKERRQ(ierr); } else { ierr = MatAXPY(MatsFwdSensipTemp[i],1.,ts->Jacprhs,SUBSET_NONZERO_PATTERN);CHKERRQ(ierr); } } } for (i=0; imat_sensip,h*b[i],rk->MatsFwdSensipTemp[i],SAME_NONZERO_PATTERN);CHKERRQ(ierr); } rk->status = TS_STEP_COMPLETE; PetscFunctionReturn(0); } static PetscErrorCode TSForwardGetStages_RK(TS ts,PetscInt *ns,Mat **stagesensip) { TS_RK *rk = (TS_RK*)ts->data; RKTableau tab = rk->tableau; PetscFunctionBegin; if (ns) *ns = tab->s; if (stagesensip) *stagesensip = rk->MatsFwdStageSensip; PetscFunctionReturn(0); } static PetscErrorCode TSForwardSetUp_RK(TS ts) { TS_RK *rk = (TS_RK*)ts->data; RKTableau tab = rk->tableau; PetscInt i; PetscErrorCode ierr; PetscFunctionBegin; /* backup sensitivity results for roll-backs */ ierr = MatDuplicate(ts->mat_sensip,MAT_DO_NOT_COPY_VALUES,&rk->MatFwdSensip0);CHKERRQ(ierr); ierr = PetscMalloc1(tab->s,&rk->MatsFwdStageSensip);CHKERRQ(ierr); ierr = PetscMalloc1(tab->s,&rk->MatsFwdSensipTemp);CHKERRQ(ierr); for (i=0; is; i++) { ierr = MatDuplicate(ts->mat_sensip,MAT_DO_NOT_COPY_VALUES,&rk->MatsFwdStageSensip[i]);CHKERRQ(ierr); ierr = MatDuplicate(ts->mat_sensip,MAT_DO_NOT_COPY_VALUES,&rk->MatsFwdSensipTemp[i]);CHKERRQ(ierr); } ierr = VecDuplicate(ts->vec_sol,&rk->VecDeltaFwdSensipCol);CHKERRQ(ierr); PetscFunctionReturn(0); } static PetscErrorCode TSForwardReset_RK(TS ts) { TS_RK *rk = (TS_RK*)ts->data; RKTableau tab = rk->tableau; PetscInt i; PetscErrorCode ierr; PetscFunctionBegin; ierr = MatDestroy(&rk->MatFwdSensip0);CHKERRQ(ierr); if (rk->MatsFwdStageSensip) { for (i=0; is; i++) { ierr = MatDestroy(&rk->MatsFwdStageSensip[i]);CHKERRQ(ierr); } ierr = PetscFree(rk->MatsFwdStageSensip);CHKERRQ(ierr); } if (rk->MatsFwdSensipTemp) { for (i=0; is; i++) { ierr = MatDestroy(&rk->MatsFwdSensipTemp[i]);CHKERRQ(ierr); } ierr = PetscFree(rk->MatsFwdSensipTemp);CHKERRQ(ierr); } ierr = VecDestroy(&rk->VecDeltaFwdSensipCol);CHKERRQ(ierr); PetscFunctionReturn(0); } static PetscErrorCode TSStep_RK(TS ts) { TS_RK *rk = (TS_RK*)ts->data; RKTableau tab = rk->tableau; const PetscInt s = tab->s; const PetscReal *A = tab->A,*c = tab->c; PetscScalar *w = rk->work; Vec *Y = rk->Y,*YdotRHS = rk->YdotRHS; PetscBool FSAL = tab->FSAL; TSAdapt adapt; PetscInt i,j; PetscInt rejections = 0; PetscBool stageok,accept = PETSC_TRUE; PetscReal next_time_step = ts->time_step; PetscErrorCode ierr; PetscFunctionBegin; if (ts->steprollback || ts->steprestart) FSAL = PETSC_FALSE; if (FSAL) { ierr = VecCopy(YdotRHS[s-1],YdotRHS[0]);CHKERRQ(ierr); } rk->status = TS_STEP_INCOMPLETE; while (!ts->reason && rk->status != TS_STEP_COMPLETE) { PetscReal t = ts->ptime; PetscReal h = ts->time_step; for (i=0; istage_time = t + h*c[i]; ierr = TSPreStage(ts,rk->stage_time);CHKERRQ(ierr); ierr = VecCopy(ts->vec_sol,Y[i]);CHKERRQ(ierr); for (j=0; jstage_time,i,Y);CHKERRQ(ierr); ierr = TSGetAdapt(ts,&adapt);CHKERRQ(ierr); ierr = TSAdaptCheckStage(adapt,ts,rk->stage_time,Y[i],&stageok);CHKERRQ(ierr); if (!stageok) goto reject_step; if (FSAL && !i) continue; ierr = TSComputeRHSFunction(ts,t+h*c[i],Y[i],YdotRHS[i]);CHKERRQ(ierr); } rk->status = TS_STEP_INCOMPLETE; ierr = TSEvaluateStep(ts,tab->order,ts->vec_sol,NULL);CHKERRQ(ierr); rk->status = TS_STEP_PENDING; ierr = TSGetAdapt(ts,&adapt);CHKERRQ(ierr); ierr = TSAdaptCandidatesClear(adapt);CHKERRQ(ierr); ierr = TSAdaptCandidateAdd(adapt,tab->name,tab->order,1,tab->ccfl,(PetscReal)tab->s,PETSC_TRUE);CHKERRQ(ierr); ierr = TSAdaptChoose(adapt,ts,ts->time_step,NULL,&next_time_step,&accept);CHKERRQ(ierr); rk->status = accept ? TS_STEP_COMPLETE : TS_STEP_INCOMPLETE; if (!accept) { /* Roll back the current step */ ierr = TSRollBack_RK(ts);CHKERRQ(ierr); ts->time_step = next_time_step; goto reject_step; } if (ts->costintegralfwd) { /* Save the info for the later use in cost integral evaluation */ rk->ptime = ts->ptime; rk->time_step = ts->time_step; } ts->ptime += ts->time_step; ts->time_step = next_time_step; break; reject_step: ts->reject++; accept = PETSC_FALSE; if (!ts->reason && ++rejections > ts->max_reject && ts->max_reject >= 0) { ts->reason = TS_DIVERGED_STEP_REJECTED; ierr = PetscInfo2(ts,"Step=%D, step rejections %D greater than current TS allowed, stopping solve\n",ts->steps,rejections);CHKERRQ(ierr); } } PetscFunctionReturn(0); } static PetscErrorCode TSAdjointSetUp_RK(TS ts) { TS_RK *rk = (TS_RK*)ts->data; RKTableau tab = rk->tableau; PetscInt s = tab->s; PetscErrorCode ierr; PetscFunctionBegin; if (ts->adjointsetupcalled++) PetscFunctionReturn(0); ierr = VecDuplicateVecs(ts->vecs_sensi[0],s*ts->numcost,&rk->VecsDeltaLam);CHKERRQ(ierr); ierr = VecDuplicateVecs(ts->vecs_sensi[0],ts->numcost,&rk->VecsSensiTemp);CHKERRQ(ierr); if (ts->vecs_sensip) { ierr = VecDuplicate(ts->vecs_sensip[0],&rk->VecDeltaMu);CHKERRQ(ierr); } if (ts->vecs_sensi2) { ierr = VecDuplicateVecs(ts->vecs_sensi[0],s*ts->numcost,&rk->VecsDeltaLam2);CHKERRQ(ierr); ierr = VecDuplicateVecs(ts->vecs_sensi2[0],ts->numcost,&rk->VecsSensi2Temp);CHKERRQ(ierr); } if (ts->vecs_sensi2p) { ierr = VecDuplicate(ts->vecs_sensi2p[0],&rk->VecDeltaMu2);CHKERRQ(ierr); } PetscFunctionReturn(0); } /* Assumptions: - TSStep_RK() always evaluates the step with b, not bembed. */ static PetscErrorCode TSAdjointStep_RK(TS ts) { TS_RK *rk = (TS_RK*)ts->data; TS quadts = ts->quadraturets; RKTableau tab = rk->tableau; Mat J,Jpre,Jquad; const PetscInt s = tab->s; const PetscReal *A = tab->A,*b = tab->b,*c = tab->c; PetscScalar *w = rk->work,*xarr; Vec *Y = rk->Y,*VecsDeltaLam = rk->VecsDeltaLam,VecDeltaMu = rk->VecDeltaMu,*VecsSensiTemp = rk->VecsSensiTemp; Vec *VecsDeltaLam2 = rk->VecsDeltaLam2,VecDeltaMu2 = rk->VecDeltaMu2,*VecsSensi2Temp = rk->VecsSensi2Temp; Vec VecDRDUTransCol = ts->vec_drdu_col,VecDRDPTransCol = ts->vec_drdp_col; PetscInt i,j,nadj; PetscReal t = ts->ptime; PetscReal h = ts->time_step; PetscErrorCode ierr; PetscFunctionBegin; rk->status = TS_STEP_INCOMPLETE; ierr = TSGetRHSJacobian(ts,&J,&Jpre,NULL,NULL);CHKERRQ(ierr); if (quadts) { ierr = TSGetRHSJacobian(quadts,&Jquad,NULL,NULL,NULL);CHKERRQ(ierr); } for (i=s-1; i>=0; i--) { if (tab->FSAL && i == s-1) { /* VecsDeltaLam[nadj*s+s-1] are initialized with zeros and the values never change.*/ continue; } rk->stage_time = t + h*(1.0-c[i]); ierr = TSComputeSNESJacobian(ts,Y[i],J,Jpre);CHKERRQ(ierr); if (quadts) { ierr = TSComputeRHSJacobian(quadts,rk->stage_time,Y[i],Jquad,Jquad);CHKERRQ(ierr); /* get r_u^T */ } if (ts->vecs_sensip) { ierr = TSComputeRHSJacobianP(ts,rk->stage_time,Y[i],ts->Jacprhs);CHKERRQ(ierr); /* get f_p */ if (quadts) { ierr = TSComputeRHSJacobianP(quadts,rk->stage_time,Y[i],quadts->Jacprhs);CHKERRQ(ierr); /* get f_p for the quadrature */ } } if (b[i]) { for (j=i+1; jnumcost; nadj++) { /* Stage values of lambda */ if (b[i]) { /* lambda_{n+1} + \sum_{j=i+1}^s a_{ji}/b[i]*lambda_{s,j} */ ierr = VecCopy(ts->vecs_sensi[nadj],VecsSensiTemp[nadj]);CHKERRQ(ierr); /* VecDeltaLam