Actual source code: glle.c

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

106: 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)
107: {
108:   TSGLLEScheme scheme;
109:   PetscInt     j;

111:   PetscFunctionBegin;
112:   PetscCheck(p >= 1, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Scheme order must be positive");
113:   PetscCheck(r >= 1, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "At least one item must be carried between steps");
114:   PetscCheck(s >= 1, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "At least one stage is required");
115:   PetscAssertPointer(inscheme, 10);
116:   *inscheme = NULL;
117:   PetscCall(PetscNew(&scheme));
118:   scheme->p = p;
119:   scheme->q = q;
120:   scheme->r = r;
121:   scheme->s = s;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

333:   PetscFunctionBegin;
334:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
335:   if (iascii) {
336:     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));
337:     PetscCall(PetscViewerASCIIPushTab(viewer));
338:     PetscCall(PetscViewerASCIIPrintf(viewer, "Stiffly accurate: %s,  FSAL: %s\n", sc->stiffly_accurate ? "yes" : "no", sc->fsal ? "yes" : "no"));
339:     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])));
340:     PetscCall(TSGLLEViewTable_Private(viewer, 1, sc->s, sc->c, "Abscissas c"));
341:     if (view_details) {
342:       PetscCall(TSGLLEViewTable_Private(viewer, sc->s, sc->s, sc->a, "A"));
343:       PetscCall(TSGLLEViewTable_Private(viewer, sc->r, sc->s, sc->b, "B"));
344:       PetscCall(TSGLLEViewTable_Private(viewer, sc->s, sc->r, sc->u, "U"));
345:       PetscCall(TSGLLEViewTable_Private(viewer, sc->r, sc->r, sc->v, "V"));

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

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

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

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

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

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

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

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

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

441:   {
442:     /* p=1,q=1, r=s=2, A- and L-stable with error estimates of order 2 and 3
443:     * Listed in Butcher & Podhaisky 2006. On error estimation in general linear methods for stiff ODE.
444:     * irks(0.3,0,[.3,1],[1],1)
445:     * Note: can be made to have classical order (not stage order) 2 by replacing 0.3 with 1-sqrt(1/2)
446:     * but doing so would sacrifice the error estimator.
447:     */
448:     const PetscScalar c[2]    = {3. / 10., 1.};
449:     const PetscScalar a[2][2] = {
450:       {3. / 10., 0       },
451:       {7. / 10., 3. / 10.}
452:     };
453:     const PetscScalar b[2][2] = {
454:       {7. / 10., 3. / 10.},
455:       {0,        1       }
456:     };
457:     const PetscScalar u[2][2] = {
458:       {1, 0},
459:       {1, 0}
460:     };
461:     const PetscScalar v[2][2] = {
462:       {1, 0},
463:       {0, 0}
464:     };
465:     PetscCall(TSGLLESchemeCreate(1, 1, 2, 2, c, *a, *b, *u, *v, &gl->schemes[gl->nschemes++]));
466:   }

