xref: /petsc/src/ts/impls/glee/glee.c (revision 2302aa1b855ebd0b8f717ac1679b74fa80c21cfb)

/*
  Code for time stepping with the General Linear with Error Estimation method

  Notes:
  The general system is written as

  Udot = F(t,U)

*/
#include <petsc/private/tsimpl.h>                /*I   "petscts.h"   I*/
#include <petscdm.h>

static TSGLEEType   TSGLEEDefaultType = TSGLEE35;
static PetscBool    TSGLEERegisterAllCalled;
static PetscBool    TSGLEEPackageInitialized;
static PetscInt     explicit_stage_time_id;

typedef struct _GLEETableau *GLEETableau;
struct _GLEETableau {
  char      *name;
  PetscInt   order;               /* Classical approximation order of the method i*/
  PetscInt   s;                   /* Number of stages */
  PetscInt   r;                   /* Number of steps */
  PetscReal  gamma;               /* LTE ratio */
  PetscReal *A,*B,*U,*V,*S,*F,*c; /* Tableau */
  PetscReal *Fembed;              /* Embedded final method coefficients */
  PetscInt   pinterp;             /* Interpolation order */
  PetscReal *binterp;             /* Interpolation coefficients */
  PetscReal  ccfl;                /* Placeholder for CFL coefficient relative to forward Euler  */
};
typedef struct _GLEETableauLink *GLEETableauLink;
struct _GLEETableauLink {
  struct _GLEETableau tab;
  GLEETableauLink     next;
};
static GLEETableauLink GLEETableauList;

typedef struct {
  GLEETableau  tableau;
  Vec          *Y;         /* Solution vector (along with auxiliary solution y~ or eps) */
  Vec          *X;         /* Temporary solution vector */
  Vec          *YStage;    /* Stage values */
  Vec          *YdotStage; /* Stage right hand side */
  Vec          W;          /* Right-hand-side for implicit stage solve */
  Vec          Ydot;       /* Work vector holding Ydot during residual evaluation */
  PetscScalar  *work;      /* Scalar work */
  PetscReal    scoeff;     /* shift = scoeff/dt */
  PetscReal    stage_time;
  TSStepStatus status;
} TS_GLEE;

/*MC
     TSGLEE23 - Second order three stage GLEE method

     This method has three stages.
     s = 3, r = 2

     Level: advanced

.seealso: TSGLEE
*/
/*MC
     TSGLEE24 - Second order four stage GLEE method

     This method has four stages.
     s = 4, r = 2

     Level: advanced

.seealso: TSGLEE
*/
/*MC
     TSGLEE25i - Second order five stage GLEE method

     This method has five stages.
     s = 5, r = 2

     Level: advanced

.seealso: TSGLEE
*/
/*MC
     TSGLEE35  - Third order five stage GLEE method

     This method has five stages.
     s = 5, r = 2

     Level: advanced

.seealso: TSGLEE
*/
/*MC
     TSGLEEEXRK2A  - Second order six stage GLEE method

     This method has six stages.
     s = 6, r = 2

     Level: advanced

.seealso: TSGLEE
*/
/*MC
     TSGLEERK32G1  - Third order eight stage GLEE method

     This method has eight stages.
     s = 8, r = 2

     Level: advanced

.seealso: TSGLEE
*/
/*MC
     TSGLEERK285EX  - Second order nine stage GLEE method

     This method has nine stages.
     s = 9, r = 2

     Level: advanced

.seealso: TSGLEE
*/

#undef __FUNCT__
#define __FUNCT__ "TSGLEERegisterAll"
/*@C
  TSGLEERegisterAll - Registers all of the General Linear with Error Estimation methods in TSGLEE

  Not Collective, but should be called by all processes which will need the schemes to be registered

  Level: advanced

.keywords: TS, TSGLEE, register, all

.seealso:  TSGLEERegisterDestroy()
@*/
PetscErrorCode TSGLEERegisterAll(void)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (TSGLEERegisterAllCalled) PetscFunctionReturn(0);
  TSGLEERegisterAllCalled = PETSC_TRUE;

