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, 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;
138: PetscCall(PetscBLASIntCast(4 * ((s + 3) * 3 + 3), &lwork));
139: PetscCall(PetscMalloc7(PetscSqr(r), &ImV, 3 * s, &H, 3 * ss, &bmat, lwork, &workscalar, 5 * (3 + r), &workreal, r + s, &sing, r + s, &ipiv));
141: /* column-major input */
142: for (i = 0; i < r - 1; i++) {
143: for (j = 0; j < r - 1; j++) ImV[i + j * r] = 1.0 * (i == j) - v[(i + 1) * r + j + 1];
144: }
145: /* Build right-hand side for alpha (tp - glm.B(2:end,:)*(glm.c.^(p)./factorial(p))) */
146: for (i = 1; i < r; i++) {
147: scheme->alpha[i] = 1. / Factorial(p + 1 - i);
148: for (j = 0; j < s; j++) scheme->alpha[i] -= b[i * s + j] * CPowF(c[j], p);
149: }
150: PetscCall(PetscBLASIntCast(r - 1, &m));
151: PetscCall(PetscBLASIntCast(r, &n));
152: PetscCallBLAS("LAPACKgesv", LAPACKgesv_(&m, &one, ImV, &n, ipiv, scheme->alpha + 1, &n, &info));
153: PetscCheck(info >= 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "Bad argument to GESV");
154: PetscCheck(info <= 0, PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Bad LU factorization");
156: /* Build right-hand side for beta (tp1 - glm.B(2:end,:)*(glm.c.^(p+1)./factorial(p+1)) - e.alpha) */
157: for (i = 1; i < r; i++) {
158: scheme->beta[i] = 1. / Factorial(p + 2 - i) - scheme->alpha[i];
159: for (j = 0; j < s; j++) scheme->beta[i] -= b[i * s + j] * CPowF(c[j], p + 1);
160: }
161: PetscCallBLAS("LAPACKgetrs", LAPACKgetrs_("No transpose", &m, &one, ImV, &n, ipiv, scheme->beta + 1, &n, &info));
162: PetscCheck(info >= 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "Bad argument to GETRS");
163: PetscCheck(info <= 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "Should not happen");
165: /* Build stage_error vector
166: xi = glm.c.^(p+1)/factorial(p+1) - glm.A*glm.c.^p/factorial(p) + glm.U(:,2:end)*e.alpha;
167: */
168: for (i = 0; i < s; i++) {
169: scheme->stage_error[i] = CPowF(c[i], p + 1);
170: for (j = 0; j < s; j++) scheme->stage_error[i] -= a[i * s + j] * CPowF(c[j], p);
171: for (j = 1; j < r; j++) scheme->stage_error[i] += u[i * r + j] * scheme->alpha[j];
172: }
174: /* alpha[0] (epsilon in B,J,W 2007)
175: epsilon = 1/factorial(p+1) - B(1,:)*c.^p/factorial(p) + V(1,2:end)*e.alpha;
176: */
177: scheme->alpha[0] = 1. / Factorial(p + 1);
178: for (j = 0; j < s; j++) scheme->alpha[0] -= b[0 * s + j] * CPowF(c[j], p);
179: for (j = 1; j < r; j++) scheme->alpha[0] += v[0 * r + j] * scheme->alpha[j];
181: /* right-hand side for gamma (glm.B(2:end,:)*e.xi - e.epsilon*eye(s-1,1)) */
182: for (i = 1; i < r; i++) {
183: scheme->gamma[i] = (i == 1 ? -1. : 0) * scheme->alpha[0];
184: for (j = 0; j < s; j++) scheme->gamma[i] += b[i * s + j] * scheme->stage_error[j];
185: }
186: PetscCallBLAS("LAPACKgetrs", LAPACKgetrs_("No transpose", &m, &one, ImV, &n, ipiv, scheme->gamma + 1, &n, &info));
187: PetscCheck(info >= 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "Bad argument to GETRS");
188: PetscCheck(info <= 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "Should not happen");
190: /* beta[0] (rho in B,J,W 2007)
191: e.rho = 1/factorial(p+2) - glm.B(1,:)*glm.c.^(p+1)/factorial(p+1) ...
192: + glm.V(1,2:end)*e.beta;% - e.epsilon;
193: % Note: The paper (B,J,W 2007) includes the last term in their definition
194: * */
195: scheme->beta[0] = 1. / Factorial(p + 2);
196: for (j = 0; j < s; j++) scheme->beta[0] -= b[0 * s + j] * CPowF(c[j], p + 1);
197: for (j = 1; j < r; j++) scheme->beta[0] += v[0 * r + j] * scheme->beta[j];
199: /* gamma[0] (sigma in B,J,W 2007)
200: * e.sigma = glm.B(1,:)*e.xi + glm.V(1,2:end)*e.gamma;
201: * */
202: scheme->gamma[0] = 0.0;
203: for (j = 0; j < s; j++) scheme->gamma[0] += b[0 * s + j] * scheme->stage_error[j];
204: for (j = 1; j < r; j++) scheme->gamma[0] += v[0 * s + j] * scheme->gamma[j];
206: /* Assemble H
207: * % " PetscInt_FMT "etermine the error estimators phi
208: H = [[cpow(glm.c,p) + C*e.alpha] [cpow(glm.c,p+1) + C*e.beta] ...