468:   {
469:     /* p=q=2, r=s=3: irks(4/9,0,[1:3]/3,[0.33852],1) */
470:     /* http://www.math.auckland.ac.nz/~hpod/atlas/i2a.html */
471:     const PetscScalar c[3]    = {1. / 3., 2. / 3., 1};
472:     const PetscScalar a[3][3] = {
473:       {4. / 9.,              0,                     0      },
474:       {1.03750643704090e+00, 4. / 9.,               0      },
475:       {7.67024779410304e-01, -3.81140216918943e-01, 4. / 9.}
476:     };
477:     const PetscScalar b[3][3] = {
478:       {0.767024779410304,  -0.381140216918943, 4. / 9.          },
479:       {0.000000000000000,  0.000000000000000,  1.000000000000000},
480:       {-2.075048385225385, 0.621728385225383,  1.277197204924873}
481:     };
482:     const PetscScalar u[3][3] = {
483:       {1.0000000000000000, -0.1111111111111109, -0.0925925925925922},
484:       {1.0000000000000000, -0.8152842148186744, -0.4199095530877056},
485:       {1.0000000000000000, 0.1696709930641948,  0.0539741070314165 }
486:     };
487:     const PetscScalar v[3][3] = {
488:       {1.0000000000000000, 0.1696709930641948, 0.0539741070314165},
489:       {0.000000000000000,  0.000000000000000,  0.000000000000000 },
490:       {0.000000000000000,  0.176122795075129,  0.000000000000000 }
491:     };
492:     PetscCall(TSGLLESchemeCreate(2, 2, 3, 3, c, *a, *b, *u, *v, &gl->schemes[gl->nschemes++]));
493:   }
494:   {
495:     /* p=q=3, r=s=4: irks(9/40,0,[1:4]/4,[0.3312 1.0050],[0.49541 1;1 0]) */
496:     const PetscScalar c[4]    = {0.25, 0.5, 0.75, 1.0};
497:     const PetscScalar a[4][4] = {
498:       {9. / 40.,             0,                     0,                 0       },
499:       {2.11286958887701e-01, 9. / 40.,              0,                 0       },
500:       {9.46338294287584e-01, -3.42942861246094e-01, 9. / 40.,          0       },
501:       {0.521490453970721,    -0.662474225622980,    0.490476425459734, 9. / 40.}
502:     };
503:     const PetscScalar b[4][4] = {
504:       {0.521490453970721,  -0.662474225622980, 0.490476425459734,  9. / 40.         },
505:       {0.000000000000000,  0.000000000000000,  0.000000000000000,  1.000000000000000},
506:       {-0.084677029310348, 1.390757514776085,  -1.568157386206001, 2.023192696767826},
507:       {0.465383797936408,  1.478273530625148,  -1.930836081010182, 1.644872111193354}
508:     };
509:     const PetscScalar u[4][4] = {
510:       {1.00000000000000000, 0.02500000000001035,  -0.02499999999999053, -0.00442708333332865},
511:       {1.00000000000000000, 0.06371304111232945,  -0.04032173972189845, -0.01389438413189452},
512:       {1.00000000000000000, -0.07839543304147778, 0.04738685705116663,  0.02032603595928376 },
513:       {1.00000000000000000, 0.42550734619251651,  0.10800718022400080,  -0.01726712647760034}
514:     };
515:     const PetscScalar v[4][4] = {
516:       {1.00000000000000000, 0.42550734619251651, 0.10800718022400080, -0.01726712647760034},
517:       {0.000000000000000,   0.000000000000000,   0.000000000000000,   0.000000000000000   },
518:       {0.000000000000000,   -1.761115796027561,  -0.521284157173780,  0.258249384305463   },
519:       {0.000000000000000,   -1.657693358744728,  -1.052227765232394,  0.521284157173780   }
520:     };
521:     PetscCall(TSGLLESchemeCreate(3, 3, 4, 4, c, *a, *b, *u, *v, &gl->schemes[gl->nschemes++]));
522:   }
523:   {
524:     /* p=q=4, r=s=5:
525:           irks(3/11,0,[1:5]/5, [0.1715   -0.1238    0.6617],...
526:           [ -0.0812    0.4079    1.0000
527:              1.0000         0         0
528:              0.8270    1.0000         0])
529:     */
530:     const PetscScalar c[5]    = {0.2, 0.4, 0.6, 0.8, 1.0};
531:     const PetscScalar a[5][5] = {
532:       {2.72727272727352e-01,  0.00000000000000e+00,  0.00000000000000e+00,  0.00000000000000e+00, 0.00000000000000e+00},
533:       {-1.03980153733431e-01, 2.72727272727405e-01,  0.00000000000000e+00,  0.00000000000000e+00, 0.00000000000000e+00},
534:       {-1.58615400341492e+00, 7.44168951881122e-01,  2.72727272727309e-01,  0.00000000000000e+00, 0.00000000000000e+00},
535:       {-8.73658042865628e-01, 5.37884671894595e-01,  -1.63298538799523e-01, 2.72727272726996e-01, 0.00000000000000e+00},
536:       {2.95489397443992e-01,  -1.18481693910097e+00, -6.68029812659953e-01, 1.00716687860943e+00, 2.72727272727288e-01}
537:     };
538:     const PetscScalar b[5][5] = {
539:       {2.95489397443992e-01,  -1.18481693910097e+00, -6.68029812659953e-01, 1.00716687860943e+00,  2.72727272727288e-01},
540:       {0.00000000000000e+00,  1.11022302462516e-16,  -2.22044604925031e-16, 0.00000000000000e+00,  1.00000000000000e+00},
541:       {-4.05882503986005e+00, -4.00924006567769e+00, -1.38930610972481e+00, 4.45223930308488e+00,  6.32331093108427e-01},
542:       {8.35690179937017e+00,  -2.26640927349732e+00, 6.86647884973826e+00,  -5.22595158025740e+00, 4.50893068837431e+00},
543:       {1.27656267027479e+01,  2.80882153840821e+00,  8.91173096522890e+00,  -1.07936444078906e+01, 4.82534148988854e+00}
544:     };
545:     const PetscScalar u[5][5] = {
546:       {1.00000000000000e+00, -7.27272727273551e-02, -3.45454545454419e-02, -4.12121212119565e-03, -2.96969696964014e-04},
547:       {1.00000000000000e+00, 2.31252881006154e-01,  -8.29487834416481e-03, -9.07191207681020e-03, -1.70378403743473e-03},
548:       {1.00000000000000e+00, 1.16925777880663e+00,  3.59268562942635e-02,  -4.09013451730615e-02, -1.02411119670164e-02},
549:       {1.00000000000000e+00, 1.02634463704356e+00,  1.59375044913405e-01,  1.89673015035370e-03,  -4.89987231897569e-03},
550:       {1.00000000000000e+00, 1.27746320298021e+00,  2.37186008132728e-01,  -8.28694373940065e-02, -5.34396510196430e-02}
551:     };
552:     const PetscScalar v[5][5] = {
553:       {1.00000000000000e+00, 1.27746320298021e+00,  2.37186008132728e-01,  -8.28694373940065e-02, -5.34396510196430e-02},
554:       {0.00000000000000e+00, -1.77635683940025e-15, -1.99840144432528e-15, -9.99200722162641e-16, -3.33066907387547e-16},
555:       {0.00000000000000e+00, 4.37280081906924e+00,  5.49221645016377e-02,  -8.88913177394943e-02, 1.12879077989154e-01 },
556:       {0.00000000000000e+00, -1.22399504837280e+01, -5.21287338448645e+00, -8.03952325565291e-01, 4.60298678047147e-01 },
557:       {0.00000000000000e+00, -1.85178762883829e+01, -5.21411849862624e+00, -1.04283436528809e+00, 7.49030161063651e-01 }
558:     };
559:     PetscCall(TSGLLESchemeCreate(4, 4, 5, 5, c, *a, *b, *u, *v, &gl->schemes[gl->nschemes++]));
560:   }
561:   {
562:     /* p=q=5, r=s=6;
563:        irks(1/3,0,[1:6]/6,...
564:           [-0.0489    0.4228   -0.8814    0.9021],...
565:           [-0.3474   -0.6617    0.6294    0.2129
566:             0.0044   -0.4256   -0.1427   -0.8936
567:            -0.8267    0.4821    0.1371   -0.2557
568:            -0.4426   -0.3855   -0.7514    0.3014])
569:     */
570:     const PetscScalar c[6]    = {1. / 6, 2. / 6, 3. / 6, 4. / 6, 5. / 6, 1.};
571:     const PetscScalar a[6][6] = {
572:       {3.33333333333940e-01,  0,                     0,                     0,                     0,                    0                   },
573:       {-8.64423857333350e-02, 3.33333333332888e-01,  0,                     0,                     0,                    0                   },
574:       {-2.16850174258252e+00, -2.23619072028839e+00, 3.33333333335204e-01,  0,                     0,                    0                   },
575:       {-4.73160970138997e+00, -3.89265344629268e+00, -2.76318716520933e-01, 3.33333333335759e-01,  0,                    0                   },
576:       {-6.75187540297338e+00, -7.90756533769377e+00, 7.90245051802259e-01,  -4.48352364517632e-01, 3.33333333328483e-01, 0                   },
577:       {-4.26488287921548e+00, -1.19320395589302e+01, 3.38924509887755e+00,  -2.23969848002481e+00, 6.62807710124007e-01, 3.33333333335440e-01}
578:     };
579:     const PetscScalar b[6][6] = {
580:       {-4.26488287921548e+00, -1.19320395589302e+01, 3.38924509887755e+00,  -2.23969848002481e+00, 6.62807710124007e-01,  3.33333333335440e-01 },
581:       {-8.88178419700125e-16, 4.44089209850063e-16,  -1.54737334057131e-15, -8.88178419700125e-16, 0.00000000000000e+00,  1.00000000000001e+00 },
582:       {-2.87780425770651e+01, -1.13520448264971e+01, 2.62002318943161e+01,  2.56943874812797e+01,  -3.06702268304488e+01, 6.68067773510103e+00 },
583:       {5.47971245256474e+01,  6.80366875868284e+01,  -6.50952588861999e+01, -8.28643975339097e+01, 8.17416943896414e+01,  -1.17819043489036e+01},
584:       {-2.33332114788869e+02, 6.12942539462634e+01,  -4.91850135865944e+01, 1.82716844135480e+02,  -1.29788173979395e+02, 3.09968095651099e+01 },
585:       {-1.72049132343751e+02, 8.60194713593999e+00,  7.98154219170200e-01,  1.50371386053218e+02,  -1.18515423962066e+02, 2.50898277784663e+01 }
586:     };
587:     const PetscScalar u[6][6] = {
588:       {1.00000000000000e+00, -1.66666666666870e-01, -4.16666666664335e-02, -3.85802469124815e-03, -2.25051440302250e-04, -9.64506172339142e-06},
589:       {1.00000000000000e+00, 8.64423857327162e-02,  -4.11484912671353e-02, -1.11450903217645e-02, -1.47651050487126e-03, -1.34395070766826e-04},
590:       {1.00000000000000e+00, 4.57135912953434e+00,  1.06514719719137e+00,  1.33517564218007e-01,  1.11365952968659e-02,  6.12382756769504e-04 },
591:       {1.00000000000000e+00, 9.23391519753404e+00,  2.22431212392095e+00,  2.91823807741891e-01,  2.52058456411084e-02,  1.22800542949647e-03 },
592:       {1.00000000000000e+00, 1.48175480533865e+01,  3.73439117461835e+00,  5.14648336541804e-01,  4.76430038853402e-02,  2.56798515502156e-03 },
593:       {1.00000000000000e+00, 1.50512347758335e+01,  4.10099701165164e+00,  5.66039141003603e-01,  3.91213893800891e-02,  -2.99136269067853e-03}
594:     };
595:     const PetscScalar v[6][6] = {
596:       {1.00000000000000e+00, 1.50512347758335e+01,  4.10099701165164e+00,  5.66039141003603e-01,  3.91213893800891e-02,  -2.99136269067853e-03},
597:       {0.00000000000000e+00, -4.88498130835069e-15, -6.43929354282591e-15, -3.55271367880050e-15, -1.22124532708767e-15, -3.12250225675825e-16},
598:       {0.00000000000000e+00, 1.22250171233141e+01,  -1.77150760606169e+00, 3.54516769879390e-01,  6.22298845883398e-01,  2.31647447450276e-01 },
599:       {0.00000000000000e+00, -4.48339457331040e+01, -3.57363126641880e-01, 5.18750173123425e-01,  6.55727990241799e-02,  1.63175368287079e-01 },
600:       {0.00000000000000e+00, 1.37297394708005e+02,  -1.60145272991317e+00, -5.05319555199441e+00, 1.55328940390990e-01,  9.16629423682464e-01 },
601:       {0.00000000000000e+00, 1.05703241119022e+02,  -1.16610260983038e+00, -2.99767252773859e+00, -1.13472315553890e-01, 1.09742849254729e+00 }
602:     };
603:     PetscCall(TSGLLESchemeCreate(5, 5, 6, 6, c, *a, *b, *u, *v, &gl->schemes[gl->nschemes++]));
604:   }
605:   PetscFunctionReturn(PETSC_SUCCESS);
606: }

