Date: 2025-03-28T21:11:17+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[] = "@ARTICLE{Constantinescu_TR2016b,\n"
     15:                                " author = {Constantinescu, E.M.},\n"
     16:                                " title = {Estimating Global Errors in Time Stepping},\n"
     17:                                " journal = {ArXiv e-prints},\n"
     18:                                " year = 2016,\n"
     19:                                " adsurl = {http://adsabs.harvard.edu/abs/2015arXiv150305166C}\n}\n";

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

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

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

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

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

     70:      Level: advanced

     72: .seealso: [](ch_ts), `TSGLEE`
     73: M*/
     74: /*MC
     75:      TSGLEE24 - Second order four stage GLEE method

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

     80:      Level: advanced

     82: .seealso: [](ch_ts), `TSGLEE`
     83: M*/
     84: /*MC
     85:      TSGLEE25i - Second order five stage GLEE method

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

     90:      Level: advanced

     92: .seealso: [](ch_ts), `TSGLEE`
     93: M*/
     94: /*MC
     95:      TSGLEE35  - Third order five stage GLEE method

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

    100:      Level: advanced

    102: .seealso: [](ch_ts), `TSGLEE`
    103: M*/
    104: /*MC
    105:      TSGLEEEXRK2A  - Second order six stage GLEE method

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

    110:      Level: advanced

    112: .seealso: [](ch_ts), `TSGLEE`
    113: M*/
    114: /*MC
    115:      TSGLEERK32G1  - Third order eight stage GLEE method

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

    120:      Level: advanced

    122: .seealso: [](ch_ts), `TSGLEE`
    123: M*/
    124: /*MC
    125:      TSGLEERK285EX  - Second order nine stage GLEE method

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

    130:      Level: advanced

    132: .seealso: [](ch_ts), `TSGLEE`
    133: M*/

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

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

    140:   Level: advanced

    142: .seealso: [](ch_ts), `TSGLEERegisterDestroy()`
    143: @*/
    144: PetscErrorCode TSGLEERegisterAll(void)
    145: {
    146:   PetscFunctionBegin;
    147:   if (TSGLEERegisterAllCalled) PetscFunctionReturn(PETSC_SUCCESS);
    148:   TSGLEERegisterAllCalled = PETSC_TRUE;