  {
    /* y-eps form */
    const PetscInt
      p = 2,
      s = 3,
      r = 2;
    const PetscReal
      gamma     = 0,
      A[3][3]   = {{0,0,0},{1,0,0},{0.25,0.25,0}},
      B[2][3]   = {{1.0/12.0,1.0/12.0,5.0/6.0},{1.0/12.0,1.0/12.0,-1.0/6.0}},
      U[3][2]   = {{1,0},{1,10},{1,-1}},
      V[2][2]   = {{1,0},{0,1}},
      S[2]      = {1,0},
      F[2]      = {1,0},
      Fembed[2] = {1,1};
    ierr = TSGLEERegister(TSGLEE23,p,s,r,gamma,&A[0][0],&B[0][0],&U[0][0],&V[0][0],S,F,NULL,Fembed,0,NULL);CHKERRQ(ierr);
  }
  {
    /* y-y~ form */
    const PetscInt
      p = 2,
      s = 4,
      r = 2;
    const PetscReal
      gamma     = 0,
      A[4][4]   = {{0,0,0,0},{0.75,0,0,0},{0.25,29.0/60.0,0,0},{-21.0/44.0,145.0/44.0,-20.0/11.0,0}},
      B[2][4]   = {{109.0/275.0,58.0/75.0,-37.0/110.0,1.0/6.0},{3.0/11.0,0,75.0/88.0,-1.0/8.0}},
      U[4][2]   = {{0,1},{75.0/58.0,-17.0/58.0},{0,1},{0,1}},
      V[2][2]   = {{1,0},{0,1}},
      S[2]      = {1,1},
      F[2]      = {1,0},
      Fembed[2] = {0,1};
      ierr = TSGLEERegister(TSGLEE24,p,s,r,gamma,&A[0][0],&B[0][0],&U[0][0],&V[0][0],S,F,NULL,Fembed,0,NULL);CHKERRQ(ierr);
  }
  {
    /* y-y~ form */
    const PetscInt
      p = 2,
      s = 5,
      r = 2;
    const PetscReal
      gamma     = 0,
      A[5][5]   = {{0,0,0,0,0},
                   {-0.94079244066783383269,0,0,0,0},
                   {0.64228187778301907108,0.10915356933958500042,0,0,0},
                   {-0.51764297742287450812,0.74414270351096040738,-0.71404164927824538121,0,0},
                   {-0.44696561556825969206,-0.76768425657590196518,0.20111608138142987881,0.93828186737840469796,0}},
      B[2][5]   = {{-0.029309178948150356153,-0.49671981884013874923,0.34275801517650053274,0.32941112623949194988,0.85385985637229662276},
                   {0.78133219686062535272,0.074238691892675897635,0.57957363498384957966,-0.24638502829674959968,-0.18875949544040123033}},
      U[5][2]   = {{0.16911424754448327735,0.83088575245551672265},
                   {0.53638465733199574340,0.46361534266800425660},
                   {0.39901579167169582526,0.60098420832830417474},
                   {0.87689005530618575480,0.12310994469381424520},
                   {0.99056100455550913009,0.0094389954444908699092}},
      V[2][2]   = {{1,0},{0,1}},
      S[2]      = {1,1},
      F[2]      = {1,0},
      Fembed[2] = {0,1};
    ierr = TSGLEERegister(TSGLEE25I,p,s,r,gamma,&A[0][0],&B[0][0],&U[0][0],&V[0][0],S,F,NULL,Fembed,0,NULL);CHKERRQ(ierr);
  }
  {
    /* y-y~ form */
    const PetscInt
      p = 3,
      s = 5,
      r = 2;
    const PetscReal
      gamma     = 0,
      A[5][5]   = {{0,0,0,0,0},
                   {- 2169604947363702313.0 /  24313474998937147335.0,0,0,0,0},
                   {46526746497697123895.0 /  94116917485856474137.0,-10297879244026594958.0 /  49199457603717988219.0,0,0,0},
                   {23364788935845982499.0 /  87425311444725389446.0,-79205144337496116638.0 / 148994349441340815519.0,40051189859317443782.0 /  36487615018004984309.0,0,0},
                   {42089522664062539205.0 / 124911313006412840286.0,-15074384760342762939.0 / 137927286865289746282.0,-62274678522253371016.0 / 125918573676298591413.0,13755475729852471739.0 /  79257927066651693390.0}},
      B[2][5]   = {{61546696837458703723.0 /  56982519523786160813.0,-55810892792806293355.0 / 206957624151308356511.0,24061048952676379087.0 / 158739347956038723465.0,3577972206874351339.0 /   7599733370677197135.0,-59449832954780563947.0 / 137360038685338563670.0},
                   {- 9738262186984159168.0 /  99299082461487742983.0,-32797097931948613195.0 /  61521565616362163366.0,42895514606418420631.0 /  71714201188501437336.0,22608567633166065068.0 /  55371917805607957003.0,94655809487476459565.0 / 151517167160302729021.0}},
      U[5][2]   = {{70820309139834661559.0 /  80863923579509469826.0,10043614439674808267.0 /  80863923579509469826.0},
                   {161694774978034105510.0 / 106187653640211060371.0,-55507121337823045139.0 / 106187653640211060371.0},
                   {78486094644566264568.0 /  88171030896733822981.0,9684936252167558413.0 /  88171030896733822981.0},
                   {65394922146334854435.0 /  84570853840405479554.0,19175931694070625119.0 /  84570853840405479554.0},
                   {8607282770183754108.0 / 108658046436496925911.0,100050763666313171803.0 / 108658046436496925911.0}},
      V[2][2]   = {{1,0},{0,1}},
      S[2]      = {1,1},
      F[2]      = {1,0},
      Fembed[2] = {0,1};
    ierr = TSGLEERegister(TSGLEE35,p,s,r,gamma,&A[0][0],&B[0][0],&U[0][0],&V[0][0],S,F,NULL,Fembed,0,NULL);CHKERRQ(ierr);
  }
  {
    /* y-eps form */
    const PetscInt
      p = 2,
      s = 6,
      r = 2;
    const PetscReal
      gamma     = 0.25,
      A[6][6]   = {{0,0,0,0,0,0},
                   {1,0,0,0,0,0},
                   {0,0,0,0,0,0},
                   {0,0,0.5,0,0,0},
                   {0,0,0.25,0.25,0,0},
                   {0,0,0.25,0.25,0.5,0}},
      B[2][6]   = {{0.5,0.5,0,0,0,0},
                   {-2.0/3.0,-2.0/3.0,1.0/3.0,1.0/3.0,1.0/3.0,1.0/3.0}},
      U[6][2]   = {{1,0},{1,0},{1,0.75},{1,0.75},{1,0.75},{1,0.75}},
      V[2][2]   = {{1,0},{0,1}},
      S[2]      = {1,0},
      F[2]      = {1,0},
      Fembed[2] = {1,0.75};
    ierr = TSGLEERegister(TSGLEEEXRK2A,p,s,r,gamma,&A[0][0],&B[0][0],&U[0][0],&V[0][0],S,F,NULL,Fembed,0,NULL);CHKERRQ(ierr);
  }
  {
    /* y-eps form */
    const PetscInt
      p = 3,
      s = 8,
      r = 2;
    const PetscReal
      gamma     = 0,
      A[8][8]   = {{0,0,0,0,0,0,0,0},
                   {0.5,0,0,0,0,0,0,0},
                   {-1,2,0,0,0,0,0,0},
                   {1.0/6.0,2.0/3.0,1.0/6.0,0,0,0,0,0},
                   {0,0,0,0,0,0,0,0},
                   {-7.0/24.0,1.0/3.0,1.0/12.0,-1.0/8.0,0.5,0,0,0},
                   {7.0/6.0,-4.0/3.0,-1.0/3.0,0.5,-1.0,2.0,0,0},
                   {0,0,0,0,1.0/6.0,2.0/3.0,1.0/6.0,0}},
      B[2][8]   = {{1.0/6.0,2.0/3.0,1.0/6.0,0,0,0,0,0},
                   {-1.0/6.0,-2.0/3.0,-1.0/6.0,0,1.0/6.0,2.0/3.0,1.0/6.0,0}},
      U[8][2]   = {{1,0},{1,0},{1,0},{1,0},{1,1},{1,1},{1,1},{1,1}},
      V[2][2]   = {{1,0},{0,1}},
      S[2]      = {1,0},
      F[2]      = {1,0},
      Fembed[2] = {1,1};
    ierr = TSGLEERegister(TSGLEERK32G1,p,s,r,gamma,&A[0][0],&B[0][0],&U[0][0],&V[0][0],S,F,NULL,Fembed,0,NULL);CHKERRQ(ierr);
  }
  {
    /* y-eps form */
    const PetscInt
      p = 2,
      s = 9,
      r = 2;
    const PetscReal
      gamma     = 0.25,
      A[9][9]   = {{0,0,0,0,0,0,0,0,0},
                   {0.585786437626904966,0,0,0,0,0,0,0,0},
                   {0.149999999999999994,0.849999999999999978,0,0,0,0,0,0,0},
                   {0,0,0,0,0,0,0,0,0},
                   {0,0,0,0.292893218813452483,0,0,0,0,0},
                   {0,0,0,0.0749999999999999972,0.424999999999999989,0,0,0,0},
                   {0,0,0,0.176776695296636893,0.176776695296636893,0.146446609406726241,0,0,0},
                   {0,0,0,0.176776695296636893,0.176776695296636893,0.146446609406726241,0.292893218813452483,0,0},
                   {0,0,0,0.176776695296636893,0.176776695296636893,0.146446609406726241,0.0749999999999999972,0.424999999999999989,0}},
      B[2][9]   = {{0.353553390593273786,0.353553390593273786,0.292893218813452483,0,0,0,0,0,0},
                   {-0.471404520791031678,-0.471404520791031678,-0.390524291751269959,0.235702260395515839,0.235702260395515839,0.195262145875634979,0.235702260395515839,0.235702260395515839,0.195262145875634979}},
      U[9][2]   = {{1,0},{1,0},{1,0},{1,0.75},{1,0.75},{1,0.75},{1,0.75},{1,0.75},{1,0.75}},
      V[2][2]   = {{1,0},{0,1}},
      S[2]      = {1,0},
      F[2]      = {1,0},
      Fembed[2] = {1,0.75};
    ierr = TSGLEERegister(TSGLEERK285EX,p,s,r,gamma,&A[0][0],&B[0][0],&U[0][0],&V[0][0],S,F,NULL,Fembed,0,NULL);CHKERRQ(ierr);
  }

