Date: 2022-03-04T17:39:35+00:00

Actual source code: glee.c

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

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

      7:   Udot = F(t,U)

      9: */
     10: #include <petsc/private/tsimpl.h>
     11: #include <petscdm.h>

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

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

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

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

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

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

     71:      Level: advanced

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

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

     81:      Level: advanced

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

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

     91:      Level: advanced

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

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

    101:      Level: advanced

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

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

    111:      Level: advanced

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

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

    121:      Level: advanced

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

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

    131:      Level: advanced

    133: .seealso: TSGLEE
    134: M*/

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

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

    141:   Level: advanced

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

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

    153:   {
    154: #define GAMMA 0.5
    155:     /* y-eps form */
    156:     const PetscInt
    157:       p = 1,
    158:       s = 3,
    159:       r = 2;
    160:     const PetscReal
    161:       A[3][3]   = {{1.0,0,0},{0,0.5,0},{0,0.5,0.5}},
    162:       B[2][3]   = {{1.0,0,0},{-2.0,1.0,1.0}},
    163:       U[3][2]   = {{1.0,0},{1.0,0.5},{1.0,0.5}},
    164:       V[2][2]   = {{1,0},{0,1}},
    165:       S[2]      = {1,0},
    166:       F[2]      = {1,0},
    167:       Fembed[2] = {1,1-GAMMA},
    168:       Ferror[2] = {0,1},
    169:       Serror[2] = {1,0};
    170:     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);
    171:   }
    172:   {
    173: #undef GAMMA
    174: #define GAMMA 0.0
    175:     /* y-eps form */
    176:     const PetscInt
    177:       p = 2,
    178:       s = 3,
    179:       r = 2;
    180:     const PetscReal
    181:       A[3][3]   = {{0,0,0},{1,0,0},{0.25,0.25,0}},
    182:       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}},
    183:       U[3][2]   = {{1,0},{1,10},{1,-1}},
    184:       V[2][2]   = {{1,0},{0,1}},
    185:       S[2]      = {1,0},
    186:       F[2]      = {1,0},
    187:       Fembed[2] = {1,1-GAMMA},
    188:       Ferror[2] = {0,1},
    189:       Serror[2] = {1,0};
    190:     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);
    191:   }
    192:   {
    193: #undef GAMMA
    194: #define GAMMA 0.0
    195:     /* y-y~ form */
    196:     const PetscInt
    197:       p = 2,
    198:       s = 4,
    199:       r = 2;
    200:     const PetscReal
    201:       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}},
    202:       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}},
    203:       U[4][2]   = {{0,1},{75.0/58.0,-17.0/58.0},{0,1},{0,1}},
    204:       V[2][2]   = {{1,0},{0,1}},
    205:       S[2]      = {1,1},
    206:       F[2]      = {1,0},
    207:       Fembed[2] = {0,1},
    208:       Ferror[2] = {-1.0/(1.0-GAMMA),1.0/(1.0-GAMMA)},
    209:       Serror[2] = {1.0-GAMMA,1.0};
    210:       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);
    211:   }
    212:   {
    213: #undef GAMMA
    214: #define GAMMA 0.0