    150:   {
    151: #define GAMMA 0.5
    152:     /* y-eps form */
    153:     const PetscInt  p = 1, s = 3, r = 2;
    154:     const PetscReal A[3][3] =
    155:       {
    156:         {1.0, 0,   0  },
    157:         {0,   0.5, 0  },
    158:         {0,   0.5, 0.5}
    159:     },
    160:                     B[2][3] = {{1.0, 0, 0}, {-2.0, 1.0, 1.0}}, U[3][2] = {{1.0, 0}, {1.0, 0.5}, {1.0, 0.5}}, V[2][2] = {{1, 0}, {0, 1}}, S[2] = {1, 0}, F[2] = {1, 0}, Fembed[2] = {1, 1 - GAMMA}, Ferror[2] = {0, 1}, Serror[2] = {1, 0};
    161:     PetscCall(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));
    162:   }
    163:   {
    164: #undef GAMMA
    165: #define GAMMA 0.0
    166:     /* y-eps form */
    167:     const PetscInt  p = 2, s = 3, r = 2;
    168:     const PetscReal A[3][3] =
    169:       {
    170:         {0,    0,    0},
    171:         {1,    0,    0},
    172:         {0.25, 0.25, 0}
    173:     },
    174:                     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 - GAMMA}, Ferror[2] = {0, 1}, Serror[2] = {1, 0};
    175:     PetscCall(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));
    176:   }
    177:   {
    178: #undef GAMMA
    179: #define GAMMA 0.0
    180:     /* y-y~ form */
    181:     const PetscInt  p = 2, s = 4, r = 2;
    182:     const PetscReal A[4][4] =
    183:       {
    184:         {0,            0,            0,            0},
    185:         {0.75,         0,            0,            0},
    186:         {0.25,         29.0 / 60.0,  0,            0},
    187:         {-21.0 / 44.0, 145.0 / 44.0, -20.0 / 11.0, 0}
    188:     },
    189:                     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}, Ferror[2] = {-1.0 / (1.0 - GAMMA), 1.0 / (1.0 - GAMMA)}, Serror[2] = {1.0 - GAMMA, 1.0};
    190:     PetscCall(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));
    191:   }
    192:   {
    193: #undef GAMMA
    194: #define GAMMA 0.0
    195:     /* y-y~ form */
    196:     const PetscInt  p = 2, s = 5, r = 2;
    197:     const PetscReal A[5][5] =
    198:       {
    199:         {0,                       0,                       0,                       0,                      0},
    200:         {-0.94079244066783383269, 0,                       0,                       0,                      0},
    201:         {0.64228187778301907108,  0.10915356933958500042,  0,                       0,                      0},
    202:         {-0.51764297742287450812, 0.74414270351096040738,  -0.71404164927824538121, 0,                      0},
    203:         {-0.44696561556825969206, -0.76768425657590196518, 0.20111608138142987881,  0.93828186737840469796, 0}
    204:     },
    205:                     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}, Ferror[2] = {-1.0 / (1.0 - GAMMA), 1.0 / (1.0 - GAMMA)}, Serror[2] = {1.0 - GAMMA, 1.0};
    206:     PetscCall(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));
    207:   }
    208:   {
    209: #undef GAMMA
    210: #define GAMMA 0.0
    211:     /* y-y~ form */
    212:     const PetscInt  p = 3, s = 5, r = 2;
    213:     const PetscReal A[5][5] =
    214:       {
    215:         {0,                                                0,                                                 0,                                                 0,                                               0},
    216:         {-2169604947363702313.0 / 24313474998937147335.0,  0,                                                 0,                                                 0,                                               0},
    217:         {46526746497697123895.0 / 94116917485856474137.0,  -10297879244026594958.0 / 49199457603717988219.0,  0,                                                 0,                                               0},
    218:         {23364788935845982499.0 / 87425311444725389446.0,  -79205144337496116638.0 / 148994349441340815519.0, 40051189859317443782.0 / 36487615018004984309.0,   0,                                               0},
    219:         {42089522664062539205.0 / 124911313006412840286.0, -15074384760342762939.0 / 137927286865289746282.0, -62274678522253371016.0 / 125918573676298591413.0, 13755475729852471739.0 / 79257927066651693390.0, 0}
    220:     },
    221:                     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}, Ferror[2] = {-1.0 / (1.0 - GAMMA), 1.0 / (1.0 - GAMMA)}, Serror[2] = {1.0 - GAMMA, 1.0};
    222:     PetscCall(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));
    223:   }
    224:   {
    225: #undef GAMMA
    226: #define GAMMA 0.25
    227:     /* y-eps form */
    228:     const PetscInt  p = 2, s = 6, r = 2;
    229:     const PetscReal A[6][6] =
    230:       {
    231:         {0, 0, 0,    0,    0,   0},
    232:         {1, 0, 0,    0,    0,   0},
    233:         {0, 0, 0,    0,    0,   0},
    234:         {0, 0, 0.5,  0,    0,   0},
    235:         {0, 0, 0.25, 0.25, 0,   0},
    236:         {0, 0, 0.25, 0.25, 0.5, 0}
    237:     },
    238:                     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, 1 - GAMMA}, Ferror[2] = {0, 1}, Serror[2] = {1, 0};
    239:     PetscCall(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));
    240:   }
    241:   {
    242: #undef GAMMA
    243: #define GAMMA 0.0
    244:     /* y-eps form */
    245:     const PetscInt  p = 3, s = 8, r = 2;
    246:     const PetscReal A[8][8] =
    247:       {
    248:         {0,           0,          0,          0,          0,         0,         0,         0},
    249:         {0.5,         0,          0,          0,          0,         0,         0,         0},
    250:         {-1,          2,          0,          0,          0,         0,         0,         0},
    251:         {1.0 / 6.0,   2.0 / 3.0,  1.0 / 6.0,  0,          0,         0,         0,         0},
    252:         {0,           0,          0,          0,          0,         0,         0,         0},
    253:         {-7.0 / 24.0, 1.0 / 3.0,  1.0 / 12.0, -1.0 / 8.0, 0.5,       0,         0,         0},
    254:         {7.0 / 6.0,   -4.0 / 3.0, -1.0 / 3.0, 0.5,        -1.0,      2.0,       0,         0},
    255:         {0,           0,          0,          0,          1.0 / 6.0, 2.0 / 3.0, 1.0 / 6.0, 0}
    256:     },
    257:                     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 - GAMMA}, Ferror[2] = {0, 1}, Serror[2] = {1, 0};
    258:     PetscCall(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));
    259:   }
    260:   {
    261: #undef GAMMA
    262: #define GAMMA 0.25
    263:     /* y-eps form */
    264:     const PetscInt  p = 2, s = 9, r = 2;
    265:     const PetscReal A[9][9] =
    266:       {
    267:         {0,                    0,                    0, 0,                     0,                    0,                    0,                     0,                    0},
    268:         {0.585786437626904966, 0,                    0, 0,                     0,                    0,                    0,                     0,                    0},
    269:         {0.149999999999999994, 0.849999999999999978, 0, 0,                     0,                    0,                    0,                     0,                    0},
    270:         {0,                    0,                    0, 0,                     0,                    0,                    0,                     0,                    0},
    271:         {0,                    0,                    0, 0.292893218813452483,  0,                    0,                    0,                     0,                    0},
    272:         {0,                    0,                    0, 0.0749999999999999972, 0.424999999999999989, 0,                    0,                     0,                    0},
    273:         {0,                    0,                    0, 0.176776695296636893,  0.176776695296636893, 0.146446609406726241, 0,                     0,                    0},
    274:         {0,                    0,                    0, 0.176776695296636893,  0.176776695296636893, 0.146446609406726241, 0.292893218813452483,  0,                    0},
    275:         {0,                    0,                    0, 0.176776695296636893,  0.176776695296636893, 0.146446609406726241, 0.0749999999999999972, 0.424999999999999989, 0}
    276:     },
    277:                     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, 1 - GAMMA}, Ferror[2] = {0, 1}, Serror[2] = {1, 0};
    278:     PetscCall(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));
    279:   }
    280:   PetscFunctionReturn(PETSC_SUCCESS);
    281: }

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

    286:   Not Collective

    288:   Level: advanced

    290: .seealso: [](ch_ts), `TSGLEERegister()`, `TSGLEERegisterAll()`
    291: @*/
    292: PetscErrorCode TSGLEERegisterDestroy(void)
    293: {
    294:   GLEETableauLink link;

    296:   PetscFunctionBegin;
    297:   while ((link = GLEETableauList)) {
    298:     GLEETableau t   = &link->tab;
    299:     GLEETableauList = link->next;
    300:     PetscCall(PetscFree5(t->A, t->B, t->U, t->V, t->c));
    301:     PetscCall(PetscFree2(t->S, t->F));
    302:     PetscCall(PetscFree(t->Fembed));
    303:     PetscCall(PetscFree(t->Ferror));
    304:     PetscCall(PetscFree(t->Serror));
    305:     PetscCall(PetscFree(t->binterp));
    306:     PetscCall(PetscFree(t->name));
    307:     PetscCall(PetscFree(link));
    308:   }
    309:   TSGLEERegisterAllCalled = PETSC_FALSE;
    310:   PetscFunctionReturn(PETSC_SUCCESS);
    311: }

    313: /*@C
    314:   TSGLEEInitializePackage - This function initializes everything in the `TSGLEE` package. It is called
    315:   from `TSInitializePackage()`.

    317:   Level: developer

    319: .seealso: [](ch_ts), `PetscInitialize()`
    320: @*/
    321: PetscErrorCode TSGLEEInitializePackage(void)
    322: {
    323:   PetscFunctionBegin;
    324:   if (TSGLEEPackageInitialized) PetscFunctionReturn(PETSC_SUCCESS);
    325:   TSGLEEPackageInitialized = PETSC_TRUE;
    326:   PetscCall(TSGLEERegisterAll());
    327:   PetscCall(PetscObjectComposedDataRegister(&explicit_stage_time_id));
    328:   PetscCall(PetscRegisterFinalize(TSGLEEFinalizePackage));
    329:   PetscFunctionReturn(PETSC_SUCCESS);
    330: }

    332: /*@C
    333:   TSGLEEFinalizePackage - This function destroys everything in the `TSGLEE` package. It is
    334:   called from `PetscFinalize()`.

