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:   }

281:   PetscFunctionReturn(PETSC_SUCCESS);
282: }

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

287:   Not Collective

289:   Level: advanced

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

297:   PetscFunctionBegin;
298:   while ((link = GLEETableauList)) {
299:     GLEETableau t   = &link->tab;
300:     GLEETableauList = link->next;
301:     PetscCall(PetscFree5(t->A, t->B, t->U, t->V, t->c));
302:     PetscCall(PetscFree2(t->S, t->F));
303:     PetscCall(PetscFree(t->Fembed));
304:     PetscCall(PetscFree(t->Ferror));
305:     PetscCall(PetscFree(t->Serror));
306:     PetscCall(PetscFree(t->binterp));
307:     PetscCall(PetscFree(t->name));
308:     PetscCall(PetscFree(link));
309:   }
310:   TSGLEERegisterAllCalled = PETSC_FALSE;
311:   PetscFunctionReturn(PETSC_SUCCESS);
312: }

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

318:   Level: developer

320: .seealso: [](ch_ts), `PetscInitialize()`
321: @*/
322: PetscErrorCode TSGLEEInitializePackage(void)
323: {
324:   PetscFunctionBegin;
325:   if (TSGLEEPackageInitialized) PetscFunctionReturn(PETSC_SUCCESS);
326:   TSGLEEPackageInitialized = PETSC_TRUE;
327:   PetscCall(TSGLEERegisterAll());
328:   PetscCall(PetscObjectComposedDataRegister(&explicit_stage_time_id));
329:   PetscCall(PetscRegisterFinalize(TSGLEEFinalizePackage));
330:   PetscFunctionReturn(PETSC_SUCCESS);
331: }

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

337:   Level: developer

339: .seealso: [](ch_ts), `PetscFinalize()`
340: @*/
341: PetscErrorCode TSGLEEFinalizePackage(void)
342: {
343:   PetscFunctionBegin;
344:   TSGLEEPackageInitialized = PETSC_FALSE;
345:   PetscCall(TSGLEERegisterDestroy());
346:   PetscFunctionReturn(PETSC_SUCCESS);
347: }

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

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

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

373:   Level: advanced

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

378: .seealso: [](ch_ts), `TSGLEE`
379: @*/
380: 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[])
381: {
382:   GLEETableauLink link;
383:   GLEETableau     t;
384:   PetscInt        i, j;

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

419:   link->next      = GLEETableauList;
420:   GLEETableauList = link;
421:   PetscFunctionReturn(PETSC_SUCCESS);
422: }

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

433:   PetscFunctionBegin;

435:   switch (glee->status) {
436:   case TS_STEP_INCOMPLETE:
437:   case TS_STEP_PENDING:
438:     h = ts->time_step;
439:     break;
440:   case TS_STEP_COMPLETE:
441:     h = ts->ptime - ts->ptime_prev;
442:     break;
443:   default:
444:     SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_PLIB, "Invalid TSStepStatus");
445:   }

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

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

479:     if (done) *done = PETSC_TRUE;
480:     PetscFunctionReturn(PETSC_SUCCESS);
481:   }
482:   if (done) *done = PETSC_FALSE;
483:   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);
484:   PetscFunctionReturn(PETSC_SUCCESS);
485: }

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

502:   PetscFunctionBegin;
503:   PetscCall(PetscCitationsRegister(citation, &cited));