209: [e.xi - C*(e.gamma + 0*e.epsilon*eye(s-1,1))]]';
210: % Paper has formula above without the 0, but that term must be left
211: % out to satisfy the conditions they propose and to make the
212: % example schemes work
213: e.H = H;
214: e.phi = (H \ [1 0 0;1 1 0;0 0 -1])';
215: e.psi = -e.phi*C;
216: * */
217: for (j = 0; j < s; j++) {
218: H[0 + j * 3] = CPowF(c[j], p);
219: H[1 + j * 3] = CPowF(c[j], p + 1);
220: H[2 + j * 3] = scheme->stage_error[j];
221: for (k = 1; k < r; k++) {
222: H[0 + j * 3] += CPowF(c[j], k - 1) * scheme->alpha[k];
223: H[1 + j * 3] += CPowF(c[j], k - 1) * scheme->beta[k];
224: H[2 + j * 3] -= CPowF(c[j], k - 1) * scheme->gamma[k];
225: }
226: }
227: bmat[0 + 0 * ss] = 1.;
228: bmat[0 + 1 * ss] = 0.;
229: bmat[0 + 2 * ss] = 0.;
230: bmat[1 + 0 * ss] = 1.;
231: bmat[1 + 1 * ss] = 1.;
232: bmat[1 + 2 * ss] = 0.;
233: bmat[2 + 0 * ss] = 0.;
234: bmat[2 + 1 * ss] = 0.;
235: bmat[2 + 2 * ss] = -1.;
236: m = 3;
237: PetscCall(PetscBLASIntCast(s, &n));
238: PetscCall(PetscBLASIntCast(ss, &ldb));
239: rcond = 1e-12;
240: #if defined(PETSC_USE_COMPLEX)
241: /* ZGELSS( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, WORK, LWORK, RWORK, INFO) */
242: PetscCallBLAS("LAPACKgelss", LAPACKgelss_(&m, &n, &m, H, &m, bmat, &ldb, sing, &rcond, &rank, workscalar, &lwork, workreal, &info));
243: #else
244: /* DGELSS( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, WORK, LWORK, INFO) */
245: PetscCallBLAS("LAPACKgelss", LAPACKgelss_(&m, &n, &m, H, &m, bmat, &ldb, sing, &rcond, &rank, workscalar, &lwork, &info));
246: #endif
247: PetscCheck(info >= 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "Bad argument to GELSS");
248: PetscCheck(info <= 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "SVD failed to converge");
250: for (j = 0; j < 3; j++) {
251: for (k = 0; k < s; k++) scheme->phi[k + j * s] = bmat[k + j * ss];
252: }
254: /* the other part of the error estimator, psi in B,J,W 2007 */
255: scheme->psi[0 * r + 0] = 0.;
256: scheme->psi[1 * r + 0] = 0.;
257: scheme->psi[2 * r + 0] = 0.;
258: for (j = 1; j < r; j++) {
259: scheme->psi[0 * r + j] = 0.;
260: scheme->psi[1 * r + j] = 0.;
261: scheme->psi[2 * r + j] = 0.;
262: for (k = 0; k < s; k++) {
263: scheme->psi[0 * r + j] -= CPowF(c[k], j - 1) * scheme->phi[0 * s + k];
264: scheme->psi[1 * r + j] -= CPowF(c[k], j - 1) * scheme->phi[1 * s + k];
265: scheme->psi[2 * r + j] -= CPowF(c[k], j - 1) * scheme->phi[2 * s + k];
266: }
267: }
268: PetscCall(PetscFree7(ImV, H, bmat, workscalar, workreal, sing, ipiv));
269: }
270: /* Check which properties are satisfied */
271: scheme->stiffly_accurate = PETSC_TRUE;
272: if (scheme->c[s - 1] != 1.) scheme->stiffly_accurate = PETSC_FALSE;
273: for (j = 0; j < s; j++)
274: if (a[(s - 1) * s + j] != b[j]) scheme->stiffly_accurate = PETSC_FALSE;
275: for (j = 0; j < r; j++)
276: if (u[(s - 1) * r + j] != v[j]) scheme->stiffly_accurate = PETSC_FALSE;
277: scheme->fsal = scheme->stiffly_accurate; /* FSAL is stronger */
278: for (j = 0; j < s - 1; j++)
279: if (r > 1 && b[1 * s + j] != 0.) scheme->fsal = PETSC_FALSE;
280: if (b[1 * s + r - 1] != 1.) scheme->fsal = PETSC_FALSE;
281: for (j = 0; j < r; j++)
282: if (r > 1 && v[1 * r + j] != 0.) scheme->fsal = PETSC_FALSE;
284: *inscheme = scheme;
285: PetscFunctionReturn(PETSC_SUCCESS);
286: }
288: static PetscErrorCode TSGLLESchemeDestroy(TSGLLEScheme sc)
289: {
290: PetscFunctionBegin;
291: PetscCall(PetscFree5(sc->c, sc->a, sc->b, sc->u, sc->v));
292: PetscCall(PetscFree6(sc->alpha, sc->beta, sc->gamma, sc->phi, sc->psi, sc->stage_error));
293: PetscCall(PetscFree(sc));
294: PetscFunctionReturn(PETSC_SUCCESS);
295: }
297: static PetscErrorCode TSGLLEDestroy_Default(TS_GLLE *gl)
298: {
299: PetscInt i;
301: PetscFunctionBegin;
302: for (i = 0; i < gl->nschemes; i++) {
303: if (gl->schemes[i]) PetscCall(TSGLLESchemeDestroy(gl->schemes[i]));
304: }
305: PetscCall(PetscFree(gl->schemes));
306: gl->nschemes = 0;
307: PetscCall(PetscMemzero(gl->type_name, sizeof(gl->type_name)));
308: PetscFunctionReturn(PETSC_SUCCESS);
309: }
311: static PetscErrorCode TSGLLEViewTable_Private(PetscViewer viewer, PetscInt m, PetscInt n, const PetscScalar a[], const char name[])
312: {
313: PetscBool iascii;
314: PetscInt i, j;
316: PetscFunctionBegin;
317: PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
318: if (iascii) {
319: PetscCall(PetscViewerASCIIPrintf(viewer, "%30s = [", name));
320: for (i = 0; i < m; i++) {
321: if (i) PetscCall(PetscViewerASCIIPrintf(viewer, "%30s [", ""));
322: PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
323: for (j = 0; j < n; j++) PetscCall(PetscViewerASCIIPrintf(viewer, " %12.8g", (double)PetscRealPart(a[i * n + j])));
324: PetscCall(PetscViewerASCIIPrintf(viewer, "]\n"));
325: PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
326: }
327: }
328: PetscFunctionReturn(PETSC_SUCCESS);
329: }
331: static PetscErrorCode TSGLLESchemeView(TSGLLEScheme sc, PetscBool view_details, PetscViewer viewer)
332: {
333: PetscBool iascii;
335: PetscFunctionBegin;
