Actual source code: glee.c

      1: /*
      2:   Code for time stepping with the General Linear with Error Estimation method

      5:   Notes:
      6:   The general system is written as

      8:   Udot = F(t,U)

     10: */
     11: #include <petsc/private/tsimpl.h>
     12: #include <petscdm.h>

     14: static PetscBool  cited = PETSC_FALSE;
     15: static const char citation[] =
     16:   "@ARTICLE{Constantinescu_TR2016b,\n"
     17:   " author = {Constantinescu, E.M.},\n"
     18:   " title = {Estimating Global Errors in Time Stepping},\n"
     19:   " journal = {ArXiv e-prints},\n"
     20:   " year = 2016,\n"
     21:   " adsurl = {http://adsabs.harvard.edu/abs/2015arXiv150305166C}\n}\n";

     23: static TSGLEEType   TSGLEEDefaultType = TSGLEE35;
     24: static PetscBool    TSGLEERegisterAllCalled;
     25: static PetscBool    TSGLEEPackageInitialized;
     26: static PetscInt     explicit_stage_time_id;

     28: typedef struct _GLEETableau *GLEETableau;
     29: struct _GLEETableau {
     30:   char      *name;
     31:   PetscInt   order;               /* Classical approximation order of the method i*/
     32:   PetscInt   s;                   /* Number of stages */
     33:   PetscInt   r;                   /* Number of steps */
     34:   PetscReal  gamma;               /* LTE ratio */
     35:   PetscReal *A,*B,*U,*V,*S,*F,*c; /* Tableau */
     36:   PetscReal *Fembed;              /* Embedded final method coefficients */
     37:   PetscReal *Ferror;              /* Coefficients for computing error   */
     38:   PetscReal *Serror;              /* Coefficients for initializing the error   */
     39:   PetscInt   pinterp;             /* Interpolation order */
     40:   PetscReal *binterp;             /* Interpolation coefficients */
     41:   PetscReal  ccfl;                /* Placeholder for CFL coefficient relative to forward Euler  */
     42: };
     43: typedef struct _GLEETableauLink *GLEETableauLink;
     44: struct _GLEETableauLink {
     45:   struct _GLEETableau tab;
     46:   GLEETableauLink     next;
     47: };
     48: static GLEETableauLink GLEETableauList;

     50: typedef struct {
     51:   GLEETableau  tableau;
     52:   Vec          *Y;         /* Solution vector (along with auxiliary solution y~ or eps) */
     53:   Vec          *X;         /* Temporary solution vector */
     54:   Vec          *YStage;    /* Stage values */
     55:   Vec          *YdotStage; /* Stage right hand side */
     56:   Vec          W;          /* Right-hand-side for implicit stage solve */
     57:   Vec          Ydot;       /* Work vector holding Ydot during residual evaluation */
     58:   Vec          yGErr;      /* Vector holding the global error after a step is completed */
     59:   PetscScalar  *swork;     /* Scalar work (size of the number of stages)*/
     60:   PetscScalar  *rwork;     /* Scalar work (size of the number of steps)*/
     61:   PetscReal    scoeff;     /* shift = scoeff/dt */
     62:   PetscReal    stage_time;
     63:   TSStepStatus status;
     64: } TS_GLEE;

     66: /*MC
     67:      TSGLEE23 - Second order three stage GLEE method

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

     72:      Level: advanced

     74: .seealso: TSGLEE
     75: M*/
     76: /*MC
     77:      TSGLEE24 - Second order four stage GLEE method

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

     82:      Level: advanced

     84: .seealso: TSGLEE
     85: M*/
     86: /*MC
     87:      TSGLEE25i - Second order five stage GLEE method

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

     92:      Level: advanced

     94: .seealso: TSGLEE
     95: M*/
     96: /*MC
     97:      TSGLEE35  - Third order five stage GLEE method

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

    102:      Level: advanced

    104: .seealso: TSGLEE
    105: M*/
    106: /*MC
    107:      TSGLEEEXRK2A  - Second order six stage GLEE method

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

    112:      Level: advanced

    114: .seealso: TSGLEE
    115: M*/
    116: /*MC
    117:      TSGLEERK32G1  - Third order eight stage GLEE method

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

    122:      Level: advanced

    124: .seealso: TSGLEE
    125: M*/
    126: /*MC
    127:      TSGLEERK285EX  - Second order nine stage GLEE method

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

    132:      Level: advanced

    134: .seealso: TSGLEE
    135: M*/

    137: /*@C
    138:   TSGLEERegisterAll - Registers all of the General Linear with Error Estimation methods in TSGLEE

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

    142:   Level: advanced

    144: .seealso:  TSGLEERegisterDestroy()
    145: @*/
    146: PetscErrorCode TSGLEERegisterAll(void)
    147: {

    151:   if (TSGLEERegisterAllCalled) return(0);
    152:   TSGLEERegisterAllCalled = PETSC_TRUE;