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

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

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

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

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

554:     /* Register only the current method as a candidate because we're not supporting multiple candidates yet. */
555:     PetscCall(TSGetAdapt(ts, &adapt));
556:     PetscCall(TSAdaptCandidatesClear(adapt));
557:     PetscCall(TSAdaptCandidateAdd(adapt, tab->name, tab->order, 1, tab->ccfl, (PetscReal)tab->s, PETSC_TRUE));
558:     PetscCall(TSAdaptChoose(adapt, ts, ts->time_step, &next_scheme, &next_time_step, &accept));
559:     if (accept) {
560:       /* ignore next_scheme for now */
561:       ts->ptime += ts->time_step;
562:       ts->time_step = next_time_step;
563:       glee->status  = TS_STEP_COMPLETE;
564:       /* compute and store the global error */
565:       /* Note: this is not needed if TSAdaptGLEE is not used */
566:       PetscCall(TSGetTimeError(ts, 0, &(glee->yGErr)));
567:       PetscCall(PetscObjectComposedDataSetReal((PetscObject)ts->vec_sol, explicit_stage_time_id, ts->ptime));
568:       break;
569:     } else { /* Roll back the current step */
570:       for (j = 0; j < r; j++) wr[j] = F[j];
571:       PetscCall(VecMAXPY(ts->vec_sol, r, wr, X));
572:       ts->time_step = next_time_step;
573:       glee->status  = TS_STEP_INCOMPLETE;
574:     }
575:   reject_step:
576:     continue;
577:   }
578:   if (glee->status != TS_STEP_COMPLETE && !ts->reason) ts->reason = TS_DIVERGED_STEP_REJECTED;
579:   PetscFunctionReturn(PETSC_SUCCESS);
580: }

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

590:   PetscFunctionBegin;
591:   PetscCheck(B, PetscObjectComm((PetscObject)ts), PETSC_ERR_SUP, "TSGLEE %s does not have an interpolation formula", glee->tableau->name);
592:   switch (glee->status) {
593:   case TS_STEP_INCOMPLETE:
594:   case TS_STEP_PENDING:
595:     h = ts->time_step;
596:     t = (itime - ts->ptime) / h;
597:     break;
598:   case TS_STEP_COMPLETE:
599:     h = ts->ptime - ts->ptime_prev;
600:     t = (itime - ts->ptime) / h + 1; /* In the interval [0,1] */
601:     break;
602:   default:
603:     SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_PLIB, "Invalid TSStepStatus");
604:   }
605:   PetscCall(PetscMalloc1(s, &b));
606:   for (i = 0; i < s; i++) b[i] = 0;
607:   for (j = 0, tt = t; j < pinterp; j++, tt *= t) {
608:     for (i = 0; i < s; i++) b[i] += h * B[i * pinterp + j] * tt;
609:   }
610:   PetscCall(VecCopy(glee->YStage[0], X));
611:   PetscCall(VecMAXPY(X, s, b, glee->YdotStage));
612:   PetscCall(PetscFree(b));
613:   PetscFunctionReturn(PETSC_SUCCESS);
614: }

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

622:   PetscFunctionBegin;
623:   if (!glee->tableau) PetscFunctionReturn(PETSC_SUCCESS);
624:   s = glee->tableau->s;
625:   r = glee->tableau->r;
626:   PetscCall(VecDestroyVecs(r, &glee->Y));
627:   PetscCall(VecDestroyVecs(r, &glee->X));
628:   PetscCall(VecDestroyVecs(s, &glee->YStage));
629:   PetscCall(VecDestroyVecs(s, &glee->YdotStage));
630:   PetscCall(VecDestroy(&glee->Ydot));
631:   PetscCall(VecDestroy(&glee->yGErr));
632:   PetscCall(VecDestroy(&glee->W));
633:   PetscCall(PetscFree2(glee->swork, glee->rwork));
634:   PetscFunctionReturn(PETSC_SUCCESS);
635: }

637: static PetscErrorCode TSGLEEGetVecs(TS ts, DM dm, Vec *Ydot)
638: {
639:   TS_GLEE *glee = (TS_GLEE *)ts->data;

641:   PetscFunctionBegin;
642:   if (Ydot) {
643:     if (dm && dm != ts->dm) {
644:       PetscCall(DMGetNamedGlobalVector(dm, "TSGLEE_Ydot", Ydot));
645:     } else *Ydot = glee->Ydot;
646:   }
647:   PetscFunctionReturn(PETSC_SUCCESS);
648: }