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

611:   Collective

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

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

620:   Level: intermediate

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

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

634: .seealso: [](ch_ts), `TS`, `TSGLLEType`, `TSGLLE`
635: @*/
636: PetscErrorCode TSGLLESetType(TS ts, TSGLLEType type)
637: {
638:   PetscFunctionBegin;
640:   PetscAssertPointer(type, 2);
641:   PetscTryMethod(ts, "TSGLLESetType_C", (TS, TSGLLEType), (ts, type));
642:   PetscFunctionReturn(PETSC_SUCCESS);
643: }

645: /*@C
646:   TSGLLESetAcceptType - sets the acceptance test for `TSGLLE`

648:   Logically Collective

650:   Input Parameters:
651: + ts   - the `TS` context
652: - type - the type

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

657:   Level: intermediate

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

663: .seealso: [](ch_ts), `TS`, `TSGLLE`, `TSGLLEAcceptRegister()`, `TSGLLEAdapt`
664: @*/
665: PetscErrorCode TSGLLESetAcceptType(TS ts, TSGLLEAcceptType type)
666: {
667:   PetscFunctionBegin;
669:   PetscAssertPointer(type, 2);
670:   PetscTryMethod(ts, "TSGLLESetAcceptType_C", (TS, TSGLLEAcceptType), (ts, type));
671:   PetscFunctionReturn(PETSC_SUCCESS);
672: }

674: /*@C
675:   TSGLLEGetAdapt - gets the `TSGLLEAdapt` object from the `TS`

677:   Not Collective

679:   Input Parameter:
680: . ts - the `TS` context

682:   Output Parameter:
683: . adapt - the `TSGLLEAdapt` context

685:   Level: advanced

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

691: .seealso: [](ch_ts), `TS`, `TSGLLE`, `TSGLLEAdapt`, `TSGLLEAdaptRegister()`
692: @*/
693: PetscErrorCode TSGLLEGetAdapt(TS ts, TSGLLEAdapt *adapt)
694: {
695:   PetscFunctionBegin;
697:   PetscAssertPointer(adapt, 2);
698:   PetscUseMethod(ts, "TSGLLEGetAdapt_C", (TS, TSGLLEAdapt *), (ts, adapt));
699:   PetscFunctionReturn(PETSC_SUCCESS);
700: }