is an vec array of size s by numcost */ ierr = VecMAXPY(VecsSensiTemp[nadj],s-i-1,w,&VecsDeltaLam[nadj*s+i+1]);CHKERRQ(ierr); ierr = MatMultTranspose(J,VecsSensiTemp[nadj],VecsDeltaLam[nadj*s+i]);CHKERRQ(ierr); /* VecsSensiTemp will be reused by 2nd-order adjoint */ ierr = VecScale(VecsDeltaLam[nadj*s+i],-h*b[i]);CHKERRQ(ierr); if (quadts) { ierr = MatDenseGetColumn(Jquad,nadj,&xarr);CHKERRQ(ierr); ierr = VecPlaceArray(VecDRDUTransCol,xarr);CHKERRQ(ierr); ierr = VecAXPY(VecsDeltaLam[nadj*s+i],-h*b[i],VecDRDUTransCol);CHKERRQ(ierr); ierr = VecResetArray(VecDRDUTransCol);CHKERRQ(ierr); ierr = MatDenseRestoreColumn(Jquad,&xarr);CHKERRQ(ierr); } } else { /* \sum_{j=i+1}^s a_{ji}*lambda_{s,j} */ ierr = VecSet(VecsSensiTemp[nadj],0);CHKERRQ(ierr); ierr = VecMAXPY(VecsSensiTemp[nadj],s-i-1,w,&VecsDeltaLam[nadj*s+i+1]);CHKERRQ(ierr); ierr = MatMultTranspose(J,VecsSensiTemp[nadj],VecsDeltaLam[nadj*s+i]);CHKERRQ(ierr); ierr = VecScale(VecsDeltaLam[nadj*s+i],-h);CHKERRQ(ierr); } /* Stage values of mu */ if (ts->vecs_sensip) { ierr = MatMultTranspose(ts->Jacprhs,VecsSensiTemp[nadj],VecDeltaMu);CHKERRQ(ierr); if (b[i]) { ierr = VecScale(VecDeltaMu,-h*b[i]);CHKERRQ(ierr); if (quadts) { ierr = MatDenseGetColumn(quadts->Jacprhs,nadj,&xarr);CHKERRQ(ierr); ierr = VecPlaceArray(VecDRDPTransCol,xarr);CHKERRQ(ierr); ierr = VecAXPY(VecDeltaMu,-h*b[i],VecDRDPTransCol);CHKERRQ(ierr); ierr = VecResetArray(VecDRDPTransCol);CHKERRQ(ierr); ierr = MatDenseRestoreColumn(quadts->Jacprhs,&xarr);CHKERRQ(ierr); } } else { ierr = VecScale(VecDeltaMu,-h);CHKERRQ(ierr); } ierr = VecAXPY(ts->vecs_sensip[nadj],1.,VecDeltaMu);CHKERRQ(ierr); /* update sensip for each stage */ } } if (ts->vecs_sensi2 && ts->forward_solve) { /* 2nd-order adjoint, TLM mode has to be turned on */ /* Get w1 at t_{n+1} from TLM matrix */ ierr = MatDenseGetColumn(rk->MatsFwdStageSensip[i],0,&xarr);CHKERRQ(ierr); ierr = VecPlaceArray(ts->vec_sensip_col,xarr);CHKERRQ(ierr); /* lambda_s^T F_UU w_1 */ ierr = TSComputeRHSHessianProductFunctionUU(ts,rk->stage_time,Y[i],VecsSensiTemp,ts->vec_sensip_col,ts->vecs_guu);CHKERRQ(ierr); if (quadts) { /* R_UU w_1 */ ierr = TSComputeRHSHessianProductFunctionUU(quadts,rk->stage_time,Y[i],NULL,ts->vec_sensip_col,ts->vecs_guu);CHKERRQ(ierr); } if (ts->vecs_sensip) { /* lambda_s^T F_UP w_2 */ ierr = TSComputeRHSHessianProductFunctionUP(ts,rk->stage_time,Y[i],VecsSensiTemp,ts->vec_dir,ts->vecs_gup);CHKERRQ(ierr); if (quadts) { /* R_UP w_2 */ ierr = TSComputeRHSHessianProductFunctionUP(quadts,rk->stage_time,Y[i],NULL,ts->vec_sensip_col,ts->vecs_gup);CHKERRQ(ierr); } } if (ts->vecs_sensi2p) { /* lambda_s^T F_PU w_1 */ ierr = TSComputeRHSHessianProductFunctionPU(ts,rk->stage_time,Y[i],VecsSensiTemp,ts->vec_sensip_col,ts->vecs_gpu);CHKERRQ(ierr); /* lambda_s^T F_PP w_2 */ ierr = TSComputeRHSHessianProductFunctionPP(ts,rk->stage_time,Y[i],VecsSensiTemp,ts->vec_dir,ts->vecs_gpp);CHKERRQ(ierr); if (b[i] && quadts) { /* R_PU w_1 */ ierr = TSComputeRHSHessianProductFunctionPU(quadts,rk->stage_time,Y[i],NULL,ts->vec_sensip_col,ts->vecs_gpu);CHKERRQ(ierr); /* R_PP w_2 */ ierr = TSComputeRHSHessianProductFunctionPP(quadts,rk->stage_time,Y[i],NULL,ts->vec_dir,ts->vecs_gpp);CHKERRQ(ierr); } } ierr = VecResetArray(ts->vec_sensip_col);CHKERRQ(ierr); ierr = MatDenseRestoreColumn(rk->MatsFwdStageSensip[i],&xarr);CHKERRQ(ierr); for (nadj=0; nadjnumcost; nadj++) { /* Stage values of lambda */ if (b[i]) { /* J_i^T*(Lambda_{n+1}+\sum_{j=i+1}^s a_{ji}/b_i*Lambda_{s,j} */ ierr = VecCopy(ts->vecs_sensi2[nadj],VecsSensi2Temp[nadj]);CHKERRQ(ierr); ierr = VecMAXPY(VecsSensi2Temp[nadj],s-i-1,w,&VecsDeltaLam2[nadj*s+i+1]);CHKERRQ(ierr); ierr = MatMultTranspose(J,VecsSensi2Temp[nadj],VecsDeltaLam2[nadj*s+i]);CHKERRQ(ierr); ierr = VecScale(VecsDeltaLam2[nadj*s+i],-h*b[i]);CHKERRQ(ierr); ierr = VecAXPY(VecsDeltaLam2[nadj*s+i],-h*b[i],ts->vecs_guu[nadj]);CHKERRQ(ierr); if (ts->vecs_sensip) { ierr = VecAXPY(VecsDeltaLam2[nadj*s+i],-h*b[i],ts->vecs_gup[nadj]);CHKERRQ(ierr); } } else { /* \sum_{j=i+1}^s a_{ji}*Lambda_{s,j} */ ierr = VecSet(VecsDeltaLam2[nadj*s+i],0);CHKERRQ(ierr); ierr = VecMAXPY(VecsSensi2Temp[nadj],s-i-1,w,&VecsDeltaLam2[nadj*s+i+1]);CHKERRQ(ierr); ierr = MatMultTranspose(J,VecsSensi2Temp[nadj],VecsDeltaLam2[nadj*s+i]);CHKERRQ(ierr); ierr = VecScale(VecsDeltaLam2[nadj*s+i],-h);CHKERRQ(ierr); ierr = VecAXPY(VecsDeltaLam2[nadj*s+i],-h,ts->vecs_guu[nadj]);CHKERRQ(ierr); if (ts->vecs_sensip) { ierr = VecAXPY(VecsDeltaLam2[nadj*s+i],-h,ts->vecs_gup[nadj]);CHKERRQ(ierr); } } if (ts->vecs_sensi2p) { /* 2nd-order adjoint for parameters */ ierr = MatMultTranspose(ts->Jacprhs,VecsSensi2Temp[nadj],VecDeltaMu2);CHKERRQ(ierr); if (b[i]) { ierr = VecScale(VecDeltaMu2,-h*b[i]);CHKERRQ(ierr); ierr = VecAXPY(VecDeltaMu2,-h*b[i],ts->vecs_gpu[nadj]);CHKERRQ(ierr); ierr = VecAXPY(VecDeltaMu2,-h*b[i],ts->vecs_gpp[nadj]);CHKERRQ(ierr); } else { ierr = VecScale(VecDeltaMu2,-h);CHKERRQ(ierr); ierr = VecAXPY(VecDeltaMu2,-h,ts->vecs_gpu[nadj]);CHKERRQ(ierr); ierr = VecAXPY(VecDeltaMu2,-h,ts->vecs_gpp[nadj]);CHKERRQ(ierr); } ierr = VecAXPY(ts->vecs_sensi2p[nadj],1,VecDeltaMu2);CHKERRQ(ierr); /* update sensi2p for each stage */ } } } } for (j=0; jnumcost; nadj++) { /* no need to do this for mu's */ ierr = VecMAXPY(ts->vecs_sensi[nadj],s,w,&VecsDeltaLam[nadj*s]);CHKERRQ(ierr); if (ts->vecs_sensi2) { ierr = VecMAXPY(ts->vecs_sensi2[nadj],s,w,&VecsDeltaLam2[nadj*s]);CHKERRQ(ierr); } } rk->status = TS_STEP_COMPLETE; PetscFunctionReturn(0); } static PetscErrorCode TSAdjointReset_RK(TS ts) { TS_RK *rk = (TS_RK*)ts->data; RKTableau tab = rk->tableau; PetscErrorCode ierr; PetscFunctionBegin; ierr = VecDestroyVecs(tab->s*ts->numcost,&rk->VecsDeltaLam);CHKERRQ(ierr); ierr = VecDestroyVecs(ts->numcost,&rk->VecsSensiTemp);CHKERRQ(ierr); ierr = VecDestroy(&rk->VecDeltaMu);CHKERRQ(ierr); ierr = VecDestroyVecs(tab->s*ts->numcost,&rk->VecsDeltaLam2);CHKERRQ(ierr); ierr = VecDestroy(&rk->VecDeltaMu2);CHKERRQ(ierr); ierr = VecDestroyVecs(ts->numcost,&rk->VecsSensi2Temp);CHKERRQ(ierr); PetscFunctionReturn(0); } static PetscErrorCode TSInterpolate_RK(TS ts,PetscReal itime,Vec X) { TS_RK *rk = (TS_RK*)ts->data; PetscInt s = rk->tableau->s,p = rk->tableau->p,i,j; PetscReal h; PetscReal tt,t; PetscScalar *b; const PetscReal *B = rk->tableau->binterp; PetscErrorCode ierr; PetscFunctionBegin; if (!B) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"TSRK %s does not have an interpolation formula",rk->tableau->name); switch (rk->status) { case TS_STEP_INCOMPLETE: case TS_STEP_PENDING: h = ts->time_step; t = (itime - ts->ptime)/h; break; case TS_STEP_COMPLETE: h = ts->ptime - ts->ptime_prev; t = (itime - ts->ptime)/h + 1; /* In the interval [0,1] */ break; default: SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_PLIB,"Invalid TSStepStatus"); } ierr = PetscMalloc1(s,&b);CHKERRQ(ierr); for (i=0; iY[0],X);CHKERRQ(ierr); ierr = VecMAXPY(X,s,b,rk->YdotRHS);CHKERRQ(ierr); ierr = PetscFree(b);CHKERRQ(ierr); PetscFunctionReturn(0); } /*------------------------------------------------------------*/ static PetscErrorCode TSRKTableauReset(TS ts) { TS_RK *rk = (TS_RK*)ts->data; RKTableau tab = rk->tableau; PetscErrorCode ierr; PetscFunctionBegin; if (!tab) PetscFunctionReturn(0); ierr = PetscFree(rk->work);CHKERRQ(ierr); ierr = VecDestroyVecs(tab->s,&rk->Y);CHKERRQ(ierr); ierr = VecDestroyVecs(tab->s,&rk->YdotRHS);CHKERRQ(ierr); ierr = VecDestroyVecs(tab->s*ts->numcost,&rk->VecsDeltaLam);CHKERRQ(ierr); ierr = VecDestroyVecs(ts->numcost,&rk->VecsSensiTemp);CHKERRQ(ierr); ierr = VecDestroy(&rk->VecDeltaMu);CHKERRQ(ierr); PetscFunctionReturn(0); } static PetscErrorCode TSReset_RK(TS ts) { PetscErrorCode ierr; PetscFunctionBegin; ierr = TSRKTableauReset(ts);CHKERRQ(ierr); if (ts->use_splitrhsfunction) { ierr = PetscTryMethod(ts,"TSReset_RK_MultirateSplit_C",(TS),(ts));CHKERRQ(ierr); } else { ierr = PetscTryMethod(ts,"TSReset_RK_MultirateNonsplit_C",(TS),(ts));CHKERRQ(ierr); } PetscFunctionReturn(0); } static PetscErrorCode DMCoarsenHook_TSRK(DM fine,DM coarse,void *ctx) { PetscFunctionBegin; PetscFunctionReturn(0); } static PetscErrorCode DMRestrictHook_TSRK(DM fine,Mat restrct,Vec rscale,Mat inject,DM coarse,void *ctx) { PetscFunctionBegin; PetscFunctionReturn(0); } static PetscErrorCode DMSubDomainHook_TSRK(DM dm,DM subdm,void *ctx) { PetscFunctionBegin; PetscFunctionReturn(0); } static PetscErrorCode DMSubDomainRestrictHook_TSRK(DM dm,VecScatter gscat,VecScatter lscat,DM subdm,void *ctx) { PetscFunctionBegin; PetscFunctionReturn(0); } static PetscErrorCode TSRKTableauSetUp(TS ts) { TS_RK *rk = (TS_RK*)ts->data; RKTableau tab = rk->tableau; PetscErrorCode ierr; PetscFunctionBegin; ierr = PetscMalloc1(tab->s,&rk->work);CHKERRQ(ierr); ierr = VecDuplicateVecs(ts->vec_sol,tab->s,&rk->Y);CHKERRQ(ierr); ierr = VecDuplicateVecs(ts->vec_sol,tab->s,&rk->YdotRHS);CHKERRQ(ierr); PetscFunctionReturn(0); } static PetscErrorCode TSSetUp_RK(TS ts) { TS quadts = ts->quadraturets; PetscErrorCode ierr; DM dm; PetscFunctionBegin; ierr = TSCheckImplicitTerm(ts);CHKERRQ(ierr); ierr = TSRKTableauSetUp(ts);CHKERRQ(ierr); if (quadts && ts->costintegralfwd) { Mat Jquad; ierr = TSGetRHSJacobian(quadts,&Jquad,NULL,NULL,NULL);CHKERRQ(ierr); } ierr = TSGetDM(ts,&dm);CHKERRQ(ierr); ierr = DMCoarsenHookAdd(dm,DMCoarsenHook_TSRK,DMRestrictHook_TSRK,ts);CHKERRQ(ierr); ierr = DMSubDomainHookAdd(dm,DMSubDomainHook_TSRK,DMSubDomainRestrictHook_TSRK,ts);CHKERRQ(ierr); if (ts->use_splitrhsfunction) { ierr = PetscTryMethod(ts,"TSSetUp_RK_MultirateSplit_C",(TS),(ts));CHKERRQ(ierr); } else { ierr = PetscTryMethod(ts,"TSSetUp_RK_MultirateNonsplit_C",(TS),(ts));CHKERRQ(ierr); } PetscFunctionReturn(0); } static PetscErrorCode TSSetFromOptions_RK(PetscOptionItems *PetscOptionsObject,TS ts) { TS_RK *rk = (TS_RK*)ts->data; PetscErrorCode ierr; PetscFunctionBegin; ierr = PetscOptionsHead(PetscOptionsObject,"RK ODE solver options");CHKERRQ(ierr); { RKTableauLink link; PetscInt count,choice; PetscBool flg,use_multirate = PETSC_FALSE; const char **namelist; for (link=RKTableauList,count=0; link; link=link->next,count++) ; ierr = PetscMalloc1(count,(char***)&namelist);CHKERRQ(ierr); for (link=RKTableauList,count=0; link; link=link->next,count++) namelist[count] = link->tab.name; ierr = PetscOptionsBool("-ts_rk_multirate","Use