336: PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
337: if (iascii) {
338: 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));
339: PetscCall(PetscViewerASCIIPushTab(viewer));
340: PetscCall(PetscViewerASCIIPrintf(viewer, "Stiffly accurate: %s, FSAL: %s\n", sc->stiffly_accurate ? "yes" : "no", sc->fsal ? "yes" : "no"));
341: 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])));
342: PetscCall(TSGLLEViewTable_Private(viewer, 1, sc->s, sc->c, "Abscissas c"));
343: if (view_details) {
344: PetscCall(TSGLLEViewTable_Private(viewer, sc->s, sc->s, sc->a, "A"));
345: PetscCall(TSGLLEViewTable_Private(viewer, sc->r, sc->s, sc->b, "B"));
346: PetscCall(TSGLLEViewTable_Private(viewer, sc->s, sc->r, sc->u, "U"));
347: PetscCall(TSGLLEViewTable_Private(viewer, sc->r, sc->r, sc->v, "V"));
349: PetscCall(TSGLLEViewTable_Private(viewer, 3, sc->s, sc->phi, "Error estimate phi"));
350: PetscCall(TSGLLEViewTable_Private(viewer, 3, sc->r, sc->psi, "Error estimate psi"));
351: PetscCall(TSGLLEViewTable_Private(viewer, 1, sc->r, sc->alpha, "Modify alpha"));
352: PetscCall(TSGLLEViewTable_Private(viewer, 1, sc->r, sc->beta, "Modify beta"));
353: PetscCall(TSGLLEViewTable_Private(viewer, 1, sc->r, sc->gamma, "Modify gamma"));
354: PetscCall(TSGLLEViewTable_Private(viewer, 1, sc->s, sc->stage_error, "Stage error xi"));
355: }
356: PetscCall(PetscViewerASCIIPopTab(viewer));
357: } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Viewer type %s not supported", ((PetscObject)viewer)->type_name);
358: PetscFunctionReturn(PETSC_SUCCESS);
359: }
361: static PetscErrorCode TSGLLEEstimateHigherMoments_Default(TSGLLEScheme sc, PetscReal h, Vec Ydot[], Vec Xold[], Vec hm[])
362: {
363: PetscInt i;
365: PetscFunctionBegin;
366: PetscCheck(sc->r <= 64 && sc->s <= 64, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Ridiculous number of stages or items passed between stages");
367: /* build error vectors*/
368: for (i = 0; i < 3; i++) {
369: PetscScalar phih[64];
370: PetscInt j;
371: for (j = 0; j < sc->s; j++) phih[j] = sc->phi[i * sc->s + j] * h;
372: PetscCall(VecZeroEntries(hm[i]));
373: PetscCall(VecMAXPY(hm[i], sc->s, phih, Ydot));
374: PetscCall(VecMAXPY(hm[i], sc->r, &sc->psi[i * sc->r], Xold));
375: }
376: PetscFunctionReturn(PETSC_SUCCESS);
377: }
379: static PetscErrorCode TSGLLECompleteStep_Rescale(TSGLLEScheme sc, PetscReal h, TSGLLEScheme next_sc, PetscReal next_h, Vec Ydot[], Vec Xold[], Vec X[])
380: {
381: PetscScalar brow[32], vrow[32];
382: PetscInt i, j, r, s;
384: PetscFunctionBegin;
385: /* Build the new solution from (X,Ydot) */
386: r = sc->r;
387: s = sc->s;
388: for (i = 0; i < r; i++) {
389: PetscCall(VecZeroEntries(X[i]));
390: for (j = 0; j < s; j++) brow[j] = h * sc->b[i * s + j];
391: PetscCall(VecMAXPY(X[i], s, brow, Ydot));
392: for (j = 0; j < r; j++) vrow[j] = sc->v[i * r + j];
393: PetscCall(VecMAXPY(X[i], r, vrow, Xold));
394: }
395: PetscFunctionReturn(PETSC_SUCCESS);
396: }
398: static PetscErrorCode TSGLLECompleteStep_RescaleAndModify(TSGLLEScheme sc, PetscReal h, TSGLLEScheme next_sc, PetscReal next_h, Vec Ydot[], Vec Xold[], Vec X[])
399: {
400: PetscScalar brow[32], vrow[32];
401: PetscReal ratio;
402: PetscInt i, j, p, r, s;
404: PetscFunctionBegin;
405: /* Build the new solution from (X,Ydot) */
406: p = sc->p;
407: r = sc->r;
408: s = sc->s;
409: ratio = next_h / h;
410: for (i = 0; i < r; i++) {
411: PetscCall(VecZeroEntries(X[i]));
412: for (j = 0; j < s; j++) {
413: 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]));
414: }
415: PetscCall(VecMAXPY(X[i], s, brow, Ydot));
416: for (j = 0; j < r; j++) {
417: 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]));
418: }
419: PetscCall(VecMAXPY(X[i], r, vrow, Xold));
420: }
421: if (r < next_sc->r) {
422: PetscCheck(r + 1 == next_sc->r, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Cannot accommodate jump in r greater than 1");
423: PetscCall(VecZeroEntries(X[r]));
424: for (j = 0; j < s; j++) brow[j] = h * PetscPowRealInt(ratio, p + 1) * sc->phi[0 * s + j];
425: PetscCall(VecMAXPY(X[r], s, brow, Ydot));
426: for (j = 0; j < r; j++) vrow[j] = PetscPowRealInt(ratio, p + 1) * sc->psi[0 * r + j];
427: PetscCall(VecMAXPY(X[r], r, vrow, Xold));
428: }
429: PetscFunctionReturn(PETSC_SUCCESS);
430: }
432: static PetscErrorCode TSGLLECreate_IRKS(TS ts)
433: {
434: TS_GLLE *gl = (TS_GLLE *)ts->data;
436: PetscFunctionBegin;
437: gl->Destroy = TSGLLEDestroy_Default;
438: gl->EstimateHigherMoments = TSGLLEEstimateHigherMoments_Default;
439: gl->CompleteStep = TSGLLECompleteStep_RescaleAndModify;
440: PetscCall(PetscMalloc1(10, &gl->schemes));
441: gl->nschemes = 0;
443: {
444: /* p=1,q=1, r=s=2, A- and L-stable with error estimates of order 2 and 3
445: * Listed in Butcher & Podhaisky 2006. On error estimation in general linear methods for stiff ODE.
446: * irks(0.3,0,[.3,1],[1],1)
447: * Note: can be made to have classical order (not stage order) 2 by replacing 0.3 with 1-sqrt(1/2)
448: * but doing so would sacrifice the error estimator.