650: static PetscErrorCode TSGLEERestoreVecs(TS ts, DM dm, Vec *Ydot)
651: {
652:   PetscFunctionBegin;
653:   if (Ydot) {
654:     if (dm && dm != ts->dm) PetscCall(DMRestoreNamedGlobalVector(dm, "TSGLEE_Ydot", Ydot));
655:   }
656:   PetscFunctionReturn(PETSC_SUCCESS);
657: }

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

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

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

680:   ts->dm = dmsave;
681:   PetscCall(TSGLEERestoreVecs(ts, dm, &Ydot));
682:   PetscFunctionReturn(PETSC_SUCCESS);
683: }

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

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

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

701:   ts->dm = dmsave;
702:   PetscCall(TSGLEERestoreVecs(ts, dm, &Ydot));
703:   PetscFunctionReturn(PETSC_SUCCESS);
704: }

706: static PetscErrorCode DMCoarsenHook_TSGLEE(DM fine, DM coarse, void *ctx)
707: {
708:   PetscFunctionBegin;
709:   PetscFunctionReturn(PETSC_SUCCESS);
710: }

712: static PetscErrorCode DMRestrictHook_TSGLEE(DM fine, Mat restrct, Vec rscale, Mat inject, DM coarse, void *ctx)
713: {
714:   PetscFunctionBegin;
715:   PetscFunctionReturn(PETSC_SUCCESS);
716: }

718: static PetscErrorCode DMSubDomainHook_TSGLEE(DM dm, DM subdm, void *ctx)
719: {
720:   PetscFunctionBegin;
721:   PetscFunctionReturn(PETSC_SUCCESS);
722: }

724: static PetscErrorCode DMSubDomainRestrictHook_TSGLEE(DM dm, VecScatter gscat, VecScatter lscat, DM subdm, void *ctx)
725: {
726:   PetscFunctionBegin;
727:   PetscFunctionReturn(PETSC_SUCCESS);
728: }

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

737:   PetscFunctionBegin;
738:   if (!glee->tableau) PetscCall(TSGLEESetType(ts, TSGLEEDefaultType));
739:   tab = glee->tableau;
740:   s   = tab->s;
741:   r   = tab->r;
742:   PetscCall(VecDuplicateVecs(ts->vec_sol, r, &glee->Y));
743:   PetscCall(VecDuplicateVecs(ts->vec_sol, r, &glee->X));
744:   PetscCall(VecDuplicateVecs(ts->vec_sol, s, &glee->YStage));
745:   PetscCall(VecDuplicateVecs(ts->vec_sol, s, &glee->YdotStage));
746:   PetscCall(VecDuplicate(ts->vec_sol, &glee->Ydot));
747:   PetscCall(VecDuplicate(ts->vec_sol, &glee->yGErr));
748:   PetscCall(VecZeroEntries(glee->yGErr));
749:   PetscCall(VecDuplicate(ts->vec_sol, &glee->W));
750:   PetscCall(PetscMalloc2(s, &glee->swork, r, &glee->rwork));
751:   PetscCall(TSGetDM(ts, &dm));
752:   PetscCall(DMCoarsenHookAdd(dm, DMCoarsenHook_TSGLEE, DMRestrictHook_TSGLEE, ts));
753:   PetscCall(DMSubDomainHookAdd(dm, DMSubDomainHook_TSGLEE, DMSubDomainRestrictHook_TSGLEE, ts));
754:   PetscFunctionReturn(PETSC_SUCCESS);
755: }

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

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

770:   PetscFunctionReturn(PETSC_SUCCESS);
771: }

773: /*------------------------------------------------------------*/

775: static PetscErrorCode TSSetFromOptions_GLEE(TS ts, PetscOptionItems *PetscOptionsObject)
776: {
777:   char gleetype[256];