interpolation-based multirate RK method","TSRKSetMultirate",rk->use_multirate,&use_multirate,&flg);CHKERRQ(ierr); if (flg) { ierr = TSRKSetMultirate(ts,use_multirate);CHKERRQ(ierr); } ierr = PetscOptionsEList("-ts_rk_type","Family of RK method","TSRKSetType",(const char*const*)namelist,count,rk->tableau->name,&choice,&flg);CHKERRQ(ierr); if (flg) {ierr = TSRKSetType(ts,namelist[choice]);CHKERRQ(ierr);} ierr = PetscFree(namelist);CHKERRQ(ierr); } ierr = PetscOptionsTail();CHKERRQ(ierr); ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)ts),NULL,"Multirate methods options","");CHKERRQ(ierr); ierr = PetscOptionsInt("-ts_rk_dtratio","time step ratio between slow and fast","",rk->dtratio,&rk->dtratio,NULL);CHKERRQ(ierr); ierr = PetscOptionsEnd();CHKERRQ(ierr); PetscFunctionReturn(0); } static PetscErrorCode TSView_RK(TS ts,PetscViewer viewer) { TS_RK *rk = (TS_RK*)ts->data; PetscBool iascii; PetscErrorCode ierr; PetscFunctionBegin; ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr); if (iascii) { RKTableau tab = rk->tableau; TSRKType rktype; const PetscReal *c; PetscInt s; char buf[512]; PetscBool FSAL; ierr = TSRKGetType(ts,&rktype);CHKERRQ(ierr); ierr = TSRKGetTableau(ts,&s,NULL,NULL,&c,NULL,NULL,NULL,&FSAL);CHKERRQ(ierr); ierr = PetscViewerASCIIPrintf(viewer," RK type %s\n",rktype);CHKERRQ(ierr); ierr = PetscViewerASCIIPrintf(viewer," Order: %D\n",tab->order);CHKERRQ(ierr); ierr = PetscViewerASCIIPrintf(viewer," FSAL property: %s\n",FSAL ? "yes" : "no");CHKERRQ(ierr); ierr = PetscFormatRealArray(buf,sizeof(buf),"% 8.6f",s,c);CHKERRQ(ierr); ierr = PetscViewerASCIIPrintf(viewer," Abscissa c = %s\n",buf);CHKERRQ(ierr); } PetscFunctionReturn(0); } static PetscErrorCode TSLoad_RK(TS ts,PetscViewer viewer) { PetscErrorCode ierr; TSAdapt adapt; PetscFunctionBegin; ierr = TSGetAdapt(ts,&adapt);CHKERRQ(ierr); ierr = TSAdaptLoad(adapt,viewer);CHKERRQ(ierr); PetscFunctionReturn(0); } /*@ TSRKGetOrder - Get the order of RK scheme Not collective Input Parameter: . ts - timestepping context Output Parameter: . order - order of RK-scheme Level: intermediate .seealso: TSRKGetType() @*/ PetscErrorCode TSRKGetOrder(TS ts,PetscInt *order) { PetscErrorCode ierr; PetscFunctionBegin; PetscValidHeaderSpecific(ts,TS_CLASSID,1); PetscValidIntPointer(order,2); ierr = PetscUseMethod(ts,"TSRKGetOrder_C",(TS,PetscInt*),(ts,order));CHKERRQ(ierr); PetscFunctionReturn(0); } /*@C TSRKSetType - Set the type of RK scheme Logically collective Input Parameters: + ts - timestepping context - rktype - type of RK-scheme Options Database: . -ts_rk_type - <1fe,2a,3,3bs,4,5f,5dp,5bs> Level: intermediate .seealso: TSRKGetType(), TSRK, TSRKType, TSRK1FE, TSRK2A, TSRK3, TSRK3BS, TSRK4, TSRK5F, TSRK5DP, TSRK5BS, TSRK6VR, TSRK7VR, TSRK8VR @*/ PetscErrorCode TSRKSetType(TS ts,TSRKType rktype) { PetscErrorCode ierr; PetscFunctionBegin; PetscValidHeaderSpecific(ts,TS_CLASSID,1); PetscValidCharPointer(rktype,2); ierr = PetscTryMethod(ts,"TSRKSetType_C",(TS,TSRKType),(ts,rktype));CHKERRQ(ierr); PetscFunctionReturn(0); } /*@C TSRKGetType - Get the type of RK scheme Not collective Input Parameter: . ts - timestepping context Output Parameter: . rktype - type of RK-scheme Level: intermediate .seealso: TSRKSetType() @*/ PetscErrorCode TSRKGetType(TS ts,TSRKType *rktype) { PetscErrorCode ierr; PetscFunctionBegin; PetscValidHeaderSpecific(ts,TS_CLASSID,1); ierr = PetscUseMethod(ts,"TSRKGetType_C",(TS,TSRKType*),(ts,rktype));CHKERRQ(ierr); PetscFunctionReturn(0); } static