449: */
450: const PetscScalar c[2] = {3. / 10., 1.};
451: const PetscScalar a[2][2] = {
452: {3. / 10., 0 },
453: {7. / 10., 3. / 10.}
454: };
455: const PetscScalar b[2][2] = {
456: {7. / 10., 3. / 10.},
457: {0, 1 }
458: };
459: const PetscScalar u[2][2] = {
460: {1, 0},
461: {1, 0}
462: };
463: const PetscScalar v[2][2] = {
464: {1, 0},
465: {0, 0}
466: };
467: PetscCall(TSGLLESchemeCreate(1, 1, 2, 2, c, *a, *b, *u, *v, &gl->schemes[gl->nschemes++]));
468: }
470: {
471: /* p=q=2, r=s=3: irks(4/9,0,[1:3]/3,[0.33852],1) */
472: /* http://www.math.auckland.ac.nz/~hpod/atlas/i2a.html */
473: const PetscScalar c[3] = {1. / 3., 2. / 3., 1};
474: const PetscScalar a[3][3] = {
475: {4. / 9., 0, 0 },
476: {1.03750643704090e+00, 4. / 9., 0 },
477: {7.67024779410304e-01, -3.81140216918943e-01, 4. / 9.}
478: };
479: const PetscScalar b[3][3] = {
480: {0.767024779410304, -0.381140216918943, 4. / 9. },
481: {0.000000000000000, 0.000000000000000, 1.000000000000000},
482: {-2.075048385225385, 0.621728385225383, 1.277197204924873}
483: };
484: const PetscScalar u[3][3] = {
485: {1.0000000000000000, -0.1111111111111109, -0.0925925925925922},
486: {1.0000000000000000, -0.8152842148186744, -0.4199095530877056},
487: {1.0000000000000000, 0.1696709930641948, 0.0539741070314165 }
488: };
489: const PetscScalar v[3][3] = {
490: {1.0000000000000000, 0.1696709930641948, 0.0539741070314165},
491: {0.000000000000000, 0.000000000000000, 0.000000000000000 },
492: {0.000000000000000, 0.176122795075129, 0.000000000000000 }
493: };
494: PetscCall(TSGLLESchemeCreate(2, 2, 3, 3, c, *a, *b, *u, *v, &gl->schemes[gl->nschemes++]));
495: }
496: {
497: /* p=q=3, r=s=4: irks(9/40,0,[1:4]/4,[0.3312 1.0050],[0.49541 1;1 0]) */
498: const PetscScalar c[4] = {0.25, 0.5, 0.75, 1.0};
499: const PetscScalar a[4][4] = {
500: {9. / 40., 0, 0, 0 },
501: {2.11286958887701e-01, 9. / 40., 0, 0 },
502: {9.46338294287584e-01, -3.42942861246094e-01, 9. / 40., 0 },
503: {0.521490453970721, -0.662474225622980, 0.490476425459734, 9. / 40.}
504: };
505: const PetscScalar b[4][4] = {
506: {0.521490453970721, -0.662474225622980, 0.490476425459734, 9. / 40. },
507: {0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
508: {-0.084677029310348, 1.390757514776085, -1.568157386206001, 2.023192696767826},
509: {0.465383797936408, 1.478273530625148, -1.930836081010182, 1.644872111193354}
510: };
511: const PetscScalar u[4][4] = {
512: {1.00000000000000000, 0.02500000000001035, -0.02499999999999053, -0.00442708333332865},
513: {1.00000000000000000, 0.06371304111232945, -0.04032173972189845, -0.01389438413189452},
514: {1.00000000000000000, -0.07839543304147778, 0.04738685705116663, 0.02032603595928376 },
515: {1.00000000000000000, 0.42550734619251651, 0.10800718022400080, -0.01726712647760034}
516: };
517: const PetscScalar v[4][4] = {
518: {1.00000000000000000, 0.42550734619251651, 0.10800718022400080, -0.01726712647760034},
519: {0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000 },
520: {0.000000000000000, -1.761115796027561, -0.521284157173780, 0.258249384305463 },
521: {0.000000000000000, -1.657693358744728, -1.052227765232394, 0.521284157173780 }
522: };
523: PetscCall(TSGLLESchemeCreate(3, 3, 4, 4, c, *a, *b, *u, *v, &gl->schemes[gl->nschemes++]));
524: }
525: {
526: /* p=q=4, r=s=5:
527: irks(3/11,0,[1:5]/5, [0.1715 -0.1238 0.6617],...
528: [ -0.0812 0.4079 1.0000
529: 1.0000 0 0
530: 0.8270 1.0000 0])
531: */
532: const PetscScalar c[5] = {0.2, 0.4, 0.6, 0.8, 1.0};
533: const PetscScalar a[5][5] = {
534: {2.72727272727352e-01, 0.00000000000000e+00, 0.00000000000000e+00, 0.00000000000000e+00, 0.00000000000000e+00},
535: {-1.03980153733431e-01, 2.72727272727405e-01, 0.00000000000000e+00, 0.00000000000000e+00, 0.00000000000000e+00},
536: {-1.58615400341492e+00, 7.44168951881122e-01, 2.72727272727309e-01, 0.00000000000000e+00, 0.00000000000000e+00},
537: {-8.73658042865628e-01, 5.37884671894595e-01, -1.63298538799523e-01, 2.72727272726996e-01, 0.00000000000000e+00},
538: {2.95489397443992e-01, -1.18481693910097e+00, -6.68029812659953e-01, 1.00716687860943e+00, 2.72727272727288e-01}
539: };
540: const PetscScalar b[5][5] = {
541: {2.95489397443992e-01, -1.18481693910097e+00, -6.68029812659953e-01, 1.00716687860943e+00, 2.72727272727288e-01},
542: {0.00000000000000e+00, 1.11022302462516e-16, -2.22044604925031e-16, 0.00000000000000e+00, 1.00000000000000e+00},
543: {-4.05882503986005e+00, -4.00924006567769e+00, -1.38930610972481e+00, 4.45223930308488e+00, 6.32331093108427e-01},
544: {8.35690179937017e+00, -2.26640927349732e+00, 6.86647884973826e+00, -5.22595158025740e+00, 4.50893068837431e+00},
545: {1.27656267027479e+01, 2.80882153840821e+00, 8.91173096522890e+00, -1.07936444078906e+01, 4.82534148988854e+00}
546: };
547: const PetscScalar u[5][5] = {
548: {1.00000000000000e+00, -7.27272727273551e-02, -3.45454545454419e-02, -4.12121212119565e-03, -2.96969696964014e-04},
549: {1.00000000000000e+00, 2.31252881006154e-01, -8.29487834416481e-03, -9.07191207681020e-03, -1.70378403743473e-03},
550: {1.00000000000000e+00, 1.16925777880663e+00, 3.59268562942635e-02, -4.09013451730615e-02, -1.02411119670164e-02},
551: {1.00000000000000e+00, 1.02634463704356e+00, 1.59375044913405e-01, 1.89673015035370e-03, -4.89987231897569e-03},
552: {1.00000000000000e+00, 1.27746320298021e+00, 2.37186008132728e-01, -8.28694373940065e-02, -5.34396510196430e-02}
553: };
554: const PetscScalar v[5][5] = {
555: {1.00000000000000e+00, 1.27746320298021e+00, 2.37186008132728e-01, -8.28694373940065e-02, -5.34396510196430e-02},
556: {0.00000000000000e+00, -1.77635683940025e-15, -1.99840144432528e-15, -9.99200722162641e-16, -3.33066907387547e-16},
557: {0.00000000000000e+00, 4.37280081906924e+00, 5.49221645016377e-02, -8.88913177394943e-02, 1.12879077989154e-01 },
558: {0.00000000000000e+00, -1.22399504837280e+01, -5.21287338448645e+00, -8.03952325565291e-01, 4.60298678047147e-01 },
559: {0.00000000000000e+00, -1.85178762883829e+01, -5.21411849862624e+00, -1.04283436528809e+00, 7.49030161063651e-01 }
560: };
561: PetscCall(TSGLLESchemeCreate(4, 4, 5, 5, c, *a, *b, *u, *v, &gl->schemes[gl->nschemes++]));
562: }
563: {
564: /* p=q=5, r=s=6;
565: irks(1/3,0,[1:6]/6,...
566: [-0.0489 0.4228 -0.8814 0.9021],...
