Actual source code: glle.c


  2: #include <../src/ts/impls/implicit/glle/glle.h>
  3: #include <petscdm.h>
  4: #include <petscblaslapack.h>

  6: static const char       *TSGLLEErrorDirections[] = {"FORWARD", "BACKWARD", "TSGLLEErrorDirection", "TSGLLEERROR_", NULL};
  7: static PetscFunctionList TSGLLEList;
  8: static PetscFunctionList TSGLLEAcceptList;
  9: static PetscBool         TSGLLEPackageInitialized;
 10: static PetscBool         TSGLLERegisterAllCalled;

 12: /* This function is pure */
 13: static PetscScalar Factorial(PetscInt n)
 14: {
 15:   PetscInt i;
 16:   if (n < 12) { /* Can compute with 32-bit integers */
 17:     PetscInt f = 1;
 18:     for (i = 2; i <= n; i++) f *= i;
 19:     return (PetscScalar)f;
 20:   } else {
 21:     PetscScalar f = 1.;
 22:     for (i = 2; i <= n; i++) f *= (PetscScalar)i;
 23:     return f;
 24:   }
 25: }

 27: /* This function is pure */
 28: static PetscScalar CPowF(PetscScalar c, PetscInt p)
 29: {
 30:   return PetscPowRealInt(PetscRealPart(c), p) / Factorial(p);
 31: }

 33: static PetscErrorCode TSGLLEGetVecs(TS ts, DM dm, Vec *Z, Vec *Ydotstage)
 34: {
 35:   TS_GLLE *gl = (TS_GLLE *)ts->data;

 37:   PetscFunctionBegin;
 38:   if (Z) {
 39:     if (dm && dm != ts->dm) {
 40:       PetscCall(DMGetNamedGlobalVector(dm, "TSGLLE_Z", Z));
 41:     } else *Z = gl->Z;
 42:   }
 43:   if (Ydotstage) {
 44:     if (dm && dm != ts->dm) {
 45:       PetscCall(DMGetNamedGlobalVector(dm, "TSGLLE_Ydot", Ydotstage));
 46:     } else *Ydotstage = gl->Ydot[gl->stage];
 47:   }
 48:   PetscFunctionReturn(PETSC_SUCCESS);
 49: }

 51: static PetscErrorCode TSGLLERestoreVecs(TS ts, DM dm, Vec *Z, Vec *Ydotstage)
 52: {
 53:   PetscFunctionBegin;
 54:   if (Z) {
 55:     if (dm && dm != ts->dm) PetscCall(DMRestoreNamedGlobalVector(dm, "TSGLLE_Z", Z));
 56:   }
 57:   if (Ydotstage) {
 58:     if (dm && dm != ts->dm) PetscCall(DMRestoreNamedGlobalVector(dm, "TSGLLE_Ydot", Ydotstage));
 59:   }
 60:   PetscFunctionReturn(PETSC_SUCCESS);
 61: }

 63: static PetscErrorCode DMCoarsenHook_TSGLLE(DM fine, DM coarse, void *ctx)
 64: {
 65:   PetscFunctionBegin;
 66:   PetscFunctionReturn(PETSC_SUCCESS);
 67: }

 69: static PetscErrorCode DMRestrictHook_TSGLLE(DM fine, Mat restrct, Vec rscale, Mat inject, DM coarse, void *ctx)
 70: {
 71:   TS  ts = (TS)ctx;
 72:   Vec Ydot, Ydot_c;

 74:   PetscFunctionBegin;
 75:   PetscCall(TSGLLEGetVecs(ts, fine, NULL, &Ydot));
 76:   PetscCall(TSGLLEGetVecs(ts, coarse, NULL, &Ydot_c));
 77:   PetscCall(MatRestrict(restrct, Ydot, Ydot_c));
 78:   PetscCall(VecPointwiseMult(Ydot_c, rscale, Ydot_c));
 79:   PetscCall(TSGLLERestoreVecs(ts, fine, NULL, &Ydot));
 80:   PetscCall(TSGLLERestoreVecs(ts, coarse, NULL, &Ydot_c));
 81:   PetscFunctionReturn(PETSC_SUCCESS);
 82: }

 84: static PetscErrorCode DMSubDomainHook_TSGLLE(DM dm, DM subdm, void *ctx)
 85: {
 86:   PetscFunctionBegin;
 87:   PetscFunctionReturn(PETSC_SUCCESS);
 88: }

 90: static PetscErrorCode DMSubDomainRestrictHook_TSGLLE(DM dm, VecScatter gscat, VecScatter lscat, DM subdm, void *ctx)
 91: {
 92:   TS  ts = (TS)ctx;
 93:   Vec Ydot, Ydot_s;

 95:   PetscFunctionBegin;
 96:   PetscCall(TSGLLEGetVecs(ts, dm, NULL, &Ydot));
 97:   PetscCall(TSGLLEGetVecs(ts, subdm, NULL, &Ydot_s));

 99:   PetscCall(VecScatterBegin(gscat, Ydot, Ydot_s, INSERT_VALUES, SCATTER_FORWARD));
100:   PetscCall(VecScatterEnd(gscat, Ydot, Ydot_s, INSERT_VALUES, SCATTER_FORWARD));

102:   PetscCall(TSGLLERestoreVecs(ts, dm, NULL, &Ydot));
103:   PetscCall(TSGLLERestoreVecs(ts, subdm, NULL, &Ydot_s));
104:   PetscFunctionReturn(PETSC_SUCCESS);
105: }

107: static PetscErrorCode TSGLLESchemeCreate(PetscInt p, PetscInt q, PetscInt r, PetscInt s, const PetscScalar *c, const PetscScalar *a, const PetscScalar *b, const PetscScalar *u, const PetscScalar *v, TSGLLEScheme *inscheme)
108: {
109:   TSGLLEScheme scheme;
110:   PetscInt     j;

112:   PetscFunctionBegin;
113:   PetscCheck(p >= 1, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Scheme order must be positive");
114:   PetscCheck(r >= 1, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "At least one item must be carried between steps");
115:   PetscCheck(s >= 1, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "At least one stage is required");
117:   *inscheme = NULL;
118:   PetscCall(PetscNew(&scheme));
119:   scheme->p = p;
120:   scheme->q = q;
121:   scheme->r = r;
122:   scheme->s = s;

124:   PetscCall(PetscMalloc5(s, &scheme->c, s * s, &scheme->a, r * s, &scheme->b, r * s, &scheme->u, r * r, &scheme->v));
125:   PetscCall(PetscArraycpy(scheme->c, c, s));
126:   for (j = 0; j < s * s; j++) scheme->a[j] = (PetscAbsScalar(a[j]) < 1e-12) ? 0 : a[j];
127:   for (j = 0; j < r * s; j++) scheme->b[j] = (PetscAbsScalar(b[j]) < 1e-12) ? 0 : b[j];
128:   for (j = 0; j < s * r; j++) scheme->u[j] = (PetscAbsScalar(u[j]) < 1e-12) ? 0 : u[j];
129:   for (j = 0; j < r * r; j++) scheme->v[j] = (PetscAbsScalar(v[j]) < 1e-12) ? 0 : v[j];

131:   PetscCall(PetscMalloc6(r, &scheme->alpha, r, &scheme->beta, r, &scheme->gamma, 3 * s, &scheme->phi, 3 * r, &scheme->psi, r, &scheme->stage_error));
132:   {
133:     PetscInt     i, j, k, ss = s + 2;
134:     PetscBLASInt m, n, one = 1, *ipiv, lwork = 4 * ((s + 3) * 3 + 3), info, ldb;
135:     PetscReal    rcond, *sing, *workreal;
136:     PetscScalar *ImV, *H, *bmat, *workscalar, *c = scheme->c, *a = scheme->a, *b = scheme->b, *u = scheme->u, *v = scheme->v;
137:     PetscBLASInt rank;
138:     PetscCall(PetscMalloc7(PetscSqr(r), &ImV, 3 * s, &H, 3 * ss, &bmat, lwork, &workscalar, 5 * (3 + r), &workreal, r + s, &sing, r + s, &ipiv));

140:     /* column-major input */
141:     for (i = 0; i < r - 1; i++) {
142:       for (j = 0; j < r - 1; j++) ImV[i + j * r] = 1.0 * (i == j) - v[(i + 1) * r + j + 1];
143:     }
144:     /* Build right hand side for alpha (tp - glm.B(2:end,:)*(glm.c.^(p)./factorial(p))) */
145:     for (i = 1; i < r; i++) {
146:       scheme->alpha[i] = 1. / Factorial(p + 1 - i);
147:       for (j = 0; j < s; j++) scheme->alpha[i] -= b[i * s + j] * CPowF(c[j], p);
148:     }
149:     PetscCall(PetscBLASIntCast(r - 1, &m));
150:     PetscCall(PetscBLASIntCast(r, &n));
151:     PetscCallBLAS("LAPACKgesv", LAPACKgesv_(&m, &one, ImV, &n, ipiv, scheme->alpha + 1, &n, &info));
152:     PetscCheck(info >= 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "Bad argument to GESV");
153:     PetscCheck(info <= 0, PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Bad LU factorization");

155:     /* Build right hand side for beta (tp1 - glm.B(2:end,:)*(glm.c.^(p+1)./factorial(p+1)) - e.alpha) */
156:     for (i = 1; i < r; i++) {
157:       scheme->beta[i] = 1. / Factorial(p + 2 - i) - scheme->alpha[i];
158:       for (j = 0; j < s; j++) scheme->beta[i] -= b[i * s + j] * CPowF(c[j], p + 1);
159:     }
160:     PetscCallBLAS("LAPACKgetrs", LAPACKgetrs_("No transpose", &m, &one, ImV, &n, ipiv, scheme->beta + 1, &n, &info));
161:     PetscCheck(info >= 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "Bad argument to GETRS");
162:     PetscCheck(info <= 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "Should not happen");

164:     /* Build stage_error vector
165:            xi = glm.c.^(p+1)/factorial(p+1) - glm.A*glm.c.^p/factorial(p) + glm.U(:,2:end)*e.alpha;
166:     */
167:     for (i = 0; i < s; i++) {
168:       scheme->stage_error[i] = CPowF(c[i], p + 1);
169:       for (j = 0; j < s; j++) scheme->stage_error[i] -= a[i * s + j] * CPowF(c[j], p);
170:       for (j = 1; j < r; j++) scheme->stage_error[i] += u[i * r + j] * scheme->alpha[j];
171:     }

173:     /* alpha[0] (epsilon in B,J,W 2007)
174:            epsilon = 1/factorial(p+1) - B(1,:)*c.^p/factorial(p) + V(1,2:end)*e.alpha;
175:     */
176:     scheme->alpha[0] = 1. / Factorial(p + 1);
177:     for (j = 0; j < s; j++) scheme->alpha[0] -= b[0 * s + j] * CPowF(c[j], p);
178:     for (j = 1; j < r; j++) scheme->alpha[0] += v[0 * r + j] * scheme->alpha[j];