702: static PetscErrorCode TSGLLEAccept_Always(TS ts, PetscReal tleft, PetscReal h, const PetscReal enorms[], PetscBool *accept)
703: {
704:   PetscFunctionBegin;
705:   *accept = PETSC_TRUE;
706:   PetscFunctionReturn(PETSC_SUCCESS);
707: }

709: static PetscErrorCode TSGLLEUpdateWRMS(TS ts)
710: {
711:   TS_GLLE     *gl = (TS_GLLE *)ts->data;
712:   PetscScalar *x, *w;
713:   PetscInt     n, i;

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

725: static PetscErrorCode TSGLLEVecNormWRMS(TS ts, Vec X, PetscReal *nrm)
726: {
727:   TS_GLLE     *gl = (TS_GLLE *)ts->data;
728:   PetscScalar *x, *w;
729:   PetscReal    sum = 0.0, gsum;
730:   PetscInt     n, N, i;

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

745: static PetscErrorCode TSGLLESetType_GLLE(TS ts, TSGLLEType type)
746: {
747:   PetscBool same;
748:   TS_GLLE  *gl = (TS_GLLE *)ts->data;
749:   PetscErrorCode (*r)(TS);

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

758:   PetscCall(PetscFunctionListFind(TSGLLEList, type, &r));
759:   PetscCheck(r, PetscObjectComm((PetscObject)ts), PETSC_ERR_ARG_UNKNOWN_TYPE, "Unknown TSGLLE type \"%s\" given", type);
760:   PetscCall((*r)(ts));
761:   PetscCall(PetscStrncpy(gl->type_name, type, sizeof(gl->type_name)));
762:   PetscFunctionReturn(PETSC_SUCCESS);
763: }

765: static PetscErrorCode TSGLLESetAcceptType_GLLE(TS ts, TSGLLEAcceptType type)
766: {
767:   TSGLLEAcceptFn *r;
768:   TS_GLLE        *gl = (TS_GLLE *)ts->data;

770:   PetscFunctionBegin;
771:   PetscCall(PetscFunctionListFind(TSGLLEAcceptList, type, &r));
772:   PetscCheck(r, PetscObjectComm((PetscObject)ts), PETSC_ERR_ARG_UNKNOWN_TYPE, "Unknown TSGLLEAccept type \"%s\" given", type);
773:   gl->Accept = r;
774:   PetscCall(PetscStrncpy(gl->accept_name, type, sizeof(gl->accept_name)));
775:   PetscFunctionReturn(PETSC_SUCCESS);
776: }

778: static PetscErrorCode TSGLLEGetAdapt_GLLE(TS ts, TSGLLEAdapt *adapt)
779: {
780:   TS_GLLE *gl = (TS_GLLE *)ts->data;

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

791: static PetscErrorCode TSGLLEChooseNextScheme(TS ts, PetscReal h, const PetscReal hmnorm[], PetscInt *next_scheme, PetscReal *next_h, PetscBool *finish)
792: {
793:   TS_GLLE  *gl = (TS_GLLE *)ts->data;
794:   PetscInt  i, n, cur_p, cur, next_sc, candidates[64], orders[64];
795:   PetscReal errors[64], costs[64], tleft;

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

822: static PetscErrorCode TSGLLEGetMaxSizes(TS ts, PetscInt *max_r, PetscInt *max_s)
823: {
824:   TS_GLLE *gl = (TS_GLLE *)ts->data;

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

832: static PetscErrorCode TSSolve_GLLE(TS ts)
833: {
834:   TS_GLLE            *gl = (TS_GLLE *)ts->data;
835:   PetscInt            i, k, its, lits, max_r, max_s;
836:   PetscBool           final_step, finish;
837:   SNESConvergedReason snesreason;

839:   PetscFunctionBegin;
840:   PetscCall(TSMonitor(ts, ts->steps, ts->ptime, ts->vec_sol));

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

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

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

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

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

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

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

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

891:     /*
892:       We only call PreStep at the start of each STEP, not each STAGE.  This is because it is
893:       possible to fail (have to restart a step) after multiple stages.
894:     */
895:     PetscCall(TSPreStep(ts));

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

906:         /*
907:         * Stage equation: Y = h A Y' + U X
908:         * We assume that A is lower-triangular so that we can solve the stages (Y,Y') sequentially
909:         * Build the affine vector z_i = -[1/(h a_ii)](h sum_j a_ij y'_j + sum_j u_ij x_j)
910:         * Then y'_i = z + 1/(h a_ii) y_i
911:         */
912:         PetscCall(VecZeroEntries(gl->Z));
913:         for (j = 0; j < r; j++) PetscCall(VecAXPY(gl->Z, -shift * u[i * r + j], X[j]));
914:         for (j = 0; j < i; j++) PetscCall(VecAXPY(gl->Z, -shift * h * a[i * s + j], Ydot[j]));
915:         /* Note: Z is used within function evaluation, Ydot = Z + shift*Y */

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

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

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

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

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

975:     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]));
976:     if (!final_step) {
977:       PetscCall(TSGLLEChooseNextScheme(ts, h, hmnorm, &next_scheme, &next_h, &final_step));
978:     } else {
979:       /* Dummy values to complete the current step in a consistent manner */
980:       next_scheme = gl->current_scheme;
981:       next_h      = h;
982:       finish      = PETSC_TRUE;
983:     }

985:     X        = gl->Xold;
986:     gl->Xold = gl->X;
987:     gl->X    = X;
988:     PetscCall((*gl->CompleteStep)(scheme, h, gl->schemes[next_scheme], next_h, Ydot, gl->Xold, gl->X));

990:     PetscCall(TSGLLEUpdateWRMS(ts));

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

997:     PetscCall(TSPostEvaluate(ts));
998:     PetscCall(TSPostStep(ts));
999:     PetscCall(TSMonitor(ts, ts->steps, ts->ptime, ts->vec_sol));