    336:   Level: developer

    338: .seealso: [](ch_ts), `PetscFinalize()`
    339: @*/
    340: PetscErrorCode TSGLEEFinalizePackage(void)
    341: {
    342:   PetscFunctionBegin;
    343:   TSGLEEPackageInitialized = PETSC_FALSE;
    344:   PetscCall(TSGLEERegisterDestroy());
    345:   PetscFunctionReturn(PETSC_SUCCESS);
    346: }

    348: /*@C
    349:   TSGLEERegister - register a new `TSGLEE` scheme by providing the entries in the Butcher tableau

    351:   Not Collective, but the same schemes should be registered on all processes on which they will be used, No Fortran Support

    353:   Input Parameters:
    354: + name    - identifier for method
    355: . order   - order of method
    356: . s       - number of stages
    357: . r       - number of steps
    358: . gamma   - LTE ratio
    359: . A       - stage coefficients (dimension s*s, row-major)
    360: . B       - step completion coefficients (dimension r*s, row-major)
    361: . U       - method coefficients (dimension s*r, row-major)
    362: . V       - method coefficients (dimension r*r, row-major)
    363: . S       - starting coefficients
    364: . F       - finishing coefficients
    365: . c       - abscissa (dimension s; NULL to use row sums of A)
    366: . Fembed  - step completion coefficients for embedded method
    367: . Ferror  - error computation coefficients
    368: . Serror  - error initialization coefficients
    369: . pinterp - order of interpolation (0 if unavailable)
    370: - binterp - array of interpolation coefficients (NULL if unavailable)

    372:   Level: advanced

    374:   Note:
    375:   Several `TSGLEE` methods are provided, this function is only needed to create new methods.

    377: .seealso: [](ch_ts), `TSGLEE`
    378: @*/
    379: 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[], const PetscReal Ferror[], const PetscReal Serror[], PetscInt pinterp, const PetscReal binterp[])
    380: {
    381:   GLEETableauLink link;
    382:   GLEETableau     t;
    383:   PetscInt        i, j;

    385:   PetscFunctionBegin;
    386:   PetscCall(TSGLEEInitializePackage());
    387:   PetscCall(PetscNew(&link));
    388:   t = &link->tab;
    389:   PetscCall(PetscStrallocpy(name, &t->name));
    390:   t->order = order;
    391:   t->s     = s;
    392:   t->r     = r;
    393:   t->gamma = gamma;
    394:   PetscCall(PetscMalloc5(s * s, &t->A, r * r, &t->V, s, &t->c, r * s, &t->B, s * r, &t->U));
    395:   PetscCall(PetscMalloc2(r, &t->S, r, &t->F));
    396:   PetscCall(PetscArraycpy(t->A, A, s * s));
    397:   PetscCall(PetscArraycpy(t->B, B, r * s));
    398:   PetscCall(PetscArraycpy(t->U, U, s * r));
    399:   PetscCall(PetscArraycpy(t->V, V, r * r));
    400:   PetscCall(PetscArraycpy(t->S, S, r));
    401:   PetscCall(PetscArraycpy(t->F, F, r));
    402:   if (c) {
    403:     PetscCall(PetscArraycpy(t->c, c, s));
    404:   } else {
    405:     for (i = 0; i < s; i++)
    406:       for (j = 0, t->c[i] = 0; j < s; j++) t->c[i] += A[i * s + j];
    407:   }
    408:   PetscCall(PetscMalloc1(r, &t->Fembed));
    409:   PetscCall(PetscMalloc1(r, &t->Ferror));
    410:   PetscCall(PetscMalloc1(r, &t->Serror));
    411:   PetscCall(PetscArraycpy(t->Fembed, Fembed, r));
    412:   PetscCall(PetscArraycpy(t->Ferror, Ferror, r));
    413:   PetscCall(PetscArraycpy(t->Serror, Serror, r));
    414:   t->pinterp = pinterp;
    415:   PetscCall(PetscMalloc1(s * pinterp, &t->binterp));
    416:   PetscCall(PetscArraycpy(t->binterp, binterp, s * pinterp));

    418:   link->next      = GLEETableauList;
    419:   GLEETableauList = link;
    420:   PetscFunctionReturn(PETSC_SUCCESS);
    421: }

    423: static PetscErrorCode TSEvaluateStep_GLEE(TS ts, PetscInt order, Vec X, PetscBool *done)
    424: {
    425:   TS_GLEE     *glee = (TS_GLEE *)ts->data;
    426:   GLEETableau  tab  = glee->tableau;
    427:   PetscReal    h, *B = tab->B, *V = tab->V, *F = tab->F, *Fembed = tab->Fembed;
    428:   PetscInt     s = tab->s, r = tab->r, i, j;
    429:   Vec         *Y = glee->Y, *YdotStage = glee->YdotStage;
    430:   PetscScalar *ws = glee->swork, *wr = glee->rwork;

    432:   PetscFunctionBegin;
    433:   switch (glee->status) {
    434:   case TS_STEP_INCOMPLETE:
    435:   case TS_STEP_PENDING:
    436:     h = ts->time_step;
    437:     break;
    438:   case TS_STEP_COMPLETE:
    439:     h = ts->ptime - ts->ptime_prev;
    440:     break;
    441:   default:
    442:     SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_PLIB, "Invalid TSStepStatus");
    443:   }

    445:   if (order == tab->order) {
    446:     /* Note: Irrespective of whether status is TS_STEP_INCOMPLETE
    447:              or TS_STEP_COMPLETE, glee->X has the solution at the
    448:              beginning of the time step. So no need to roll-back.
    449:     */
    450:     if (glee->status == TS_STEP_INCOMPLETE) {
    451:       for (i = 0; i < r; i++) {
    452:         PetscCall(VecZeroEntries(Y[i]));
    453:         for (j = 0; j < r; j++) wr[j] = V[i * r + j];
    454:         PetscCall(VecMAXPY(Y[i], r, wr, glee->X));
    455:         for (j = 0; j < s; j++) ws[j] = h * B[i * s + j];
    456:         PetscCall(VecMAXPY(Y[i], s, ws, YdotStage));
    457:       }
    458:       PetscCall(VecZeroEntries(X));
    459:       for (j = 0; j < r; j++) wr[j] = F[j];
    460:       PetscCall(VecMAXPY(X, r, wr, Y));
    461:     } else PetscCall(VecCopy(ts->vec_sol, X));
    462:     PetscFunctionReturn(PETSC_SUCCESS);