    154:   {
    155: #define GAMMA 0.5
    156:     /* y-eps form */
    157:     const PetscInt
    158:       p = 1,
    159:       s = 3,
    160:       r = 2;
    161:     const PetscReal
    162:       A[3][3]   = {{1.0,0,0},{0,0.5,0},{0,0.5,0.5}},
    163:       B[2][3]   = {{1.0,0,0},{-2.0,1.0,1.0}},
    164:       U[3][2]   = {{1.0,0},{1.0,0.5},{1.0,0.5}},
    165:       V[2][2]   = {{1,0},{0,1}},
    166:       S[2]      = {1,0},
    167:       F[2]      = {1,0},
    168:       Fembed[2] = {1,1-GAMMA},
    169:       Ferror[2] = {0,1},
    170:       Serror[2] = {1,0};
    171:     TSGLEERegister(TSGLEEi1,p,s,r,GAMMA,&A[0][0],&B[0][0],&U[0][0],&V[0][0],S,F,NULL,Fembed,Ferror,Serror,0,NULL);
    172:   }
    173:   {
    174: #undef GAMMA
    175: #define GAMMA 0.0
    176:     /* y-eps form */
    177:     const PetscInt
    178:       p = 2,
    179:       s = 3,
    180:       r = 2;
    181:     const PetscReal
    182:       A[3][3]   = {{0,0,0},{1,0,0},{0.25,0.25,0}},
    183:       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}},
    184:       U[3][2]   = {{1,0},{1,10},{1,-1}},
    185:       V[2][2]   = {{1,0},{0,1}},
    186:       S[2]      = {1,0},
    187:       F[2]      = {1,0},
    188:       Fembed[2] = {1,1-GAMMA},
    189:       Ferror[2] = {0,1},
    190:       Serror[2] = {1,0};
    191:     TSGLEERegister(TSGLEE23,p,s,r,GAMMA,&A[0][0],&B[0][0],&U[0][0],&V[0][0],S,F,NULL,Fembed,Ferror,Serror,0,NULL);
    192:   }
    193:   {
    194: #undef GAMMA
    195: #define GAMMA 0.0
    196:     /* y-y~ form */
    197:     const PetscInt
    198:       p = 2,
    199:       s = 4,
    200:       r = 2;
    201:     const PetscReal
    202:       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}},
    203:       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}},
    204:       U[4][2]   = {{0,1},{75.0/58.0,-17.0/58.0},{0,1},{0,1}},
    205:       V[2][2]   = {{1,0},{0,1}},
    206:       S[2]      = {1,1},
    207:       F[2]      = {1,0},
    208:       Fembed[2] = {0,1},
    209:       Ferror[2] = {-1.0/(1.0-GAMMA),1.0/(1.0-GAMMA)},
    210:       Serror[2] = {1.0-GAMMA,1.0};
    211:       TSGLEERegister(TSGLEE24,p,s,r,GAMMA,&A[0][0],&B[0][0],&U[0][0],&V[0][0],S,F,NULL,Fembed,Ferror,Serror,0,NULL);
    212:   }
    213:   {
    214: #undef GAMMA
    215: #define GAMMA 0.0
    216:     /* y-y~ form */
    217:     const PetscInt
    218:       p = 2,
    219:       s = 5,
    220:       r = 2;
    221:     const PetscReal
    222:       A[5][5]   = {{0,0,0,0,0},
    223:                    {-0.94079244066783383269,0,0,0,0},
    224:                    {0.64228187778301907108,0.10915356933958500042,0,0,0},
    225:                    {-0.51764297742287450812,0.74414270351096040738,-0.71404164927824538121,0,0},
    226:                    {-0.44696561556825969206,-0.76768425657590196518,0.20111608138142987881,0.93828186737840469796,0}},
    227:       B[2][5]   = {{-0.029309178948150356153,-0.49671981884013874923,0.34275801517650053274,0.32941112623949194988,0.85385985637229662276},
    228:                    {0.78133219686062535272,0.074238691892675897635,0.57957363498384957966,-0.24638502829674959968,-0.18875949544040123033}},
    229:       U[5][2]   = {{0.16911424754448327735,0.83088575245551672265},
    230:                    {0.53638465733199574340,0.46361534266800425660},
    231:                    {0.39901579167169582526,0.60098420832830417474},
    232:                    {0.87689005530618575480,0.12310994469381424520},
    233:                    {0.99056100455550913009,0.0094389954444908699092}},
    234:       V[2][2]   = {{1,0},{0,1}},
    235:       S[2]      = {1,1},
    236:       F[2]      = {1,0},
    237:       Fembed[2] = {0,1},
    238:       Ferror[2] = {-1.0/(1.0-GAMMA),1.0/(1.0-GAMMA)},
    239:       Serror[2] = {1.0-GAMMA,1.0};
    240:     TSGLEERegister(TSGLEE25I,p,s,r,GAMMA,&A[0][0],&B[0][0],&U[0][0],&V[0][0],S,F,NULL,Fembed,Ferror,Serror,0,NULL);
    241:   }
    242:   {
    243: #undef GAMMA
    244: #define GAMMA 0.0
    245:     /* y-y~ form */
    246:     const PetscInt
    247:       p = 3,
    248:       s = 5,
    249:       r = 2;
    250:     const PetscReal
    251:       A[5][5]   = {{0,0,0,0,0},
    252:                    {- 2169604947363702313.0 /  24313474998937147335.0,0,0,0,0},
    253:                    {46526746497697123895.0 /  94116917485856474137.0,-10297879244026594958.0 /  49199457603717988219.0,0,0,0},
    254:                    {23364788935845982499.0 /  87425311444725389446.0,-79205144337496116638.0 / 148994349441340815519.0,40051189859317443782.0 /  36487615018004984309.0,0,0},
    255:                    {42089522664062539205.0 / 124911313006412840286.0,-15074384760342762939.0 / 137927286865289746282.0,-62274678522253371016.0 / 125918573676298591413.0,13755475729852471739.0 /  79257927066651693390.0,0}},
    256:       B[2][5]   = {{61546696837458703723.0 /  56982519523786160813.0,-55810892792806293355.0 / 206957624151308356511.0,24061048952676379087.0 / 158739347956038723465.0,3577972206874351339.0 /   7599733370677197135.0,-59449832954780563947.0 / 137360038685338563670.0},
    257:                    {- 9738262186984159168.0 /  99299082461487742983.0,-32797097931948613195.0 /  61521565616362163366.0,42895514606418420631.0 /  71714201188501437336.0,22608567633166065068.0 /  55371917805607957003.0,94655809487476459565.0 / 151517167160302729021.0}},
    258:       U[5][2]   = {{70820309139834661559.0 /  80863923579509469826.0,10043614439674808267.0 /  80863923579509469826.0},
    259:                    {161694774978034105510.0 / 106187653640211060371.0,-55507121337823045139.0 / 106187653640211060371.0},
    260:                    {78486094644566264568.0 /  88171030896733822981.0,9684936252167558413.0 /  88171030896733822981.0},
    261:                    {65394922146334854435.0 /  84570853840405479554.0,19175931694070625119.0 /  84570853840405479554.0},
    262:                    {8607282770183754108.0 / 108658046436496925911.0,100050763666313171803.0 / 108658046436496925911.0}},
    263:       V[2][2]   = {{1,0},{0,1}},
    264:       S[2]      = {1,1},
    265:       F[2]      = {1,0},
    266:       Fembed[2] = {0,1},
    267:       Ferror[2] = {-1.0/(1.0-GAMMA),1.0/(1.0-GAMMA)},
    268:       Serror[2] = {1.0-GAMMA,1.0};
    269:     TSGLEERegister(TSGLEE35,p,s,r,GAMMA,&A[0][0],&B[0][0],&U[0][0],&V[0][0],S,F,NULL,Fembed,Ferror,Serror,0,NULL);
    270:   }
    271:   {
    272: #undef GAMMA
    273: #define GAMMA 0.25
    274:     /* y-eps form */
    275:     const PetscInt
    276:       p = 2,
    277:       s = 6,
    278:       r = 2;
    279:     const PetscReal
    280:       A[6][6]   = {{0,0,0,0,0,0},
    281:                    {1,0,0,0,0,0},
    282:                    {0,0,0,0,0,0},
    283:                    {0,0,0.5,0,0,0},
    284:                    {0,0,0.25,0.25,0,0},
    285:                    {0,0,0.25,0.25,0.5,0}},
    286:       B[2][6]   = {{0.5,0.5,0,0,0,0},
    287:                    {-2.0/3.0,-2.0/3.0,1.0/3.0,1.0/3.0,1.0/3.0,1.0/3.0}},
    288:       U[6][2]   = {{1,0},{1,0},{1,0.75},{1,0.75},{1,0.75},{1,0.75}},
    289:       V[2][2]   = {{1,0},{0,1}},
    290:       S[2]      = {1,0},
    291:       F[2]      = {1,0},
    292:       Fembed[2] = {1,1-GAMMA},
    293:       Ferror[2] = {0,1},
    294:       Serror[2] = {1,0};
    295:     TSGLEERegister(TSGLEEEXRK2A,p,s,r,GAMMA,&A[0][0],&B[0][0],&U[0][0],&V[0][0],S,F,NULL,Fembed,Ferror,Serror,0,NULL);
    296:   }
    297:   {
    298: #undef GAMMA
    299: #define GAMMA 0.0
    300:     /* y-eps form */
    301:     const PetscInt
    302:       p = 3,
    303:       s = 8,
    304:       r = 2;
    305:     const PetscReal
    306:       A[8][8]   = {{0,0,0,0,0,0,0,0},
    307:                    {0.5,0,0,0,0,0,0,0},
    308:                    {-1,2,0,0,0,0,0,0},
    309:                    {1.0/6.0,2.0/3.0,1.0/6.0,0,0,0,0,0},
    310:                    {0,0,0,0,0,0,0,0},
    311:                    {-7.0/24.0,1.0/3.0,1.0/12.0,-1.0/8.0,0.5,0,0,0},
    312:                    {7.0/6.0,-4.0/3.0,-1.0/3.0,0.5,-1.0,2.0,0,0},
    313:                    {0,0,0,0,1.0/6.0,2.0/3.0,1.0/6.0,0}},
    314:       B[2][8]   = {{1.0/6.0,2.0/3.0,1.0/6.0,0,0,0,0,0},
    315:                    {-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}},
    316:       U[8][2]   = {{1,0},{1,0},{1,0},{1,0},{1,1},{1,1},{1,1},{1,1}},
    317:       V[2][2]   = {{1,0},{0,1}},
    318:       S[2]      = {1,0},
    319:       F[2]      = {1,0},
    320:       Fembed[2] = {1,1-GAMMA},
    321:       Ferror[2] = {0,1},
    322:       Serror[2] = {1,0};
    323:     TSGLEERegister(TSGLEERK32G1,p,s,r,GAMMA,&A[0][0],&B[0][0],&U[0][0],&V[0][0],S,F,NULL,Fembed,Ferror,Serror,0,NULL);
    324:   }
    325:   {
    326: #undef GAMMA
    327: #define GAMMA 0.25
    328:     /* y-eps form */
    329:     const PetscInt
    330:       p = 2,
    331:       s = 9,
    332:       r = 2;
    333:     const PetscReal
    334:       A[9][9]   = {{0,0,0,0,0,0,0,0,0},
    335:                    {0.585786437626904966,0,0,0,0,0,0,0,0},
    336:                    {0.149999999999999994,0.849999999999999978,0,0,0,0,0,0,0},
    337:                    {0,0,0,0,0,0,0,0,0},
    338:                    {0,0,0,0.292893218813452483,0,0,0,0,0},
    339:                    {0,0,0,0.0749999999999999972,0.424999999999999989,0,0,0,0},
    340:                    {0,0,0,0.176776695296636893,0.176776695296636893,0.146446609406726241,0,0,0},
    341:                    {0,0,0,0.176776695296636893,0.176776695296636893,0.146446609406726241,0.292893218813452483,0,0},
    342:                    {0,0,0,0.176776695296636893,0.176776695296636893,0.146446609406726241,0.0749999999999999972,0.424999999999999989,0}},
    343:       B[2][9]   = {{0.353553390593273786,0.353553390593273786,0.292893218813452483,0,0,0,0,0,0},
    344:                    {-0.471404520791031678,-0.471404520791031678,-0.390524291751269959,0.235702260395515839,0.235702260395515839,0.195262145875634979,0.235702260395515839,0.235702260395515839,0.195262145875634979}},
    345:       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}},
    346:       V[2][2]   = {{1,0},{0,1}},
    347:       S[2]      = {1,0},
    348:       F[2]      = {1,0},
    349:       Fembed[2] = {1,1-GAMMA},
    350:       Ferror[2] = {0,1},
    351:       Serror[2] = {1,0};
    352:     TSGLEERegister(TSGLEERK285EX,p,s,r,GAMMA,&A[0][0],&B[0][0],&U[0][0],&V[0][0],S,F,NULL,Fembed,Ferror,Serror,0,NULL);
    353:   }