    215:     /* y-y~ form */
    216:     const PetscInt
    217:       p = 2,
    218:       s = 5,
    219:       r = 2;
    220:     const PetscReal
    221:       A[5][5]   = {{0,0,0,0,0},
    222:                    {-0.94079244066783383269,0,0,0,0},
    223:                    {0.64228187778301907108,0.10915356933958500042,0,0,0},
    224:                    {-0.51764297742287450812,0.74414270351096040738,-0.71404164927824538121,0,0},
    225:                    {-0.44696561556825969206,-0.76768425657590196518,0.20111608138142987881,0.93828186737840469796,0}},
    226:       B[2][5]   = {{-0.029309178948150356153,-0.49671981884013874923,0.34275801517650053274,0.32941112623949194988,0.85385985637229662276},
    227:                    {0.78133219686062535272,0.074238691892675897635,0.57957363498384957966,-0.24638502829674959968,-0.18875949544040123033}},
    228:       U[5][2]   = {{0.16911424754448327735,0.83088575245551672265},
    229:                    {0.53638465733199574340,0.46361534266800425660},
    230:                    {0.39901579167169582526,0.60098420832830417474},
    231:                    {0.87689005530618575480,0.12310994469381424520},
    232:                    {0.99056100455550913009,0.0094389954444908699092}},
    233:       V[2][2]   = {{1,0},{0,1}},
    234:       S[2]      = {1,1},
    235:       F[2]      = {1,0},
    236:       Fembed[2] = {0,1},
    237:       Ferror[2] = {-1.0/(1.0-GAMMA),1.0/(1.0-GAMMA)},
    238:       Serror[2] = {1.0-GAMMA,1.0};
    239:     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);
    240:   }
    241:   {
    242: #undef GAMMA
    243: #define GAMMA 0.0
    244:     /* y-y~ form */
    245:     const PetscInt
    246:       p = 3,
    247:       s = 5,
    248:       r = 2;
    249:     const PetscReal
    250:       A[5][5]   = {{0,0,0,0,0},
    251:                    {- 2169604947363702313.0 /  24313474998937147335.0,0,0,0,0},
    252:                    {46526746497697123895.0 /  94116917485856474137.0,-10297879244026594958.0 /  49199457603717988219.0,0,0,0},
    253:                    {23364788935845982499.0 /  87425311444725389446.0,-79205144337496116638.0 / 148994349441340815519.0,40051189859317443782.0 /  36487615018004984309.0,0,0},
    254:                    {42089522664062539205.0 / 124911313006412840286.0,-15074384760342762939.0 / 137927286865289746282.0,-62274678522253371016.0 / 125918573676298591413.0,13755475729852471739.0 /  79257927066651693390.0,0}},
    255:       B[2][5]   = {{61546696837458703723.0 /  56982519523786160813.0,-55810892792806293355.0 / 206957624151308356511.0,24061048952676379087.0 / 158739347956038723465.0,3577972206874351339.0 /   7599733370677197135.0,-59449832954780563947.0 / 137360038685338563670.0},
    256:                    {- 9738262186984159168.0 /  99299082461487742983.0,-32797097931948613195.0 /  61521565616362163366.0,42895514606418420631.0 /  71714201188501437336.0,22608567633166065068.0 /  55371917805607957003.0,94655809487476459565.0 / 151517167160302729021.0}},
    257:       U[5][2]   = {{70820309139834661559.0 /  80863923579509469826.0,10043614439674808267.0 /  80863923579509469826.0},
    258:                    {161694774978034105510.0 / 106187653640211060371.0,-55507121337823045139.0 / 106187653640211060371.0},
    259:                    {78486094644566264568.0 /  88171030896733822981.0,9684936252167558413.0 /  88171030896733822981.0},
    260:                    {65394922146334854435.0 /  84570853840405479554.0,19175931694070625119.0 /  84570853840405479554.0},
    261:                    {8607282770183754108.0 / 108658046436496925911.0,100050763666313171803.0 / 108658046436496925911.0}},
    262:       V[2][2]   = {{1,0},{0,1}},
    263:       S[2]      = {1,1},
    264:       F[2]      = {1,0},
    265:       Fembed[2] = {0,1},
    266:       Ferror[2] = {-1.0/(1.0-GAMMA),1.0/(1.0-GAMMA)},
    267:       Serror[2] = {1.0-GAMMA,1.0};