    464:   } else if (order == tab->order - 1) {
    465:     /* Complete with the embedded method (Fembed) */
    466:     for (i = 0; i < r; i++) {
    467:       PetscCall(VecZeroEntries(Y[i]));
    468:       for (j = 0; j < r; j++) wr[j] = V[i * r + j];
    469:       PetscCall(VecMAXPY(Y[i], r, wr, glee->X));
    470:       for (j = 0; j < s; j++) ws[j] = h * B[i * s + j];
    471:       PetscCall(VecMAXPY(Y[i], s, ws, YdotStage));
    472:     }
    473:     PetscCall(VecZeroEntries(X));
    474:     for (j = 0; j < r; j++) wr[j] = Fembed[j];
    475:     PetscCall(VecMAXPY(X, r, wr, Y));

    477:     if (done) *done = PETSC_TRUE;
    478:     PetscFunctionReturn(PETSC_SUCCESS);
    479:   }
    480:   if (done) *done = PETSC_FALSE;
    481:   else SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_SUP, "GLEE '%s' of order %" PetscInt_FMT " cannot evaluate step at order %" PetscInt_FMT, tab->name, tab->order, order);
    482:   PetscFunctionReturn(PETSC_SUCCESS);
    483: }

    485: static PetscErrorCode TSStep_GLEE(TS ts)
    486: {
    487:   TS_GLEE       *glee = (TS_GLEE *)ts->data;
    488:   GLEETableau    tab  = glee->tableau;
    489:   const PetscInt s = tab->s, r = tab->r;
    490:   PetscReal     *A = tab->A, *U = tab->U, *F = tab->F, *c = tab->c;
    491:   Vec           *Y = glee->Y, *X = glee->X, *YStage = glee->YStage, *YdotStage = glee->YdotStage, W = glee->W;
    492:   SNES           snes;
    493:   PetscScalar   *ws = glee->swork, *wr = glee->rwork;
    494:   TSAdapt        adapt;
    495:   PetscInt       i, j, reject, next_scheme, its, lits;
    496:   PetscReal      next_time_step;
    497:   PetscReal      t;
    498:   PetscBool      accept;

    500:   PetscFunctionBegin;
    501:   PetscCall(PetscCitationsRegister(citation, &cited));

    503:   for (i = 0; i < r; i++) PetscCall(VecCopy(Y[i], X[i]));

    505:   PetscCall(TSGetSNES(ts, &snes));
    506:   next_time_step = ts->time_step;
    507:   t              = ts->ptime;
    508:   accept         = PETSC_TRUE;
    509:   glee->status   = TS_STEP_INCOMPLETE;

    511:   for (reject = 0; reject < ts->max_reject && !ts->reason; reject++, ts->reject++) {
    512:     PetscReal h = ts->time_step;
    513:     PetscCall(TSPreStep(ts));

    515:     for (i = 0; i < s; i++) {
    516:       glee->stage_time = t + h * c[i];
    517:       PetscCall(TSPreStage(ts, glee->stage_time));

    519:       if (A[i * s + i] == 0) { /* Explicit stage */
    520:         PetscCall(VecZeroEntries(YStage[i]));
    521:         for (j = 0; j < r; j++) wr[j] = U[i * r + j];
    522:         PetscCall(VecMAXPY(YStage[i], r, wr, X));
    523:         for (j = 0; j < i; j++) ws[j] = h * A[i * s + j];
    524:         PetscCall(VecMAXPY(YStage[i], i, ws, YdotStage));
    525:       } else { /* Implicit stage */
    526:         glee->scoeff = 1.0 / A[i * s + i];
    527:         /* compute right-hand side */
    528:         PetscCall(VecZeroEntries(W));
    529:         for (j = 0; j < r; j++) wr[j] = U[i * r + j];
    530:         PetscCall(VecMAXPY(W, r, wr, X));
    531:         for (j = 0; j < i; j++) ws[j] = h * A[i * s + j];
    532:         PetscCall(VecMAXPY(W, i, ws, YdotStage));
    533:         PetscCall(VecScale(W, glee->scoeff / h));
    534:         /* set initial guess */
    535:         PetscCall(VecCopy(i > 0 ? YStage[i - 1] : ts->vec_sol, YStage[i]));
    536:         /* solve for this stage */
    537:         PetscCall(SNESSolve(snes, W, YStage[i]));
    538:         PetscCall(SNESGetIterationNumber(snes, &its));
    539:         PetscCall(SNESGetLinearSolveIterations(snes, &lits));
    540:         ts->snes_its += its;
    541:         ts->ksp_its += lits;
    542:       }
    543:       PetscCall(TSGetAdapt(ts, &adapt));
    544:       PetscCall(TSAdaptCheckStage(adapt, ts, glee->stage_time, YStage[i], &accept));
    545:       if (!accept) goto reject_step;
    546:       PetscCall(TSPostStage(ts, glee->stage_time, i, YStage));
    547:       PetscCall(TSComputeRHSFunction(ts, t + h * c[i], YStage[i], YdotStage[i]));
    548:     }
    549:     PetscCall(TSEvaluateStep(ts, tab->order, ts->vec_sol, NULL));
    550:     glee->status = TS_STEP_PENDING;