1001:     gl->current_scheme = next_scheme;
1002:     ts->time_step      = next_h;
1003:   }
1004:   PetscFunctionReturn(PETSC_SUCCESS);
1005: }

1007: /*------------------------------------------------------------*/

1009: static PetscErrorCode TSReset_GLLE(TS ts)
1010: {
1011:   TS_GLLE *gl = (TS_GLLE *)ts->data;
1012:   PetscInt max_r, max_s;

1014:   PetscFunctionBegin;
1015:   if (gl->setupcalled) {
1016:     PetscCall(TSGLLEGetMaxSizes(ts, &max_r, &max_s));
1017:     PetscCall(VecDestroyVecs(max_r, &gl->Xold));
1018:     PetscCall(VecDestroyVecs(max_r, &gl->X));
1019:     PetscCall(VecDestroyVecs(max_s, &gl->Ydot));
1020:     PetscCall(VecDestroyVecs(3, &gl->himom));
1021:     PetscCall(VecDestroy(&gl->W));
1022:     PetscCall(VecDestroy(&gl->Y));
1023:     PetscCall(VecDestroy(&gl->Z));
1024:   }
1025:   gl->setupcalled = PETSC_FALSE;
1026:   PetscFunctionReturn(PETSC_SUCCESS);
1027: }

1029: static PetscErrorCode TSDestroy_GLLE(TS ts)
1030: {
1031:   TS_GLLE *gl = (TS_GLLE *)ts->data;

1033:   PetscFunctionBegin;
1034:   PetscCall(TSReset_GLLE(ts));
1035:   if (ts->dm) {
1036:     PetscCall(DMCoarsenHookRemove(ts->dm, DMCoarsenHook_TSGLLE, DMRestrictHook_TSGLLE, ts));
1037:     PetscCall(DMSubDomainHookRemove(ts->dm, DMSubDomainHook_TSGLLE, DMSubDomainRestrictHook_TSGLLE, ts));
1038:   }
1039:   if (gl->adapt) PetscCall(TSGLLEAdaptDestroy(&gl->adapt));
1040:   if (gl->Destroy) PetscCall((*gl->Destroy)(gl));
1041:   PetscCall(PetscFree(ts->data));
1042:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSGLLESetType_C", NULL));
1043:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSGLLESetAcceptType_C", NULL));
1044:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSGLLEGetAdapt_C", NULL));
1045:   PetscFunctionReturn(PETSC_SUCCESS);
1046: }

1048: /*
1049:     This defines the nonlinear equation that is to be solved with SNES
1050:     g(x) = f(t,x,z+shift*x) = 0
1051: */
1052: static PetscErrorCode SNESTSFormFunction_GLLE(SNES snes, Vec x, Vec f, TS ts)
1053: {
1054:   TS_GLLE *gl = (TS_GLLE *)ts->data;
1055:   Vec      Z, Ydot;
1056:   DM       dm, dmsave;

1058:   PetscFunctionBegin;
1059:   PetscCall(SNESGetDM(snes, &dm));
1060:   PetscCall(TSGLLEGetVecs(ts, dm, &Z, &Ydot));
1061:   PetscCall(VecWAXPY(Ydot, gl->scoeff / ts->time_step, x, Z));
1062:   dmsave = ts->dm;
1063:   ts->dm = dm;
1064:   PetscCall(TSComputeIFunction(ts, gl->stage_time, x, Ydot, f, PETSC_FALSE));
1065:   ts->dm = dmsave;
1066:   PetscCall(TSGLLERestoreVecs(ts, dm, &Z, &Ydot));
1067:   PetscFunctionReturn(PETSC_SUCCESS);
1068: }

1070: static PetscErrorCode SNESTSFormJacobian_GLLE(SNES snes, Vec x, Mat A, Mat B, TS ts)
1071: {
1072:   TS_GLLE *gl = (TS_GLLE *)ts->data;
1073:   Vec      Z, Ydot;
1074:   DM       dm, dmsave;

1076:   PetscFunctionBegin;
1077:   PetscCall(SNESGetDM(snes, &dm));
1078:   PetscCall(TSGLLEGetVecs(ts, dm, &Z, &Ydot));
1079:   dmsave = ts->dm;
1080:   ts->dm = dm;
1081:   /* gl->Xdot will have already been computed in SNESTSFormFunction_GLLE */
1082:   PetscCall(TSComputeIJacobian(ts, gl->stage_time, x, gl->Ydot[gl->stage], gl->scoeff / ts->time_step, A, B, PETSC_FALSE));
1083:   ts->dm = dmsave;
1084:   PetscCall(TSGLLERestoreVecs(ts, dm, &Z, &Ydot));
1085:   PetscFunctionReturn(PETSC_SUCCESS);
1086: }

1088: static PetscErrorCode TSSetUp_GLLE(TS ts)
1089: {
1090:   TS_GLLE *gl = (TS_GLLE *)ts->data;
1091:   PetscInt max_r, max_s;
1092:   DM       dm;

1094:   PetscFunctionBegin;
1095:   gl->setupcalled = PETSC_TRUE;
1096:   PetscCall(TSGLLEGetMaxSizes(ts, &max_r, &max_s));
1097:   PetscCall(VecDuplicateVecs(ts->vec_sol, max_r, &gl->X));
1098:   PetscCall(VecDuplicateVecs(ts->vec_sol, max_r, &gl->Xold));
1099:   PetscCall(VecDuplicateVecs(ts->vec_sol, max_s, &gl->Ydot));
1100:   PetscCall(VecDuplicateVecs(ts->vec_sol, 3, &gl->himom));
1101:   PetscCall(VecDuplicate(ts->vec_sol, &gl->W));
1102:   PetscCall(VecDuplicate(ts->vec_sol, &gl->Y));
1103:   PetscCall(VecDuplicate(ts->vec_sol, &gl->Z));

1105:   /* Default acceptance tests and adaptivity */
1106:   if (!gl->Accept) PetscCall(TSGLLESetAcceptType(ts, TSGLLEACCEPT_ALWAYS));
1107:   if (!gl->adapt) PetscCall(TSGLLEGetAdapt(ts, &gl->adapt));