    355:   return(0);
    356: }

    358: /*@C
    359:    TSGLEERegisterDestroy - Frees the list of schemes that were registered by TSGLEERegister().

    361:    Not Collective

    363:    Level: advanced

    365: .seealso: TSGLEERegister(), TSGLEERegisterAll()
    366: @*/
    367: PetscErrorCode TSGLEERegisterDestroy(void)
    368: {
    370:   GLEETableauLink link;

    373:   while ((link = GLEETableauList)) {
    374:     GLEETableau t = &link->tab;
    375:     GLEETableauList = link->next;
    376:     PetscFree5(t->A,t->B,t->U,t->V,t->c);
    377:     PetscFree2(t->S,t->F);
    378:     PetscFree (t->Fembed);
    379:     PetscFree (t->Ferror);
    380:     PetscFree (t->Serror);
    381:     PetscFree (t->binterp);
    382:     PetscFree (t->name);
    383:     PetscFree (link);
    384:   }
    385:   TSGLEERegisterAllCalled = PETSC_FALSE;
    386:   return(0);
    387: }

    389: /*@C
    390:   TSGLEEInitializePackage - This function initializes everything in the TSGLEE package. It is called
    391:   from TSInitializePackage().

    393:   Level: developer

    395: .seealso: PetscInitialize()
    396: @*/
    397: PetscErrorCode TSGLEEInitializePackage(void)
    398: {

    402:   if (TSGLEEPackageInitialized) return(0);
    403:   TSGLEEPackageInitialized = PETSC_TRUE;
    404:   TSGLEERegisterAll();
    405:   PetscObjectComposedDataRegister(&explicit_stage_time_id);
    406:   PetscRegisterFinalize(TSGLEEFinalizePackage);
    407:   return(0);
    408: }

    410: /*@C
    411:   TSGLEEFinalizePackage - This function destroys everything in the TSGLEE package. It is
    412:   called from PetscFinalize().