    552:     /* Register only the current method as a candidate because we're not supporting multiple candidates yet. */
    553:     PetscCall(TSGetAdapt(ts, &adapt));
    554:     PetscCall(TSAdaptCandidatesClear(adapt));
    555:     PetscCall(TSAdaptCandidateAdd(adapt, tab->name, tab->order, 1, tab->ccfl, (PetscReal)tab->s, PETSC_TRUE));
    556:     PetscCall(TSAdaptChoose(adapt, ts, ts->time_step, &next_scheme, &next_time_step, &accept));
    557:     if (accept) {
    558:       /* ignore next_scheme for now */
    559:       ts->ptime += ts->time_step;
    560:       ts->time_step = next_time_step;
    561:       glee->status  = TS_STEP_COMPLETE;
    562:       /* compute and store the global error */
    563:       /* Note: this is not needed if TSAdaptGLEE is not used */
    564:       PetscCall(TSGetTimeError(ts, 0, &glee->yGErr));
    565:       PetscCall(PetscObjectComposedDataSetReal((PetscObject)ts->vec_sol, explicit_stage_time_id, ts->ptime));
    566:       break;
    567:     } else { /* Roll back the current step */
    568:       for (j = 0; j < r; j++) wr[j] = F[j];
    569:       PetscCall(VecMAXPY(ts->vec_sol, r, wr, X));
    570:       ts->time_step = next_time_step;
    571:       glee->status  = TS_STEP_INCOMPLETE;
    572:     }
    573:   reject_step:
    574:     continue;
    575:   }
    576:   if (glee->status != TS_STEP_COMPLETE && !ts->reason) ts->reason = TS_DIVERGED_STEP_REJECTED;
    577:   PetscFunctionReturn(PETSC_SUCCESS);
    578: }

    580: static PetscErrorCode TSInterpolate_GLEE(TS ts, PetscReal itime, Vec X)
    581: {
    582:   TS_GLEE         *glee = (TS_GLEE *)ts->data;
    583:   PetscInt         s = glee->tableau->s, pinterp = glee->tableau->pinterp, i, j;
    584:   PetscReal        h, tt, t;
    585:   PetscScalar     *b;
    586:   const PetscReal *B = glee->tableau->binterp;

    588:   PetscFunctionBegin;
    589:   PetscCheck(B, PetscObjectComm((PetscObject)ts), PETSC_ERR_SUP, "TSGLEE %s does not have an interpolation formula", glee->tableau->name);
    590:   switch (glee->status) {
    591:   case TS_STEP_INCOMPLETE:
    592:   case TS_STEP_PENDING:
    593:     h = ts->time_step;
    594:     t = (itime - ts->ptime) / h;
    595:     break;
    596:   case TS_STEP_COMPLETE:
    597:     h = ts->ptime - ts->ptime_prev;
    598:     t = (itime - ts->ptime) / h + 1; /* In the interval [0,1] */
    599:     break;
    600:   default:
    601:     SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_PLIB, "Invalid TSStepStatus");
    602:   }
    603:   PetscCall(PetscMalloc1(s, &b));
    604:   for (i = 0; i < s; i++) b[i] = 0;
    605:   for (j = 0, tt = t; j < pinterp; j++, tt *= t) {
    606:     for (i = 0; i < s; i++) b[i] += h * B[i * pinterp + j] * tt;
    607:   }
    608:   PetscCall(VecCopy(glee->YStage[0], X));
    609:   PetscCall(VecMAXPY(X, s, b, glee->YdotStage));
    610:   PetscCall(PetscFree(b));
    611:   PetscFunctionReturn(PETSC_SUCCESS);
    612: }

    614: /*------------------------------------------------------------*/
    615: static PetscErrorCode TSReset_GLEE(TS ts)
    616: {
    617:   TS_GLEE *glee = (TS_GLEE *)ts->data;
    618:   PetscInt s, r;

    620:   PetscFunctionBegin;
    621:   if (!glee->tableau) PetscFunctionReturn(PETSC_SUCCESS);
    622:   s = glee->tableau->s;
    623:   r = glee->tableau->r;
    624:   PetscCall(VecDestroyVecs(r, &glee->Y));
    625:   PetscCall(VecDestroyVecs(r, &glee->X));
    626:   PetscCall(VecDestroyVecs(s, &glee->YStage));
    627:   PetscCall(VecDestroyVecs(s, &glee->YdotStage));
    628:   PetscCall(VecDestroy(&glee->Ydot));
    629:   PetscCall(VecDestroy(&glee->yGErr));
    630:   PetscCall(VecDestroy(&glee->W));
    631:   PetscCall(PetscFree2(glee->swork, glee->rwork));
    632:   PetscFunctionReturn(PETSC_SUCCESS);
    633: }

    635: static PetscErrorCode TSGLEEGetVecs(TS ts, DM dm, Vec *Ydot)
    636: {
    637:   TS_GLEE *glee = (TS_GLEE *)ts->data;

    639:   PetscFunctionBegin;
    640:   if (Ydot) {
    641:     if (dm && dm != ts->dm) {
    642:       PetscCall(DMGetNamedGlobalVector(dm, "TSGLEE_Ydot", Ydot));
    643:     } else *Ydot = glee->Ydot;
    644:   }
    645:   PetscFunctionReturn(PETSC_SUCCESS);
    646: }

    648: static PetscErrorCode TSGLEERestoreVecs(TS ts, DM dm, Vec *Ydot)
    649: {
    650:   PetscFunctionBegin;
    651:   if (Ydot) {
    652:     if (dm && dm != ts->dm) PetscCall(DMRestoreNamedGlobalVector(dm, "TSGLEE_Ydot", Ydot));
    653:   }
    654:   PetscFunctionReturn(PETSC_SUCCESS);
    655: }

    657: /*
    658:   This defines the nonlinear equation that is to be solved with SNES
    659: */
    660: static PetscErrorCode SNESTSFormFunction_GLEE(SNES snes, Vec X, Vec F, TS ts)
    661: {
    662:   TS_GLEE  *glee = (TS_GLEE *)ts->data;
    663:   DM        dm, dmsave;
    664:   Vec       Ydot;
    665:   PetscReal shift = glee->scoeff / ts->time_step;

    667:   PetscFunctionBegin;
    668:   PetscCall(SNESGetDM(snes, &dm));
    669:   PetscCall(TSGLEEGetVecs(ts, dm, &Ydot));
    670:   /* Set Ydot = shift*X */
    671:   PetscCall(VecCopy(X, Ydot));
    672:   PetscCall(VecScale(Ydot, shift));
    673:   dmsave = ts->dm;
    674:   ts->dm = dm;

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

    678:   ts->dm = dmsave;
    679:   PetscCall(TSGLEERestoreVecs(ts, dm, &Ydot));
    680:   PetscFunctionReturn(PETSC_SUCCESS);
    681: }