  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "TSGLEERegisterDestroy"
/*@C
   TSGLEERegisterDestroy - Frees the list of schemes that were registered by TSGLEERegister().

   Not Collective

   Level: advanced

.keywords: TSGLEE, register, destroy
.seealso: TSGLEERegister(), TSGLEERegisterAll()
@*/
PetscErrorCode TSGLEERegisterDestroy(void)
{
  PetscErrorCode ierr;
  GLEETableauLink link;

  PetscFunctionBegin;
  while ((link = GLEETableauList)) {
    GLEETableau t = &link->tab;
    GLEETableauList = link->next;
    ierr = PetscFree5(t->A,t->B,t->U,t->V,t->c);  CHKERRQ(ierr);
    ierr = PetscFree2(t->S,t->F);                 CHKERRQ(ierr);
    ierr = PetscFree (t->Fembed);                 CHKERRQ(ierr);
    ierr = PetscFree (t->binterp);                CHKERRQ(ierr);
    ierr = PetscFree (t->name);                   CHKERRQ(ierr);
    ierr = PetscFree (link);                      CHKERRQ(ierr);
  }
  TSGLEERegisterAllCalled = PETSC_FALSE;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "TSGLEEInitializePackage"
/*@C
  TSGLEEInitializePackage - This function initializes everything in the TSGLEE package. It is called
  from PetscDLLibraryRegister() when using dynamic libraries, and on the first call to TSCreate_GLEE()
  when using static libraries.

  Level: developer

.keywords: TS, TSGLEE, initialize, package
.seealso: PetscInitialize()
@*/
PetscErrorCode TSGLEEInitializePackage(void)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (TSGLEEPackageInitialized) PetscFunctionReturn(0);
  TSGLEEPackageInitialized = PETSC_TRUE;
  ierr = TSGLEERegisterAll();CHKERRQ(ierr);
  ierr = PetscObjectComposedDataRegister(&explicit_stage_time_id);CHKERRQ(ierr);
  ierr = PetscRegisterFinalize(TSGLEEFinalizePackage);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "TSGLEEFinalizePackage"
/*@C
  TSGLEEFinalizePackage - This function destroys everything in the TSGLEE package. It is
  called from PetscFinalize().

  Level: developer

.keywords: Petsc, destroy, package
.seealso: PetscFinalize()
@*/
PetscErrorCode TSGLEEFinalizePackage(void)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  TSGLEEPackageInitialized = PETSC_FALSE;
  ierr = TSGLEERegisterDestroy();CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "TSGLEERegister"
/*@C
   TSGLEERegister - register an GLEE scheme by providing the entries in the Butcher tableau

   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  - order of method
.  s - number of stages
.  r - number of steps
.  gamma - LTE ratio
.  A - stage coefficients (dimension s*s, row-major)
.  B - step completion coefficients (dimension r*s, row-major)
.  U - method coefficients (dimension s*r, row-major)
.  V - method coefficients (dimension r*r, row-major)
.  S - starting coefficients
.  F - finishing coefficients
.  c - abscissa (dimension s; NULL to use row sums of A)
.  Fembed - step completion coefficients for embedded method
.  pinterp - order of interpolation (0 if unavailable)
-  binterp - array of interpolation coefficients (NULL if unavailable)

   Notes:
   Several GLEE methods are provided, this function is only needed to create new methods.