1109:   if (gl->current_scheme < 0) {
1110:     PetscInt i;
1111:     for (i = 0;; i++) {
1112:       if (gl->schemes[i]->p == gl->start_order) break;
1113:       PetscCheck(i + 1 != gl->nschemes, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "No schemes available with requested start order %" PetscInt_FMT, i);
1114:     }
1115:     gl->current_scheme = i;
1116:   }
1117:   PetscCall(TSGetDM(ts, &dm));
1118:   PetscCall(DMCoarsenHookAdd(dm, DMCoarsenHook_TSGLLE, DMRestrictHook_TSGLLE, ts));
1119:   PetscCall(DMSubDomainHookAdd(dm, DMSubDomainHook_TSGLLE, DMSubDomainRestrictHook_TSGLLE, ts));
1120:   PetscFunctionReturn(PETSC_SUCCESS);
1121: }
1122: /*------------------------------------------------------------*/

1124: static PetscErrorCode TSSetFromOptions_GLLE(TS ts, PetscOptionItems *PetscOptionsObject)
1125: {
1126:   TS_GLLE *gl         = (TS_GLLE *)ts->data;
1127:   char     tname[256] = TSGLLE_IRKS, completef[256] = "rescale-and-modify";

1129:   PetscFunctionBegin;
1130:   PetscOptionsHeadBegin(PetscOptionsObject, "General Linear ODE solver options");
1131:   {
1132:     PetscBool flg;
1133:     PetscCall(PetscOptionsFList("-ts_gl_type", "Type of GL method", "TSGLLESetType", TSGLLEList, gl->type_name[0] ? gl->type_name : tname, tname, sizeof(tname), &flg));
1134:     if (flg || !gl->type_name[0]) PetscCall(TSGLLESetType(ts, tname));
1135:     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));
1136:     PetscCall(PetscOptionsInt("-ts_gl_max_order", "Maximum order to try", "TSGLLESetMaxOrder", gl->max_order, &gl->max_order, NULL));
1137:     PetscCall(PetscOptionsInt("-ts_gl_min_order", "Minimum order to try", "TSGLLESetMinOrder", gl->min_order, &gl->min_order, NULL));
1138:     PetscCall(PetscOptionsInt("-ts_gl_start_order", "Initial order to try", "TSGLLESetMinOrder", gl->start_order, &gl->start_order, NULL));
1139:     PetscCall(PetscOptionsEnum("-ts_gl_error_direction", "Which direction to look when estimating error", "TSGLLESetErrorDirection", TSGLLEErrorDirections, (PetscEnum)gl->error_direction, (PetscEnum *)&gl->error_direction, NULL));
1140:     PetscCall(PetscOptionsBool("-ts_gl_extrapolate", "Extrapolate stage solution from previous solution (sometimes unstable)", "TSGLLESetExtrapolate", gl->extrapolate, &gl->extrapolate, NULL));
1141:     PetscCall(PetscOptionsReal("-ts_gl_atol", "Absolute tolerance", "TSGLLESetTolerances", gl->wrms_atol, &gl->wrms_atol, NULL));
1142:     PetscCall(PetscOptionsReal("-ts_gl_rtol", "Relative tolerance", "TSGLLESetTolerances", gl->wrms_rtol, &gl->wrms_rtol, NULL));
1143:     PetscCall(PetscOptionsString("-ts_gl_complete", "Method to use for completing the step", "none", completef, completef, sizeof(completef), &flg));
1144:     if (flg) {
1145:       PetscBool match1, match2;
1146:       PetscCall(PetscStrcmp(completef, "rescale", &match1));
1147:       PetscCall(PetscStrcmp(completef, "rescale-and-modify", &match2));
1148:       if (match1) gl->CompleteStep = TSGLLECompleteStep_Rescale;
1149:       else if (match2) gl->CompleteStep = TSGLLECompleteStep_RescaleAndModify;
1150:       else SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_ARG_UNKNOWN_TYPE, "%s", completef);
1151:     }
1152:     {
1153:       char type[256] = TSGLLEACCEPT_ALWAYS;
1154:       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));
1155:       if (flg || !gl->accept_name[0]) PetscCall(TSGLLESetAcceptType(ts, type));
1156:     }
1157:     {
1158:       TSGLLEAdapt adapt;
1159:       PetscCall(TSGLLEGetAdapt(ts, &adapt));
1160:       PetscCall(TSGLLEAdaptSetFromOptions(adapt, PetscOptionsObject));
1161:     }
1162:   }
1163:   PetscOptionsHeadEnd();
1164:   PetscFunctionReturn(PETSC_SUCCESS);
1165: }

1167: static PetscErrorCode TSView_GLLE(TS ts, PetscViewer viewer)
1168: {
1169:   TS_GLLE  *gl = (TS_GLLE *)ts->data;
1170:   PetscInt  i;
1171:   PetscBool iascii, details;

1173:   PetscFunctionBegin;
1174:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
1175:   if (iascii) {
1176:     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));
1177:     PetscCall(PetscViewerASCIIPrintf(viewer, "  Error estimation: %s\n", TSGLLEErrorDirections[gl->error_direction]));
1178:     PetscCall(PetscViewerASCIIPrintf(viewer, "  Extrapolation: %s\n", gl->extrapolate ? "yes" : "no"));
1179:     PetscCall(PetscViewerASCIIPrintf(viewer, "  Acceptance test: %s\n", gl->accept_name[0] ? gl->accept_name : "(not yet set)"));
1180:     PetscCall(PetscViewerASCIIPushTab(viewer));
1181:     PetscCall(TSGLLEAdaptView(gl->adapt, viewer));
1182:     PetscCall(PetscViewerASCIIPopTab(viewer));
1183:     PetscCall(PetscViewerASCIIPrintf(viewer, "  type: %s\n", gl->type_name[0] ? gl->type_name : "(not yet set)"));
1184:     PetscCall(PetscViewerASCIIPrintf(viewer, "Schemes within family (%" PetscInt_FMT "):\n", gl->nschemes));
1185:     details = PETSC_FALSE;
1186:     PetscCall(PetscOptionsGetBool(((PetscObject)ts)->options, ((PetscObject)ts)->prefix, "-ts_gl_view_detailed", &details, NULL));
1187:     PetscCall(PetscViewerASCIIPushTab(viewer));
1188:     for (i = 0; i < gl->nschemes; i++) PetscCall(TSGLLESchemeView(gl->schemes[i], details, viewer));
1189:     if (gl->View) PetscCall((*gl->View)(gl, viewer));
1190:     PetscCall(PetscViewerASCIIPopTab(viewer));
1191:   }
1192:   PetscFunctionReturn(PETSC_SUCCESS);
1193: }