180:     /* right hand side for gamma (glm.B(2:end,:)*e.xi - e.epsilon*eye(s-1,1)) */
181:     for (i = 1; i < r; i++) {
182:       scheme->gamma[i] = (i == 1 ? -1. : 0) * scheme->alpha[0];
183:       for (j = 0; j < s; j++) scheme->gamma[i] += b[i * s + j] * scheme->stage_error[j];
184:     }
185:     PetscCallBLAS("LAPACKgetrs", LAPACKgetrs_("No transpose", &m, &one, ImV, &n, ipiv, scheme->gamma + 1, &n, &info));
186:     PetscCheck(info >= 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "Bad argument to GETRS");
187:     PetscCheck(info <= 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "Should not happen");

189:     /* beta[0] (rho in B,J,W 2007)
190:         e.rho = 1/factorial(p+2) - glm.B(1,:)*glm.c.^(p+1)/factorial(p+1) ...
191:             + glm.V(1,2:end)*e.beta;% - e.epsilon;
192:     % Note: The paper (B,J,W 2007) includes the last term in their definition
193:     * */
194:     scheme->beta[0] = 1. / Factorial(p + 2);
195:     for (j = 0; j < s; j++) scheme->beta[0] -= b[0 * s + j] * CPowF(c[j], p + 1);
196:     for (j = 1; j < r; j++) scheme->beta[0] += v[0 * r + j] * scheme->beta[j];

198:     /* gamma[0] (sigma in B,J,W 2007)
199:     *   e.sigma = glm.B(1,:)*e.xi + glm.V(1,2:end)*e.gamma;
200:     * */
201:     scheme->gamma[0] = 0.0;
202:     for (j = 0; j < s; j++) scheme->gamma[0] += b[0 * s + j] * scheme->stage_error[j];
203:     for (j = 1; j < r; j++) scheme->gamma[0] += v[0 * s + j] * scheme->gamma[j];

205:     /* Assemble H
206:     *    % " PetscInt_FMT "etermine the error estimators phi
207:        H = [[cpow(glm.c,p) + C*e.alpha] [cpow(glm.c,p+1) + C*e.beta] ...
208:                [e.xi - C*(e.gamma + 0*e.epsilon*eye(s-1,1))]]';
209:     % Paper has formula above without the 0, but that term must be left
210:     % out to satisfy the conditions they propose and to make the
211:     % example schemes work
212:     e.H = H;
213:     e.phi = (H \ [1 0 0;1 1 0;0 0 -1])';
214:     e.psi = -e.phi*C;
215:     * */
216:     for (j = 0; j < s; j++) {
217:       H[0 + j * 3] = CPowF(c[j], p);
218:       H[1 + j * 3] = CPowF(c[j], p + 1);
219:       H[2 + j * 3] = scheme->stage_error[j];
220:       for (k = 1; k < r; k++) {
221:         H[0 + j * 3] += CPowF(c[j], k - 1) * scheme->alpha[k];
222:         H[1 + j * 3] += CPowF(c[j], k - 1) * scheme->beta[k];
223:         H[2 + j * 3] -= CPowF(c[j], k - 1) * scheme->gamma[k];
224:       }
225:     }
226:     bmat[0 + 0 * ss] = 1.;
227:     bmat[0 + 1 * ss] = 0.;
228:     bmat[0 + 2 * ss] = 0.;
229:     bmat[1 + 0 * ss] = 1.;
230:     bmat[1 + 1 * ss] = 1.;
231:     bmat[1 + 2 * ss] = 0.;
232:     bmat[2 + 0 * ss] = 0.;
233:     bmat[2 + 1 * ss] = 0.;
234:     bmat[2 + 2 * ss] = -1.;
235:     m                = 3;
236:     PetscCall(PetscBLASIntCast(s, &n));
237:     PetscCall(PetscBLASIntCast(ss, &ldb));
238:     rcond = 1e-12;
239: #if defined(PETSC_USE_COMPLEX)
240:     /* ZGELSS( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, WORK, LWORK, RWORK, INFO) */
241:     PetscCallBLAS("LAPACKgelss", LAPACKgelss_(&m, &n, &m, H, &m, bmat, &ldb, sing, &rcond, &rank, workscalar, &lwork, workreal, &info));
242: #else
243:     /* DGELSS( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, WORK, LWORK, INFO) */
244:     PetscCallBLAS("LAPACKgelss", LAPACKgelss_(&m, &n, &m, H, &m, bmat, &ldb, sing, &rcond, &rank, workscalar, &lwork, &info));
245: #endif
246:     PetscCheck(info >= 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "Bad argument to GELSS");
247:     PetscCheck(info <= 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "SVD failed to converge");

249:     for (j = 0; j < 3; j++) {
250:       for (k = 0; k < s; k++) scheme->phi[k + j * s] = bmat[k + j * ss];
251:     }

253:     /* the other part of the error estimator, psi in B,J,W 2007 */
254:     scheme->psi[0 * r + 0] = 0.;
255:     scheme->psi[1 * r + 0] = 0.;
256:     scheme->psi[2 * r + 0] = 0.;
257:     for (j = 1; j < r; j++) {
258:       scheme->psi[0 * r + j] = 0.;
259:       scheme->psi[1 * r + j] = 0.;
260:       scheme->psi[2 * r + j] = 0.;
261:       for (k = 0; k < s; k++) {
262:         scheme->psi[0 * r + j] -= CPowF(c[k], j - 1) * scheme->phi[0 * s + k];
263:         scheme->psi[1 * r + j] -= CPowF(c[k], j - 1) * scheme->phi[1 * s + k];
264:         scheme->psi[2 * r + j] -= CPowF(c[k], j - 1) * scheme->phi[2 * s + k];
265:       }
266:     }
267:     PetscCall(PetscFree7(ImV, H, bmat, workscalar, workreal, sing, ipiv));
268:   }
269:   /* Check which properties are satisfied */
270:   scheme->stiffly_accurate = PETSC_TRUE;
271:   if (scheme->c[s - 1] != 1.) scheme->stiffly_accurate = PETSC_FALSE;
272:   for (j = 0; j < s; j++)
273:     if (a[(s - 1) * s + j] != b[j]) scheme->stiffly_accurate = PETSC_FALSE;
274:   for (j = 0; j < r; j++)
275:     if (u[(s - 1) * r + j] != v[j]) scheme->stiffly_accurate = PETSC_FALSE;
276:   scheme->fsal = scheme->stiffly_accurate; /* FSAL is stronger */
277:   for (j = 0; j < s - 1; j++)
278:     if (r > 1 && b[1 * s + j] != 0.) scheme->fsal = PETSC_FALSE;
279:   if (b[1 * s + r - 1] != 1.) scheme->fsal = PETSC_FALSE;
280:   for (j = 0; j < r; j++)
281:     if (r > 1 && v[1 * r + j] != 0.) scheme->fsal = PETSC_FALSE;

283:   *inscheme = scheme;
284:   PetscFunctionReturn(PETSC_SUCCESS);
285: }

287: static PetscErrorCode TSGLLESchemeDestroy(TSGLLEScheme sc)
288: {
289:   PetscFunctionBegin;
290:   PetscCall(PetscFree5(sc->c, sc->a, sc->b, sc->u, sc->v));
291:   PetscCall(PetscFree6(sc->alpha, sc->beta, sc->gamma, sc->phi, sc->psi, sc->stage_error));
292:   PetscCall(PetscFree(sc));
293:   PetscFunctionReturn(PETSC_SUCCESS);
294: }

296: static PetscErrorCode TSGLLEDestroy_Default(TS_GLLE *gl)
297: {
298:   PetscInt i;

300:   PetscFunctionBegin;
301:   for (i = 0; i < gl->nschemes; i++) {
302:     if (gl->schemes[i]) PetscCall(TSGLLESchemeDestroy(gl->schemes[i]));
303:   }
304:   PetscCall(PetscFree(gl->schemes));
305:   gl->nschemes = 0;
306:   PetscCall(PetscMemzero(gl->type_name, sizeof(gl->type_name)));
307:   PetscFunctionReturn(PETSC_SUCCESS);
308: }

310: static PetscErrorCode TSGLLEViewTable_Private(PetscViewer viewer, PetscInt m, PetscInt n, const PetscScalar a[], const char name[])
311: {
312:   PetscBool iascii;
313:   PetscInt  i, j;

315:   PetscFunctionBegin;
316:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
317:   if (iascii) {
318:     PetscCall(PetscViewerASCIIPrintf(viewer, "%30s = [", name));
319:     for (i = 0; i < m; i++) {
320:       if (i) PetscCall(PetscViewerASCIIPrintf(viewer, "%30s   [", ""));
321:       PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
322:       for (j = 0; j < n; j++) PetscCall(PetscViewerASCIIPrintf(viewer, " %12.8g", (double)PetscRealPart(a[i * n + j])));
323:       PetscCall(PetscViewerASCIIPrintf(viewer, "]\n"));
324:       PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
325:     }
326:   }
327:   PetscFunctionReturn(PETSC_SUCCESS);
328: }

330: static PetscErrorCode TSGLLESchemeView(TSGLLEScheme sc, PetscBool view_details, PetscViewer viewer)
331: {
332:   PetscBool iascii;

334:   PetscFunctionBegin;
335:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
336:   if (iascii) {
337:     PetscCall(PetscViewerASCIIPrintf(viewer, "GL scheme p,q,r,s = %" PetscInt_FMT ",%" PetscInt_FMT ",%" PetscInt_FMT ",%" PetscInt_FMT "\n", sc->p, sc->q, sc->r, sc->s));
338:     PetscCall(PetscViewerASCIIPushTab(viewer));
339:     PetscCall(PetscViewerASCIIPrintf(viewer, "Stiffly accurate: %s,  FSAL: %s\n", sc->stiffly_accurate ? "yes" : "no", sc->fsal ? "yes" : "no"));
340:     PetscCall(PetscViewerASCIIPrintf(viewer, "Leading error constants: %10.3e  %10.3e  %10.3e\n", (double)PetscRealPart(sc->alpha[0]), (double)PetscRealPart(sc->beta[0]), (double)PetscRealPart(sc->gamma[0])));
341:     PetscCall(TSGLLEViewTable_Private(viewer, 1, sc->s, sc->c, "Abscissas c"));
342:     if (view_details) {
343:       PetscCall(TSGLLEViewTable_Private(viewer, sc->s, sc->s, sc->a, "A"));
344:       PetscCall(TSGLLEViewTable_Private(viewer, sc->r, sc->s, sc->b, "B"));
345:       PetscCall(TSGLLEViewTable_Private(viewer, sc->s, sc->r, sc->u, "U"));
346:       PetscCall(TSGLLEViewTable_Private(viewer, sc->r, sc->r, sc->v, "V"));