    268:     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);
    269:   }
    270:   {
    271: #undef GAMMA
    272: #define GAMMA 0.25
    273:     /* y-eps form */
    274:     const PetscInt
    275:       p = 2,
    276:       s = 6,
    277:       r = 2;
    278:     const PetscReal
    279:       A[6][6]   = {{0,0,0,0,0,0},
    280:                    {1,0,0,0,0,0},
    281:                    {0,0,0,0,0,0},
    282:                    {0,0,0.5,0,0,0},
    283:                    {0,0,0.25,0.25,0,0},
    284:                    {0,0,0.25,0.25,0.5,0}},
    285:       B[2][6]   = {{0.5,0.5,0,0,0,0},
    286:                    {-2.0/3.0,-2.0/3.0,1.0/3.0,1.0/3.0,1.0/3.0,1.0/3.0}},
    287:       U[6][2]   = {{1,0},{1,0},{1,0.75},{1,0.75},{1,0.75},{1,0.75}},
    288:       V[2][2]   = {{1,0},{0,1}},
    289:       S[2]      = {1,0},
    290:       F[2]      = {1,0},
    291:       Fembed[2] = {1,1-GAMMA},
    292:       Ferror[2] = {0,1},
    293:       Serror[2] = {1,0};
    294:     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);
    295:   }
    296:   {
    297: #undef GAMMA
    298: #define GAMMA 0.0
    299:     /* y-eps form */
    300:     const PetscInt
    301:       p = 3,
    302:       s = 8,
    303:       r = 2;
    304:     const PetscReal
    305:       A[8][8]   = {{0,0,0,0,0,0,0,0},
    306:                    {0.5,0,0,0,0,0,0,0},
    307:                    {-1,2,0,0,0,0,0,0},
    308:                    {1.0/6.0,2.0/3.0,1.0/6.0,0,0,0,0,0},
    309:                    {0,0,0,0,0,0,0,0},
    310:                    {-7.0/24.0,1.0/3.0,1.0/12.0,-1.0/8.0,0.5,0,0,0},
    311:                    {7.0/6.0,-4.0/3.0,-1.0/3.0,0.5,-1.0,2.0,0,0},
    312:                    {0,0,0,0,1.0/6.0,2.0/3.0,1.0/6.0,0}},
    313:       B[2][8]   = {{1.0/6.0,2.0/3.0,1.0/6.0,0,0,0,0,0},
    314:                    {-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}},
    315:       U[8][2]   = {{1,0},{1,0},{1,0},{1,0},{1,1},{1,1},{1,1},{1,1}},
    316:       V[2][2]   = {{1,0},{0,1}},
    317:       S[2]      = {1,0},
    318:       F[2]      = {1,0},
    319:       Fembed[2] = {1,1-GAMMA},
    320:       Ferror[2] = {0,1},
    321:       Serror[2] = {1,0};
    322:     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);
    323:   }
    324:   {
    325: #undef GAMMA
    326: #define GAMMA 0.25
    327:     /* y-eps form */
    328:     const PetscInt
    329:       p = 2,
    330:       s = 9,
    331:       r = 2;
    332:     const PetscReal
    333:       A[9][9]   = {{0,0,0,0,0,0,0,0,0},
    334:                    {0.585786437626904966,0,0,0,0,0,0,0,0},
    335:                    {0.149999999999999994,0.849999999999999978,0,0,0,0,0,0,0},
    336:                    {0,0,0,0,0,0,0,0,0},
    337:                    {0,0,0,0.292893218813452483,0,0,0,0,0},
    338:                    {0,0,0,0.0749999999999999972,0.424999999999999989,0,0,0,0},
    339:                    {0,0,0,0.176776695296636893,0.176776695296636893,0.146446609406726241,0,0,0},
    340:                    {0,0,0,0.176776695296636893,0.176776695296636893,0.146446609406726241,0.292893218813452483,0,0},
    341:                    {0,0,0,0.176776695296636893,0.176776695296636893,0.146446609406726241,0.0749999999999999972,0.424999999999999989,0}},
    342:       B[2][9]   = {{0.353553390593273786,0.353553390593273786,0.292893218813452483,0,0,0,0,0,0},
    343:                    {-0.471404520791031678,-0.471404520791031678,-0.390524291751269959,0.235702260395515839,0.235702260395515839,0.195262145875634979,0.235702260395515839,0.235702260395515839,0.195262145875634979}},
    344:       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}},
    345:       V[2][2]   = {{1,0},{0,1}},
    346:       S[2]      = {1,0},
    347:       F[2]      = {1,0},
    348:       Fembed[2] = {1,1-GAMMA},
    349:       Ferror[2] = {0,1},
    350:       Serror[2] = {1,0};
    351:     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);
    352:   }