1195: /*@C
1196:   TSGLLERegister -  adds a `TSGLLE` implementation

1198:   Not Collective

1200:   Input Parameters:
1201: + sname    - name of user-defined general linear scheme
1202: - function - routine to create method context

1204:   Level: advanced

1206:   Note:
1207:   `TSGLLERegister()` may be called multiple times to add several user-defined families.

1209:   Example Usage:
1210: .vb
1211:   TSGLLERegister("my_scheme", MySchemeCreate);
1212: .ve

1214:   Then, your scheme can be chosen with the procedural interface via
1215: $ TSGLLESetType(ts, "my_scheme")
1216:   or at runtime via the option
1217: $ -ts_gl_type my_scheme

1219: .seealso: [](ch_ts), `TSGLLE`, `TSGLLEType`, `TSGLLERegisterAll()`
1220: @*/
1221: PetscErrorCode TSGLLERegister(const char sname[], PetscErrorCode (*function)(TS))
1222: {
1223:   PetscFunctionBegin;
1224:   PetscCall(TSGLLEInitializePackage());
1225:   PetscCall(PetscFunctionListAdd(&TSGLLEList, sname, function));
1226:   PetscFunctionReturn(PETSC_SUCCESS);
1227: }

1229: /*@C
1230:   TSGLLEAcceptRegister -  adds a `TSGLLE` acceptance scheme

1232:   Not Collective

1234:   Input Parameters:
1235: + sname    - name of user-defined acceptance scheme
1236: - function - routine to create method context, see `TSGLLEAcceptFn` for the calling sequence

1238:   Level: advanced

1240:   Note:
1241:   `TSGLLEAcceptRegister()` may be called multiple times to add several user-defined families.

1243:   Example Usage:
1244: .vb
1245:   TSGLLEAcceptRegister("my_scheme", MySchemeCreate);
1246: .ve

1248:   Then, your scheme can be chosen with the procedural interface via
1249: .vb
1250:   TSGLLESetAcceptType(ts, "my_scheme")
1251: .ve
1252:   or at runtime via the option `-ts_gl_accept_type my_scheme`

1254: .seealso: [](ch_ts), `TSGLLE`, `TSGLLEType`, `TSGLLERegisterAll()`, `TSGLLEAcceptFn`
1255: @*/
1256: PetscErrorCode TSGLLEAcceptRegister(const char sname[], TSGLLEAcceptFn *function)
1257: {
1258:   PetscFunctionBegin;
1259:   PetscCall(PetscFunctionListAdd(&TSGLLEAcceptList, sname, function));
1260:   PetscFunctionReturn(PETSC_SUCCESS);
1261: }

1263: /*@C
1264:   TSGLLERegisterAll - Registers all of the general linear methods in `TSGLLE`

1266:   Not Collective

1268:   Level: advanced

1270: .seealso: [](ch_ts), `TSGLLE`, `TSGLLERegisterDestroy()`
1271: @*/
1272: PetscErrorCode TSGLLERegisterAll(void)
1273: {
1274:   PetscFunctionBegin;
1275:   if (TSGLLERegisterAllCalled) PetscFunctionReturn(PETSC_SUCCESS);
1276:   TSGLLERegisterAllCalled = PETSC_TRUE;

1278:   PetscCall(TSGLLERegister(TSGLLE_IRKS, TSGLLECreate_IRKS));
1279:   PetscCall(TSGLLEAcceptRegister(TSGLLEACCEPT_ALWAYS, TSGLLEAccept_Always));
1280:   PetscFunctionReturn(PETSC_SUCCESS);
1281: }

1283: /*@C
1284:   TSGLLEInitializePackage - This function initializes everything in the `TSGLLE` package. It is called
1285:   from `TSInitializePackage()`.

1287:   Level: developer

1289: .seealso: [](ch_ts), `PetscInitialize()`, `TSInitializePackage()`, `TSGLLEFinalizePackage()`
1290: @*/
1291: PetscErrorCode TSGLLEInitializePackage(void)
1292: {
1293:   PetscFunctionBegin;
1294:   if (TSGLLEPackageInitialized) PetscFunctionReturn(PETSC_SUCCESS);
1295:   TSGLLEPackageInitialized = PETSC_TRUE;
1296:   PetscCall(TSGLLERegisterAll());
1297:   PetscCall(PetscRegisterFinalize(TSGLLEFinalizePackage));
1298:   PetscFunctionReturn(PETSC_SUCCESS);
1299: }

1301: /*@C
1302:   TSGLLEFinalizePackage - This function destroys everything in the `TSGLLE` package. It is
1303:   called from `PetscFinalize()`.