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

787:     PetscCall(PetscStrncpy(gleetype, TSGLEEDefaultType, sizeof(gleetype)));
788:     for (link = GLEETableauList, count = 0; link; link = link->next, count++)
789:       ;
790:     PetscCall(PetscMalloc1(count, (char ***)&namelist));
791:     for (link = GLEETableauList, count = 0; link; link = link->next, count++) namelist[count] = link->tab.name;
792:     PetscCall(PetscOptionsEList("-ts_glee_type", "Family of GLEE method", "TSGLEESetType", (const char *const *)namelist, count, gleetype, &choice, &flg));
793:     PetscCall(TSGLEESetType(ts, flg ? namelist[choice] : gleetype));
794:     PetscCall(PetscFree(namelist));
795:   }
796:   PetscOptionsHeadEnd();
797:   PetscFunctionReturn(PETSC_SUCCESS);
798: }

800: static PetscErrorCode TSView_GLEE(TS ts, PetscViewer viewer)
801: {
802:   TS_GLEE    *glee = (TS_GLEE *)ts->data;
803:   GLEETableau tab  = glee->tableau;
804:   PetscBool   iascii;

806:   PetscFunctionBegin;
807:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
808:   if (iascii) {
809:     TSGLEEType gleetype;
810:     char       buf[512];
811:     PetscCall(TSGLEEGetType(ts, &gleetype));
812:     PetscCall(PetscViewerASCIIPrintf(viewer, "  GLEE type %s\n", gleetype));
813:     PetscCall(PetscFormatRealArray(buf, sizeof(buf), "% 8.6f", tab->s, tab->c));
814:     PetscCall(PetscViewerASCIIPrintf(viewer, "  Abscissa     c = %s\n", buf));
815:     /* Note: print out r as well */
816:   }
817:   PetscFunctionReturn(PETSC_SUCCESS);
818: }

820: static PetscErrorCode TSLoad_GLEE(TS ts, PetscViewer viewer)
821: {
822:   SNES    snes;
823:   TSAdapt tsadapt;

825:   PetscFunctionBegin;
826:   PetscCall(TSGetAdapt(ts, &tsadapt));
827:   PetscCall(TSAdaptLoad(tsadapt, viewer));
828:   PetscCall(TSGetSNES(ts, &snes));
829:   PetscCall(SNESLoad(snes, viewer));
830:   /* function and Jacobian context for SNES when used with TS is always ts object */
831:   PetscCall(SNESSetFunction(snes, NULL, NULL, ts));
832:   PetscCall(SNESSetJacobian(snes, NULL, NULL, NULL, ts));
833:   PetscFunctionReturn(PETSC_SUCCESS);
834: }

836: /*@C
837:   TSGLEESetType - Set the type of `TSGLEE` scheme

839:   Logically Collective

841:   Input Parameters:
842: + ts       - timestepping context
843: - gleetype - type of `TSGLEE` scheme

845:   Level: intermediate

847: .seealso: [](ch_ts), `TSGLEEGetType()`, `TSGLEE`
848: @*/
849: PetscErrorCode TSGLEESetType(TS ts, TSGLEEType gleetype)
850: {
851:   PetscFunctionBegin;
853:   PetscAssertPointer(gleetype, 2);
854:   PetscTryMethod(ts, "TSGLEESetType_C", (TS, TSGLEEType), (ts, gleetype));
855:   PetscFunctionReturn(PETSC_SUCCESS);
856: }

858: /*@C
859:   TSGLEEGetType - Get the type of `TSGLEE` scheme

861:   Logically Collective

863:   Input Parameter:
864: . ts - timestepping context

866:   Output Parameter:
867: . gleetype - type of `TSGLEE` scheme

869:   Level: intermediate

871: .seealso: [](ch_ts), `TSGLEE`, `TSGLEESetType()`
872: @*/
873: PetscErrorCode TSGLEEGetType(TS ts, TSGLEEType *gleetype)
874: {
875:   PetscFunctionBegin;
877:   PetscUseMethod(ts, "TSGLEEGetType_C", (TS, TSGLEEType *), (ts, gleetype));
878:   PetscFunctionReturn(PETSC_SUCCESS);
879: }