    354:   return(0);
    355: }

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

    360:    Not Collective

    362:    Level: advanced

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

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

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

    392:   Level: developer

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

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

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

    413:   Level: developer

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

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

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

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

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

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

    454:    Level: advanced

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

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

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

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

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

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

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

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

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

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

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

    597:   PetscCitationsRegister(citation,&cited);

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

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

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

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

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

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

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

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

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

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

    712: /*------------------------------------------------------------*/
    713: static PetscErrorCode TSReset_GLEE(TS ts)
    714: {
    715:   TS_GLEE        *glee = (TS_GLEE*)ts->data;
    716:   PetscInt       s, r;

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

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

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

    748: static PetscErrorCode TSGLEERestoreVecs(TS ts,DM dm,Vec *Ydot)
    749: {

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

    761: /*
    762:   This defines the nonlinear equation that is to be solved with SNES
    763: */
    764: static PetscErrorCode SNESTSFormFunction_GLEE(SNES snes,Vec X,Vec F,TS ts)
    765: {
    766:   TS_GLEE       *glee = (TS_GLEE*)ts->data;
    767:   DM             dm,dmsave;
    768:   Vec            Ydot;
    769:   PetscReal      shift = glee->scoeff / ts->time_step;

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

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

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

    788: static PetscErrorCode SNESTSFormJacobian_GLEE(SNES snes,Vec X,Mat A,Mat B,TS ts)
    789: {
    790:   TS_GLEE        *glee = (TS_GLEE*)ts->data;
    791:   DM             dm,dmsave;
    792:   Vec            Ydot;
    793:   PetscReal      shift = glee->scoeff / ts->time_step;

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

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

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

    810: static PetscErrorCode DMCoarsenHook_TSGLEE(DM fine,DM coarse,void *ctx)
    811: {
    813:   return(0);
    814: }

    816: static PetscErrorCode DMRestrictHook_TSGLEE(DM fine,Mat restrct,Vec rscale,Mat inject,DM coarse,void *ctx)
    817: {
    819:   return(0);
    820: }

    822: static PetscErrorCode DMSubDomainHook_TSGLEE(DM dm,DM subdm,void *ctx)
    823: {
    825:   return(0);
    826: }

    828: static PetscErrorCode DMSubDomainRestrictHook_TSGLEE(DM dm,VecScatter gscat,VecScatter lscat,DM subdm,void *ctx)
    829: {
    831:   return(0);
    832: }

    834: static PetscErrorCode TSSetUp_GLEE(TS ts)
    835: {
    836:   TS_GLEE        *glee = (TS_GLEE*)ts->data;
    837:   GLEETableau    tab;
    838:   PetscInt       s,r;
    840:   DM             dm;

    843:   if (!glee->tableau) {
    844:     TSGLEESetType(ts,TSGLEEDefaultType);
    845:   }
    846:   tab  = glee->tableau;
    847:   s    = tab->s;
    848:   r    = tab->r;
    849:   VecDuplicateVecs(ts->vec_sol,r,&glee->Y);
    850:   VecDuplicateVecs(ts->vec_sol,r,&glee->X);
    851:   VecDuplicateVecs(ts->vec_sol,s,&glee->YStage);
    852:   VecDuplicateVecs(ts->vec_sol,s,&glee->YdotStage);
    853:   VecDuplicate(ts->vec_sol,&glee->Ydot);
    854:   VecDuplicate(ts->vec_sol,&glee->yGErr);
    855:   VecZeroEntries(glee->yGErr);
    856:   VecDuplicate(ts->vec_sol,&glee->W);
    857:   PetscMalloc2(s,&glee->swork,r,&glee->rwork);
    858:   TSGetDM(ts,&dm);
    859:   DMCoarsenHookAdd(dm,DMCoarsenHook_TSGLEE,DMRestrictHook_TSGLEE,ts);
    860:   DMSubDomainHookAdd(dm,DMSubDomainHook_TSGLEE,DMSubDomainRestrictHook_TSGLEE,ts);
    861:   return(0);
    862: }