567: [-0.3474 -0.6617 0.6294 0.2129
568: 0.0044 -0.4256 -0.1427 -0.8936
569: -0.8267 0.4821 0.1371 -0.2557
570: -0.4426 -0.3855 -0.7514 0.3014])
571: */
572: const PetscScalar c[6] = {1. / 6, 2. / 6, 3. / 6, 4. / 6, 5. / 6, 1.};
573: const PetscScalar a[6][6] = {
574: {3.33333333333940e-01, 0, 0, 0, 0, 0 },
575: {-8.64423857333350e-02, 3.33333333332888e-01, 0, 0, 0, 0 },
576: {-2.16850174258252e+00, -2.23619072028839e+00, 3.33333333335204e-01, 0, 0, 0 },
577: {-4.73160970138997e+00, -3.89265344629268e+00, -2.76318716520933e-01, 3.33333333335759e-01, 0, 0 },
578: {-6.75187540297338e+00, -7.90756533769377e+00, 7.90245051802259e-01, -4.48352364517632e-01, 3.33333333328483e-01, 0 },
579: {-4.26488287921548e+00, -1.19320395589302e+01, 3.38924509887755e+00, -2.23969848002481e+00, 6.62807710124007e-01, 3.33333333335440e-01}
580: };
581: const PetscScalar b[6][6] = {
582: {-4.26488287921548e+00, -1.19320395589302e+01, 3.38924509887755e+00, -2.23969848002481e+00, 6.62807710124007e-01, 3.33333333335440e-01 },
583: {-8.88178419700125e-16, 4.44089209850063e-16, -1.54737334057131e-15, -8.88178419700125e-16, 0.00000000000000e+00, 1.00000000000001e+00 },
584: {-2.87780425770651e+01, -1.13520448264971e+01, 2.62002318943161e+01, 2.56943874812797e+01, -3.06702268304488e+01, 6.68067773510103e+00 },
585: {5.47971245256474e+01, 6.80366875868284e+01, -6.50952588861999e+01, -8.28643975339097e+01, 8.17416943896414e+01, -1.17819043489036e+01},
586: {-2.33332114788869e+02, 6.12942539462634e+01, -4.91850135865944e+01, 1.82716844135480e+02, -1.29788173979395e+02, 3.09968095651099e+01 },
587: {-1.72049132343751e+02, 8.60194713593999e+00, 7.98154219170200e-01, 1.50371386053218e+02, -1.18515423962066e+02, 2.50898277784663e+01 }
588: };
589: const PetscScalar u[6][6] = {
590: {1.00000000000000e+00, -1.66666666666870e-01, -4.16666666664335e-02, -3.85802469124815e-03, -2.25051440302250e-04, -9.64506172339142e-06},
591: {1.00000000000000e+00, 8.64423857327162e-02, -4.11484912671353e-02, -1.11450903217645e-02, -1.47651050487126e-03, -1.34395070766826e-04},
592: {1.00000000000000e+00, 4.57135912953434e+00, 1.06514719719137e+00, 1.33517564218007e-01, 1.11365952968659e-02, 6.12382756769504e-04 },
593: {1.00000000000000e+00, 9.23391519753404e+00, 2.22431212392095e+00, 2.91823807741891e-01, 2.52058456411084e-02, 1.22800542949647e-03 },
594: {1.00000000000000e+00, 1.48175480533865e+01, 3.73439117461835e+00, 5.14648336541804e-01, 4.76430038853402e-02, 2.56798515502156e-03 },
595: {1.00000000000000e+00, 1.50512347758335e+01, 4.10099701165164e+00, 5.66039141003603e-01, 3.91213893800891e-02, -2.99136269067853e-03}
596: };
597: const PetscScalar v[6][6] = {
598: {1.00000000000000e+00, 1.50512347758335e+01, 4.10099701165164e+00, 5.66039141003603e-01, 3.91213893800891e-02, -2.99136269067853e-03},
599: {0.00000000000000e+00, -4.88498130835069e-15, -6.43929354282591e-15, -3.55271367880050e-15, -1.22124532708767e-15, -3.12250225675825e-16},
600: {0.00000000000000e+00, 1.22250171233141e+01, -1.77150760606169e+00, 3.54516769879390e-01, 6.22298845883398e-01, 2.31647447450276e-01 },
601: {0.00000000000000e+00, -4.48339457331040e+01, -3.57363126641880e-01, 5.18750173123425e-01, 6.55727990241799e-02, 1.63175368287079e-01 },
602: {0.00000000000000e+00, 1.37297394708005e+02, -1.60145272991317e+00, -5.05319555199441e+00, 1.55328940390990e-01, 9.16629423682464e-01 },
603: {0.00000000000000e+00, 1.05703241119022e+02, -1.16610260983038e+00, -2.99767252773859e+00, -1.13472315553890e-01, 1.09742849254729e+00 }
604: };
605: PetscCall(TSGLLESchemeCreate(5, 5, 6, 6, c, *a, *b, *u, *v, &gl->schemes[gl->nschemes++]));
606: }
607: PetscFunctionReturn(PETSC_SUCCESS);
608: }
610: /*@
611: TSGLLESetType - sets the class of general linear method, `TSGLLE` to use for time-stepping
613: Collective
615: Input Parameters:
616: + ts - the `TS` context
617: - type - a method
619: Options Database Key:
620: . -ts_gl_type <type> - sets the method, use -help for a list of available method (e.g. irks)
622: Level: intermediate
624: Notes:
625: See "petsc/include/petscts.h" for available methods (for instance)
626: . TSGLLE_IRKS - Diagonally implicit methods with inherent Runge-Kutta stability (for stiff problems)
628: Normally, it is best to use the `TSSetFromOptions()` command and then set the `TSGLLE` type
629: from the options database rather than by using this routine. Using the options database
630: provides the user with maximum flexibility in evaluating the many different solvers. The
631: `TSGLLESetType()` routine is provided for those situations where it is necessary to set the
632: timestepping solver independently of the command line or options database. This might be the
633: case, for example, when the choice of solver changes during the execution of the program, and
634: the user's application is taking responsibility for choosing the appropriate method.
636: .seealso: [](ch_ts), `TS`, `TSGLLEType`, `TSGLLE`
637: @*/
638: PetscErrorCode TSGLLESetType(TS ts, TSGLLEType type)
639: {
640: PetscFunctionBegin;
642: PetscAssertPointer(type, 2);
643: PetscTryMethod(ts, "TSGLLESetType_C", (TS, TSGLLEType), (ts, type));
644: PetscFunctionReturn(PETSC_SUCCESS);
645: }
647: /*@C
648: TSGLLESetAcceptType - sets the acceptance test for `TSGLLE`
650: Logically Collective
652: Input Parameters:
653: + ts - the `TS` context
654: - type - the type
656: Options Database Key:
657: . -ts_gl_accept_type <type> - sets the method used to determine whether to accept or reject a step
659: Level: intermediate
661: Notes:
662: Time integrators that need to control error must have the option to reject a time step based
663: on local error estimates. This function allows different schemes to be set.