    414:   Level: developer

    416: .seealso: PetscFinalize()
    417: @*/
    418: PetscErrorCode TSGLEEFinalizePackage(void)
    419: {

    423:   TSGLEEPackageInitialized = PETSC_FALSE;
    424:   TSGLEERegisterDestroy();
    425:   return(0);
    426: }

    428: /*@C
    429:    TSGLEERegister - register an GLEE scheme by providing the entries in the Butcher tableau

    431:    Not Collective, but the same schemes should be registered on all processes on which they will be used

    433:    Input Parameters:
    434: +  name   - identifier for method
    435: .  order  - order of method
    436: .  s - number of stages
    437: .  r - number of steps
    438: .  gamma - LTE ratio
    439: .  A - stage coefficients (dimension s*s, row-major)
    440: .  B - step completion coefficients (dimension r*s, row-major)
    441: .  U - method coefficients (dimension s*r, row-major)
    442: .  V - method coefficients (dimension r*r, row-major)
    443: .  S - starting coefficients
    444: .  F - finishing coefficients
    445: .  c - abscissa (dimension s; NULL to use row sums of A)
    446: .  Fembed - step completion coefficients for embedded method
    447: .  Ferror - error computation coefficients
    448: .  Serror - error initialization coefficients
    449: .  pinterp - order of interpolation (0 if unavailable)
    450: -  binterp - array of interpolation coefficients (NULL if unavailable)

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

    455:    Level: advanced

    457: .seealso: TSGLEE
    458: @*/
    459: PetscErrorCode TSGLEERegister(TSGLEEType name,PetscInt order,PetscInt s, PetscInt r,
    460:                               PetscReal gamma,
    461:                               const PetscReal A[],const PetscReal B[],
    462:                               const PetscReal U[],const PetscReal V[],
    463:                               const PetscReal S[],const PetscReal F[],
    464:                               const PetscReal c[],
    465:                               const PetscReal Fembed[],const PetscReal Ferror[],
    466:                               const PetscReal Serror[],
    467:                               PetscInt pinterp, const PetscReal binterp[])
    468: {
    469:   PetscErrorCode    ierr;
    470:   GLEETableauLink   link;
    471:   GLEETableau       t;
    472:   PetscInt          i,j;

    475:   TSGLEEInitializePackage();
    476:   PetscNew(&link);
    477:   t        = &link->tab;
    478:   PetscStrallocpy(name,&t->name);
    479:   t->order = order;
    480:   t->s     = s;
    481:   t->r     = r;
    482:   t->gamma = gamma;
    483:   PetscMalloc5(s*s,&t->A,r*r,&t->V,s,&t->c,r*s,&t->B,s*r,&t->U);
    484:   PetscMalloc2(r,&t->S,r,&t->F);
    485:   PetscArraycpy(t->A,A,s*s);
    486:   PetscArraycpy(t->B,B,r*s);
    487:   PetscArraycpy(t->U,U,s*r);
    488:   PetscArraycpy(t->V,V,r*r);
    489:   PetscArraycpy(t->S,S,r);
    490:   PetscArraycpy(t->F,F,r);
    491:   if (c) {
    492:     PetscArraycpy(t->c,c,s);
    493:   } else {
    494:     for (i=0; i<s; i++) for (j=0,t->c[i]=0; j<s; j++) t->c[i] += A[i*s+j];
    495:   }
    496:   PetscMalloc1(r,&t->Fembed);
    497:   PetscMalloc1(r,&t->Ferror);
    498:   PetscMalloc1(r,&t->Serror);
    499:   PetscArraycpy(t->Fembed,Fembed,r);
    500:   PetscArraycpy(t->Ferror,Ferror,r);
    501:   PetscArraycpy(t->Serror,Serror,r);
    502:   t->pinterp = pinterp;
    503:   PetscMalloc1(s*pinterp,&t->binterp);
    504:   PetscArraycpy(t->binterp,binterp,s*pinterp);

    506:   link->next      = GLEETableauList;
    507:   GLEETableauList = link;
    508:   return(0);
    509: }

    511: static PetscErrorCode TSEvaluateStep_GLEE(TS ts,PetscInt order,Vec X,PetscBool *done)
    512: {
    513:   TS_GLEE         *glee = (TS_GLEE*) ts->data;
    514:   GLEETableau     tab = glee->tableau;
    515:   PetscReal       h, *B = tab->B, *V = tab->V,
    516:                   *F = tab->F,
    517:                   *Fembed = tab->Fembed;
    518:   PetscInt        s = tab->s, r = tab->r, i, j;
    519:   Vec             *Y = glee->Y, *YdotStage = glee->YdotStage;
    520:   PetscScalar     *ws = glee->swork, *wr = glee->rwork;
    521:   PetscErrorCode  ierr;

    525:   switch (glee->status) {
    526:     case TS_STEP_INCOMPLETE:
    527:     case TS_STEP_PENDING:
    528:       h = ts->time_step; break;
    529:     case TS_STEP_COMPLETE:
    530:       h = ts->ptime - ts->ptime_prev; break;
    531:     default: SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_PLIB,"Invalid TSStepStatus");
    532:   }

    534:   if (order == tab->order) {

    536:     /* Note: Irrespective of whether status is TS_STEP_INCOMPLETE
    537:              or TS_STEP_COMPLETE, glee->X has the solution at the
    538:              beginning of the time step. So no need to roll-back.
    539:     */
    540:     if (glee->status == TS_STEP_INCOMPLETE) {
    541:       for (i=0; i<r; i++) {
    542:         VecZeroEntries(Y[i]);
    543:         for (j=0; j<r; j++) wr[j] = V[i*r+j];
    544:         VecMAXPY(Y[i],r,wr,glee->X);
    545:         for (j=0; j<s; j++) ws[j] = h*B[i*s+j];
    546:         VecMAXPY(Y[i],s,ws,YdotStage);
    547:       }
    548:       VecZeroEntries(X);
    549:       for (j=0; j<r; j++) wr[j] = F[j];
    550:       VecMAXPY(X,r,wr,Y);
    551:     } else {VecCopy(ts->vec_sol,X);}
    552:     return(0);

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

    556:     /* Complete with the embedded method (Fembed) */
    557:     for (i=0; i<r; i++) {
    558:       VecZeroEntries(Y[i]);
    559:       for (j=0; j<r; j++) wr[j] = V[i*r+j];
    560:       VecMAXPY(Y[i],r,wr,glee->X);
    561:       for (j=0; j<s; j++) ws[j] = h*B[i*s+j];
    562:       VecMAXPY(Y[i],s,ws,YdotStage);
    563:     }
    564:     VecZeroEntries(X);
    565:     for (j=0; j<r; j++) wr[j] = Fembed[j];
    566:     VecMAXPY(X,r,wr,Y);