    864: PetscErrorCode TSStartingMethod_GLEE(TS ts)
    865: {
    866:   TS_GLEE        *glee = (TS_GLEE*)ts->data;
    867:   GLEETableau    tab  = glee->tableau;
    868:   PetscInt       r=tab->r,i;
    869:   PetscReal      *S=tab->S;

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

    878:   return(0);
    879: }

    881: /*------------------------------------------------------------*/

    883: static PetscErrorCode TSSetFromOptions_GLEE(PetscOptionItems *PetscOptionsObject,TS ts)
    884: {
    886:   char           gleetype[256];

    889:   PetscOptionsHead(PetscOptionsObject,"GLEE ODE solver options");
    890:   {
    891:     GLEETableauLink link;
    892:     PetscInt        count,choice;
    893:     PetscBool       flg;
    894:     const char      **namelist;

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

    908: static PetscErrorCode TSView_GLEE(TS ts,PetscViewer viewer)
    909: {
    910:   TS_GLEE        *glee   = (TS_GLEE*)ts->data;
    911:   GLEETableau    tab  = glee->tableau;
    912:   PetscBool      iascii;

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

    929: static PetscErrorCode TSLoad_GLEE(TS ts,PetscViewer viewer)
    930: {
    932:   SNES           snes;
    933:   TSAdapt        tsadapt;

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

    946: /*@C
    947:   TSGLEESetType - Set the type of GLEE scheme

    949:   Logically collective

    951:   Input Parameters:
    952: +  ts - timestepping context
    953: -  gleetype - type of GLEE-scheme

    955:   Level: intermediate

    957: .seealso: TSGLEEGetType(), TSGLEE
    958: @*/
    959: PetscErrorCode TSGLEESetType(TS ts,TSGLEEType gleetype)
    960: {

    966:   PetscTryMethod(ts,"TSGLEESetType_C",(TS,TSGLEEType),(ts,gleetype));
    967:   return(0);
    968: }

    970: /*@C
    971:   TSGLEEGetType - Get the type of GLEE scheme

    973:   Logically collective

    975:   Input Parameter:
    976: .  ts - timestepping context

    978:   Output Parameter:
    979: .  gleetype - type of GLEE-scheme

    981:   Level: intermediate

    983: .seealso: TSGLEESetType()
    984: @*/
    985: PetscErrorCode TSGLEEGetType(TS ts,TSGLEEType *gleetype)
    986: {

    991:   PetscUseMethod(ts,"TSGLEEGetType_C",(TS,TSGLEEType*),(ts,gleetype));
    992:   return(0);
    993: }

    995: PetscErrorCode  TSGLEEGetType_GLEE(TS ts,TSGLEEType *gleetype)
    996: {
    997:   TS_GLEE     *glee = (TS_GLEE*)ts->data;

    1001:   if (!glee->tableau) {
    1002:     TSGLEESetType(ts,TSGLEEDefaultType);
    1003:   }
    1004:   *gleetype = glee->tableau->name;
    1005:   return(0);
    1006: }
    1007: PetscErrorCode  TSGLEESetType_GLEE(TS ts,TSGLEEType gleetype)
    1008: {
    1009:   TS_GLEE         *glee = (TS_GLEE*)ts->data;
    1010:   PetscErrorCode  ierr;
    1011:   PetscBool       match;
    1012:   GLEETableauLink link;