665: .seealso: [](ch_ts), `TS`, `TSGLLE`, `TSGLLEAcceptRegister()`, `TSGLLEAdapt`
666: @*/
667: PetscErrorCode TSGLLESetAcceptType(TS ts, TSGLLEAcceptType type)
668: {
669: PetscFunctionBegin;
671: PetscAssertPointer(type, 2);
672: PetscTryMethod(ts, "TSGLLESetAcceptType_C", (TS, TSGLLEAcceptType), (ts, type));
673: PetscFunctionReturn(PETSC_SUCCESS);
674: }
676: /*@
677: TSGLLEGetAdapt - gets the `TSGLLEAdapt` object from the `TS`
679: Not Collective
681: Input Parameter:
682: . ts - the `TS` context
684: Output Parameter:
685: . adapt - the `TSGLLEAdapt` context
687: Level: advanced
689: Note:
690: This allows the user set options on the `TSGLLEAdapt` object. Usually it is better to do this
691: using the options database, so this function is rarely needed.
693: .seealso: [](ch_ts), `TS`, `TSGLLE`, `TSGLLEAdapt`, `TSGLLEAdaptRegister()`
694: @*/
695: PetscErrorCode TSGLLEGetAdapt(TS ts, TSGLLEAdapt *adapt)
696: {
697: PetscFunctionBegin;
699: PetscAssertPointer(adapt, 2);
700: PetscUseMethod(ts, "TSGLLEGetAdapt_C", (TS, TSGLLEAdapt *), (ts, adapt));
701: PetscFunctionReturn(PETSC_SUCCESS);
702: }
704: static PetscErrorCode TSGLLEAccept_Always(TS ts, PetscReal tleft, PetscReal h, const PetscReal enorms[], PetscBool *accept)
705: {
706: PetscFunctionBegin;
707: *accept = PETSC_TRUE;
708: PetscFunctionReturn(PETSC_SUCCESS);
709: }
711: static PetscErrorCode TSGLLEUpdateWRMS(TS ts)
712: {
713: TS_GLLE *gl = (TS_GLLE *)ts->data;
714: PetscScalar *x, *w;
715: PetscInt n, i;
717: PetscFunctionBegin;
718: PetscCall(VecGetArray(gl->X[0], &x));
719: PetscCall(VecGetArray(gl->W, &w));
720: PetscCall(VecGetLocalSize(gl->W, &n));
721: for (i = 0; i < n; i++) w[i] = 1. / (gl->wrms_atol + gl->wrms_rtol * PetscAbsScalar(x[i]));
722: PetscCall(VecRestoreArray(gl->X[0], &x));
723: PetscCall(VecRestoreArray(gl->W, &w));
724: PetscFunctionReturn(PETSC_SUCCESS);
725: }
727: static PetscErrorCode TSGLLEVecNormWRMS(TS ts, Vec X, PetscReal *nrm)
728: {
729: TS_GLLE *gl = (TS_GLLE *)ts->data;
730: PetscScalar *x, *w;
731: PetscReal sum = 0.0, gsum;
732: PetscInt n, N, i;
734: PetscFunctionBegin;
735: PetscCall(VecGetArray(X, &x));
736: PetscCall(VecGetArray(gl->W, &w));
737: PetscCall(VecGetLocalSize(gl->W, &n));
738: for (i = 0; i < n; i++) sum += PetscAbsScalar(PetscSqr(x[i] * w[i]));
739: PetscCall(VecRestoreArray(X, &x));
740: PetscCall(VecRestoreArray(gl->W, &w));
741: PetscCallMPI(MPIU_Allreduce(&sum, &gsum, 1, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject)ts)));
742: PetscCall(VecGetSize(gl->W, &N));
743: *nrm = PetscSqrtReal(gsum / (1. * N));
744: PetscFunctionReturn(PETSC_SUCCESS);
745: }
747: static PetscErrorCode TSGLLESetType_GLLE(TS ts, TSGLLEType type)
748: {
749: PetscBool same;
750: TS_GLLE *gl = (TS_GLLE *)ts->data;
751: PetscErrorCode (*r)(TS);
753: PetscFunctionBegin;
754: if (gl->type_name[0]) {
755: PetscCall(PetscStrcmp(gl->type_name, type, &same));
756: if (same) PetscFunctionReturn(PETSC_SUCCESS);
757: PetscCall((*gl->Destroy)(gl));
758: }
760: PetscCall(PetscFunctionListFind(TSGLLEList, type, &r));
761: PetscCheck(r, PetscObjectComm((PetscObject)ts), PETSC_ERR_ARG_UNKNOWN_TYPE, "Unknown TSGLLE type \"%s\" given", type);
762: PetscCall((*r)(ts));
763: PetscCall(PetscStrncpy(gl->type_name, type, sizeof(gl->type_name)));
764: PetscFunctionReturn(PETSC_SUCCESS);
765: }
767: static PetscErrorCode TSGLLESetAcceptType_GLLE(TS ts, TSGLLEAcceptType type)
768: {
769: TSGLLEAcceptFn *r;
770: TS_GLLE *gl = (TS_GLLE *)ts->data;
772: PetscFunctionBegin;
773: PetscCall(PetscFunctionListFind(TSGLLEAcceptList, type, &r));
774: PetscCheck(r, PetscObjectComm((PetscObject)ts), PETSC_ERR_ARG_UNKNOWN_TYPE, "Unknown TSGLLEAccept type \"%s\" given", type);
775: gl->Accept = r;
776: PetscCall(PetscStrncpy(gl->accept_name, type, sizeof(gl->accept_name)));
777: PetscFunctionReturn(PETSC_SUCCESS);
778: }
780: static PetscErrorCode TSGLLEGetAdapt_GLLE(TS ts, TSGLLEAdapt *adapt)
781: {
782: TS_GLLE *gl = (TS_GLLE *)ts->data;
784: PetscFunctionBegin;
785: if (!gl->adapt) {
786: PetscCall(TSGLLEAdaptCreate(PetscObjectComm((PetscObject)ts), &gl->adapt));
787: PetscCall(PetscObjectIncrementTabLevel((PetscObject)gl->adapt, (PetscObject)ts, 1));
788: }
789: *adapt = gl->adapt;
790: PetscFunctionReturn(PETSC_SUCCESS);
791: }
793: static PetscErrorCode TSGLLEChooseNextScheme(TS ts, PetscReal h, const PetscReal hmnorm[], PetscInt *next_scheme, PetscReal *next_h, PetscBool *finish)
794: {
795: TS_GLLE *gl = (TS_GLLE *)ts->data;
796: PetscInt i, n, cur_p, cur, next_sc, candidates[64], orders[64];
797: PetscReal errors[64], costs[64], tleft;
799: PetscFunctionBegin;
800: cur = -1;
801: cur_p = gl->schemes[gl->current_scheme]->p;
802: tleft = ts->max_time - (ts->ptime + ts->time_step);
803: for (i = 0, n = 0; i < gl->nschemes; i++) {
804: TSGLLEScheme sc = gl->schemes[i];
805: if (sc->p < gl->min_order || gl->max_order < sc->p) continue;
806: if (sc->p == cur_p - 1) errors[n] = PetscAbsScalar(sc->alpha[0]) * hmnorm[0];
807: else if (sc->p == cur_p) errors[n] = PetscAbsScalar(sc->alpha[0]) * hmnorm[1];
808: else if (sc->p == cur_p + 1) errors[n] = PetscAbsScalar(sc->alpha[0]) * (hmnorm[2] + hmnorm[3]);
809: else continue;