348:       PetscCall(TSGLLEViewTable_Private(viewer, 3, sc->s, sc->phi, "Error estimate phi"));
349:       PetscCall(TSGLLEViewTable_Private(viewer, 3, sc->r, sc->psi, "Error estimate psi"));
350:       PetscCall(TSGLLEViewTable_Private(viewer, 1, sc->r, sc->alpha, "Modify alpha"));
351:       PetscCall(TSGLLEViewTable_Private(viewer, 1, sc->r, sc->beta, "Modify beta"));
352:       PetscCall(TSGLLEViewTable_Private(viewer, 1, sc->r, sc->gamma, "Modify gamma"));
353:       PetscCall(TSGLLEViewTable_Private(viewer, 1, sc->s, sc->stage_error, "Stage error xi"));
354:     }
355:     PetscCall(PetscViewerASCIIPopTab(viewer));
356:   } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Viewer type %s not supported", ((PetscObject)viewer)->type_name);
357:   PetscFunctionReturn(PETSC_SUCCESS);
358: }

360: static PetscErrorCode TSGLLEEstimateHigherMoments_Default(TSGLLEScheme sc, PetscReal h, Vec Ydot[], Vec Xold[], Vec hm[])
361: {
362:   PetscInt i;

364:   PetscFunctionBegin;
365:   PetscCheck(sc->r <= 64 && sc->s <= 64, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Ridiculous number of stages or items passed between stages");
366:   /* build error vectors*/
367:   for (i = 0; i < 3; i++) {
368:     PetscScalar phih[64];
369:     PetscInt    j;
370:     for (j = 0; j < sc->s; j++) phih[j] = sc->phi[i * sc->s + j] * h;
371:     PetscCall(VecZeroEntries(hm[i]));
372:     PetscCall(VecMAXPY(hm[i], sc->s, phih, Ydot));
373:     PetscCall(VecMAXPY(hm[i], sc->r, &sc->psi[i * sc->r], Xold));
374:   }
375:   PetscFunctionReturn(PETSC_SUCCESS);
376: }

378: static PetscErrorCode TSGLLECompleteStep_Rescale(TSGLLEScheme sc, PetscReal h, TSGLLEScheme next_sc, PetscReal next_h, Vec Ydot[], Vec Xold[], Vec X[])
379: {
380:   PetscScalar brow[32], vrow[32];
381:   PetscInt    i, j, r, s;

383:   PetscFunctionBegin;
384:   /* Build the new solution from (X,Ydot) */
385:   r = sc->r;
386:   s = sc->s;
387:   for (i = 0; i < r; i++) {
388:     PetscCall(VecZeroEntries(X[i]));
389:     for (j = 0; j < s; j++) brow[j] = h * sc->b[i * s + j];
390:     PetscCall(VecMAXPY(X[i], s, brow, Ydot));
391:     for (j = 0; j < r; j++) vrow[j] = sc->v[i * r + j];
392:     PetscCall(VecMAXPY(X[i], r, vrow, Xold));
393:   }
394:   PetscFunctionReturn(PETSC_SUCCESS);
395: }

397: static PetscErrorCode TSGLLECompleteStep_RescaleAndModify(TSGLLEScheme sc, PetscReal h, TSGLLEScheme next_sc, PetscReal next_h, Vec Ydot[], Vec Xold[], Vec X[])
398: {
399:   PetscScalar brow[32], vrow[32];
400:   PetscReal   ratio;
401:   PetscInt    i, j, p, r, s;

403:   PetscFunctionBegin;
404:   /* Build the new solution from (X,Ydot) */
405:   p     = sc->p;
406:   r     = sc->r;
407:   s     = sc->s;
408:   ratio = next_h / h;
409:   for (i = 0; i < r; i++) {
410:     PetscCall(VecZeroEntries(X[i]));
411:     for (j = 0; j < s; j++) {
412:       brow[j] = h * (PetscPowRealInt(ratio, i) * sc->b[i * s + j] + (PetscPowRealInt(ratio, i) - PetscPowRealInt(ratio, p + 1)) * (+sc->alpha[i] * sc->phi[0 * s + j]) + (PetscPowRealInt(ratio, i) - PetscPowRealInt(ratio, p + 2)) * (+sc->beta[i] * sc->phi[1 * s + j] + sc->gamma[i] * sc->phi[2 * s + j]));
413:     }
414:     PetscCall(VecMAXPY(X[i], s, brow, Ydot));
415:     for (j = 0; j < r; j++) {
416:       vrow[j] = (PetscPowRealInt(ratio, i) * sc->v[i * r + j] + (PetscPowRealInt(ratio, i) - PetscPowRealInt(ratio, p + 1)) * (+sc->alpha[i] * sc->psi[0 * r + j]) + (PetscPowRealInt(ratio, i) - PetscPowRealInt(ratio, p + 2)) * (+sc->beta[i] * sc->psi[1 * r + j] + sc->gamma[i] * sc->psi[2 * r + j]));
417:     }
418:     PetscCall(VecMAXPY(X[i], r, vrow, Xold));
419:   }
420:   if (r < next_sc->r) {
421:     PetscCheck(r + 1 == next_sc->r, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Cannot accommodate jump in r greater than 1");
422:     PetscCall(VecZeroEntries(X[r]));
423:     for (j = 0; j < s; j++) brow[j] = h * PetscPowRealInt(ratio, p + 1) * sc->phi[0 * s + j];
424:     PetscCall(VecMAXPY(X[r], s, brow, Ydot));
425:     for (j = 0; j < r; j++) vrow[j] = PetscPowRealInt(ratio, p + 1) * sc->psi[0 * r + j];
426:     PetscCall(VecMAXPY(X[r], r, vrow, Xold));
427:   }
428:   PetscFunctionReturn(PETSC_SUCCESS);
429: }

431: static PetscErrorCode TSGLLECreate_IRKS(TS ts)
432: {
433:   TS_GLLE *gl = (TS_GLLE *)ts->data;

435:   PetscFunctionBegin;
436:   gl->Destroy               = TSGLLEDestroy_Default;
437:   gl->EstimateHigherMoments = TSGLLEEstimateHigherMoments_Default;
438:   gl->CompleteStep          = TSGLLECompleteStep_RescaleAndModify;
439:   PetscCall(PetscMalloc1(10, &gl->schemes));
440:   gl->nschemes = 0;

442:   {
443:     /* p=1,q=1, r=s=2, A- and L-stable with error estimates of order 2 and 3
444:     * Listed in Butcher & Podhaisky 2006. On error estimation in general linear methods for stiff ODE.
445:     * irks(0.3,0,[.3,1],[1],1)
446:     * Note: can be made to have classical order (not stage order) 2 by replacing 0.3 with 1-sqrt(1/2)
447:     * but doing so would sacrifice the error estimator.
448:     */
449:     const PetscScalar c[2]    = {3. / 10., 1.};
450:     const PetscScalar a[2][2] = {
451:       {3. / 10., 0       },
452:       {7. / 10., 3. / 10.}
453:     };
454:     const PetscScalar b[2][2] = {
455:       {7. / 10., 3. / 10.},
456:       {0,        1       }
457:     };
458:     const PetscScalar u[2][2] = {
459:       {1, 0},
460:       {1, 0}
461:     };
462:     const PetscScalar v[2][2] = {
463:       {1, 0},
464:       {0, 0}
465:     };
466:     PetscCall(TSGLLESchemeCreate(1, 1, 2, 2, c, *a, *b, *u, *v, &gl->schemes[gl->nschemes++]));
467:   }