   Level: advanced

.keywords: TS, register

.seealso: TSGLEE
@*/
PetscErrorCode TSGLEERegister(TSGLEEType name,PetscInt order,PetscInt s, PetscInt r,
                              PetscReal gamma,
                              const PetscReal A[],const PetscReal B[],
                              const PetscReal U[],const PetscReal V[],
                              const PetscReal S[],const PetscReal F[],
                              const PetscReal c[],const PetscReal Fembed[],
                              PetscInt pinterp, const PetscReal binterp[])
{
  PetscErrorCode    ierr;
  GLEETableauLink   link;
  GLEETableau       t;
  PetscInt          i,j;

  PetscFunctionBegin;
  ierr     = PetscMalloc(sizeof(*link),&link);CHKERRQ(ierr);
  ierr     = PetscMemzero(link,sizeof(*link));CHKERRQ(ierr);
  t        = &link->tab;
  ierr     = PetscStrallocpy(name,&t->name);CHKERRQ(ierr);
  t->order = order;
  t->s     = s;
  t->r     = r;
  t->gamma = gamma;
  ierr     = PetscMalloc5(s*s,&t->A,r*r,&t->V,s,&t->c,r*s,&t->B,s*r,&t->U); CHKERRQ(ierr);
  ierr     = PetscMalloc2(r,&t->S,r,&t->F); CHKERRQ(ierr);
  ierr     = PetscMemcpy(t->A,A,s*s*sizeof(A[0]));CHKERRQ(ierr);
  ierr     = PetscMemcpy(t->B,B,r*s*sizeof(B[0]));CHKERRQ(ierr);
  ierr     = PetscMemcpy(t->U,U,s*r*sizeof(U[0]));CHKERRQ(ierr);
  ierr     = PetscMemcpy(t->V,V,r*r*sizeof(V[0]));CHKERRQ(ierr);
  ierr     = PetscMemcpy(t->S,S,r  *sizeof(S[0]));CHKERRQ(ierr);
  ierr     = PetscMemcpy(t->F,F,r  *sizeof(F[0]));CHKERRQ(ierr);
  if (c) {
    ierr   = PetscMemcpy(t->c,c,s*sizeof(c[0])); CHKERRQ(ierr);
  } else {
    for (i=0; i<s; i++) for (j=0,t->c[i]=0; j<s; j++) t->c[i] += A[i*s+j];
  }
  ierr = PetscMalloc1(r,&t->Fembed);CHKERRQ(ierr);
  ierr = PetscMemcpy(t->Fembed,Fembed,r*sizeof(Fembed[0]));CHKERRQ(ierr);
  t->pinterp = pinterp;
  ierr       = PetscMalloc1(s*pinterp,&t->binterp);CHKERRQ(ierr);
  ierr       = PetscMemcpy(t->binterp,binterp,s*pinterp*sizeof(binterp[0]));CHKERRQ(ierr);

  link->next      = GLEETableauList;
  GLEETableauList = link;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "TSEvaluateStep_GLEE"
static PetscErrorCode TSEvaluateStep_GLEE(TS ts,PetscInt order,Vec X,PetscBool *done)
{
  TS_GLEE         *glee = (TS_GLEE*) ts->data;
  GLEETableau     tab = glee->tableau;
  PetscReal       h, *B = tab->B, *V = tab->V,
                  *F = tab->F, *Fembed = tab->Fembed;
  PetscInt        s = tab->s, r = tab->r, i, j;
  Vec             *Y = glee->Y, *YdotStage = glee->YdotStage;
  PetscScalar     *w = glee->work;
  PetscErrorCode  ierr;

  PetscFunctionBegin;

  switch (glee->status) {
    case TS_STEP_INCOMPLETE:
    case TS_STEP_PENDING:
      h = ts->time_step; break;
    case TS_STEP_COMPLETE:
      h = ts->time_step_prev; break;
    default: SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_PLIB,"Invalid TSStepStatus");
  }

  if (order == tab->order) {

    /* Note: Irrespective of whether status is TS_STEP_INCOMPLETE
             or TS_STEP_COMPLETE, glee-X has the solution at the
             beginning of the time step. So no need to roll-back.
    */

    if (glee->status == TS_STEP_INCOMPLETE) {
      for (i=0; i<r; i++) {
        ierr = VecZeroEntries(Y[i]); CHKERRQ(ierr);
        ierr = VecMAXPY(Y[i],r,(V+i*r),glee->X); CHKERRQ(ierr);
        for (j=0; j<s; j++) w[j] = h*B[i*s+j];
        ierr = VecMAXPY(Y[i],s,w,YdotStage); CHKERRQ(ierr);
      }
      ierr = VecZeroEntries(X);CHKERRQ(ierr);
      ierr = VecMAXPY(X,r,F,Y);CHKERRQ(ierr);
    } else {ierr = VecCopy(ts->vec_sol,X);CHKERRQ(ierr);}
    PetscFunctionReturn(0);

  } else if (order == tab->order-1) {

    /* Complete with the embedded method (Fembed) */
    for (i=0; i<r; i++) {
      ierr = VecZeroEntries(Y[i]); CHKERRQ(ierr);
      ierr = VecMAXPY(Y[i],r,(V+i*r),glee->X); CHKERRQ(ierr);
      for (j=0; j<s; j++) w[j] = h*B[i*s+j];
      ierr = VecMAXPY(Y[i],s,w,YdotStage); CHKERRQ(ierr);
    }
    ierr = VecZeroEntries(X);CHKERRQ(ierr);
    ierr = VecMAXPY(X,r,Fembed,Y);CHKERRQ(ierr);
    if (done) *done = PETSC_TRUE;
    PetscFunctionReturn(0);
  }
  if (done) *done = PETSC_FALSE;
  else SETERRQ3(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"GLEE '%s' of order %D cannot evaluate step at order %D",tab->name,tab->order,order);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "TSStep_GLEE"
static PetscErrorCode TSStep_GLEE(TS ts)
{
  TS_GLEE         *glee = (TS_GLEE*)ts->data;
  GLEETableau     tab = glee->tableau;
  const PetscInt  s = tab->s, r = tab->r;
  PetscReal       *A = tab->A, *U = tab->U,
                  *F = tab->F,
                  *c = tab->c;
  Vec             *Y = glee->Y, *X = glee->X,
                  *YStage = glee->YStage,
                  *YdotStage = glee->YdotStage,
                  W = glee->W;
  SNES            snes;
  PetscScalar     *w = glee->work;
  TSAdapt         adapt;
  PetscInt        i,j,reject,next_scheme,its,lits;
  PetscReal       next_time_step;
  PetscReal       t;
  PetscBool       accept;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  for (i=0; i<r; i++) { ierr = VecCopy(Y[i],X[i]); CHKERRQ(ierr); }