    568:     if (done) *done = PETSC_TRUE;
    569:     return(0);
    570:   }
    571:   if (done) *done = PETSC_FALSE;
    572:   else SETERRQ3(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"GLEE '%s' of order %D cannot evaluate step at order %D",tab->name,tab->order,order);
    573:   return(0);
    574: }

    576: static PetscErrorCode TSStep_GLEE(TS ts)
    577: {
    578:   TS_GLEE         *glee = (TS_GLEE*)ts->data;
    579:   GLEETableau     tab = glee->tableau;
    580:   const PetscInt  s = tab->s, r = tab->r;
    581:   PetscReal       *A = tab->A, *U = tab->U,
    582:                   *F = tab->F,
    583:                   *c = tab->c;
    584:   Vec             *Y = glee->Y, *X = glee->X,
    585:                   *YStage = glee->YStage,
    586:                   *YdotStage = glee->YdotStage,
    587:                   W = glee->W;
    588:   SNES            snes;
    589:   PetscScalar     *ws = glee->swork, *wr = glee->rwork;
    590:   TSAdapt         adapt;
    591:   PetscInt        i,j,reject,next_scheme,its,lits;
    592:   PetscReal       next_time_step;
    593:   PetscReal       t;
    594:   PetscBool       accept;
    595:   PetscErrorCode  ierr;

    598:   PetscCitationsRegister(citation,&cited);

    600:   for (i=0; i<r; i++) { VecCopy(Y[i],X[i]); }

    602:   TSGetSNES(ts,&snes);
    603:   next_time_step = ts->time_step;
    604:   t              = ts->ptime;
    605:   accept         = PETSC_TRUE;
    606:   glee->status   = TS_STEP_INCOMPLETE;

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

    610:     PetscReal h = ts->time_step;
    611:     TSPreStep(ts);

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

    615:       glee->stage_time = t + h*c[i];
    616:       TSPreStage(ts,glee->stage_time);

    618:       if (A[i*s+i] == 0) {  /* Explicit stage */
    619:         VecZeroEntries(YStage[i]);
    620:         for (j=0; j<r; j++) wr[j] = U[i*r+j];
    621:         VecMAXPY(YStage[i],r,wr,X);
    622:         for (j=0; j<i; j++) ws[j] = h*A[i*s+j];
    623:         VecMAXPY(YStage[i],i,ws,YdotStage);
    624:       } else {              /* Implicit stage */
    625:         glee->scoeff = 1.0/A[i*s+i];
    626:         /* compute right-hand-side */
    627:         VecZeroEntries(W);
    628:         for (j=0; j<r; j++) wr[j] = U[i*r+j];
    629:         VecMAXPY(W,r,wr,X);
    630:         for (j=0; j<i; j++) ws[j] = h*A[i*s+j];
    631:         VecMAXPY(W,i,ws,YdotStage);
    632:         VecScale(W,glee->scoeff/h);
    633:         /* set initial guess */
    634:         VecCopy(i>0 ? YStage[i-1] : ts->vec_sol,YStage[i]);
    635:         /* solve for this stage */
    636:         SNESSolve(snes,W,YStage[i]);
    637:         SNESGetIterationNumber(snes,&its);
    638:         SNESGetLinearSolveIterations(snes,&lits);
    639:         ts->snes_its += its; ts->ksp_its += lits;
    640:       }
    641:       TSGetAdapt(ts,&adapt);
    642:       TSAdaptCheckStage(adapt,ts,glee->stage_time,YStage[i],&accept);
    643:       if (!accept) goto reject_step;
    644:       TSPostStage(ts,glee->stage_time,i,YStage);
    645:       TSComputeRHSFunction(ts,t+h*c[i],YStage[i],YdotStage[i]);
    646:     }
    647:     TSEvaluateStep(ts,tab->order,ts->vec_sol,NULL);
    648:     glee->status = TS_STEP_PENDING;

    650:     /* Register only the current method as a candidate because we're not supporting multiple candidates yet. */
    651:     TSGetAdapt(ts,&adapt);
    652:     TSAdaptCandidatesClear(adapt);
    653:     TSAdaptCandidateAdd(adapt,tab->name,tab->order,1,tab->ccfl,(PetscReal)tab->s,PETSC_TRUE);
    654:     TSAdaptChoose(adapt,ts,ts->time_step,&next_scheme,&next_time_step,&accept);
    655:     if (accept) {
    656:       /* ignore next_scheme for now */
    657:       ts->ptime     += ts->time_step;
    658:       ts->time_step  = next_time_step;
    659:       glee->status = TS_STEP_COMPLETE;
    660:       /* compute and store the global error */
    661:       /* Note: this is not needed if TSAdaptGLEE is not used */
    662:       TSGetTimeError(ts,0,&(glee->yGErr));
    663:       PetscObjectComposedDataSetReal((PetscObject)ts->vec_sol,explicit_stage_time_id,ts->ptime);
    664:       break;
    665:     } else {                    /* Roll back the current step */
    666:       for (j=0; j<r; j++) wr[j] = F[j];
    667:       VecMAXPY(ts->vec_sol,r,wr,X);
    668:       ts->time_step = next_time_step;
    669:       glee->status  = TS_STEP_INCOMPLETE;
    670:     }
    671: reject_step: continue;
    672:   }
    673:   if (glee->status != TS_STEP_COMPLETE && !ts->reason) ts->reason = TS_DIVERGED_STEP_REJECTED;
    674:   return(0);
    675: }

    677: static PetscErrorCode TSInterpolate_GLEE(TS ts,PetscReal itime,Vec X)
    678: {
    679:   TS_GLEE         *glee = (TS_GLEE*)ts->data;
    680:   PetscInt        s=glee->tableau->s, pinterp=glee->tableau->pinterp,i,j;
    681:   PetscReal       h,tt,t;
    682:   PetscScalar     *b;
    683:   const PetscReal *B = glee->tableau->binterp;
    684:   PetscErrorCode  ierr;