469:   {
470:     /* p=q=2, r=s=3: irks(4/9,0,[1:3]/3,[0.33852],1) */
471:     /* http://www.math.auckland.ac.nz/~hpod/atlas/i2a.html */
472:     const PetscScalar c[3]    = {1. / 3., 2. / 3., 1};
473:     const PetscScalar a[3][3] = {
474:       {4. / 9.,              0,                     0      },
475:       {1.03750643704090e+00, 4. / 9.,               0      },
476:       {7.67024779410304e-01, -3.81140216918943e-01, 4. / 9.}
477:     };
478:     const PetscScalar b[3][3] = {
479:       {0.767024779410304,  -0.381140216918943, 4. / 9.          },
480:       {0.000000000000000,  0.000000000000000,  1.000000000000000},
481:       {-2.075048385225385, 0.621728385225383,  1.277197204924873}
482:     };
483:     const PetscScalar u[3][3] = {
484:       {1.0000000000000000, -0.1111111111111109, -0.0925925925925922},
485:       {1.0000000000000000, -0.8152842148186744, -0.4199095530877056},
486:       {1.0000000000000000, 0.1696709930641948,  0.0539741070314165 }
487:     };
488:     const PetscScalar v[3][3] = {
489:       {1.0000000000000000, 0.1696709930641948, 0.0539741070314165},
490:       {0.000000000000000,  0.000000000000000,  0.000000000000000 },
491:       {0.000000000000000,  0.176122795075129,  0.000000000000000 }
492:     };
493:     PetscCall(TSGLLESchemeCreate(2, 2, 3, 3, c, *a, *b, *u, *v, &gl->schemes[gl->nschemes++]));
494:   }
495:   {
496:     /* p=q=3, r=s=4: irks(9/40,0,[1:4]/4,[0.3312 1.0050],[0.49541 1;1 0]) */
497:     const PetscScalar c[4]    = {0.25, 0.5, 0.75, 1.0};
498:     const PetscScalar a[4][4] = {
499:       {9. / 40.,             0,                     0,                 0       },
500:       {2.11286958887701e-01, 9. / 40.,              0,                 0       },
501:       {9.46338294287584e-01, -3.42942861246094e-01, 9. / 40.,          0       },
502:       {0.521490453970721,    -0.662474225622980,    0.490476425459734, 9. / 40.}
503:     };
504:     const PetscScalar b[4][4] = {
505:       {0.521490453970721,  -0.662474225622980, 0.490476425459734,  9. / 40.         },
506:       {0.000000000000000,  0.000000000000000,  0.000000000000000,  1.000000000000000},
507:       {-0.084677029310348, 1.390757514776085,  -1.568157386206001, 2.023192696767826},
508:       {0.465383797936408,  1.478273530625148,  -1.930836081010182, 1.644872111193354}
509:     };
510:     const PetscScalar u[4][4] = {
511:       {1.00000000000000000, 0.02500000000001035,  -0.02499999999999053, -0.00442708333332865},
512:       {1.00000000000000000, 0.06371304111232945,  -0.04032173972189845, -0.01389438413189452},
513:       {1.00000000000000000, -0.07839543304147778, 0.04738685705116663,  0.02032603595928376 },
514:       {1.00000000000000000, 0.42550734619251651,  0.10800718022400080,  -0.01726712647760034}
515:     };
516:     const PetscScalar v[4][4] = {
517:       {1.00000000000000000, 0.42550734619251651, 0.10800718022400080, -0.01726712647760034},
518:       {0.000000000000000,   0.000000000000000,   0.000000000000000,   0.000000000000000   },
519:       {0.000000000000000,   -1.761115796027561,  -0.521284157173780,  0.258249384305463   },
520:       {0.000000000000000,   -1.657693358744728,  -1.052227765232394,  0.521284157173780   }
521:     };
522:     PetscCall(TSGLLESchemeCreate(3, 3, 4, 4, c, *a, *b, *u, *v, &gl->schemes[gl->nschemes++]));
523:   }
524:   {
525:     /* p=q=4, r=s=5:
526:           irks(3/11,0,[1:5]/5, [0.1715   -0.1238    0.6617],...
527:           [ -0.0812    0.4079    1.0000
528:              1.0000         0         0
529:              0.8270    1.0000         0])
530:     */
531:     const PetscScalar c[5]    = {0.2, 0.4, 0.6, 0.8, 1.0};
532:     const PetscScalar a[5][5] = {
533:       {2.72727272727352e-01,  0.00000000000000e+00,  0.00000000000000e+00,  0.00000000000000e+00, 0.00000000000000e+00},
534:       {-1.03980153733431e-01, 2.72727272727405e-01,  0.00000000000000e+00,  0.00000000000000e+00, 0.00000000000000e+00},
535:       {-1.58615400341492e+00, 7.44168951881122e-01,  2.72727272727309e-01,  0.00000000000000e+00, 0.00000000000000e+00},
536:       {-8.73658042865628e-01, 5.37884671894595e-01,  -1.63298538799523e-01, 2.72727272726996e-01, 0.00000000000000e+00},
537:       {2.95489397443992e-01,  -1.18481693910097e+00, -6.68029812659953e-01, 1.00716687860943e+00, 2.72727272727288e-01}
538:     };
539:     const PetscScalar b[5][5] = {
540:       {2.95489397443992e-01,  -1.18481693910097e+00, -6.68029812659953e-01, 1.00716687860943e+00,  2.72727272727288e-01},
541:       {0.00000000000000e+00,  1.11022302462516e-16,  -2.22044604925031e-16, 0.00000000000000e+00,  1.00000000000000e+00},
542:       {-4.05882503986005e+00, -4.00924006567769e+00, -1.38930610972481e+00, 4.45223930308488e+00,  6.32331093108427e-01},
543:       {8.35690179937017e+00,  -2.26640927349732e+00, 6.86647884973826e+00,  -5.22595158025740e+00, 4.50893068837431e+00},
544:       {1.27656267027479e+01,  2.80882153840821e+00,  8.91173096522890e+00,  -1.07936444078906e+01, 4.82534148988854e+00}
545:     };
546:     const PetscScalar u[5][5] = {
547:       {1.00000000000000e+00, -7.27272727273551e-02, -3.45454545454419e-02, -4.12121212119565e-03, -2.96969696964014e-04},
548:       {1.00000000000000e+00, 2.31252881006154e-01,  -8.29487834416481e-03, -9.07191207681020e-03, -1.70378403743473e-03},
549:       {1.00000000000000e+00, 1.16925777880663e+00,  3.59268562942635e-02,  -4.09013451730615e-02, -1.02411119670164e-02},
550:       {1.00000000000000e+00, 1.02634463704356e+00,  1.59375044913405e-01,  1.89673015035370e-03,  -4.89987231897569e-03},
551:       {1.00000000000000e+00, 1.27746320298021e+00,  2.37186008132728e-01,  -8.28694373940065e-02, -5.34396510196430e-02}
552:     };
553:     const PetscScalar v[5][5] = {
554:       {1.00000000000000e+00, 1.27746320298021e+00,  2.37186008132728e-01,  -8.28694373940065e-02, -5.34396510196430e-02},
555:       {0.00000000000000e+00, -1.77635683940025e-15, -1.99840144432528e-15, -9.99200722162641e-16, -3.33066907387547e-16},
556:       {0.00000000000000e+00, 4.37280081906924e+00,  5.49221645016377e-02,  -8.88913177394943e-02, 1.12879077989154e-01 },
557:       {0.00000000000000e+00, -1.22399504837280e+01, -5.21287338448645e+00, -8.03952325565291e-01, 4.60298678047147e-01 },
558:       {0.00000000000000e+00, -1.85178762883829e+01, -5.21411849862624e+00, -1.04283436528809e+00, 7.49030161063651e-01 }
559:     };
560:     PetscCall(TSGLLESchemeCreate(4, 4, 5, 5, c, *a, *b, *u, *v, &gl->schemes[gl->nschemes++]));
561:   }
562:   {
563:     /* p=q=5, r=s=6;
564:        irks(1/3,0,[1:6]/6,...
565:           [-0.0489    0.4228   -0.8814    0.9021],...
566:           [-0.3474   -0.6617    0.6294    0.2129
567:             0.0044   -0.4256   -0.1427   -0.8936
568:            -0.8267    0.4821    0.1371   -0.2557
569:            -0.4426   -0.3855   -0.7514    0.3014])
570:     */
571:     const PetscScalar c[6]    = {1. / 6, 2. / 6, 3. / 6, 4. / 6, 5. / 6, 1.};
572:     const PetscScalar a[6][6] = {
573:       {3.33333333333940e-01,  0,                     0,                     0,                     0,                    0                   },
574:       {-8.64423857333350e-02, 3.33333333332888e-01,  0,                     0,                     0,                    0                   },
575:       {-2.16850174258252e+00, -2.23619072028839e+00, 3.33333333335204e-01,  0,                     0,                    0                   },
576:       {-4.73160970138997e+00, -3.89265344629268e+00, -2.76318716520933e-01, 3.33333333335759e-01,  0,                    0                   },
577:       {-6.75187540297338e+00, -7.90756533769377e+00, 7.90245051802259e-01,  -4.48352364517632e-01, 3.33333333328483e-01, 0                   },
578:       {-4.26488287921548e+00, -1.19320395589302e+01, 3.38924509887755e+00,  -2.23969848002481e+00, 6.62807710124007e-01, 3.33333333335440e-01}
579:     };
580:     const PetscScalar b[6][6] = {
581:       {-4.26488287921548e+00, -1.19320395589302e+01, 3.38924509887755e+00,  -2.23969848002481e+00, 6.62807710124007e-01,  3.33333333335440e-01 },
582:       {-8.88178419700125e-16, 4.44089209850063e-16,  -1.54737334057131e-15, -8.88178419700125e-16, 0.00000000000000e+00,  1.00000000000001e+00 },
583:       {-2.87780425770651e+01, -1.13520448264971e+01, 2.62002318943161e+01,  2.56943874812797e+01,  -3.06702268304488e+01, 6.68067773510103e+00 },
584:       {5.47971245256474e+01,  6.80366875868284e+01,  -6.50952588861999e+01, -8.28643975339097e+01, 8.17416943896414e+01,  -1.17819043489036e+01},
585:       {-2.33332114788869e+02, 6.12942539462634e+01,  -4.91850135865944e+01, 1.82716844135480e+02,  -1.29788173979395e+02, 3.09968095651099e+01 },
586:       {-1.72049132343751e+02, 8.60194713593999e+00,  7.98154219170200e-01,  1.50371386053218e+02,  -1.18515423962066e+02, 2.50898277784663e+01 }
587:     };
588:     const PetscScalar u[6][6] = {
589:       {1.00000000000000e+00, -1.66666666666870e-01, -4.16666666664335e-02, -3.85802469124815e-03, -2.25051440302250e-04, -9.64506172339142e-06},
590:       {1.00000000000000e+00, 8.64423857327162e-02,  -4.11484912671353e-02, -1.11450903217645e-02, -1.47651050487126e-03, -1.34395070766826e-04},
591:       {1.00000000000000e+00, 4.57135912953434e+00,  1.06514719719137e+00,  1.33517564218007e-01,  1.11365952968659e-02,  6.12382756769504e-04 },
592:       {1.00000000000000e+00, 9.23391519753404e+00,  2.22431212392095e+00,  2.91823807741891e-01,  2.52058456411084e-02,  1.22800542949647e-03 },
593:       {1.00000000000000e+00, 1.48175480533865e+01,  3.73439117461835e+00,  5.14648336541804e-01,  4.76430038853402e-02,  2.56798515502156e-03 },
594:       {1.00000000000000e+00, 1.50512347758335e+01,  4.10099701165164e+00,  5.66039141003603e-01,  3.91213893800891e-02,  -2.99136269067853e-03}
595:     };
596:     const PetscScalar v[6][6] = {
597:       {1.00000000000000e+00, 1.50512347758335e+01,  4.10099701165164e+00,  5.66039141003603e-01,  3.91213893800891e-02,  -2.99136269067853e-03},
598:       {0.00000000000000e+00, -4.88498130835069e-15, -6.43929354282591e-15, -3.55271367880050e-15, -1.22124532708767e-15, -3.12250225675825e-16},
599:       {0.00000000000000e+00, 1.22250171233141e+01,  -1.77150760606169e+00, 3.54516769879390e-01,  6.22298845883398e-01,  2.31647447450276e-01 },
600:       {0.00000000000000e+00, -4.48339457331040e+01, -3.57363126641880e-01, 5.18750173123425e-01,  6.55727990241799e-02,  1.63175368287079e-01 },
601:       {0.00000000000000e+00, 1.37297394708005e+02,  -1.60145272991317e+00, -5.05319555199441e+00, 1.55328940390990e-01,  9.16629423682464e-01 },
602:       {0.00000000000000e+00, 1.05703241119022e+02,  -1.16610260983038e+00, -2.99767252773859e+00, -1.13472315553890e-01, 1.09742849254729e+00 }
603:     };
604:     PetscCall(TSGLLESchemeCreate(5, 5, 6, 6, c, *a, *b, *u, *v, &gl->schemes[gl->nschemes++]));
605:   }
606:   PetscFunctionReturn(PETSC_SUCCESS);
607: }

609: /*@C
610:    TSGLLESetType - sets the class of general linear method, `TSGLLE` to use for time-stepping

612:    Collective

614:    Input Parameters:
615: +  ts - the `TS` context
616: -  type - a method

618:    Options Database Key:
619: .  -ts_gl_type <type> - sets the method, use -help for a list of available method (e.g. irks)

621:    Level: intermediate

623:    Notes:
624:    See "petsc/include/petscts.h" for available methods (for instance)
625: .    TSGLLE_IRKS - Diagonally implicit methods with inherent Runge-Kutta stability (for stiff problems)

627:    Normally, it is best to use the `TSSetFromOptions()` command and
628:    then set the `TSGLLE` type from the options database rather than by using
629:    this routine.  Using the options database provides the user with
630:    maximum flexibility in evaluating the many different solvers.
631:    The `TSGLLESetType()` routine is provided for those situations where it
632:    is necessary to set the timestepping solver independently of the
633:    command line or options database.  This might be the case, for example,
634:    when the choice of solver changes during the execution of the
635:    program, and the user's application is taking responsibility for
636:    choosing the appropriate method.

638: .seealso: [](ch_ts), `TS`, `TSGLLEType`, `TSGLLE`
639: @*/
640: PetscErrorCode TSGLLESetType(TS ts, TSGLLEType type)
641: {
642:   PetscFunctionBegin;
645:   PetscTryMethod(ts, "TSGLLESetType_C", (TS, TSGLLEType), (ts, type));
646:   PetscFunctionReturn(PETSC_SUCCESS);
647: }

649: /*@C
650:    TSGLLESetAcceptType - sets the acceptance test for `TSGLLE`

652:    Time integrators that need to control error must have the option to reject a time step based on local error
653:    estimates.  This function allows different schemes to be set.