  ierr           = TSGetSNES(ts,&snes);CHKERRQ(ierr);
  next_time_step = ts->time_step;
  t              = ts->ptime;
  accept         = PETSC_TRUE;
  glee->status   = TS_STEP_INCOMPLETE;

  for (reject=0; reject<ts->max_reject && !ts->reason; reject++,ts->reject++) {

    PetscReal h = ts->time_step;
    ierr = TSPreStep(ts);CHKERRQ(ierr);

    for (i=0; i<s; i++) {

      glee->stage_time = t + h*c[i];
      ierr = TSPreStage(ts,glee->stage_time); CHKERRQ(ierr);

      if (A[i*s+i] == 0) {  /* Explicit stage */
        ierr = VecZeroEntries(YStage[i]);CHKERRQ(ierr);
        ierr = VecMAXPY(YStage[i],r,(U+i*r),X);CHKERRQ(ierr);
        for (j=0; j<i; j++) w[j] = h*A[i*s+j];
        ierr = VecMAXPY(YStage[i],i,w,YdotStage);CHKERRQ(ierr);
      } else {              /* Implicit stage */
        glee->scoeff = 1.0/A[i*s+i];
        /* compute right-hand-side */
        ierr = VecZeroEntries(W);CHKERRQ(ierr);
        ierr = VecMAXPY(W,r,(U+i*r),X);CHKERRQ(ierr);
        for (j=0; j<i; j++) w[j] = h*A[i*s+j];
        ierr = VecMAXPY(W,i,w,YdotStage);CHKERRQ(ierr);
        ierr = VecScale(W,glee->scoeff/h);CHKERRQ(ierr);
        /* set initial guess */
        ierr = VecCopy(i>0 ? YStage[i-1] : ts->vec_sol,YStage[i]);CHKERRQ(ierr);
        /* solve for this stage */
        ierr = SNESSolve(snes,W,YStage[i]);CHKERRQ(ierr);
        ierr = SNESGetIterationNumber(snes,&its);CHKERRQ(ierr);
        ierr = SNESGetLinearSolveIterations(snes,&lits);CHKERRQ(ierr);
        ts->snes_its += its; ts->ksp_its += lits;
      }
      ierr = TSGetAdapt(ts,&adapt);CHKERRQ(ierr);
      ierr = TSAdaptCheckStage(adapt,ts,&accept);CHKERRQ(ierr);
      if (!accept) goto reject_step;
      ierr = TSPostStage(ts,glee->stage_time,i,YStage); CHKERRQ(ierr);
      ierr = TSComputeRHSFunction(ts,t+h*c[i],YStage[i],YdotStage[i]);CHKERRQ(ierr);
    }
    ierr = TSEvaluateStep(ts,tab->order,ts->vec_sol,NULL);CHKERRQ(ierr);
    glee->status = TS_STEP_PENDING;

    /* Register only the current method as a candidate because we're not supporting multiple candidates yet. */
    ierr = TSGetAdapt(ts,&adapt);CHKERRQ(ierr);
    ierr = TSAdaptCandidatesClear(adapt);CHKERRQ(ierr);
    ierr = TSAdaptCandidateAdd(adapt,tab->name,tab->order,1,tab->ccfl,1.*tab->s,PETSC_TRUE);CHKERRQ(ierr);
    ierr = TSAdaptChoose(adapt,ts,ts->time_step,&next_scheme,&next_time_step,&accept);CHKERRQ(ierr);
    if (accept) {
      /* ignore next_scheme for now */
      ts->ptime     += ts->time_step;
      ts->time_step  = next_time_step;
      ts->steps++;
      glee->status = TS_STEP_COMPLETE;
      ierr = PetscObjectComposedDataSetReal((PetscObject)ts->vec_sol,explicit_stage_time_id,ts->ptime);CHKERRQ(ierr);
      break;
    } else {                    /* Roll back the current step */
      ierr = VecMAXPY(ts->vec_sol,r,F,X);CHKERRQ(ierr);
      ts->time_step = next_time_step;
      glee->status  = TS_STEP_INCOMPLETE;
    }
reject_step: continue;
  }
  if (glee->status != TS_STEP_COMPLETE && !ts->reason) ts->reason = TS_DIVERGED_STEP_REJECTED;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "TSInterpolate_GLEE"
static PetscErrorCode TSInterpolate_GLEE(TS ts,PetscReal itime,Vec X)
{
  TS_GLEE         *glee = (TS_GLEE*)ts->data;
  PetscInt        s=glee->tableau->s, pinterp=glee->tableau->pinterp,i,j;
  PetscReal       h,tt,t;
  PetscScalar     *b;
  const PetscReal *B = glee->tableau->binterp;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  if (!B) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"TSGLEE %s does not have an interpolation formula",glee->tableau->name);
  switch (glee->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->time_step_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; i<s; i++) b[i] = 0;
  for (j=0,tt=t; j<pinterp; j++,tt*=t) {
    for (i=0; i<s; i++) {
      b[i]  += h * B[i*pinterp+j] * tt;
    }
  }
  ierr = VecCopy(glee->YStage[0],X);CHKERRQ(ierr);
  ierr = VecMAXPY(X,s,b,glee->YdotStage);CHKERRQ(ierr);
  ierr = PetscFree(b);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*------------------------------------------------------------*/
#undef __FUNCT__
#define __FUNCT__ "TSReset_GLEE"
static PetscErrorCode TSReset_GLEE(TS ts)
{
  TS_GLEE        *glee = (TS_GLEE*)ts->data;
  PetscInt       s, r;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (!glee->tableau) PetscFunctionReturn(0);
  s    = glee->tableau->s;
  r    = glee->tableau->r;
  ierr = VecDestroyVecs(r,&glee->Y);CHKERRQ(ierr);
  ierr = VecDestroyVecs(r,&glee->X);CHKERRQ(ierr);
  ierr = VecDestroyVecs(s,&glee->YStage);CHKERRQ(ierr);
  ierr = VecDestroyVecs(s,&glee->YdotStage);CHKERRQ(ierr);
  ierr = VecDestroy(&glee->Ydot);CHKERRQ(ierr);
  ierr = VecDestroy(&glee->W);CHKERRQ(ierr);
  ierr = PetscFree(glee->work);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "TSDestroy_GLEE"
static PetscErrorCode TSDestroy_GLEE(TS ts)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = TSReset_GLEE(ts);CHKERRQ(ierr);
  ierr = PetscFree(ts->data);CHKERRQ(ierr);
  ierr = PetscObjectComposeFunction((PetscObject)ts,"TSGLEEGetType_C",NULL);CHKERRQ(ierr);
  ierr = PetscObjectComposeFunction((PetscObject)ts,"TSGLEESetType_C",NULL);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "TSGLEEGetVecs"
static PetscErrorCode TSGLEEGetVecs(TS ts,DM dm,Vec *Ydot)
{
  TS_GLEE     *glee = (TS_GLEE*)ts->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (Ydot) {
    if (dm && dm != ts->dm) {
      ierr = DMGetNamedGlobalVector(dm,"TSGLEE_Ydot",Ydot);CHKERRQ(ierr);
    } else *Ydot = glee->Ydot;
  }
  PetscFunctionReturn(0);
}