810: candidates[n] = i;
811: orders[n] = PetscMin(sc->p, sc->q); /* order of global truncation error */
812: costs[n] = sc->s; /* estimate the cost as the number of stages */
813: if (i == gl->current_scheme) cur = n;
814: n++;
815: }
816: PetscCheck(cur >= 0 && gl->nschemes > cur, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Current scheme not found in scheme list");
817: PetscCall(TSGLLEAdaptChoose(gl->adapt, n, orders, errors, costs, cur, h, tleft, &next_sc, next_h, finish));
818: *next_scheme = candidates[next_sc];
819: 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,
820: gl->schemes[*next_scheme]->r, gl->schemes[*next_scheme]->s, (double)*next_h, PetscBools[*finish]));
821: PetscFunctionReturn(PETSC_SUCCESS);
822: }
824: static PetscErrorCode TSGLLEGetMaxSizes(TS ts, PetscInt *max_r, PetscInt *max_s)
825: {
826: TS_GLLE *gl = (TS_GLLE *)ts->data;
828: PetscFunctionBegin;
829: *max_r = gl->schemes[gl->nschemes - 1]->r;
830: *max_s = gl->schemes[gl->nschemes - 1]->s;
831: PetscFunctionReturn(PETSC_SUCCESS);
832: }
834: static PetscErrorCode TSSolve_GLLE(TS ts)
835: {
836: TS_GLLE *gl = (TS_GLLE *)ts->data;
837: PetscInt i, k, its, lits, max_r, max_s;
838: PetscBool final_step, finish;
839: SNESConvergedReason snesreason;
841: PetscFunctionBegin;
842: PetscCall(TSMonitor(ts, ts->steps, ts->ptime, ts->vec_sol));
844: PetscCall(TSGLLEGetMaxSizes(ts, &max_r, &max_s));
845: PetscCall(VecCopy(ts->vec_sol, gl->X[0]));
846: for (i = 1; i < max_r; i++) PetscCall(VecZeroEntries(gl->X[i]));
847: PetscCall(TSGLLEUpdateWRMS(ts));
849: if (0) {
850: /* Find consistent initial data for DAE */
851: gl->stage_time = ts->ptime + ts->time_step;
852: gl->scoeff = 1.;
853: gl->stage = 0;
855: PetscCall(VecCopy(ts->vec_sol, gl->Z));
856: PetscCall(VecCopy(ts->vec_sol, gl->Y));
857: PetscCall(SNESSolve(ts->snes, NULL, gl->Y));
858: PetscCall(SNESGetIterationNumber(ts->snes, &its));
859: PetscCall(SNESGetLinearSolveIterations(ts->snes, &lits));
860: PetscCall(SNESGetConvergedReason(ts->snes, &snesreason));
862: ts->snes_its += its;
863: ts->ksp_its += lits;
864: if (snesreason < 0 && ts->max_snes_failures != PETSC_UNLIMITED && ++ts->num_snes_failures >= ts->max_snes_failures) {
865: ts->reason = TS_DIVERGED_NONLINEAR_SOLVE;
866: 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));
867: PetscFunctionReturn(PETSC_SUCCESS);
868: }
869: }
871: PetscCheck(gl->current_scheme >= 0, PETSC_COMM_SELF, PETSC_ERR_ORDER, "A starting scheme has not been provided");
873: for (k = 0, final_step = PETSC_FALSE, finish = PETSC_FALSE; k < ts->max_steps && !finish; k++) {
874: PetscInt j, r, s, next_scheme = 0, rejections;
875: PetscReal h, hmnorm[4], enorm[3], next_h;
876: PetscBool accept;
877: const PetscScalar *c, *a, *u;
878: Vec *X, *Ydot, Y;
879: TSGLLEScheme scheme = gl->schemes[gl->current_scheme];
881: r = scheme->r;
882: s = scheme->s;
883: c = scheme->c;
884: a = scheme->a;
885: u = scheme->u;
886: h = ts->time_step;
887: X = gl->X;
888: Ydot = gl->Ydot;
889: Y = gl->Y;
891: if (ts->ptime > ts->max_time) break;
893: /*
894: We only call PreStep at the start of each STEP, not each STAGE. This is because it is
895: possible to fail (have to restart a step) after multiple stages.
896: */
897: PetscCall(TSPreStep(ts));
899: rejections = 0;
900: while (1) {
901: for (i = 0; i < s; i++) {
902: PetscScalar shift;
903: gl->scoeff = 1. / PetscRealPart(a[i * s + i]);
904: shift = gl->scoeff / ts->time_step;
905: gl->stage = i;
906: gl->stage_time = ts->ptime + PetscRealPart(c[i]) * h;
908: /*
909: * Stage equation: Y = h A Y' + U X
910: * We assume that A is lower-triangular so that we can solve the stages (Y,Y') sequentially
911: * Build the affine vector z_i = -[1/(h a_ii)](h sum_j a_ij y'_j + sum_j u_ij x_j)
912: * Then y'_i = z + 1/(h a_ii) y_i
913: */
914: PetscCall(VecZeroEntries(gl->Z));
915: for (j = 0; j < r; j++) PetscCall(VecAXPY(gl->Z, -shift * u[i * r + j], X[j]));
916: for (j = 0; j < i; j++) PetscCall(VecAXPY(gl->Z, -shift * h * a[i * s + j], Ydot[j]));
917: /* Note: Z is used within function evaluation, Ydot = Z + shift*Y */
919: /* Compute an estimate of Y to start Newton iteration */
920: if (gl->extrapolate) {
921: if (i == 0) {
922: /* Linear extrapolation on the first stage */
923: PetscCall(VecWAXPY(Y, c[i] * h, X[1], X[0]));
924: } else {
925: /* Linear extrapolation from the last stage */
926: PetscCall(VecAXPY(Y, (c[i] - c[i - 1]) * h, Ydot[i - 1]));
927: }
928: } else if (i == 0) { /* Directly use solution from the last step, otherwise reuse the last stage (do nothing) */
929: PetscCall(VecCopy(X[0], Y));
930: }
932: /* Solve this stage (Ydot[i] is computed during function evaluation) */
933: PetscCall(SNESSolve(ts->snes, NULL, Y));
934: PetscCall(SNESGetIterationNumber(ts->snes, &its));
935: PetscCall(SNESGetLinearSolveIterations(ts->snes, &lits));
936: PetscCall(SNESGetConvergedReason(ts->snes, &snesreason));
937: ts->snes_its += its;
938: ts->ksp_its += lits;
939: if (snesreason < 0 && ts->max_snes_failures != PETSC_UNLIMITED && ++ts->num_snes_failures >= ts->max_snes_failures) {
940: ts->reason = TS_DIVERGED_NONLINEAR_SOLVE;
941: 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));