655:    Logically Collective

657:    Input Parameters:
658: +  ts - the `TS` context
659: -  type - the type

661:    Options Database Key:
662: .  -ts_gl_accept_type <type> - sets the method used to determine whether to accept or reject a step

664:    Level: intermediate

666: .seealso: [](ch_ts), `TS`, `TSGLLE`, `TSGLLEAcceptRegister()`, `TSGLLEAdapt`
667: @*/
668: PetscErrorCode TSGLLESetAcceptType(TS ts, TSGLLEAcceptType type)
669: {
670:   PetscFunctionBegin;
673:   PetscTryMethod(ts, "TSGLLESetAcceptType_C", (TS, TSGLLEAcceptType), (ts, type));
674:   PetscFunctionReturn(PETSC_SUCCESS);
675: }

677: /*@C
678:    TSGLLEGetAdapt - gets the `TSGLLEAdapt` object from the `TS`

680:    Not Collective

682:    Input Parameter:
683: .  ts - the `TS` context

685:    Output Parameter:
686: .  adapt - the `TSGLLEAdapt` context

688:    Level: advanced

690:    Note:
691:    This allows the user set options on the `TSGLLEAdapt` object.  Usually it is better to do this using the options
692:    database, so this function is rarely needed.

694: .seealso: [](ch_ts), `TS`, `TSGLLE`, `TSGLLEAdapt`, `TSGLLEAdaptRegister()`
695: @*/
696: PetscErrorCode TSGLLEGetAdapt(TS ts, TSGLLEAdapt *adapt)
697: {
698:   PetscFunctionBegin;
701:   PetscUseMethod(ts, "TSGLLEGetAdapt_C", (TS, TSGLLEAdapt *), (ts, adapt));
702:   PetscFunctionReturn(PETSC_SUCCESS);
703: }

705: static PetscErrorCode TSGLLEAccept_Always(TS ts, PetscReal tleft, PetscReal h, const PetscReal enorms[], PetscBool *accept)
706: {
707:   PetscFunctionBegin;
708:   *accept = PETSC_TRUE;
709:   PetscFunctionReturn(PETSC_SUCCESS);
710: }

712: static PetscErrorCode TSGLLEUpdateWRMS(TS ts)
713: {
714:   TS_GLLE     *gl = (TS_GLLE *)ts->data;
715:   PetscScalar *x, *w;
716:   PetscInt     n, i;

718:   PetscFunctionBegin;
719:   PetscCall(VecGetArray(gl->X[0], &x));
720:   PetscCall(VecGetArray(gl->W, &w));
721:   PetscCall(VecGetLocalSize(gl->W, &n));
722:   for (i = 0; i < n; i++) w[i] = 1. / (gl->wrms_atol + gl->wrms_rtol * PetscAbsScalar(x[i]));
723:   PetscCall(VecRestoreArray(gl->X[0], &x));
724:   PetscCall(VecRestoreArray(gl->W, &w));
725:   PetscFunctionReturn(PETSC_SUCCESS);
726: }

728: static PetscErrorCode TSGLLEVecNormWRMS(TS ts, Vec X, PetscReal *nrm)
729: {
730:   TS_GLLE     *gl = (TS_GLLE *)ts->data;
731:   PetscScalar *x, *w;
732:   PetscReal    sum = 0.0, gsum;
733:   PetscInt     n, N, i;

735:   PetscFunctionBegin;
736:   PetscCall(VecGetArray(X, &x));
737:   PetscCall(VecGetArray(gl->W, &w));
738:   PetscCall(VecGetLocalSize(gl->W, &n));
739:   for (i = 0; i < n; i++) sum += PetscAbsScalar(PetscSqr(x[i] * w[i]));
740:   PetscCall(VecRestoreArray(X, &x));
741:   PetscCall(VecRestoreArray(gl->W, &w));
742:   PetscCall(MPIU_Allreduce(&sum, &gsum, 1, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject)ts)));
743:   PetscCall(VecGetSize(gl->W, &N));
744:   *nrm = PetscSqrtReal(gsum / (1. * N));
745:   PetscFunctionReturn(PETSC_SUCCESS);
746: }

748: static PetscErrorCode TSGLLESetType_GLLE(TS ts, TSGLLEType type)
749: {
750:   PetscBool same;
751:   TS_GLLE  *gl = (TS_GLLE *)ts->data;
752:   PetscErrorCode (*r)(TS);

754:   PetscFunctionBegin;
755:   if (gl->type_name[0]) {
756:     PetscCall(PetscStrcmp(gl->type_name, type, &same));
757:     if (same) PetscFunctionReturn(PETSC_SUCCESS);
758:     PetscCall((*gl->Destroy)(gl));
759:   }

761:   PetscCall(PetscFunctionListFind(TSGLLEList, type, &r));
762:   PetscCheck(r, PETSC_COMM_SELF, PETSC_ERR_ARG_UNKNOWN_TYPE, "Unknown TSGLLE type \"%s\" given", type);
763:   PetscCall((*r)(ts));
764:   PetscCall(PetscStrncpy(gl->type_name, type, sizeof(gl->type_name)));
765:   PetscFunctionReturn(PETSC_SUCCESS);
766: }

768: static PetscErrorCode TSGLLESetAcceptType_GLLE(TS ts, TSGLLEAcceptType type)
769: {
770:   TSGLLEAcceptFunction r;
771:   TS_GLLE             *gl = (TS_GLLE *)ts->data;

773:   PetscFunctionBegin;
774:   PetscCall(PetscFunctionListFind(TSGLLEAcceptList, type, &r));
775:   PetscCheck(r, PETSC_COMM_SELF, PETSC_ERR_ARG_UNKNOWN_TYPE, "Unknown TSGLLEAccept type \"%s\" given", type);
776:   gl->Accept = r;
777:   PetscCall(PetscStrncpy(gl->accept_name, type, sizeof(gl->accept_name)));
778:   PetscFunctionReturn(PETSC_SUCCESS);
779: }

781: static PetscErrorCode TSGLLEGetAdapt_GLLE(TS ts, TSGLLEAdapt *adapt)
782: {
783:   TS_GLLE *gl = (TS_GLLE *)ts->data;

785:   PetscFunctionBegin;
786:   if (!gl->adapt) {
787:     PetscCall(TSGLLEAdaptCreate(PetscObjectComm((PetscObject)ts), &gl->adapt));
788:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)gl->adapt, (PetscObject)ts, 1));
789:   }
790:   *adapt = gl->adapt;
791:   PetscFunctionReturn(PETSC_SUCCESS);
792: }

794: static PetscErrorCode TSGLLEChooseNextScheme(TS ts, PetscReal h, const PetscReal hmnorm[], PetscInt *next_scheme, PetscReal *next_h, PetscBool *finish)
795: {
796:   TS_GLLE  *gl = (TS_GLLE *)ts->data;
797:   PetscInt  i, n, cur_p, cur, next_sc, candidates[64], orders[64];
798:   PetscReal errors[64], costs[64], tleft;

800:   PetscFunctionBegin;
801:   cur   = -1;
802:   cur_p = gl->schemes[gl->current_scheme]->p;
803:   tleft = ts->max_time - (ts->ptime + ts->time_step);
804:   for (i = 0, n = 0; i < gl->nschemes; i++) {
805:     TSGLLEScheme sc = gl->schemes[i];
806:     if (sc->p < gl->min_order || gl->max_order < sc->p) continue;
807:     if (sc->p == cur_p - 1) errors[n] = PetscAbsScalar(sc->alpha[0]) * hmnorm[0];
808:     else if (sc->p == cur_p) errors[n] = PetscAbsScalar(sc->alpha[0]) * hmnorm[1];
809:     else if (sc->p == cur_p + 1) errors[n] = PetscAbsScalar(sc->alpha[0]) * (hmnorm[2] + hmnorm[3]);
810:     else continue;
811:     candidates[n] = i;
812:     orders[n]     = PetscMin(sc->p, sc->q); /* order of global truncation error */
813:     costs[n]      = sc->s;                  /* estimate the cost as the number of stages */
814:     if (i == gl->current_scheme) cur = n;
815:     n++;
816:   }
817:   PetscCheck(cur >= 0 && gl->nschemes > cur, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Current scheme not found in scheme list");
818:   PetscCall(TSGLLEAdaptChoose(gl->adapt, n, orders, errors, costs, cur, h, tleft, &next_sc, next_h, finish));
819:   *next_scheme = candidates[next_sc];
820:   PetscCall(PetscInfo(ts, "Adapt chose scheme %" PetscInt_FMT " (%" PetscInt_FMT ",%" PetscInt_FMT ",%" PetscInt_FMT ",%" PetscInt_FMT ") with step size %6.2e, finish=%s\n", *next_scheme, gl->schemes[*next_scheme]->p, gl->schemes[*next_scheme]->q,
821:                       gl->schemes[*next_scheme]->r, gl->schemes[*next_scheme]->s, (double)*next_h, PetscBools[*finish]));
822:   PetscFunctionReturn(PETSC_SUCCESS);
823: }

825: static PetscErrorCode TSGLLEGetMaxSizes(TS ts, PetscInt *max_r, PetscInt *max_s)
826: {
827:   TS_GLLE *gl = (TS_GLLE *)ts->data;

829:   PetscFunctionBegin;
830:   *max_r = gl->schemes[gl->nschemes - 1]->r;
831:   *max_s = gl->schemes[gl->nschemes - 1]->s;
832:   PetscFunctionReturn(PETSC_SUCCESS);
833: }

835: static PetscErrorCode TSSolve_GLLE(TS ts)
836: {
837:   TS_GLLE            *gl = (TS_GLLE *)ts->data;
838:   PetscInt            i, k, its, lits, max_r, max_s;
839:   PetscBool           final_step, finish;
840:   SNESConvergedReason snesreason;

842:   PetscFunctionBegin;
843:   PetscCall(TSMonitor(ts, ts->steps, ts->ptime, ts->vec_sol));

845:   PetscCall(TSGLLEGetMaxSizes(ts, &max_r, &max_s));
846:   PetscCall(VecCopy(ts->vec_sol, gl->X[0]));
847:   for (i = 1; i < max_r; i++) PetscCall(VecZeroEntries(gl->X[i]));
848:   PetscCall(TSGLLEUpdateWRMS(ts));

850:   if (0) {
851:     /* Find consistent initial data for DAE */
852:     gl->stage_time = ts->ptime + ts->time_step;
853:     gl->scoeff     = 1.;
854:     gl->stage      = 0;

856:     PetscCall(VecCopy(ts->vec_sol, gl->Z));
857:     PetscCall(VecCopy(ts->vec_sol, gl->Y));
858:     PetscCall(SNESSolve(ts->snes, NULL, gl->Y));
859:     PetscCall(SNESGetIterationNumber(ts->snes, &its));
860:     PetscCall(SNESGetLinearSolveIterations(ts->snes, &lits));
861:     PetscCall(SNESGetConvergedReason(ts->snes, &snesreason));