PetscErrorCode TSRKGetOrder_RK(TS ts,PetscInt *order) { TS_RK *rk = (TS_RK*)ts->data; PetscFunctionBegin; *order = rk->tableau->order; PetscFunctionReturn(0); } static PetscErrorCode TSRKGetType_RK(TS ts,TSRKType *rktype) { TS_RK *rk = (TS_RK*)ts->data; PetscFunctionBegin; *rktype = rk->tableau->name; PetscFunctionReturn(0); } static PetscErrorCode TSRKSetType_RK(TS ts,TSRKType rktype) { TS_RK *rk = (TS_RK*)ts->data; PetscErrorCode ierr; PetscBool match; RKTableauLink link; PetscFunctionBegin; if (rk->tableau) { ierr = PetscStrcmp(rk->tableau->name,rktype,&match);CHKERRQ(ierr); if (match) PetscFunctionReturn(0); } for (link = RKTableauList; link; link=link->next) { ierr = PetscStrcmp(link->tab.name,rktype,&match);CHKERRQ(ierr); if (match) { if (ts->setupcalled) {ierr = TSRKTableauReset(ts);CHKERRQ(ierr);} rk->tableau = &link->tab; if (ts->setupcalled) {ierr = TSRKTableauSetUp(ts);CHKERRQ(ierr);} ts->default_adapt_type = rk->tableau->bembed ? TSADAPTBASIC : TSADAPTNONE; PetscFunctionReturn(0); } } SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_UNKNOWN_TYPE,"Could not find '%s'",rktype); } static PetscErrorCode TSGetStages_RK(TS ts,PetscInt *ns,Vec **Y) { TS_RK *rk = (TS_RK*)ts->data; PetscFunctionBegin; if (ns) *ns = rk->tableau->s; if (Y) *Y = rk->Y; PetscFunctionReturn(0); } static PetscErrorCode TSDestroy_RK(TS ts) { PetscErrorCode ierr; PetscFunctionBegin; ierr = TSReset_RK(ts);CHKERRQ(ierr); if (ts->dm) { ierr = DMCoarsenHookRemove(ts->dm,DMCoarsenHook_TSRK,DMRestrictHook_TSRK,ts);CHKERRQ(ierr); ierr = DMSubDomainHookRemove(ts->dm,DMSubDomainHook_TSRK,DMSubDomainRestrictHook_TSRK,ts);CHKERRQ(ierr); } ierr = PetscFree(ts->data);CHKERRQ(ierr); ierr = PetscObjectComposeFunction((PetscObject)ts,"TSRKGetOrder_C",NULL);CHKERRQ(ierr); ierr = PetscObjectComposeFunction((PetscObject)ts,"TSRKGetType_C",NULL);CHKERRQ(ierr); ierr = PetscObjectComposeFunction((PetscObject)ts,"TSRKSetType_C",NULL);CHKERRQ(ierr); ierr = PetscObjectComposeFunction((PetscObject)ts,"TSRKGetTableau_C",NULL);CHKERRQ(ierr); ierr = PetscObjectComposeFunction((PetscObject)ts,"TSRKSetMultirate_C",NULL);CHKERRQ(ierr); ierr = PetscObjectComposeFunction((PetscObject)ts,"TSRKGetMultirate_C",NULL);CHKERRQ(ierr); PetscFunctionReturn(0); } /* This defines the nonlinear equation that is to be solved with SNES We do not need to solve the equation; we just use SNES to approximate the Jacobian */ static PetscErrorCode SNESTSFormFunction_RK(SNES snes,Vec x,Vec y,TS ts) { TS_RK *rk = (TS_RK*)ts->data; DM dm,dmsave; PetscErrorCode ierr; PetscFunctionBegin; ierr = SNESGetDM(snes,&dm);CHKERRQ(ierr); /* DM monkey-business allows user code to call TSGetDM() inside of functions evaluated on levels of FAS */ dmsave = ts->dm; ts->dm = dm; ierr = TSComputeRHSFunction(ts,rk->stage_time,x,y);CHKERRQ(ierr); ts->dm = dmsave; PetscFunctionReturn(0); } static PetscErrorCode SNESTSFormJacobian_RK(SNES snes,Vec x,Mat A,Mat B,TS ts) { TS_RK *rk = (TS_RK*)ts->data; DM dm,dmsave; PetscErrorCode ierr; PetscFunctionBegin; ierr = SNESGetDM(snes,&dm);CHKERRQ(ierr); dmsave = ts->dm; ts->dm = dm; ierr = TSComputeRHSJacobian(ts,rk->stage_time,x,A,B);CHKERRQ(ierr); ts->dm = dmsave; PetscFunctionReturn(0); } /*@C TSRKSetMultirate - Use the interpolation-based multirate RK method Logically collective Input Parameters: + ts - timestepping context - use_multirate - PETSC_TRUE enables