    687:   if (!B) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"TSGLEE %s does not have an interpolation formula",glee->tableau->name);
    688:   switch (glee->status) {
    689:     case TS_STEP_INCOMPLETE:
    690:     case TS_STEP_PENDING:
    691:       h = ts->time_step;
    692:       t = (itime - ts->ptime)/h;
    693:       break;
    694:     case TS_STEP_COMPLETE:
    695:       h = ts->ptime - ts->ptime_prev;
    696:       t = (itime - ts->ptime)/h + 1; /* In the interval [0,1] */
    697:       break;
    698:     default: SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_PLIB,"Invalid TSStepStatus");
    699:   }
    700:   PetscMalloc1(s,&b);
    701:   for (i=0; i<s; i++) b[i] = 0;
    702:   for (j=0,tt=t; j<pinterp; j++,tt*=t) {
    703:     for (i=0; i<s; i++) {
    704:       b[i]  += h * B[i*pinterp+j] * tt;
    705:     }
    706:   }
    707:   VecCopy(glee->YStage[0],X);
    708:   VecMAXPY(X,s,b,glee->YdotStage);
    709:   PetscFree(b);
    710:   return(0);
    711: }

    713: /*------------------------------------------------------------*/
    714: static PetscErrorCode TSReset_GLEE(TS ts)
    715: {
    716:   TS_GLEE        *glee = (TS_GLEE*)ts->data;
    717:   PetscInt       s, r;

    721:   if (!glee->tableau) return(0);
    722:   s    = glee->tableau->s;
    723:   r    = glee->tableau->r;
    724:   VecDestroyVecs(r,&glee->Y);
    725:   VecDestroyVecs(r,&glee->X);
    726:   VecDestroyVecs(s,&glee->YStage);
    727:   VecDestroyVecs(s,&glee->YdotStage);
    728:   VecDestroy(&glee->Ydot);
    729:   VecDestroy(&glee->yGErr);
    730:   VecDestroy(&glee->W);
    731:   PetscFree2(glee->swork,glee->rwork);
    732:   return(0);
    733: }

    735: static PetscErrorCode TSGLEEGetVecs(TS ts,DM dm,Vec *Ydot)
    736: {
    737:   TS_GLEE     *glee = (TS_GLEE*)ts->data;

    741:   if (Ydot) {
    742:     if (dm && dm != ts->dm) {
    743:       DMGetNamedGlobalVector(dm,"TSGLEE_Ydot",Ydot);
    744:     } else *Ydot = glee->Ydot;
    745:   }
    746:   return(0);
    747: }

    750: static PetscErrorCode TSGLEERestoreVecs(TS ts,DM dm,Vec *Ydot)
    751: {

    755:   if (Ydot) {
    756:     if (dm && dm != ts->dm) {
    757:       DMRestoreNamedGlobalVector(dm,"TSGLEE_Ydot",Ydot);
    758:     }
    759:   }
    760:   return(0);
    761: }

    763: /*
    764:   This defines the nonlinear equation that is to be solved with SNES
    765: */
    766: static PetscErrorCode SNESTSFormFunction_GLEE(SNES snes,Vec X,Vec F,TS ts)
    767: {
    768:   TS_GLEE       *glee = (TS_GLEE*)ts->data;
    769:   DM             dm,dmsave;
    770:   Vec            Ydot;
    771:   PetscReal      shift = glee->scoeff / ts->time_step;

    775:   SNESGetDM(snes,&dm);
    776:   TSGLEEGetVecs(ts,dm,&Ydot);
    777:   /* Set Ydot = shift*X */
    778:   VecCopy(X,Ydot);
    779:   VecScale(Ydot,shift);
    780:   dmsave = ts->dm;
    781:   ts->dm = dm;

    783:   TSComputeIFunction(ts,glee->stage_time,X,Ydot,F,PETSC_FALSE);

    785:   ts->dm = dmsave;
    786:   TSGLEERestoreVecs(ts,dm,&Ydot);
    787:   return(0);
    788: }

    790: static PetscErrorCode SNESTSFormJacobian_GLEE(SNES snes,Vec X,Mat A,Mat B,TS ts)
    791: {
    792:   TS_GLEE        *glee = (TS_GLEE*)ts->data;
    793:   DM             dm,dmsave;
    794:   Vec            Ydot;
    795:   PetscReal      shift = glee->scoeff / ts->time_step;

    799:   SNESGetDM(snes,&dm);
    800:   TSGLEEGetVecs(ts,dm,&Ydot);
    801:   /* glee->Ydot has already been computed in SNESTSFormFunction_GLEE (SNES guarantees this) */
    802:   dmsave = ts->dm;
    803:   ts->dm = dm;

    805:   TSComputeIJacobian(ts,glee->stage_time,X,Ydot,shift,A,B,PETSC_FALSE);

    807:   ts->dm = dmsave;
    808:   TSGLEERestoreVecs(ts,dm,&Ydot);
    809:   return(0);
    810: }

    812: static PetscErrorCode DMCoarsenHook_TSGLEE(DM fine,DM coarse,void *ctx)
    813: {
    815:   return(0);
    816: }

    818: static PetscErrorCode DMRestrictHook_TSGLEE(DM fine,Mat restrct,Vec rscale,Mat inject,DM coarse,void *ctx)
    819: {
    821:   return(0);
    822: }

    825: static PetscErrorCode DMSubDomainHook_TSGLEE(DM dm,DM subdm,void *ctx)
    826: {
    828:   return(0);
    829: }

    831: static PetscErrorCode DMSubDomainRestrictHook_TSGLEE(DM dm,VecScatter gscat,VecScatter lscat,DM subdm,void *ctx)
    832: {
    834:   return(0);
    835: }

    837: static PetscErrorCode TSSetUp_GLEE(TS ts)
    838: {
    839:   TS_GLEE        *glee = (TS_GLEE*)ts->data;
    840:   GLEETableau    tab;
    841:   PetscInt       s,r;
    843:   DM             dm;

    846:   if (!glee->tableau) {
    847:     TSGLEESetType(ts,TSGLEEDefaultType);
    848:   }
    849:   tab  = glee->tableau;
    850:   s    = tab->s;
    851:   r    = tab->r;
    852:   VecDuplicateVecs(ts->vec_sol,r,&glee->Y);
    853:   VecDuplicateVecs(ts->vec_sol,r,&glee->X);
    854:   VecDuplicateVecs(ts->vec_sol,s,&glee->YStage);
    855:   VecDuplicateVecs(ts->vec_sol,s,&glee->YdotStage);
    856:   VecDuplicate(ts->vec_sol,&glee->Ydot);
    857:   VecDuplicate(ts->vec_sol,&glee->yGErr);
    858:   VecZeroEntries(glee->yGErr);
    859:   VecDuplicate(ts->vec_sol,&glee->W);
    860:   PetscMalloc2(s,&glee->swork,r,&glee->rwork);
    861:   TSGetDM(ts,&dm);
    862:   DMCoarsenHookAdd(dm,DMCoarsenHook_TSGLEE,DMRestrictHook_TSGLEE,ts);
    863:   DMSubDomainHookAdd(dm,DMSubDomainHook_TSGLEE,DMSubDomainRestrictHook_TSGLEE,ts);
    864:   return(0);
    865: }