    683: static PetscErrorCode SNESTSFormJacobian_GLEE(SNES snes, Vec X, Mat A, Mat B, TS ts)
    684: {
    685:   TS_GLEE  *glee = (TS_GLEE *)ts->data;
    686:   DM        dm, dmsave;
    687:   Vec       Ydot;
    688:   PetscReal shift = glee->scoeff / ts->time_step;

    690:   PetscFunctionBegin;
    691:   PetscCall(SNESGetDM(snes, &dm));
    692:   PetscCall(TSGLEEGetVecs(ts, dm, &Ydot));
    693:   /* glee->Ydot has already been computed in SNESTSFormFunction_GLEE (SNES guarantees this) */
    694:   dmsave = ts->dm;
    695:   ts->dm = dm;

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

    699:   ts->dm = dmsave;
    700:   PetscCall(TSGLEERestoreVecs(ts, dm, &Ydot));
    701:   PetscFunctionReturn(PETSC_SUCCESS);
    702: }

    704: static PetscErrorCode DMCoarsenHook_TSGLEE(DM fine, DM coarse, void *ctx)
    705: {
    706:   PetscFunctionBegin;
    707:   PetscFunctionReturn(PETSC_SUCCESS);
    708: }

    710: static PetscErrorCode DMRestrictHook_TSGLEE(DM fine, Mat restrct, Vec rscale, Mat inject, DM coarse, void *ctx)
    711: {
    712:   PetscFunctionBegin;
    713:   PetscFunctionReturn(PETSC_SUCCESS);
    714: }

    716: static PetscErrorCode DMSubDomainHook_TSGLEE(DM dm, DM subdm, void *ctx)
    717: {
    718:   PetscFunctionBegin;
    719:   PetscFunctionReturn(PETSC_SUCCESS);
    720: }

    722: static PetscErrorCode DMSubDomainRestrictHook_TSGLEE(DM dm, VecScatter gscat, VecScatter lscat, DM subdm, void *ctx)
    723: {
    724:   PetscFunctionBegin;
    725:   PetscFunctionReturn(PETSC_SUCCESS);
    726: }

    728: static PetscErrorCode TSSetUp_GLEE(TS ts)
    729: {
    730:   TS_GLEE    *glee = (TS_GLEE *)ts->data;
    731:   GLEETableau tab;
    732:   PetscInt    s, r;
    733:   DM          dm;

    735:   PetscFunctionBegin;
    736:   if (!glee->tableau) PetscCall(TSGLEESetType(ts, TSGLEEDefaultType));
    737:   tab = glee->tableau;
    738:   s   = tab->s;
    739:   r   = tab->r;
    740:   PetscCall(VecDuplicateVecs(ts->vec_sol, r, &glee->Y));
    741:   PetscCall(VecDuplicateVecs(ts->vec_sol, r, &glee->X));
    742:   PetscCall(VecDuplicateVecs(ts->vec_sol, s, &glee->YStage));
    743:   PetscCall(VecDuplicateVecs(ts->vec_sol, s, &glee->YdotStage));
    744:   PetscCall(VecDuplicate(ts->vec_sol, &glee->Ydot));
    745:   PetscCall(VecDuplicate(ts->vec_sol, &glee->yGErr));
    746:   PetscCall(VecZeroEntries(glee->yGErr));
    747:   PetscCall(VecDuplicate(ts->vec_sol, &glee->W));
    748:   PetscCall(PetscMalloc2(s, &glee->swork, r, &glee->rwork));
    749:   PetscCall(TSGetDM(ts, &dm));
    750:   PetscCall(DMCoarsenHookAdd(dm, DMCoarsenHook_TSGLEE, DMRestrictHook_TSGLEE, ts));
    751:   PetscCall(DMSubDomainHookAdd(dm, DMSubDomainHook_TSGLEE, DMSubDomainRestrictHook_TSGLEE, ts));
    752:   PetscFunctionReturn(PETSC_SUCCESS);
    753: }

    755: static PetscErrorCode TSStartingMethod_GLEE(TS ts)
    756: {
    757:   TS_GLEE    *glee = (TS_GLEE *)ts->data;
    758:   GLEETableau tab  = glee->tableau;
    759:   PetscInt    r    = tab->r, i;
    760:   PetscReal  *S    = tab->S;

    762:   PetscFunctionBegin;
    763:   for (i = 0; i < r; i++) {
    764:     PetscCall(VecZeroEntries(glee->Y[i]));
    765:     PetscCall(VecAXPY(glee->Y[i], S[i], ts->vec_sol));
    766:   }
    767:   PetscFunctionReturn(PETSC_SUCCESS);
    768: }

    770: /*------------------------------------------------------------*/

    772: static PetscErrorCode TSSetFromOptions_GLEE(TS ts, PetscOptionItems *PetscOptionsObject)
    773: {
    774:   char gleetype[256];

    776:   PetscFunctionBegin;
    777:   PetscOptionsHeadBegin(PetscOptionsObject, "GLEE ODE solver options");
    778:   {
    779:     GLEETableauLink link;
    780:     PetscInt        count, choice;
    781:     PetscBool       flg;
    782:     const char    **namelist;

    784:     PetscCall(PetscStrncpy(gleetype, TSGLEEDefaultType, sizeof(gleetype)));
    785:     for (link = GLEETableauList, count = 0; link; link = link->next, count++);
    786:     PetscCall(PetscMalloc1(count, (char ***)&namelist));
    787:     for (link = GLEETableauList, count = 0; link; link = link->next, count++) namelist[count] = link->tab.name;
    788:     PetscCall(PetscOptionsEList("-ts_glee_type", "Family of GLEE method", "TSGLEESetType", (const char *const *)namelist, count, gleetype, &choice, &flg));
    789:     PetscCall(TSGLEESetType(ts, flg ? namelist[choice] : gleetype));
    790:     PetscCall(PetscFree(namelist));
    791:   }
    792:   PetscOptionsHeadEnd();
    793:   PetscFunctionReturn(PETSC_SUCCESS);
    794: }

    796: static PetscErrorCode TSView_GLEE(TS ts, PetscViewer viewer)
    797: {
    798:   TS_GLEE    *glee = (TS_GLEE *)ts->data;
    799:   GLEETableau tab  = glee->tableau;
    800:   PetscBool   iascii;