881: static PetscErrorCode TSGLEEGetType_GLEE(TS ts, TSGLEEType *gleetype)
882: {
883:   TS_GLEE *glee = (TS_GLEE *)ts->data;

885:   PetscFunctionBegin;
886:   if (!glee->tableau) PetscCall(TSGLEESetType(ts, TSGLEEDefaultType));
887:   *gleetype = glee->tableau->name;
888:   PetscFunctionReturn(PETSC_SUCCESS);
889: }
890: static PetscErrorCode TSGLEESetType_GLEE(TS ts, TSGLEEType gleetype)
891: {
892:   TS_GLEE        *glee = (TS_GLEE *)ts->data;
893:   PetscBool       match;
894:   GLEETableauLink link;

896:   PetscFunctionBegin;
897:   if (glee->tableau) {
898:     PetscCall(PetscStrcmp(glee->tableau->name, gleetype, &match));
899:     if (match) PetscFunctionReturn(PETSC_SUCCESS);
900:   }
901:   for (link = GLEETableauList; link; link = link->next) {
902:     PetscCall(PetscStrcmp(link->tab.name, gleetype, &match));
903:     if (match) {
904:       PetscCall(TSReset_GLEE(ts));
905:       glee->tableau = &link->tab;
906:       PetscFunctionReturn(PETSC_SUCCESS);
907:     }
908:   }
909:   SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_ARG_UNKNOWN_TYPE, "Could not find '%s'", gleetype);
910: }

912: static PetscErrorCode TSGetStages_GLEE(TS ts, PetscInt *ns, Vec **Y)
913: {
914:   TS_GLEE *glee = (TS_GLEE *)ts->data;

916:   PetscFunctionBegin;
917:   if (ns) *ns = glee->tableau->s;
918:   if (Y) *Y = glee->YStage;
919:   PetscFunctionReturn(PETSC_SUCCESS);
920: }

922: static PetscErrorCode TSGetSolutionComponents_GLEE(TS ts, PetscInt *n, Vec *Y)
923: {
924:   TS_GLEE    *glee = (TS_GLEE *)ts->data;
925:   GLEETableau tab  = glee->tableau;

927:   PetscFunctionBegin;
928:   if (!Y) *n = tab->r;
929:   else {
930:     if ((*n >= 0) && (*n < tab->r)) {
931:       PetscCall(VecCopy(glee->Y[*n], *Y));
932:     } else SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_ARG_OUTOFRANGE, "Second argument (%" PetscInt_FMT ") out of range[0,%" PetscInt_FMT "].", *n, tab->r - 1);
933:   }
934:   PetscFunctionReturn(PETSC_SUCCESS);
935: }

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

947:   PetscFunctionBegin;
948:   PetscCall(VecZeroEntries(*X));
949:   for (i = 0; i < r; i++) wr[i] = F[i];
950:   PetscCall(VecMAXPY((*X), r, wr, Y));
951:   PetscFunctionReturn(PETSC_SUCCESS);
952: }

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

964:   PetscFunctionBegin;
965:   PetscCall(VecZeroEntries(*X));
966:   if (n == 0) {
967:     for (i = 0; i < r; i++) wr[i] = F[i];
968:     PetscCall(VecMAXPY((*X), r, wr, Y));
969:   } else if (n == -1) {
970:     *X = glee->yGErr;
971:   }
972:   PetscFunctionReturn(PETSC_SUCCESS);
973: }

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

983:   PetscFunctionBegin;
984:   PetscCheck(r == 2, PetscObjectComm((PetscObject)ts), PETSC_ERR_SUP, "TSSetTimeError_GLEE not supported for '%s' with r=%" PetscInt_FMT ".", tab->name, tab->r);
985:   for (i = 1; i < r; i++) {
986:     PetscCall(VecCopy(ts->vec_sol, Y[i]));
987:     PetscCall(VecAXPBY(Y[i], S[0], S[1], X));
988:     PetscCall(VecCopy(X, glee->yGErr));
989:   }
990:   PetscFunctionReturn(PETSC_SUCCESS);
991: }