the multirate RK method, sets the basic method to be RK2A and sets the ratio between slow stepsize and fast stepsize to be 2 Options Database: . -ts_rk_multirate - Notes: The multirate method requires interpolation. The default interpolation works for 1st- and 2nd- order RK, but not for high-order RKs except TSRK5DP which comes with the interpolation coeffcients (binterp). Level: intermediate .seealso: TSRKGetMultirate() @*/ PetscErrorCode TSRKSetMultirate(TS ts,PetscBool use_multirate) { PetscErrorCode ierr; PetscFunctionBegin; ierr = PetscTryMethod(ts,"TSRKSetMultirate_C",(TS,PetscBool),(ts,use_multirate));CHKERRQ(ierr); PetscFunctionReturn(0); } /*@C TSRKGetMultirate - Gets whether to Use the interpolation-based multirate RK method Not collective Input Parameter: . ts - timestepping context Output Parameter: . use_multirate - PETSC_TRUE if the multirate RK method is enabled, PETSC_FALSE otherwise Level: intermediate .seealso: TSRKSetMultirate() @*/ PetscErrorCode TSRKGetMultirate(TS ts,PetscBool *use_multirate) { PetscErrorCode ierr; PetscFunctionBegin; ierr = PetscUseMethod(ts,"TSRKGetMultirate_C",(TS,PetscBool*),(ts,use_multirate));CHKERRQ(ierr); PetscFunctionReturn(0); } /*MC TSRK - ODE and DAE solver using Runge-Kutta schemes The user should provide the right hand side of the equation using TSSetRHSFunction(). Notes: The default is TSRK3BS, it can be changed with TSRKSetType() or -ts_rk_type Level: beginner .seealso: TSCreate(), TS, TSSetType(), TSRKSetType(), TSRKGetType(), TSRK2D, TTSRK2E, TSRK3, TSRK4, TSRK5, TSRKPRSSP2, TSRKBPR3, TSRKType, TSRKRegister(), TSRKSetMultirate(), TSRKGetMultirate() M*/ PETSC_EXTERN PetscErrorCode TSCreate_RK(TS ts) { TS_RK *rk; PetscErrorCode ierr; PetscFunctionBegin; ierr = TSRKInitializePackage();CHKERRQ(ierr); ts->ops->reset = TSReset_RK; ts->ops->destroy = TSDestroy_RK; ts->ops->view = TSView_RK; ts->ops->load = TSLoad_RK; ts->ops->setup = TSSetUp_RK; ts->ops->interpolate = TSInterpolate_RK; ts->ops->step = TSStep_RK; ts->ops->evaluatestep = TSEvaluateStep_RK; ts->ops->rollback = TSRollBack_RK; ts->ops->setfromoptions = TSSetFromOptions_RK; ts->ops->getstages = TSGetStages_RK; ts->ops->snesfunction = SNESTSFormFunction_RK; ts->ops->snesjacobian = SNESTSFormJacobian_RK; ts->ops->adjointintegral = TSAdjointCostIntegral_RK; ts->ops->adjointsetup = TSAdjointSetUp_RK; ts->ops->adjointstep = TSAdjointStep_RK; ts->ops->adjointreset = TSAdjointReset_RK; ts->ops->forwardintegral = TSForwardCostIntegral_RK; ts->ops->forwardsetup = TSForwardSetUp_RK; ts->ops->forwardreset = TSForwardReset_RK; ts->ops->forwardstep = TSForwardStep_RK; ts->ops->forwardgetstages= TSForwardGetStages_RK; ierr = PetscNewLog(ts,&rk);CHKERRQ(ierr); ts->data = (void*)rk; ierr = PetscObjectComposeFunction((PetscObject)ts,"TSRKGetOrder_C",TSRKGetOrder_RK);CHKERRQ(ierr); ierr = PetscObjectComposeFunction((PetscObject)ts,"TSRKGetType_C",TSRKGetType_RK);CHKERRQ(ierr); ierr = PetscObjectComposeFunction((PetscObject)ts,"TSRKSetType_C",TSRKSetType_RK);CHKERRQ(ierr); ierr = PetscObjectComposeFunction((PetscObject)ts,"TSRKGetTableau_C",TSRKGetTableau_RK);CHKERRQ(ierr); ierr = PetscObjectComposeFunction((PetscObject)ts,"TSRKSetMultirate_C",TSRKSetMultirate_RK);CHKERRQ(ierr); ierr = PetscObjectComposeFunction((PetscObject)ts,"TSRKGetMultirate_C",TSRKGetMultirate_RK);CHKERRQ(ierr); ierr = TSRKSetType(ts,TSRKDefault);CHKERRQ(ierr); rk->dtratio = 1; PetscFunctionReturn(0); }