863:     ts->snes_its += its;
864:     ts->ksp_its += lits;
865:     if (snesreason < 0 && ts->max_snes_failures > 0 && ++ts->num_snes_failures >= ts->max_snes_failures) {
866:       ts->reason = TS_DIVERGED_NONLINEAR_SOLVE;
867:       PetscCall(PetscInfo(ts, "Step=%" PetscInt_FMT ", nonlinear solve solve failures %" PetscInt_FMT " greater than current TS allowed, stopping solve\n", ts->steps, ts->num_snes_failures));
868:       PetscFunctionReturn(PETSC_SUCCESS);
869:     }
870:   }

872:   PetscCheck(gl->current_scheme >= 0, PETSC_COMM_SELF, PETSC_ERR_ORDER, "A starting scheme has not been provided");

874:   for (k = 0, final_step = PETSC_FALSE, finish = PETSC_FALSE; k < ts->max_steps && !finish; k++) {
875:     PetscInt           j, r, s, next_scheme = 0, rejections;
876:     PetscReal          h, hmnorm[4], enorm[3], next_h;
877:     PetscBool          accept;
878:     const PetscScalar *c, *a, *u;
879:     Vec               *X, *Ydot, Y;
880:     TSGLLEScheme       scheme = gl->schemes[gl->current_scheme];

882:     r    = scheme->r;
883:     s    = scheme->s;
884:     c    = scheme->c;
885:     a    = scheme->a;
886:     u    = scheme->u;
887:     h    = ts->time_step;
888:     X    = gl->X;
889:     Ydot = gl->Ydot;
890:     Y    = gl->Y;

892:     if (ts->ptime > ts->max_time) break;

894:     /*
895:       We only call PreStep at the start of each STEP, not each STAGE.  This is because it is
896:       possible to fail (have to restart a step) after multiple stages.
897:     */
898:     PetscCall(TSPreStep(ts));

900:     rejections = 0;
901:     while (1) {
902:       for (i = 0; i < s; i++) {
903:         PetscScalar shift;
904:         gl->scoeff     = 1. / PetscRealPart(a[i * s + i]);
905:         shift          = gl->scoeff / ts->time_step;
906:         gl->stage      = i;
907:         gl->stage_time = ts->ptime + PetscRealPart(c[i]) * h;

909:         /*
910:         * Stage equation: Y = h A Y' + U X
911:         * We assume that A is lower-triangular so that we can solve the stages (Y,Y') sequentially
912:         * Build the affine vector z_i = -[1/(h a_ii)](h sum_j a_ij y'_j + sum_j u_ij x_j)
913:         * Then y'_i = z + 1/(h a_ii) y_i
914:         */
915:         PetscCall(VecZeroEntries(gl->Z));
916:         for (j = 0; j < r; j++) PetscCall(VecAXPY(gl->Z, -shift * u[i * r + j], X[j]));
917:         for (j = 0; j < i; j++) PetscCall(VecAXPY(gl->Z, -shift * h * a[i * s + j], Ydot[j]));
918:         /* Note: Z is used within function evaluation, Ydot = Z + shift*Y */

920:         /* Compute an estimate of Y to start Newton iteration */
921:         if (gl->extrapolate) {
922:           if (i == 0) {
923:             /* Linear extrapolation on the first stage */
924:             PetscCall(VecWAXPY(Y, c[i] * h, X[1], X[0]));
925:           } else {
926:             /* Linear extrapolation from the last stage */
927:             PetscCall(VecAXPY(Y, (c[i] - c[i - 1]) * h, Ydot[i - 1]));
928:           }
929:         } else if (i == 0) { /* Directly use solution from the last step, otherwise reuse the last stage (do nothing) */
930:           PetscCall(VecCopy(X[0], Y));
931:         }

933:         /* Solve this stage (Ydot[i] is computed during function evaluation) */
934:         PetscCall(SNESSolve(ts->snes, NULL, Y));
935:         PetscCall(SNESGetIterationNumber(ts->snes, &its));
936:         PetscCall(SNESGetLinearSolveIterations(ts->snes, &lits));
937:         PetscCall(SNESGetConvergedReason(ts->snes, &snesreason));
938:         ts->snes_its += its;
939:         ts->ksp_its += lits;
940:         if (snesreason < 0 && ts->max_snes_failures > 0 && ++ts->num_snes_failures >= ts->max_snes_failures) {
941:           ts->reason = TS_DIVERGED_NONLINEAR_SOLVE;
942:           PetscCall(PetscInfo(ts, "Step=%" PetscInt_FMT ", nonlinear solve solve failures %" PetscInt_FMT " greater than current TS allowed, stopping solve\n", ts->steps, ts->num_snes_failures));
943:           PetscFunctionReturn(PETSC_SUCCESS);
944:         }
945:       }

947:       gl->stage_time = ts->ptime + ts->time_step;

949:       PetscCall((*gl->EstimateHigherMoments)(scheme, h, Ydot, gl->X, gl->himom));
950:       /* hmnorm[i] = h^{p+i}x^{(p+i)} with i=0,1,2; hmnorm[3] = h^{p+2}(dx'/dx) x^{(p+1)} */
951:       for (i = 0; i < 3; i++) PetscCall(TSGLLEVecNormWRMS(ts, gl->himom[i], &hmnorm[i + 1]));
952:       enorm[0] = PetscRealPart(scheme->alpha[0]) * hmnorm[1];
953:       enorm[1] = PetscRealPart(scheme->beta[0]) * hmnorm[2];
954:       enorm[2] = PetscRealPart(scheme->gamma[0]) * hmnorm[3];
955:       PetscCall((*gl->Accept)(ts, ts->max_time - gl->stage_time, h, enorm, &accept));
956:       if (accept) goto accepted;
957:       rejections++;
958:       PetscCall(PetscInfo(ts, "Step %" PetscInt_FMT " (t=%g) not accepted, rejections=%" PetscInt_FMT "\n", k, (double)gl->stage_time, rejections));
959:       if (rejections > gl->max_step_rejections) break;
960:       /*
961:         There are lots of reasons why a step might be rejected, including solvers not converging and other factors that
962:         TSGLLEChooseNextScheme does not support.  Additionally, the error estimates may be very screwed up, so I'm not
963:         convinced that it's safe to just compute a new error estimate using the same interface as the current adaptor
964:         (the adaptor interface probably has to change).  Here we make an arbitrary and naive choice.  This assumes that
965:         steps were written in Nordsieck form.  The "correct" method would be to re-complete the previous time step with
966:         the correct "next" step size.  It is unclear to me whether the present ad-hoc method of rescaling X is stable.
967:       */
968:       h *= 0.5;
969:       for (i = 1; i < scheme->r; i++) PetscCall(VecScale(X[i], PetscPowRealInt(0.5, i)));
970:     }
971:     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_CONV_FAILED, "Time step %" PetscInt_FMT " (t=%g) not accepted after %" PetscInt_FMT " failures", k, (double)gl->stage_time, rejections);

973:   accepted:
974:     /* This term is not error, but it *would* be the leading term for a lower order method */
975:     PetscCall(TSGLLEVecNormWRMS(ts, gl->X[scheme->r - 1], &hmnorm[0]));
976:     /* Correct scaling so that these are equivalent to norms of the Nordsieck vectors */

978:     PetscCall(PetscInfo(ts, "Last moment norm %10.2e, estimated error norms %10.2e %10.2e %10.2e\n", (double)hmnorm[0], (double)enorm[0], (double)enorm[1], (double)enorm[2]));
979:     if (!final_step) {
980:       PetscCall(TSGLLEChooseNextScheme(ts, h, hmnorm, &next_scheme, &next_h, &final_step));
981:     } else {
982:       /* Dummy values to complete the current step in a consistent manner */
983:       next_scheme = gl->current_scheme;
984:       next_h      = h;
985:       finish      = PETSC_TRUE;
986:     }

988:     X        = gl->Xold;
989:     gl->Xold = gl->X;
990:     gl->X    = X;
991:     PetscCall((*gl->CompleteStep)(scheme, h, gl->schemes[next_scheme], next_h, Ydot, gl->Xold, gl->X));

993:     PetscCall(TSGLLEUpdateWRMS(ts));

995:     /* Post the solution for the user, we could avoid this copy with a small bit of cleverness */
996:     PetscCall(VecCopy(gl->X[0], ts->vec_sol));
997:     ts->ptime += h;
998:     ts->steps++;

1000:     PetscCall(TSPostEvaluate(ts));
1001:     PetscCall(TSPostStep(ts));
1002:     PetscCall(TSMonitor(ts, ts->steps, ts->ptime, ts->vec_sol));

1004:     gl->current_scheme = next_scheme;
1005:     ts->time_step      = next_h;
1006:   }
1007:   PetscFunctionReturn(PETSC_SUCCESS);
1008: }

1010: /*------------------------------------------------------------*/

1012: static PetscErrorCode TSReset_GLLE(TS ts)
1013: {
1014:   TS_GLLE *gl = (TS_GLLE *)ts->data;
1015:   PetscInt max_r, max_s;

1017:   PetscFunctionBegin;
1018:   if (gl->setupcalled) {
1019:     PetscCall(TSGLLEGetMaxSizes(ts, &max_r, &max_s));
1020:     PetscCall(VecDestroyVecs(max_r, &gl->Xold));
1021:     PetscCall(VecDestroyVecs(max_r, &gl->X));
1022:     PetscCall(VecDestroyVecs(max_s, &gl->Ydot));
1023:     PetscCall(VecDestroyVecs(3, &gl->himom));
1024:     PetscCall(VecDestroy(&gl->W));
1025:     PetscCall(VecDestroy(&gl->Y));
1026:     PetscCall(VecDestroy(&gl->Z));
1027:   }
1028:   gl->setupcalled = PETSC_FALSE;
1029:   PetscFunctionReturn(PETSC_SUCCESS);
1030: }

1032: static PetscErrorCode TSDestroy_GLLE(TS ts)
1033: {
1034:   TS_GLLE *gl = (TS_GLLE *)ts->data;

1036:   PetscFunctionBegin;
1037:   PetscCall(TSReset_GLLE(ts));
1038:   if (ts->dm) {
1039:     PetscCall(DMCoarsenHookRemove(ts->dm, DMCoarsenHook_TSGLLE, DMRestrictHook_TSGLLE, ts));
1040:     PetscCall(DMSubDomainHookRemove(ts->dm, DMSubDomainHook_TSGLLE, DMSubDomainRestrictHook_TSGLLE, ts));
1041:   }
1042:   if (gl->adapt) PetscCall(TSGLLEAdaptDestroy(&gl->adapt));
1043:   if (gl->Destroy) PetscCall((*gl->Destroy)(gl));
1044:   PetscCall(PetscFree(ts->data));
1045:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSGLLESetType_C", NULL));
1046:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSGLLESetAcceptType_C", NULL));
1047:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSGLLEGetAdapt_C", NULL));
1048:   PetscFunctionReturn(PETSC_SUCCESS);
1049: }