    802:   PetscFunctionBegin;
    803:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
    804:   if (iascii) {
    805:     TSGLEEType gleetype;
    806:     char       buf[512];
    807:     PetscCall(TSGLEEGetType(ts, &gleetype));
    808:     PetscCall(PetscViewerASCIIPrintf(viewer, "  GLEE type %s\n", gleetype));
    809:     PetscCall(PetscFormatRealArray(buf, sizeof(buf), "% 8.6f", tab->s, tab->c));
    810:     PetscCall(PetscViewerASCIIPrintf(viewer, "  Abscissa     c = %s\n", buf));
    811:     /* Note: print out r as well */
    812:   }
    813:   PetscFunctionReturn(PETSC_SUCCESS);
    814: }

    816: static PetscErrorCode TSLoad_GLEE(TS ts, PetscViewer viewer)
    817: {
    818:   SNES    snes;
    819:   TSAdapt tsadapt;

    821:   PetscFunctionBegin;
    822:   PetscCall(TSGetAdapt(ts, &tsadapt));
    823:   PetscCall(TSAdaptLoad(tsadapt, viewer));
    824:   PetscCall(TSGetSNES(ts, &snes));
    825:   PetscCall(SNESLoad(snes, viewer));
    826:   /* function and Jacobian context for SNES when used with TS is always ts object */
    827:   PetscCall(SNESSetFunction(snes, NULL, NULL, ts));
    828:   PetscCall(SNESSetJacobian(snes, NULL, NULL, NULL, ts));
    829:   PetscFunctionReturn(PETSC_SUCCESS);
    830: }

    832: /*@
    833:   TSGLEESetType - Set the type of `TSGLEE` scheme

    835:   Logically Collective

    837:   Input Parameters:
    838: + ts       - timestepping context
    839: - gleetype - type of `TSGLEE` scheme

    841:   Level: intermediate

    843: .seealso: [](ch_ts), `TSGLEEGetType()`, `TSGLEE`
    844: @*/
    845: PetscErrorCode TSGLEESetType(TS ts, TSGLEEType gleetype)
    846: {
    847:   PetscFunctionBegin;
    849:   PetscAssertPointer(gleetype, 2);
    850:   PetscTryMethod(ts, "TSGLEESetType_C", (TS, TSGLEEType), (ts, gleetype));
    851:   PetscFunctionReturn(PETSC_SUCCESS);
    852: }

    854: /*@
    855:   TSGLEEGetType - Get the type of `TSGLEE` scheme

    857:   Logically Collective

    859:   Input Parameter:
    860: . ts - timestepping context

    862:   Output Parameter:
    863: . gleetype - type of `TSGLEE` scheme

    865:   Level: intermediate

    867: .seealso: [](ch_ts), `TSGLEE`, `TSGLEESetType()`
    868: @*/
    869: PetscErrorCode TSGLEEGetType(TS ts, TSGLEEType *gleetype)
    870: {
    871:   PetscFunctionBegin;
    873:   PetscUseMethod(ts, "TSGLEEGetType_C", (TS, TSGLEEType *), (ts, gleetype));
    874:   PetscFunctionReturn(PETSC_SUCCESS);
    875: }

    877: static PetscErrorCode TSGLEEGetType_GLEE(TS ts, TSGLEEType *gleetype)
    878: {
    879:   TS_GLEE *glee = (TS_GLEE *)ts->data;

    881:   PetscFunctionBegin;
    882:   if (!glee->tableau) PetscCall(TSGLEESetType(ts, TSGLEEDefaultType));
    883:   *gleetype = glee->tableau->name;
    884:   PetscFunctionReturn(PETSC_SUCCESS);
    885: }
    886: static PetscErrorCode TSGLEESetType_GLEE(TS ts, TSGLEEType gleetype)
    887: {
    888:   TS_GLEE        *glee = (TS_GLEE *)ts->data;
    889:   PetscBool       match;
    890:   GLEETableauLink link;

    892:   PetscFunctionBegin;
    893:   if (glee->tableau) {
    894:     PetscCall(PetscStrcmp(glee->tableau->name, gleetype, &match));
    895:     if (match) PetscFunctionReturn(PETSC_SUCCESS);
    896:   }
    897:   for (link = GLEETableauList; link; link = link->next) {
    898:     PetscCall(PetscStrcmp(link->tab.name, gleetype, &match));
    899:     if (match) {
    900:       PetscCall(TSReset_GLEE(ts));
    901:       glee->tableau = &link->tab;
    902:       PetscFunctionReturn(PETSC_SUCCESS);
    903:     }
    904:   }
    905:   SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_ARG_UNKNOWN_TYPE, "Could not find '%s'", gleetype);
    906: }

    908: static PetscErrorCode TSGetStages_GLEE(TS ts, PetscInt *ns, Vec **Y)
    909: {
    910:   TS_GLEE *glee = (TS_GLEE *)ts->data;

    912:   PetscFunctionBegin;
    913:   if (ns) *ns = glee->tableau->s;
    914:   if (Y) *Y = glee->YStage;
    915:   PetscFunctionReturn(PETSC_SUCCESS);
    916: }

    918: static PetscErrorCode TSGetSolutionComponents_GLEE(TS ts, PetscInt *n, Vec *Y)
    919: {
    920:   TS_GLEE    *glee = (TS_GLEE *)ts->data;
    921:   GLEETableau tab  = glee->tableau;

    923:   PetscFunctionBegin;
    924:   if (!Y) *n = tab->r;
    925:   else {
    926:     if ((*n >= 0) && (*n < tab->r)) {
    927:       PetscCall(VecCopy(glee->Y[*n], *Y));
    928:     } else SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_ARG_OUTOFRANGE, "Second argument (%" PetscInt_FMT ") out of range[0,%" PetscInt_FMT "].", *n, tab->r - 1);
    929:   }
    930:   PetscFunctionReturn(PETSC_SUCCESS);
    931: }

    933: static PetscErrorCode TSGetAuxSolution_GLEE(TS ts, Vec *X)
    934: {
    935:   TS_GLEE     *glee = (TS_GLEE *)ts->data;
    936:   GLEETableau  tab  = glee->tableau;
    937:   PetscReal   *F    = tab->Fembed;
    938:   PetscInt     r    = tab->r;
    939:   Vec         *Y    = glee->Y;
    940:   PetscScalar *wr   = glee->rwork;
    941:   PetscInt     i;