993: static PetscErrorCode TSDestroy_GLEE(TS ts)
994: {
995:   PetscFunctionBegin;
996:   PetscCall(TSReset_GLEE(ts));
997:   if (ts->dm) {
998:     PetscCall(DMCoarsenHookRemove(ts->dm, DMCoarsenHook_TSGLEE, DMRestrictHook_TSGLEE, ts));
999:     PetscCall(DMSubDomainHookRemove(ts->dm, DMSubDomainHook_TSGLEE, DMSubDomainRestrictHook_TSGLEE, ts));
1000:   }
1001:   PetscCall(PetscFree(ts->data));
1002:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSGLEEGetType_C", NULL));
1003:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSGLEESetType_C", NULL));
1004:   PetscFunctionReturn(PETSC_SUCCESS);
1005: }

1007: /* ------------------------------------------------------------ */
1008: /*MC
1009:       TSGLEE - ODE and DAE solver using General Linear with Error Estimation schemes

1011:   The user should provide the right hand side of the equation using `TSSetRHSFunction()`.

1013:   Level: beginner

1015:   Note:
1016:   The default is `TSGLEE35`, it can be changed with `TSGLEESetType()` or -ts_glee_type

1018: .seealso: [](ch_ts), `TSCreate()`, `TS`, `TSSetType()`, `TSGLEESetType()`, `TSGLEEGetType()`,
1019:           `TSGLEE23`, `TTSGLEE24`, `TSGLEE35`, `TSGLEE25I`, `TSGLEEEXRK2A`,
1020:           `TSGLEERK32G1`, `TSGLEERK285EX`, `TSGLEEType`, `TSGLEERegister()`, `TSType`
1021: M*/
1022: PETSC_EXTERN PetscErrorCode TSCreate_GLEE(TS ts)
1023: {
1024:   TS_GLEE *th;

1026:   PetscFunctionBegin;
1027:   PetscCall(TSGLEEInitializePackage());

1029:   ts->ops->reset                 = TSReset_GLEE;
1030:   ts->ops->destroy               = TSDestroy_GLEE;
1031:   ts->ops->view                  = TSView_GLEE;
1032:   ts->ops->load                  = TSLoad_GLEE;
1033:   ts->ops->setup                 = TSSetUp_GLEE;
1034:   ts->ops->step                  = TSStep_GLEE;
1035:   ts->ops->interpolate           = TSInterpolate_GLEE;
1036:   ts->ops->evaluatestep          = TSEvaluateStep_GLEE;
1037:   ts->ops->setfromoptions        = TSSetFromOptions_GLEE;
1038:   ts->ops->getstages             = TSGetStages_GLEE;
1039:   ts->ops->snesfunction          = SNESTSFormFunction_GLEE;
1040:   ts->ops->snesjacobian          = SNESTSFormJacobian_GLEE;
1041:   ts->ops->getsolutioncomponents = TSGetSolutionComponents_GLEE;
1042:   ts->ops->getauxsolution        = TSGetAuxSolution_GLEE;
1043:   ts->ops->gettimeerror          = TSGetTimeError_GLEE;
1044:   ts->ops->settimeerror          = TSSetTimeError_GLEE;
1045:   ts->ops->startingmethod        = TSStartingMethod_GLEE;
1046:   ts->default_adapt_type         = TSADAPTGLEE;

1048:   ts->usessnes = PETSC_TRUE;

1050:   PetscCall(PetscNew(&th));
1051:   ts->data = (void *)th;

1053:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSGLEEGetType_C", TSGLEEGetType_GLEE));
1054:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSGLEESetType_C", TSGLEESetType_GLEE));
1055:   PetscFunctionReturn(PETSC_SUCCESS);
1056: }