#undef __FUNCT__
#define __FUNCT__ "TSGLEERestoreVecs"
static PetscErrorCode TSGLEERestoreVecs(TS ts,DM dm,Vec *Ydot)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (Ydot) {
    if (dm && dm != ts->dm) {
      ierr = DMRestoreNamedGlobalVector(dm,"TSGLEE_Ydot",Ydot);CHKERRQ(ierr);
    }
  }
  PetscFunctionReturn(0);
}

/*
  This defines the nonlinear equation that is to be solved with SNES
*/
#undef __FUNCT__
#define __FUNCT__ "SNESTSFormFunction_GLEE"
static PetscErrorCode SNESTSFormFunction_GLEE(SNES snes,Vec X,Vec F,TS ts)
{
  TS_GLEE       *glee = (TS_GLEE*)ts->data;
  DM             dm,dmsave;
  Vec            Ydot;
  PetscReal      shift = glee->scoeff / ts->time_step;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr   = SNESGetDM(snes,&dm);CHKERRQ(ierr);
  ierr   = TSGLEEGetVecs(ts,dm,&Ydot);CHKERRQ(ierr);
  /* Set Ydot = shift*X */
  ierr   = VecCopy(X,Ydot);CHKERRQ(ierr);
  ierr   = VecScale(Ydot,shift);CHKERRQ(ierr);
  dmsave = ts->dm;
  ts->dm = dm;

  ierr = TSComputeIFunction(ts,glee->stage_time,X,Ydot,F,PETSC_FALSE);CHKERRQ(ierr);

  ts->dm = dmsave;
  ierr   = TSGLEERestoreVecs(ts,dm,&Ydot);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "SNESTSFormJacobian_GLEE"
static PetscErrorCode SNESTSFormJacobian_GLEE(SNES snes,Vec X,Mat A,Mat B,TS ts)
{
  TS_GLEE        *glee = (TS_GLEE*)ts->data;
  DM             dm,dmsave;
  Vec            Ydot;
  PetscReal      shift = glee->scoeff / ts->time_step;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = SNESGetDM(snes,&dm);CHKERRQ(ierr);
  ierr = TSGLEEGetVecs(ts,dm,&Ydot);CHKERRQ(ierr);
  /* glee->Ydot has already been computed in SNESTSFormFunction_GLEE (SNES guarantees this) */
  dmsave = ts->dm;
  ts->dm = dm;

  ierr = TSComputeIJacobian(ts,glee->stage_time,X,Ydot,shift,A,B,PETSC_FALSE);CHKERRQ(ierr);

  ts->dm = dmsave;
  ierr   = TSGLEERestoreVecs(ts,dm,&Ydot);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMCoarsenHook_TSGLEE"
static PetscErrorCode DMCoarsenHook_TSGLEE(DM fine,DM coarse,void *ctx)
{
  PetscFunctionBegin;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMRestrictHook_TSGLEE"
static PetscErrorCode DMRestrictHook_TSGLEE(DM fine,Mat restrct,Vec rscale,Mat inject,DM coarse,void *ctx)
{
  PetscFunctionBegin;
  PetscFunctionReturn(0);
}


#undef __FUNCT__
#define __FUNCT__ "DMSubDomainHook_TSGLEE"
static PetscErrorCode DMSubDomainHook_TSGLEE(DM dm,DM subdm,void *ctx)
{
  PetscFunctionBegin;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMSubDomainRestrictHook_TSGLEE"
static PetscErrorCode DMSubDomainRestrictHook_TSGLEE(DM dm,VecScatter gscat,VecScatter lscat,DM subdm,void *ctx)
{
  PetscFunctionBegin;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "TSSetUp_GLEE"
static PetscErrorCode TSSetUp_GLEE(TS ts)
{
  TS_GLEE        *glee = (TS_GLEE*)ts->data;
  GLEETableau    tab;
  PetscInt       s,r;
  PetscErrorCode ierr;
  DM             dm;