    943:   PetscFunctionBegin;
    944:   PetscCall(VecZeroEntries(*X));
    945:   for (i = 0; i < r; i++) wr[i] = F[i];
    946:   PetscCall(VecMAXPY(*X, r, wr, Y));
    947:   PetscFunctionReturn(PETSC_SUCCESS);
    948: }

    950: static PetscErrorCode TSGetTimeError_GLEE(TS ts, PetscInt n, Vec *X)
    951: {
    952:   TS_GLEE     *glee = (TS_GLEE *)ts->data;
    953:   GLEETableau  tab  = glee->tableau;
    954:   PetscReal   *F    = tab->Ferror;
    955:   PetscInt     r    = tab->r;
    956:   Vec         *Y    = glee->Y;
    957:   PetscScalar *wr   = glee->rwork;
    958:   PetscInt     i;

    960:   PetscFunctionBegin;
    961:   PetscCall(VecZeroEntries(*X));
    962:   if (n == 0) {
    963:     for (i = 0; i < r; i++) wr[i] = F[i];
    964:     PetscCall(VecMAXPY(*X, r, wr, Y));
    965:   } else if (n == -1) {
    966:     *X = glee->yGErr;
    967:   }
    968:   PetscFunctionReturn(PETSC_SUCCESS);
    969: }

    971: static PetscErrorCode TSSetTimeError_GLEE(TS ts, Vec X)
    972: {
    973:   TS_GLEE    *glee = (TS_GLEE *)ts->data;
    974:   GLEETableau tab  = glee->tableau;
    975:   PetscReal  *S    = tab->Serror;
    976:   PetscInt    r    = tab->r, i;
    977:   Vec        *Y    = glee->Y;

    979:   PetscFunctionBegin;
    980:   PetscCheck(r == 2, PetscObjectComm((PetscObject)ts), PETSC_ERR_SUP, "TSSetTimeError_GLEE not supported for '%s' with r=%" PetscInt_FMT ".", tab->name, tab->r);
    981:   for (i = 1; i < r; i++) {
    982:     PetscCall(VecCopy(ts->vec_sol, Y[i]));
    983:     PetscCall(VecAXPBY(Y[i], S[0], S[1], X));
    984:     PetscCall(VecCopy(X, glee->yGErr));
    985:   }
    986:   PetscFunctionReturn(PETSC_SUCCESS);
    987: }

    989: static PetscErrorCode TSDestroy_GLEE(TS ts)
    990: {
    991:   PetscFunctionBegin;
    992:   PetscCall(TSReset_GLEE(ts));
    993:   if (ts->dm) {
    994:     PetscCall(DMCoarsenHookRemove(ts->dm, DMCoarsenHook_TSGLEE, DMRestrictHook_TSGLEE, ts));
    995:     PetscCall(DMSubDomainHookRemove(ts->dm, DMSubDomainHook_TSGLEE, DMSubDomainRestrictHook_TSGLEE, ts));
    996:   }
    997:   PetscCall(PetscFree(ts->data));
    998:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSGLEEGetType_C", NULL));
    999:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSGLEESetType_C", NULL));
    1000:   PetscFunctionReturn(PETSC_SUCCESS);
    1001: }

    1003: /* ------------------------------------------------------------ */
    1004: /*MC
    1005:       TSGLEE - ODE and DAE solver using General Linear with Error Estimation schemes

    1007:   The user should provide the right-hand side of the equation using `TSSetRHSFunction()`.

    1009:   Level: beginner

    1011:   Note:
    1012:   The default is `TSGLEE35`, it can be changed with `TSGLEESetType()` or -ts_glee_type

    1014: .seealso: [](ch_ts), `TSCreate()`, `TS`, `TSSetType()`, `TSGLEESetType()`, `TSGLEEGetType()`,
    1015:           `TSGLEE23`, `TSGLEE24`, `TSGLEE35`, `TSGLEE25I`, `TSGLEEEXRK2A`,
    1016:           `TSGLEERK32G1`, `TSGLEERK285EX`, `TSGLEEType`, `TSGLEERegister()`, `TSType`
    1017: M*/
    1018: PETSC_EXTERN PetscErrorCode TSCreate_GLEE(TS ts)
    1019: {
    1020:   TS_GLEE *th;

    1022:   PetscFunctionBegin;
    1023:   PetscCall(TSGLEEInitializePackage());

    1025:   ts->ops->reset                 = TSReset_GLEE;
    1026:   ts->ops->destroy               = TSDestroy_GLEE;
    1027:   ts->ops->view                  = TSView_GLEE;
    1028:   ts->ops->load                  = TSLoad_GLEE;
    1029:   ts->ops->setup                 = TSSetUp_GLEE;
    1030:   ts->ops->step                  = TSStep_GLEE;
    1031:   ts->ops->interpolate           = TSInterpolate_GLEE;
    1032:   ts->ops->evaluatestep          = TSEvaluateStep_GLEE;
    1033:   ts->ops->setfromoptions        = TSSetFromOptions_GLEE;
    1034:   ts->ops->getstages             = TSGetStages_GLEE;
    1035:   ts->ops->snesfunction          = SNESTSFormFunction_GLEE;
    1036:   ts->ops->snesjacobian          = SNESTSFormJacobian_GLEE;
    1037:   ts->ops->getsolutioncomponents = TSGetSolutionComponents_GLEE;
    1038:   ts->ops->getauxsolution        = TSGetAuxSolution_GLEE;
    1039:   ts->ops->gettimeerror          = TSGetTimeError_GLEE;
    1040:   ts->ops->settimeerror          = TSSetTimeError_GLEE;
    1041:   ts->ops->startingmethod        = TSStartingMethod_GLEE;
    1042:   ts->default_adapt_type         = TSADAPTGLEE;

    1044:   ts->usessnes = PETSC_TRUE;

    1046:   PetscCall(PetscNew(&th));
    1047:   ts->data = (void *)th;

    1049:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSGLEEGetType_C", TSGLEEGetType_GLEE));
    1050:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSGLEESetType_C", TSGLEESetType_GLEE));
    1051:   PetscFunctionReturn(PETSC_SUCCESS);
    1052: }