    867: PetscErrorCode TSStartingMethod_GLEE(TS ts)
    868: {
    869:   TS_GLEE        *glee = (TS_GLEE*)ts->data;
    870:   GLEETableau    tab  = glee->tableau;
    871:   PetscInt       r=tab->r,i;
    872:   PetscReal      *S=tab->S;

    876:   for (i=0; i<r; i++) {
    877:     VecZeroEntries(glee->Y[i]);
    878:     VecAXPY(glee->Y[i],S[i],ts->vec_sol);
    879:   }

    881:   return(0);
    882: }

    885: /*------------------------------------------------------------*/

    887: static PetscErrorCode TSSetFromOptions_GLEE(PetscOptionItems *PetscOptionsObject,TS ts)
    888: {
    890:   char           gleetype[256];

    893:   PetscOptionsHead(PetscOptionsObject,"GLEE ODE solver options");
    894:   {
    895:     GLEETableauLink link;
    896:     PetscInt        count,choice;
    897:     PetscBool       flg;
    898:     const char      **namelist;

    900:     PetscStrncpy(gleetype,TSGLEEDefaultType,sizeof(gleetype));
    901:     for (link=GLEETableauList,count=0; link; link=link->next,count++) ;
    902:     PetscMalloc1(count,(char***)&namelist);
    903:     for (link=GLEETableauList,count=0; link; link=link->next,count++) namelist[count] = link->tab.name;
    904:     PetscOptionsEList("-ts_glee_type","Family of GLEE method","TSGLEESetType",(const char*const*)namelist,count,gleetype,&choice,&flg);
    905:     TSGLEESetType(ts,flg ? namelist[choice] : gleetype);
    906:     PetscFree(namelist);
    907:   }
    908:   PetscOptionsTail();
    909:   return(0);
    910: }

    912: static PetscErrorCode TSView_GLEE(TS ts,PetscViewer viewer)
    913: {
    914:   TS_GLEE        *glee   = (TS_GLEE*)ts->data;
    915:   GLEETableau    tab  = glee->tableau;
    916:   PetscBool      iascii;

    920:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
    921:   if (iascii) {
    922:     TSGLEEType gleetype;
    923:     char       buf[512];
    924:     TSGLEEGetType(ts,&gleetype);
    925:     PetscViewerASCIIPrintf(viewer,"  GLEE type %s\n",gleetype);
    926:     PetscFormatRealArray(buf,sizeof(buf),"% 8.6f",tab->s,tab->c);
    927:     PetscViewerASCIIPrintf(viewer,"  Abscissa     c = %s\n",buf);
    928:     /* Note: print out r as well */
    929:   }
    930:   return(0);
    931: }

    933: static PetscErrorCode TSLoad_GLEE(TS ts,PetscViewer viewer)
    934: {
    936:   SNES           snes;
    937:   TSAdapt        tsadapt;

    940:   TSGetAdapt(ts,&tsadapt);
    941:   TSAdaptLoad(tsadapt,viewer);
    942:   TSGetSNES(ts,&snes);
    943:   SNESLoad(snes,viewer);
    944:   /* function and Jacobian context for SNES when used with TS is always ts object */
    945:   SNESSetFunction(snes,NULL,NULL,ts);
    946:   SNESSetJacobian(snes,NULL,NULL,NULL,ts);
    947:   return(0);
    948: }

    950: /*@C
    951:   TSGLEESetType - Set the type of GLEE scheme

    953:   Logically collective

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

    959:   Level: intermediate

    961: .seealso: TSGLEEGetType(), TSGLEE
    962: @*/
    963: PetscErrorCode TSGLEESetType(TS ts,TSGLEEType gleetype)
    964: {

    970:   PetscTryMethod(ts,"TSGLEESetType_C",(TS,TSGLEEType),(ts,gleetype));
    971:   return(0);
    972: }

    974: /*@C
    975:   TSGLEEGetType - Get the type of GLEE scheme

    977:   Logically collective

    979:   Input Parameter:
    980: .  ts - timestepping context

    982:   Output Parameter:
    983: .  gleetype - type of GLEE-scheme

    985:   Level: intermediate

    987: .seealso: TSGLEESetType()
    988: @*/
    989: PetscErrorCode TSGLEEGetType(TS ts,TSGLEEType *gleetype)
    990: {

    995:   PetscUseMethod(ts,"TSGLEEGetType_C",(TS,TSGLEEType*),(ts,gleetype));
    996:   return(0);
    997: }

    999: PetscErrorCode  TSGLEEGetType_GLEE(TS ts,TSGLEEType *gleetype)
    1000: {
    1001:   TS_GLEE     *glee = (TS_GLEE*)ts->data;

    1005:   if (!glee->tableau) {
    1006:     TSGLEESetType(ts,TSGLEEDefaultType);
    1007:   }
    1008:   *gleetype = glee->tableau->name;
    1009:   return(0);
    1010: }
    1011: PetscErrorCode  TSGLEESetType_GLEE(TS ts,TSGLEEType gleetype)
    1012: {
    1013:   TS_GLEE         *glee = (TS_GLEE*)ts->data;
    1014:   PetscErrorCode  ierr;
    1015:   PetscBool       match;
    1016:   GLEETableauLink link;

    1019:   if (glee->tableau) {
    1020:     PetscStrcmp(glee->tableau->name,gleetype,&match);
    1021:     if (match) return(0);
    1022:   }
    1023:   for (link = GLEETableauList; link; link=link->next) {
    1024:     PetscStrcmp(link->tab.name,gleetype,&match);
    1025:     if (match) {
    1026:       TSReset_GLEE(ts);
    1027:       glee->tableau = &link->tab;
    1028:       return(0);
    1029:     }
    1030:   }
    1031:   SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_UNKNOWN_TYPE,"Could not find '%s'",gleetype);
    1032: }

    1034: static PetscErrorCode  TSGetStages_GLEE(TS ts,PetscInt *ns,Vec **Y)
    1035: {
    1036:   TS_GLEE *glee = (TS_GLEE*)ts->data;

    1039:   if (ns) *ns = glee->tableau->s;
    1040:   if (Y)  *Y  = glee->YStage;
    1041:   return(0);
    1042: }

    1044: PetscErrorCode TSGetSolutionComponents_GLEE(TS ts,PetscInt *n,Vec *Y)
    1045: {
    1046:   TS_GLEE         *glee = (TS_GLEE*)ts->data;
    1047:   GLEETableau     tab   = glee->tableau;
    1048:   PetscErrorCode  ierr;