  PetscFunctionBegin;
  if (!glee->tableau) {
    ierr = TSGLEESetType(ts,TSGLEEDefaultType);CHKERRQ(ierr);
  }
  tab  = glee->tableau;
  s    = tab->s;
  r    = tab->r;
  ierr = VecDuplicateVecs(ts->vec_sol,r,&glee->Y);CHKERRQ(ierr);
  ierr = VecDuplicateVecs(ts->vec_sol,r,&glee->X);CHKERRQ(ierr);
  ierr = VecDuplicateVecs(ts->vec_sol,s,&glee->YStage);CHKERRQ(ierr);
  ierr = VecDuplicateVecs(ts->vec_sol,s,&glee->YdotStage);CHKERRQ(ierr);
  ierr = VecDuplicate(ts->vec_sol,&glee->Ydot);CHKERRQ(ierr);
  ierr = VecDuplicate(ts->vec_sol,&glee->W);CHKERRQ(ierr);
  ierr = PetscMalloc1(s,&glee->work);CHKERRQ(ierr);
  ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
  if (dm) {
    ierr = DMCoarsenHookAdd(dm,DMCoarsenHook_TSGLEE,DMRestrictHook_TSGLEE,ts);CHKERRQ(ierr);
    ierr = DMSubDomainHookAdd(dm,DMSubDomainHook_TSGLEE,DMSubDomainRestrictHook_TSGLEE,ts);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "TSStartingMethod_GLEE"
PetscErrorCode TSStartingMethod_GLEE(TS ts)
{
  TS_GLEE        *glee = (TS_GLEE*)ts->data;
  GLEETableau    tab;
  PetscInt       r,i;
  PetscReal      *S;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (!glee->tableau) {
    ierr = TSGLEESetType(ts,TSGLEEDefaultType);CHKERRQ(ierr);
  }
  tab  = glee->tableau;
  r    = tab->r;
  S    = tab->S;
  ierr = VecDuplicateVecs(ts->vec_sol,r,&glee->Y);CHKERRQ(ierr);
  for (i=0; i<r; i++) {
    ierr = VecZeroEntries(glee->Y[i]);CHKERRQ(ierr);
    ierr = VecAXPY(glee->Y[i],S[i],ts->vec_sol);CHKERRQ(ierr);
  }

  PetscFunctionReturn(0);
}


/*------------------------------------------------------------*/

#undef __FUNCT__
#define __FUNCT__ "TSSetFromOptions_GLEE"
static PetscErrorCode TSSetFromOptions_GLEE(PetscOptions *PetscOptionsObject,TS ts)
{
  PetscErrorCode ierr;
  char           gleetype[256];

  PetscFunctionBegin;
  ierr = PetscOptionsHead(PetscOptionsObject,"GLEE ODE solver options");CHKERRQ(ierr);
  {
    GLEETableauLink link;
    PetscInt        count,choice;
    PetscBool       flg;
    const char      **namelist;

    ierr = PetscStrncpy(gleetype,TSGLEEDefaultType,sizeof(gleetype));CHKERRQ(ierr);
    for (link=GLEETableauList,count=0; link; link=link->next,count++) ;
    ierr = PetscMalloc1(count,&namelist);CHKERRQ(ierr);
    for (link=GLEETableauList,count=0; link; link=link->next,count++) namelist[count] = link->tab.name;
    ierr = PetscOptionsEList("-ts_glee_type","Family of GLEE method","TSGLEESetType",(const char*const*)namelist,count,gleetype,&choice,&flg);CHKERRQ(ierr);
    ierr = TSGLEESetType(ts,flg ? namelist[choice] : gleetype);CHKERRQ(ierr);
    ierr = PetscFree(namelist);CHKERRQ(ierr);
  }
  ierr = PetscOptionsTail();CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PetscFormatRealArray"
static PetscErrorCode PetscFormatRealArray(char buf[],size_t len,const char *fmt,PetscInt n,const PetscReal x[])
{
  PetscErrorCode ierr;
  PetscInt       i;
  size_t         left,count;
  char           *p;

  PetscFunctionBegin;
  for (i=0,p=buf,left=len; i<n; i++) {
    ierr = PetscSNPrintfCount(p,left,fmt,&count,x[i]);CHKERRQ(ierr);
    if (count >= left) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Insufficient space in buffer");
    left -= count;
    p    += count;
    *p++  = ' ';
  }
  p[i ? 0 : -1] = 0;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "TSView_GLEE"
static PetscErrorCode TSView_GLEE(TS ts,PetscViewer viewer)
{
  TS_GLEE        *glee   = (TS_GLEE*)ts->data;
  GLEETableau    tab  = glee->tableau;
  PetscBool      iascii;
  PetscErrorCode ierr;
  TSAdapt        adapt;

  PetscFunctionBegin;
  ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
  if (iascii) {
    TSGLEEType gleetype;
    char   buf[512];
    ierr = TSGLEEGetType(ts,&gleetype);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(viewer,"  GLEE %s\n",gleetype);CHKERRQ(ierr);
    ierr = PetscFormatRealArray(buf,sizeof(buf),"% 8.6f",tab->s,tab->c);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(viewer,"  Abscissa     c = %s\n",buf);CHKERRQ(ierr);
    /* Note: print out r as well */
  }
  ierr = TSGetAdapt(ts,&adapt);CHKERRQ(ierr);
  ierr = TSAdaptView(adapt,viewer);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "TSLoad_GLEE"
static PetscErrorCode TSLoad_GLEE(TS ts,PetscViewer viewer)
{
  PetscErrorCode ierr;
  SNES           snes;
  TSAdapt        tsadapt;