1305:   Level: developer

1307: .seealso: [](ch_ts), `PetscFinalize()`, `TSGLLEInitializePackage()`, `TSInitializePackage()`
1308: @*/
1309: PetscErrorCode TSGLLEFinalizePackage(void)
1310: {
1311:   PetscFunctionBegin;
1312:   PetscCall(PetscFunctionListDestroy(&TSGLLEList));
1313:   PetscCall(PetscFunctionListDestroy(&TSGLLEAcceptList));
1314:   TSGLLEPackageInitialized = PETSC_FALSE;
1315:   TSGLLERegisterAllCalled  = PETSC_FALSE;
1316:   PetscFunctionReturn(PETSC_SUCCESS);
1317: }

1319: /* ------------------------------------------------------------ */
1320: /*MC
1321:   TSGLLE - DAE solver using implicit General Linear methods {cite}`butcher_2007` {cite}`butcher2016numerical`

1323:   Options Database Keys:
1324: +  -ts_gl_type <type> - the class of general linear method (irks)
1325: .  -ts_gl_rtol <tol>  - relative error
1326: .  -ts_gl_atol <tol>  - absolute error
1327: .  -ts_gl_min_order <p> - minimum order method to consider (default=1)
1328: .  -ts_gl_max_order <p> - maximum order method to consider (default=3)
1329: .  -ts_gl_start_order <p> - order of starting method (default=1)
1330: .  -ts_gl_complete <method> - method to use for completing the step (rescale-and-modify or rescale)
1331: -  -ts_adapt_type <method> - adaptive controller to use (none step both)

1333:   Level: beginner

1335:   Notes:
1336:   These methods contain Runge-Kutta and multistep schemes as special cases. These special cases
1337:   have some fundamental limitations. For example, diagonally implicit Runge-Kutta cannot have
1338:   stage order greater than 1 which limits their applicability to very stiff systems.
1339:   Meanwhile, multistep methods cannot be A-stable for order greater than 2 and BDF are not
1340:   0-stable for order greater than 6. GL methods can be A- and L-stable with arbitrarily high
1341:   stage order and reliable error estimates for both 1 and 2 orders higher to facilitate
1342:   adaptive step sizes and adaptive order schemes. All this is possible while preserving a
1343:   singly diagonally implicit structure.

1345:   This integrator can be applied to DAE.

1347:   Diagonally implicit general linear (DIGL) methods are a generalization of diagonally implicit
1348:   Runge-Kutta (DIRK). 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
1357:   triangular. A step of the general method reads

1359:   $$
1360:   \begin{align*}
1361:   [ Y ] = [A  U] [  Y'   ] \\
1362:   [X^k] = [B  V] [X^{k-1}]
1363:   \end{align*}
1364:   $$

1366:   where Y is the multivector of stage values, $Y'$ is the multivector of stage derivatives, $X^k$
1367:   is the Nordsieck vector of the solution at step $k$. The Nordsieck vector consists of the first
1368:   $r$ moments of the solution, given by

1370:   $$
1371:   X = [x_0,x_1,...,x_{r-1}] = [x, h x', h^2 x'', ..., h^{r-1} x^{(r-1)} ]
1372:   $$

1374:   If $A$ is lower triangular, we can solve the stages $(Y, Y')$ sequentially

1376:   $$
1377:   y_i = h \sum_{j=0}^{s-1} (a_{ij} y'_j) + \sum_{j=0}^{r-1} u_{ij} x_j, \, \,   i=0,...,{s-1}
1378:   $$

1380:   and then construct the pieces to carry to the next step

1382:   $$
1383:   xx_i = h \sum_{j=0}^{s-1} b_{ij} y'_j  + \sum_{j=0}^{r-1} v_{ij} x_j,  \, \,  i=0,...,{r-1}
1384:   $$

1386:   Note that when the equations are cast in implicit form, we are using the stage equation to
1387:   define $y'_i$ in terms of $y_i$ and known stuff ($y_j$ for $j<i$ and $x_j$ for all $j$).

1389:   Error estimation

1391:   At present, the most attractive GL methods for stiff problems are singly diagonally implicit
1392:   schemes which posses Inherent Runge-Kutta Stability (`TSIRKS`).  These methods have $r=s$, the
1393:   number of items passed between steps is equal to the number of stages.  The order and
1394:   stage-order are one less than the number of stages.  We use the error estimates in the 2007
1395:   paper which provide the following estimates

1397:   $$
1398:   \begin{align*}
1399:   h^{p+1} X^{(p+1)}          = \phi_0^T Y' + [0 \psi_0^T] Xold \\
1400:   h^{p+2} X^{(p+2)}          = \phi_1^T Y' + [0 \psi_1^T] Xold \\
1401:   h^{p+2} (dx'/dx) X^{(p+1)} = \phi_2^T Y' + [0 \psi_2^T] Xold
1402:   \end{align*}
1403:   $$

1405:   These estimates are accurate to $ O(h^{p+3})$.

1407:   Changing the step size

1409:   Uses the generalized "rescale and modify" scheme, see equation (4.5) of {cite}`butcher_2007`.

1411: .seealso: [](ch_ts), `TSCreate()`, `TS`, `TSSetType()`, `TSType`
1412: M*/
1413: PETSC_EXTERN PetscErrorCode TSCreate_GLLE(TS ts)
1414: {
1415:   TS_GLLE *gl;

1417:   PetscFunctionBegin;
1418:   PetscCall(TSGLLEInitializePackage());

1420:   PetscCall(PetscNew(&gl));
1421:   ts->data = (void *)gl;

1423:   ts->ops->reset          = TSReset_GLLE;
1424:   ts->ops->destroy        = TSDestroy_GLLE;
1425:   ts->ops->view           = TSView_GLLE;
1426:   ts->ops->setup          = TSSetUp_GLLE;
1427:   ts->ops->solve          = TSSolve_GLLE;
1428:   ts->ops->setfromoptions = TSSetFromOptions_GLLE;
1429:   ts->ops->snesfunction   = SNESTSFormFunction_GLLE;
1430:   ts->ops->snesjacobian   = SNESTSFormJacobian_GLLE;

1432:   ts->usessnes = PETSC_TRUE;

1434:   gl->max_step_rejections = 1;
1435:   gl->min_order           = 1;
1436:   gl->max_order           = 3;
1437:   gl->start_order         = 1;
1438:   gl->current_scheme      = -1;
1439:   gl->extrapolate         = PETSC_FALSE;

1441:   gl->wrms_atol = 1e-8;
1442:   gl->wrms_rtol = 1e-5;

1444:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSGLLESetType_C", &TSGLLESetType_GLLE));
1445:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSGLLESetAcceptType_C", &TSGLLESetAcceptType_GLLE));
1446:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSGLLEGetAdapt_C", &TSGLLEGetAdapt_GLLE));
1447:   PetscFunctionReturn(PETSC_SUCCESS);
1448: }