1051: /*
1052:     This defines the nonlinear equation that is to be solved with SNES
1053:     g(x) = f(t,x,z+shift*x) = 0
1054: */
1055: static PetscErrorCode SNESTSFormFunction_GLLE(SNES snes, Vec x, Vec f, TS ts)
1056: {
1057:   TS_GLLE *gl = (TS_GLLE *)ts->data;
1058:   Vec      Z, Ydot;
1059:   DM       dm, dmsave;

1061:   PetscFunctionBegin;
1062:   PetscCall(SNESGetDM(snes, &dm));
1063:   PetscCall(TSGLLEGetVecs(ts, dm, &Z, &Ydot));
1064:   PetscCall(VecWAXPY(Ydot, gl->scoeff / ts->time_step, x, Z));
1065:   dmsave = ts->dm;
1066:   ts->dm = dm;
1067:   PetscCall(TSComputeIFunction(ts, gl->stage_time, x, Ydot, f, PETSC_FALSE));
1068:   ts->dm = dmsave;
1069:   PetscCall(TSGLLERestoreVecs(ts, dm, &Z, &Ydot));
1070:   PetscFunctionReturn(PETSC_SUCCESS);
1071: }

1073: static PetscErrorCode SNESTSFormJacobian_GLLE(SNES snes, Vec x, Mat A, Mat B, TS ts)
1074: {
1075:   TS_GLLE *gl = (TS_GLLE *)ts->data;
1076:   Vec      Z, Ydot;
1077:   DM       dm, dmsave;

1079:   PetscFunctionBegin;
1080:   PetscCall(SNESGetDM(snes, &dm));
1081:   PetscCall(TSGLLEGetVecs(ts, dm, &Z, &Ydot));
1082:   dmsave = ts->dm;
1083:   ts->dm = dm;
1084:   /* gl->Xdot will have already been computed in SNESTSFormFunction_GLLE */
1085:   PetscCall(TSComputeIJacobian(ts, gl->stage_time, x, gl->Ydot[gl->stage], gl->scoeff / ts->time_step, A, B, PETSC_FALSE));
1086:   ts->dm = dmsave;
1087:   PetscCall(TSGLLERestoreVecs(ts, dm, &Z, &Ydot));
1088:   PetscFunctionReturn(PETSC_SUCCESS);
1089: }

1091: static PetscErrorCode TSSetUp_GLLE(TS ts)
1092: {
1093:   TS_GLLE *gl = (TS_GLLE *)ts->data;
1094:   PetscInt max_r, max_s;
1095:   DM       dm;

1097:   PetscFunctionBegin;
1098:   gl->setupcalled = PETSC_TRUE;
1099:   PetscCall(TSGLLEGetMaxSizes(ts, &max_r, &max_s));
1100:   PetscCall(VecDuplicateVecs(ts->vec_sol, max_r, &gl->X));
1101:   PetscCall(VecDuplicateVecs(ts->vec_sol, max_r, &gl->Xold));
1102:   PetscCall(VecDuplicateVecs(ts->vec_sol, max_s, &gl->Ydot));
1103:   PetscCall(VecDuplicateVecs(ts->vec_sol, 3, &gl->himom));
1104:   PetscCall(VecDuplicate(ts->vec_sol, &gl->W));
1105:   PetscCall(VecDuplicate(ts->vec_sol, &gl->Y));
1106:   PetscCall(VecDuplicate(ts->vec_sol, &gl->Z));

1108:   /* Default acceptance tests and adaptivity */
1109:   if (!gl->Accept) PetscCall(TSGLLESetAcceptType(ts, TSGLLEACCEPT_ALWAYS));
1110:   if (!gl->adapt) PetscCall(TSGLLEGetAdapt(ts, &gl->adapt));

1112:   if (gl->current_scheme < 0) {
1113:     PetscInt i;
1114:     for (i = 0;; i++) {
1115:       if (gl->schemes[i]->p == gl->start_order) break;
1116:       PetscCheck(i + 1 != gl->nschemes, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "No schemes available with requested start order %" PetscInt_FMT, i);
1117:     }
1118:     gl->current_scheme = i;
1119:   }
1120:   PetscCall(TSGetDM(ts, &dm));
1121:   PetscCall(DMCoarsenHookAdd(dm, DMCoarsenHook_TSGLLE, DMRestrictHook_TSGLLE, ts));
1122:   PetscCall(DMSubDomainHookAdd(dm, DMSubDomainHook_TSGLLE, DMSubDomainRestrictHook_TSGLLE, ts));
1123:   PetscFunctionReturn(PETSC_SUCCESS);
1124: }
1125: /*------------------------------------------------------------*/

1127: static PetscErrorCode TSSetFromOptions_GLLE(TS ts, PetscOptionItems *PetscOptionsObject)
1128: {
1129:   TS_GLLE *gl         = (TS_GLLE *)ts->data;
1130:   char     tname[256] = TSGLLE_IRKS, completef[256] = "rescale-and-modify";

1132:   PetscFunctionBegin;
1133:   PetscOptionsHeadBegin(PetscOptionsObject, "General Linear ODE solver options");
1134:   {
1135:     PetscBool flg;
1136:     PetscCall(PetscOptionsFList("-ts_gl_type", "Type of GL method", "TSGLLESetType", TSGLLEList, gl->type_name[0] ? gl->type_name : tname, tname, sizeof(tname), &flg));
1137:     if (flg || !gl->type_name[0]) PetscCall(TSGLLESetType(ts, tname));
1138:     PetscCall(PetscOptionsInt("-ts_gl_max_step_rejections", "Maximum number of times to attempt a step", "None", gl->max_step_rejections, &gl->max_step_rejections, NULL));
1139:     PetscCall(PetscOptionsInt("-ts_gl_max_order", "Maximum order to try", "TSGLLESetMaxOrder", gl->max_order, &gl->max_order, NULL));
1140:     PetscCall(PetscOptionsInt("-ts_gl_min_order", "Minimum order to try", "TSGLLESetMinOrder", gl->min_order, &gl->min_order, NULL));
1141:     PetscCall(PetscOptionsInt("-ts_gl_start_order", "Initial order to try", "TSGLLESetMinOrder", gl->start_order, &gl->start_order, NULL));
1142:     PetscCall(PetscOptionsEnum("-ts_gl_error_direction", "Which direction to look when estimating error", "TSGLLESetErrorDirection", TSGLLEErrorDirections, (PetscEnum)gl->error_direction, (PetscEnum *)&gl->error_direction, NULL));
1143:     PetscCall(PetscOptionsBool("-ts_gl_extrapolate", "Extrapolate stage solution from previous solution (sometimes unstable)", "TSGLLESetExtrapolate", gl->extrapolate, &gl->extrapolate, NULL));
1144:     PetscCall(PetscOptionsReal("-ts_gl_atol", "Absolute tolerance", "TSGLLESetTolerances", gl->wrms_atol, &gl->wrms_atol, NULL));
1145:     PetscCall(PetscOptionsReal("-ts_gl_rtol", "Relative tolerance", "TSGLLESetTolerances", gl->wrms_rtol, &gl->wrms_rtol, NULL));
1146:     PetscCall(PetscOptionsString("-ts_gl_complete", "Method to use for completing the step", "none", completef, completef, sizeof(completef), &flg));
1147:     if (flg) {
1148:       PetscBool match1, match2;
1149:       PetscCall(PetscStrcmp(completef, "rescale", &match1));
1150:       PetscCall(PetscStrcmp(completef, "rescale-and-modify", &match2));
1151:       if (match1) gl->CompleteStep = TSGLLECompleteStep_Rescale;
1152:       else if (match2) gl->CompleteStep = TSGLLECompleteStep_RescaleAndModify;
1153:       else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_UNKNOWN_TYPE, "%s", completef);
1154:     }
1155:     {
1156:       char type[256] = TSGLLEACCEPT_ALWAYS;
1157:       PetscCall(PetscOptionsFList("-ts_gl_accept_type", "Method to use for determining whether to accept a step", "TSGLLESetAcceptType", TSGLLEAcceptList, gl->accept_name[0] ? gl->accept_name : type, type, sizeof(type), &flg));
1158:       if (flg || !gl->accept_name[0]) PetscCall(TSGLLESetAcceptType(ts, type));
1159:     }
1160:     {
1161:       TSGLLEAdapt adapt;
1162:       PetscCall(TSGLLEGetAdapt(ts, &adapt));
1163:       PetscCall(TSGLLEAdaptSetFromOptions(adapt, PetscOptionsObject));
1164:     }
1165:   }
1166:   PetscOptionsHeadEnd();
1167:   PetscFunctionReturn(PETSC_SUCCESS);
1168: }

1170: static PetscErrorCode TSView_GLLE(TS ts, PetscViewer viewer)
1171: {
1172:   TS_GLLE  *gl = (TS_GLLE *)ts->data;
1173:   PetscInt  i;
1174:   PetscBool iascii, details;

1176:   PetscFunctionBegin;
1177:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
1178:   if (iascii) {
1179:     PetscCall(PetscViewerASCIIPrintf(viewer, "  min order %" PetscInt_FMT ", max order %" PetscInt_FMT ", current order %" PetscInt_FMT "\n", gl->min_order, gl->max_order, gl->schemes[gl->current_scheme]->p));
1180:     PetscCall(PetscViewerASCIIPrintf(viewer, "  Error estimation: %s\n", TSGLLEErrorDirections[gl->error_direction]));
1181:     PetscCall(PetscViewerASCIIPrintf(viewer, "  Extrapolation: %s\n", gl->extrapolate ? "yes" : "no"));
1182:     PetscCall(PetscViewerASCIIPrintf(viewer, "  Acceptance test: %s\n", gl->accept_name[0] ? gl->accept_name : "(not yet set)"));
1183:     PetscCall(PetscViewerASCIIPushTab(viewer));
1184:     PetscCall(TSGLLEAdaptView(gl->adapt, viewer));
1185:     PetscCall(PetscViewerASCIIPopTab(viewer));
1186:     PetscCall(PetscViewerASCIIPrintf(viewer, "  type: %s\n", gl->type_name[0] ? gl->type_name : "(not yet set)"));
1187:     PetscCall(PetscViewerASCIIPrintf(viewer, "Schemes within family (%" PetscInt_FMT "):\n", gl->nschemes));
1188:     details = PETSC_FALSE;
1189:     PetscCall(PetscOptionsGetBool(((PetscObject)ts)->options, ((PetscObject)ts)->prefix, "-ts_gl_view_detailed", &details, NULL));
1190:     PetscCall(PetscViewerASCIIPushTab(viewer));
1191:     for (i = 0; i < gl->nschemes; i++) PetscCall(TSGLLESchemeView(gl->schemes[i], details, viewer));
1192:     if (gl->View) PetscCall((*gl->View)(gl, viewer));
1193:     PetscCall(PetscViewerASCIIPopTab(viewer));
1194:   }
1195:   PetscFunctionReturn(PETSC_SUCCESS);
1196: }

1198: /*@C
1199:    TSGLLERegister -  adds a `TSGLLE` implementation

1201:    Not Collective

1203:    Input Parameters:
1204: +  sname - name of user-defined general linear scheme
1205: -  function - routine to create method context

1207:    Level: advanced

1209:    Note:
1210:    `TSGLLERegister()` may be called multiple times to add several user-defined families.