  PetscFunctionBegin;
  ierr = TSGetAdapt(ts,&tsadapt);CHKERRQ(ierr);
  ierr = TSAdaptLoad(tsadapt,viewer);CHKERRQ(ierr);
  ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
  ierr = SNESLoad(snes,viewer);CHKERRQ(ierr);
  /* function and Jacobian context for SNES when used with TS is always ts object */
  ierr = SNESSetFunction(snes,NULL,NULL,ts);CHKERRQ(ierr);
  ierr = SNESSetJacobian(snes,NULL,NULL,NULL,ts);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "TSGLEESetType"
/*@C
  TSGLEESetType - Set the type of GLEE scheme

  Logically collective

  Input Parameter:
+  ts - timestepping context
-  gleetype - type of GLEE-scheme

  Level: intermediate

.seealso: TSGLEEGetType(), TSGLEE
@*/
PetscErrorCode TSGLEESetType(TS ts,TSGLEEType gleetype)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  ierr = PetscTryMethod(ts,"TSGLEESetType_C",(TS,TSGLEEType),(ts,gleetype));CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "TSGLEEGetType"
/*@C
  TSGLEEGetType - Get the type of GLEE scheme

  Logically collective

  Input Parameter:
.  ts - timestepping context

  Output Parameter:
.  gleetype - type of GLEE-scheme

  Level: intermediate

.seealso: TSGLEESetType()
@*/
PetscErrorCode TSGLEEGetType(TS ts,TSGLEEType *gleetype)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  ierr = PetscUseMethod(ts,"TSGLEEGetType_C",(TS,TSGLEEType*),(ts,gleetype));CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "TSGLEEGetType_GLEE"
PetscErrorCode  TSGLEEGetType_GLEE(TS ts,TSGLEEType *gleetype)
{
  TS_GLEE     *glee = (TS_GLEE*)ts->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (!glee->tableau) {
    ierr = TSGLEESetType(ts,TSGLEEDefaultType);CHKERRQ(ierr);
  }
  *gleetype = glee->tableau->name;
  PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "TSGLEESetType_GLEE"
PetscErrorCode  TSGLEESetType_GLEE(TS ts,TSGLEEType gleetype)
{
  TS_GLEE         *glee = (TS_GLEE*)ts->data;
  PetscErrorCode  ierr;
  PetscBool       match;
  GLEETableauLink link;

  PetscFunctionBegin;
  if (glee->tableau) {
    ierr = PetscStrcmp(glee->tableau->name,gleetype,&match);CHKERRQ(ierr);
    if (match) PetscFunctionReturn(0);
  }
  for (link = GLEETableauList; link; link=link->next) {
    ierr = PetscStrcmp(link->tab.name,gleetype,&match);CHKERRQ(ierr);
    if (match) {
      ierr = TSReset_GLEE(ts);CHKERRQ(ierr);
      glee->tableau = &link->tab;
      PetscFunctionReturn(0);
    }
  }
  SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_UNKNOWN_TYPE,"Could not find '%s'",gleetype);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "TSGetStages_GLEE"
static PetscErrorCode  TSGetStages_GLEE(TS ts,PetscInt *ns,Vec **Y)
{
  TS_GLEE *glee = (TS_GLEE*)ts->data;

  PetscFunctionBegin;
  *ns = glee->tableau->s;
  if(Y) *Y  = glee->Y;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "TSGetAuxSolution_GLEE"
PetscErrorCode TSGetAuxSolution_GLEE(TS ts,PetscInt *n,Vec *Y)
{
  TS_GLEE     *glee = (TS_GLEE*)ts->data;
  GLEETableau tab   = glee->tableau;

  PetscFunctionBegin;
  if (!Y) *n = tab->r - 1;
  else {
    if ((*n > 0) && (*n < tab->r)) *Y = glee->Y[*n];
    else {
      /* XXX: Error message for invalid value of n */
    }
  }
  PetscFunctionReturn(0);
}

/* ------------------------------------------------------------ */
/*MC
      TSGLEE - ODE and DAE solver using General Linear with Error Estimation schemes

  The user should provide the right hand side of the equation
  using TSSetRHSFunction().

  Notes:
  The default is TSGLEE35, it can be changed with TSGLEESetType() or -ts_glee_type

  Level: beginner

.seealso:  TSCreate(), TS, TSSetType(), TSGLEESetType(), TSGLEEGetType(),
           TSGLEE23, TTSGLEE24, TSGLEE35, TSGLEE25I, TSGLEEEXRK2A,
           TSGLEERK32G1, TSGLEERK285EX, TSGLEEType, TSGLEERegister()

M*/
#undef __FUNCT__
#define __FUNCT__ "TSCreate_GLEE"
PETSC_EXTERN PetscErrorCode TSCreate_GLEE(TS ts)
{
  TS_GLEE         *th;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
#if !defined(PETSC_USE_DYNAMIC_LIBRARIES)
  ierr = TSGLEEInitializePackage();CHKERRQ(ierr);
#endif

  ts->ops->reset          = TSReset_GLEE;
  ts->ops->destroy        = TSDestroy_GLEE;
  ts->ops->view           = TSView_GLEE;
  ts->ops->load           = TSLoad_GLEE;
  ts->ops->setup          = TSSetUp_GLEE;
  ts->ops->step           = TSStep_GLEE;
  ts->ops->interpolate    = TSInterpolate_GLEE;
  ts->ops->evaluatestep   = TSEvaluateStep_GLEE;
  ts->ops->setfromoptions = TSSetFromOptions_GLEE;
  ts->ops->getstages      = TSGetStages_GLEE;
  ts->ops->snesfunction   = SNESTSFormFunction_GLEE;
  ts->ops->snesjacobian   = SNESTSFormJacobian_GLEE;
  ts->ops->getauxsolution = TSGetAuxSolution_GLEE;
  ts->ops->startingmethod = TSStartingMethod_GLEE;

  ierr = PetscNewLog(ts,&th);CHKERRQ(ierr);
  ts->data = (void*)th;

  ierr = PetscObjectComposeFunction((PetscObject)ts,"TSGLEEGetType_C",TSGLEEGetType_GLEE);CHKERRQ(ierr);
  ierr = PetscObjectComposeFunction((PetscObject)ts,"TSGLEESetType_C",TSGLEESetType_GLEE);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}