    1015:   if (glee->tableau) {
    1016:     PetscStrcmp(glee->tableau->name,gleetype,&match);
    1017:     if (match) return(0);
    1018:   }
    1019:   for (link = GLEETableauList; link; link=link->next) {
    1020:     PetscStrcmp(link->tab.name,gleetype,&match);
    1021:     if (match) {
    1022:       TSReset_GLEE(ts);
    1023:       glee->tableau = &link->tab;
    1024:       return(0);
    1025:     }
    1026:   }
    1027:   SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_UNKNOWN_TYPE,"Could not find '%s'",gleetype);
    1028: }

    1030: static PetscErrorCode  TSGetStages_GLEE(TS ts,PetscInt *ns,Vec **Y)
    1031: {
    1032:   TS_GLEE *glee = (TS_GLEE*)ts->data;

    1035:   if (ns) *ns = glee->tableau->s;
    1036:   if (Y)  *Y  = glee->YStage;
    1037:   return(0);
    1038: }

    1040: PetscErrorCode TSGetSolutionComponents_GLEE(TS ts,PetscInt *n,Vec *Y)
    1041: {
    1042:   TS_GLEE         *glee = (TS_GLEE*)ts->data;
    1043:   GLEETableau     tab   = glee->tableau;
    1044:   PetscErrorCode  ierr;

    1047:   if (!Y) *n = tab->r;
    1048:   else {
    1049:     if ((*n >= 0) && (*n < tab->r)) {
    1050:       VecCopy(glee->Y[*n],*Y);
    1051:     } else SETERRQ3(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_OUTOFRANGE,"Second argument (%d) out of range[%d,%d].",*n,0,tab->r-1);
    1052:   }
    1053:   return(0);
    1054: }

    1056: PetscErrorCode TSGetAuxSolution_GLEE(TS ts,Vec *X)
    1057: {
    1058:   TS_GLEE         *glee = (TS_GLEE*)ts->data;
    1059:   GLEETableau     tab   = glee->tableau;
    1060:   PetscReal       *F    = tab->Fembed;
    1061:   PetscInt        r     = tab->r;
    1062:   Vec             *Y    = glee->Y;
    1063:   PetscScalar     *wr   = glee->rwork;
    1064:   PetscInt        i;
    1065:   PetscErrorCode  ierr;

    1068:   VecZeroEntries(*X);
    1069:   for (i=0; i<r; i++) wr[i] = F[i];
    1070:   VecMAXPY((*X),r,wr,Y);
    1071:   return(0);
    1072: }

    1074: PetscErrorCode TSGetTimeError_GLEE(TS ts,PetscInt n,Vec *X)
    1075: {
    1076:   TS_GLEE         *glee = (TS_GLEE*)ts->data;
    1077:   GLEETableau     tab   = glee->tableau;
    1078:   PetscReal       *F    = tab->Ferror;
    1079:   PetscInt        r     = tab->r;
    1080:   Vec             *Y    = glee->Y;
    1081:   PetscScalar     *wr   = glee->rwork;
    1082:   PetscInt        i;
    1083:   PetscErrorCode  ierr;

    1086:   VecZeroEntries(*X);
    1087:   if (n==0) {
    1088:     for (i=0; i<r; i++) wr[i] = F[i];
    1089:     VecMAXPY((*X),r,wr,Y);
    1090:   } else if (n==-1) {
    1091:     *X=glee->yGErr;
    1092:   }
    1093:   return(0);
    1094: }

    1096: PetscErrorCode TSSetTimeError_GLEE(TS ts,Vec X)
    1097: {
    1098:   TS_GLEE         *glee = (TS_GLEE*)ts->data;
    1099:   GLEETableau     tab   = glee->tableau;
    1100:   PetscReal       *S    = tab->Serror;
    1101:   PetscInt        r     = tab->r,i;
    1102:   Vec             *Y    = glee->Y;
    1103:   PetscErrorCode  ierr;

    1106:   if (r != 2) SETERRQ2(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"TSSetTimeError_GLEE not supported for '%s' with r=%D.",tab->name,tab->r);
    1107:   for (i=1; i<r; i++) {
    1108:     VecCopy(ts->vec_sol,Y[i]);
    1109:     VecAXPBY(Y[i],S[0],S[1],X);
    1110:     VecCopy(X,glee->yGErr);
    1111:   }
    1112:   return(0);
    1113: }