1212:    Sample usage:
1213: .vb
1214:    TSGLLERegister("my_scheme", MySchemeCreate);
1215: .ve

1217:    Then, your scheme can be chosen with the procedural interface via
1218: $     TSGLLESetType(ts, "my_scheme")
1219:    or at runtime via the option
1220: $     -ts_gl_type my_scheme

1222: .seealso: [](ch_ts), `TSGLLE`, `TSGLLEType`, `TSGLLERegisterAll()`
1223: @*/
1224: PetscErrorCode TSGLLERegister(const char sname[], PetscErrorCode (*function)(TS))
1225: {
1226:   PetscFunctionBegin;
1227:   PetscCall(TSGLLEInitializePackage());
1228:   PetscCall(PetscFunctionListAdd(&TSGLLEList, sname, function));
1229:   PetscFunctionReturn(PETSC_SUCCESS);
1230: }

1232: /*@C
1233:    TSGLLEAcceptRegister -  adds a `TSGLLE` acceptance scheme

1235:    Not Collective

1237:    Input Parameters:
1238: +  sname - name of user-defined acceptance scheme
1239: -  function - routine to create method context

1241:    Level: advanced

1243:    Note:
1244:    `TSGLLEAcceptRegister()` may be called multiple times to add several user-defined families.

1246:    Sample usage:
1247: .vb
1248:    TSGLLEAcceptRegister("my_scheme", MySchemeCreate);
1249: .ve

1251:    Then, your scheme can be chosen with the procedural interface via
1252: $     TSGLLESetAcceptType(ts, "my_scheme")
1253:    or at runtime via the option
1254: $     -ts_gl_accept_type my_scheme

1256: .seealso: [](ch_ts), `TSGLLE`, `TSGLLEType`, `TSGLLERegisterAll()`, `TSGLLEAcceptFunction`
1257: @*/
1258: PetscErrorCode TSGLLEAcceptRegister(const char sname[], TSGLLEAcceptFunction function)
1259: {
1260:   PetscFunctionBegin;
1261:   PetscCall(PetscFunctionListAdd(&TSGLLEAcceptList, sname, function));
1262:   PetscFunctionReturn(PETSC_SUCCESS);
1263: }

1265: /*@C
1266:   TSGLLERegisterAll - Registers all of the general linear methods in `TSGLLE`

1268:   Not Collective

1270:   Level: advanced

1272: .seealso: [](ch_ts), `TSGLLE`, `TSGLLERegisterDestroy()`
1273: @*/
1274: PetscErrorCode TSGLLERegisterAll(void)
1275: {
1276:   PetscFunctionBegin;
1277:   if (TSGLLERegisterAllCalled) PetscFunctionReturn(PETSC_SUCCESS);
1278:   TSGLLERegisterAllCalled = PETSC_TRUE;

1280:   PetscCall(TSGLLERegister(TSGLLE_IRKS, TSGLLECreate_IRKS));
1281:   PetscCall(TSGLLEAcceptRegister(TSGLLEACCEPT_ALWAYS, TSGLLEAccept_Always));
1282:   PetscFunctionReturn(PETSC_SUCCESS);
1283: }

1285: /*@C
1286:   TSGLLEInitializePackage - This function initializes everything in the `TSGLLE` package. It is called
1287:   from `TSInitializePackage()`.

1289:   Level: developer

1291: .seealso: [](ch_ts), `PetscInitialize()`, `TSInitializePackage()`, `TSGLLEFinalizePackage()`
1292: @*/
1293: PetscErrorCode TSGLLEInitializePackage(void)
1294: {
1295:   PetscFunctionBegin;
1296:   if (TSGLLEPackageInitialized) PetscFunctionReturn(PETSC_SUCCESS);
1297:   TSGLLEPackageInitialized = PETSC_TRUE;
1298:   PetscCall(TSGLLERegisterAll());
1299:   PetscCall(PetscRegisterFinalize(TSGLLEFinalizePackage));
1300:   PetscFunctionReturn(PETSC_SUCCESS);
1301: }

1303: /*@C
1304:   TSGLLEFinalizePackage - This function destroys everything in the `TSGLLE` package. It is
1305:   called from `PetscFinalize()`.

1307:   Level: developer

1309: .seealso: [](ch_ts), `PetscFinalize()`, `TSGLLEInitializePackage()`, `TSInitializePackage()`
1310: @*/
1311: PetscErrorCode TSGLLEFinalizePackage(void)
1312: {
1313:   PetscFunctionBegin;
1314:   PetscCall(PetscFunctionListDestroy(&TSGLLEList));
1315:   PetscCall(PetscFunctionListDestroy(&TSGLLEAcceptList));
1316:   TSGLLEPackageInitialized = PETSC_FALSE;
1317:   TSGLLERegisterAllCalled  = PETSC_FALSE;
1318:   PetscFunctionReturn(PETSC_SUCCESS);
1319: }

1321: /* ------------------------------------------------------------ */
1322: /*MC
1323:       TSGLLE - DAE solver using implicit General Linear methods

1325:   These methods contain Runge-Kutta and multistep schemes as special cases.  These special cases have some fundamental
1326:   limitations.  For example, diagonally implicit Runge-Kutta cannot have stage order greater than 1 which limits their
1327:   applicability to very stiff systems.  Meanwhile, multistep methods cannot be A-stable for order greater than 2 and BDF
1328:   are not 0-stable for order greater than 6.  GL methods can be A- and L-stable with arbitrarily high stage order and
1329:   reliable error estimates for both 1 and 2 orders higher to facilitate adaptive step sizes and adaptive order schemes.
1330:   All this is possible while preserving a singly diagonally implicit structure.

1332:   Options Database Keys:
1333: +  -ts_gl_type <type> - the class of general linear method (irks)
1334: .  -ts_gl_rtol <tol>  - relative error
1335: .  -ts_gl_atol <tol>  - absolute error
1336: .  -ts_gl_min_order <p> - minimum order method to consider (default=1)
1337: .  -ts_gl_max_order <p> - maximum order method to consider (default=3)
1338: .  -ts_gl_start_order <p> - order of starting method (default=1)
1339: .  -ts_gl_complete <method> - method to use for completing the step (rescale-and-modify or rescale)
1340: -  -ts_adapt_type <method> - adaptive controller to use (none step both)

1342:   Level: beginner

1344:   Notes:
1345:   This integrator can be applied to DAE.

1347:   Diagonally implicit general linear (DIGL) methods are a generalization of diagonally implicit Runge-Kutta (DIRK).
1348:   They are represented by the tableau

1350: .vb
1351:   A  |  U
1352:   -------
1353:   B  |  V
1354: .ve

1356:   combined with a vector c of abscissa.  "Diagonally implicit" means that A is lower triangular.
1357:   A step of the general method reads

1359: .vb
1360:   [ Y ] = [A  U] [  Y'   ]
1361:   [X^k] = [B  V] [X^{k-1}]
1362: .ve

1364:   where Y is the multivector of stage values, Y' is the multivector of stage derivatives, X^k is the Nordsieck vector of
1365:   the solution at step k.  The Nordsieck vector consists of the first r moments of the solution, given by

1367: .vb
1368:   X = [x_0,x_1,...,x_{r-1}] = [x, h x', h^2 x'', ..., h^{r-1} x^{(r-1)} ]
1369: .ve

1371:   If A is lower triangular, we can solve the stages (Y,Y') sequentially

1373: .vb
1374:   y_i = h sum_{j=0}^{s-1} (a_ij y'_j) + sum_{j=0}^{r-1} u_ij x_j,    i=0,...,{s-1}
1375: .ve

1377:   and then construct the pieces to carry to the next step

1379: .vb
1380:   xx_i = h sum_{j=0}^{s-1} b_ij y'_j  + sum_{j=0}^{r-1} v_ij x_j,    i=0,...,{r-1}
1381: .ve

1383:   Note that when the equations are cast in implicit form, we are using the stage equation to define y'_i
1384:   in terms of y_i and known stuff (y_j for j<i and x_j for all j).

1386:   Error estimation

1388:   At present, the most attractive GL methods for stiff problems are singly diagonally implicit schemes which posses
1389:   Inherent Runge-Kutta Stability (`TSIRKS`).  These methods have r=s, the number of items passed between steps is equal to
1390:   the number of stages.  The order and stage-order are one less than the number of stages.  We use the error estimates
1391:   in the 2007 paper which provide the following estimates

1393: .vb
1394:   h^{p+1} X^{(p+1)}          = phi_0^T Y' + [0 psi_0^T] Xold
1395:   h^{p+2} X^{(p+2)}          = phi_1^T Y' + [0 psi_1^T] Xold
1396:   h^{p+2} (dx'/dx) X^{(p+1)} = phi_2^T Y' + [0 psi_2^T] Xold
1397: .ve

1399:   These estimates are accurate to O(h^{p+3}).

1401:   Changing the step size

1403:   We use the generalized "rescale and modify" scheme, see equation (4.5) of the 2007 paper.

1405:   References:
1406: + * - John Butcher and Z. Jackieweicz and W. Wright, On error propagation in general linear methods for
1407:   ordinary differential equations, Journal of Complexity, Vol 23, 2007.
1408: - * - John Butcher, Numerical methods for ordinary differential equations, second edition, Wiley, 2009.

1410: .seealso: [](ch_ts), `TSCreate()`, `TS`, `TSSetType()`, `TSType`
1411: M*/
1412: PETSC_EXTERN PetscErrorCode TSCreate_GLLE(TS ts)
1413: {
1414:   TS_GLLE *gl;

1416:   PetscFunctionBegin;
1417:   PetscCall(TSGLLEInitializePackage());

1419:   PetscCall(PetscNew(&gl));
1420:   ts->data = (void *)gl;

1422:   ts->ops->reset          = TSReset_GLLE;
1423:   ts->ops->destroy        = TSDestroy_GLLE;
1424:   ts->ops->view           = TSView_GLLE;
1425:   ts->ops->setup          = TSSetUp_GLLE;
1426:   ts->ops->solve          = TSSolve_GLLE;
1427:   ts->ops->setfromoptions = TSSetFromOptions_GLLE;
1428:   ts->ops->snesfunction   = SNESTSFormFunction_GLLE;
1429:   ts->ops->snesjacobian   = SNESTSFormJacobian_GLLE;

1431:   ts->usessnes = PETSC_TRUE;

1433:   gl->max_step_rejections = 1;
1434:   gl->min_order           = 1;
1435:   gl->max_order           = 3;
1436:   gl->start_order         = 1;
1437:   gl->current_scheme      = -1;
1438:   gl->extrapolate         = PETSC_FALSE;

1440:   gl->wrms_atol = 1e-8;
1441:   gl->wrms_rtol = 1e-5;

1443:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSGLLESetType_C", &TSGLLESetType_GLLE));
1444:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSGLLESetAcceptType_C", &TSGLLESetAcceptType_GLLE));
1445:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSGLLEGetAdapt_C", &TSGLLEGetAdapt_GLLE));
1446:   PetscFunctionReturn(PETSC_SUCCESS);
1447: }