    1051:   if (!Y) *n = tab->r;
    1052:   else {
    1053:     if ((*n >= 0) && (*n < tab->r)) {
    1054:       VecCopy(glee->Y[*n],*Y);
    1055:     } else SETERRQ3(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_OUTOFRANGE,"Second argument (%d) out of range[%d,%d].",*n,0,tab->r-1);
    1056:   }
    1057:   return(0);
    1058: }

    1060: PetscErrorCode TSGetAuxSolution_GLEE(TS ts,Vec *X)
    1061: {
    1062:   TS_GLEE         *glee = (TS_GLEE*)ts->data;
    1063:   GLEETableau     tab   = glee->tableau;
    1064:   PetscReal       *F    = tab->Fembed;
    1065:   PetscInt        r     = tab->r;
    1066:   Vec             *Y    = glee->Y;
    1067:   PetscScalar     *wr   = glee->rwork;
    1068:   PetscInt        i;
    1069:   PetscErrorCode  ierr;

    1072:   VecZeroEntries(*X);
    1073:   for (i=0; i<r; i++) wr[i] = F[i];
    1074:   VecMAXPY((*X),r,wr,Y);
    1075:   return(0);
    1076: }

    1078: PetscErrorCode TSGetTimeError_GLEE(TS ts,PetscInt n,Vec *X)
    1079: {
    1080:   TS_GLEE         *glee = (TS_GLEE*)ts->data;
    1081:   GLEETableau     tab   = glee->tableau;
    1082:   PetscReal       *F    = tab->Ferror;
    1083:   PetscInt        r     = tab->r;
    1084:   Vec             *Y    = glee->Y;
    1085:   PetscScalar     *wr   = glee->rwork;
    1086:   PetscInt        i;
    1087:   PetscErrorCode  ierr;

    1090:   VecZeroEntries(*X);
    1091:   if (n==0){
    1092:     for (i=0; i<r; i++) wr[i] = F[i];
    1093:     VecMAXPY((*X),r,wr,Y);
    1094:   } else if (n==-1) {
    1095:     *X=glee->yGErr;
    1096:   }
    1097:   return(0);
    1098: }

    1100: PetscErrorCode TSSetTimeError_GLEE(TS ts,Vec X)
    1101: {
    1102:   TS_GLEE         *glee = (TS_GLEE*)ts->data;
    1103:   GLEETableau     tab   = glee->tableau;
    1104:   PetscReal       *S    = tab->Serror;
    1105:   PetscInt        r     = tab->r,i;
    1106:   Vec             *Y    = glee->Y;
    1107:   PetscErrorCode  ierr;

    1110:   if (r != 2) SETERRQ2(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"TSSetTimeError_GLEE not supported for '%s' with r=%D.",tab->name,tab->r);
    1111:   for (i=1; i<r; i++) {
    1112:     VecCopy(ts->vec_sol,Y[i]);
    1113:     VecAXPBY(Y[i],S[0],S[1],X);
    1114:     VecCopy(X,glee->yGErr);
    1115:   }
    1116:   return(0);
    1117: }

    1119: static PetscErrorCode TSDestroy_GLEE(TS ts)
    1120: {

    1124:   TSReset_GLEE(ts);
    1125:   if (ts->dm) {
    1126:     DMCoarsenHookRemove(ts->dm,DMCoarsenHook_TSGLEE,DMRestrictHook_TSGLEE,ts);
    1127:     DMSubDomainHookRemove(ts->dm,DMSubDomainHook_TSGLEE,DMSubDomainRestrictHook_TSGLEE,ts);
    1128:   }
    1129:   PetscFree(ts->data);
    1130:   PetscObjectComposeFunction((PetscObject)ts,"TSGLEEGetType_C",NULL);
    1131:   PetscObjectComposeFunction((PetscObject)ts,"TSGLEESetType_C",NULL);
    1132:   return(0);
    1133: }

    1135: /* ------------------------------------------------------------ */
    1136: /*MC
    1137:       TSGLEE - ODE and DAE solver using General Linear with Error Estimation schemes

    1139:   The user should provide the right hand side of the equation
    1140:   using TSSetRHSFunction().

    1142:   Notes:
    1143:   The default is TSGLEE35, it can be changed with TSGLEESetType() or -ts_glee_type

    1145:   Level: beginner

    1147: .seealso:  TSCreate(), TS, TSSetType(), TSGLEESetType(), TSGLEEGetType(),
    1148:            TSGLEE23, TTSGLEE24, TSGLEE35, TSGLEE25I, TSGLEEEXRK2A,
    1149:            TSGLEERK32G1, TSGLEERK285EX, TSGLEEType, TSGLEERegister()

    1151: M*/
    1152: PETSC_EXTERN PetscErrorCode TSCreate_GLEE(TS ts)
    1153: {
    1154:   TS_GLEE         *th;
    1155:   PetscErrorCode  ierr;

    1158:   TSGLEEInitializePackage();

    1160:   ts->ops->reset                  = TSReset_GLEE;
    1161:   ts->ops->destroy                = TSDestroy_GLEE;
    1162:   ts->ops->view                   = TSView_GLEE;
    1163:   ts->ops->load                   = TSLoad_GLEE;
    1164:   ts->ops->setup                  = TSSetUp_GLEE;
    1165:   ts->ops->step                   = TSStep_GLEE;
    1166:   ts->ops->interpolate            = TSInterpolate_GLEE;
    1167:   ts->ops->evaluatestep           = TSEvaluateStep_GLEE;
    1168:   ts->ops->setfromoptions         = TSSetFromOptions_GLEE;
    1169:   ts->ops->getstages              = TSGetStages_GLEE;
    1170:   ts->ops->snesfunction           = SNESTSFormFunction_GLEE;
    1171:   ts->ops->snesjacobian           = SNESTSFormJacobian_GLEE;
    1172:   ts->ops->getsolutioncomponents  = TSGetSolutionComponents_GLEE;
    1173:   ts->ops->getauxsolution         = TSGetAuxSolution_GLEE;
    1174:   ts->ops->gettimeerror           = TSGetTimeError_GLEE;
    1175:   ts->ops->settimeerror           = TSSetTimeError_GLEE;
    1176:   ts->ops->startingmethod         = TSStartingMethod_GLEE;
    1177:   ts->default_adapt_type          = TSADAPTGLEE;

    1179:   ts->usessnes = PETSC_TRUE;

    1181:   PetscNewLog(ts,&th);
    1182:   ts->data = (void*)th;

    1184:   PetscObjectComposeFunction((PetscObject)ts,"TSGLEEGetType_C",TSGLEEGetType_GLEE);
    1185:   PetscObjectComposeFunction((PetscObject)ts,"TSGLEESetType_C",TSGLEESetType_GLEE);
    1186:   return(0);
    1187: }