    1115: static PetscErrorCode TSDestroy_GLEE(TS ts)
    1116: {

    1120:   TSReset_GLEE(ts);
    1121:   if (ts->dm) {
    1122:     DMCoarsenHookRemove(ts->dm,DMCoarsenHook_TSGLEE,DMRestrictHook_TSGLEE,ts);
    1123:     DMSubDomainHookRemove(ts->dm,DMSubDomainHook_TSGLEE,DMSubDomainRestrictHook_TSGLEE,ts);
    1124:   }
    1125:   PetscFree(ts->data);
    1126:   PetscObjectComposeFunction((PetscObject)ts,"TSGLEEGetType_C",NULL);
    1127:   PetscObjectComposeFunction((PetscObject)ts,"TSGLEESetType_C",NULL);
    1128:   return(0);
    1129: }

    1131: /* ------------------------------------------------------------ */
    1132: /*MC
    1133:       TSGLEE - ODE and DAE solver using General Linear with Error Estimation schemes

    1135:   The user should provide the right hand side of the equation
    1136:   using TSSetRHSFunction().

    1138:   Notes:
    1139:   The default is TSGLEE35, it can be changed with TSGLEESetType() or -ts_glee_type

    1141:   Level: beginner

    1143: .seealso:  TSCreate(), TS, TSSetType(), TSGLEESetType(), TSGLEEGetType(),
    1144:            TSGLEE23, TTSGLEE24, TSGLEE35, TSGLEE25I, TSGLEEEXRK2A,
    1145:            TSGLEERK32G1, TSGLEERK285EX, TSGLEEType, TSGLEERegister()

    1147: M*/
    1148: PETSC_EXTERN PetscErrorCode TSCreate_GLEE(TS ts)
    1149: {
    1150:   TS_GLEE         *th;
    1151:   PetscErrorCode  ierr;

    1154:   TSGLEEInitializePackage();

    1156:   ts->ops->reset                  = TSReset_GLEE;
    1157:   ts->ops->destroy                = TSDestroy_GLEE;
    1158:   ts->ops->view                   = TSView_GLEE;
    1159:   ts->ops->load                   = TSLoad_GLEE;
    1160:   ts->ops->setup                  = TSSetUp_GLEE;
    1161:   ts->ops->step                   = TSStep_GLEE;
    1162:   ts->ops->interpolate            = TSInterpolate_GLEE;
    1163:   ts->ops->evaluatestep           = TSEvaluateStep_GLEE;
    1164:   ts->ops->setfromoptions         = TSSetFromOptions_GLEE;
    1165:   ts->ops->getstages              = TSGetStages_GLEE;
    1166:   ts->ops->snesfunction           = SNESTSFormFunction_GLEE;
    1167:   ts->ops->snesjacobian           = SNESTSFormJacobian_GLEE;
    1168:   ts->ops->getsolutioncomponents  = TSGetSolutionComponents_GLEE;
    1169:   ts->ops->getauxsolution         = TSGetAuxSolution_GLEE;
    1170:   ts->ops->gettimeerror           = TSGetTimeError_GLEE;
    1171:   ts->ops->settimeerror           = TSSetTimeError_GLEE;
    1172:   ts->ops->startingmethod         = TSStartingMethod_GLEE;
    1173:   ts->default_adapt_type          = TSADAPTGLEE;

    1175:   ts->usessnes = PETSC_TRUE;

    1177:   PetscNewLog(ts,&th);
    1178:   ts->data = (void*)th;

    1180:   PetscObjectComposeFunction((PetscObject)ts,"TSGLEEGetType_C",TSGLEEGetType_GLEE);
    1181:   PetscObjectComposeFunction((PetscObject)ts,"TSGLEESetType_C",TSGLEESetType_GLEE);
    1182:   return(0);
    1183: }