942: PetscFunctionReturn(PETSC_SUCCESS);
943: }
944: }
946: gl->stage_time = ts->ptime + ts->time_step;
948: PetscCall((*gl->EstimateHigherMoments)(scheme, h, Ydot, gl->X, gl->himom));
949: /* hmnorm[i] = h^{p+i}x^{(p+i)} with i=0,1,2; hmnorm[3] = h^{p+2}(dx'/dx) x^{(p+1)} */
950: for (i = 0; i < 3; i++) PetscCall(TSGLLEVecNormWRMS(ts, gl->himom[i], &hmnorm[i + 1]));
951: enorm[0] = PetscRealPart(scheme->alpha[0]) * hmnorm[1];
952: enorm[1] = PetscRealPart(scheme->beta[0]) * hmnorm[2];
953: enorm[2] = PetscRealPart(scheme->gamma[0]) * hmnorm[3];
954: PetscCall((*gl->Accept)(ts, ts->max_time - gl->stage_time, h, enorm, &accept));
955: if (accept) goto accepted;
956: rejections++;
957: PetscCall(PetscInfo(ts, "Step %" PetscInt_FMT " (t=%g) not accepted, rejections=%" PetscInt_FMT "\n", k, (double)gl->stage_time, rejections));
958: if (rejections > gl->max_step_rejections) break;
959: /*
960: There are lots of reasons why a step might be rejected, including solvers not converging and other factors that
961: TSGLLEChooseNextScheme does not support. Additionally, the error estimates may be very screwed up, so I'm not
962: convinced that it's safe to just compute a new error estimate using the same interface as the current adaptor
963: (the adaptor interface probably has to change). Here we make an arbitrary and naive choice. This assumes that
964: steps were written in Nordsieck form. The "correct" method would be to re-complete the previous time step with
965: the correct "next" step size. It is unclear to me whether the present ad-hoc method of rescaling X is stable.
966: */
967: h *= 0.5;
968: for (i = 1; i < scheme->r; i++) PetscCall(VecScale(X[i], PetscPowRealInt(0.5, i)));
969: }
970: 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);
972: accepted:
973: /* This term is not error, but it *would* be the leading term for a lower order method */
974: PetscCall(TSGLLEVecNormWRMS(ts, gl->X[scheme->r - 1], &hmnorm[0]));
975: /* Correct scaling so that these are equivalent to norms of the Nordsieck vectors */
977: 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]));
978: if (!final_step) {
979: PetscCall(TSGLLEChooseNextScheme(ts, h, hmnorm, &next_scheme, &next_h, &final_step));
980: } else {
981: /* Dummy values to complete the current step in a consistent manner */
982: next_scheme = gl->current_scheme;
983: next_h = h;
984: finish = PETSC_TRUE;
985: }
987: X = gl->Xold;
988: gl->Xold = gl->X;
989: gl->X = X;
990: PetscCall((*gl->CompleteStep)(scheme, h, gl->schemes[next_scheme], next_h, Ydot, gl->Xold, gl->X));
992: PetscCall(TSGLLEUpdateWRMS(ts));
994: /* Post the solution for the user, we could avoid this copy with a small bit of cleverness */
995: PetscCall(VecCopy(gl->X[0], ts->vec_sol));
996: ts->ptime += h;
997: ts->steps++;
999: PetscCall(TSPostEvaluate(ts));
1000: PetscCall(TSPostStep(ts));
1001: PetscCall(TSMonitor(ts, ts->steps, ts->ptime, ts->vec_sol));
1003: gl->current_scheme = next_scheme;
1004: ts->time_step = next_h;
1005: }
1006: PetscFunctionReturn(PETSC_SUCCESS);
1007: }
1009: /*------------------------------------------------------------*/
1011: static PetscErrorCode TSReset_GLLE(TS ts)
1012: {
1013: TS_GLLE *gl = (TS_GLLE *)ts->data;
1014: PetscInt max_r, max_s;
1016: PetscFunctionBegin;
1017: if (gl->setupcalled) {
1018: PetscCall(TSGLLEGetMaxSizes(ts, &max_r, &max_s));
1019: PetscCall(VecDestroyVecs(max_r, &gl->Xold));
1020: PetscCall(VecDestroyVecs(max_r, &gl->X));
1021: PetscCall(VecDestroyVecs(max_s, &gl->Ydot));
1022: PetscCall(VecDestroyVecs(3, &gl->himom));
1023: PetscCall(VecDestroy(&gl->W));
1024: PetscCall(VecDestroy(&gl->Y));
1025: PetscCall(VecDestroy(&gl->Z));
1026: }
1027: gl->setupcalled = PETSC_FALSE;
1028: PetscFunctionReturn(PETSC_SUCCESS);
1029: }
1031: static PetscErrorCode TSDestroy_GLLE(TS ts)
1032: {
1033: TS_GLLE *gl = (TS_GLLE *)ts->data;
1035: PetscFunctionBegin;
1036: PetscCall(TSReset_GLLE(ts));
1037: if (ts->dm) {
1038: PetscCall(DMCoarsenHookRemove(ts->dm, DMCoarsenHook_TSGLLE, DMRestrictHook_TSGLLE, ts));
1039: PetscCall(DMSubDomainHookRemove(ts->dm, DMSubDomainHook_TSGLLE, DMSubDomainRestrictHook_TSGLLE, ts));
1040: }
1041: if (gl->adapt) PetscCall(TSGLLEAdaptDestroy(&gl->adapt));
1042: if (gl->Destroy) PetscCall((*gl->Destroy)(gl));
1043: PetscCall(PetscFree(ts->data));
1044: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSGLLESetType_C", NULL));
1045: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSGLLESetAcceptType_C", NULL));
1046: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSGLLEGetAdapt_C", NULL));
1047: PetscFunctionReturn(PETSC_SUCCESS);
1048: }
1050: /*
1051: This defines the nonlinear equation that is to be solved with SNES
1052: g(x) = f(t,x,z+shift*x) = 0
1053: */
1054: static PetscErrorCode SNESTSFormFunction_GLLE(SNES snes, Vec x, Vec f, TS ts)
1055: {
1056: TS_GLLE *gl = (TS_GLLE *)ts->data;
1057: Vec Z, Ydot;
1058: DM dm, dmsave;
1060: PetscFunctionBegin;
1061: PetscCall(SNESGetDM(snes, &dm));
1062: PetscCall(TSGLLEGetVecs(ts, dm, &Z, &Ydot));
1063: PetscCall(VecWAXPY(Ydot, gl->scoeff / ts->time_step, x, Z));
1064: dmsave = ts->dm;
1065: ts->dm = dm;
1066: PetscCall(TSComputeIFunction(ts, gl->stage_time, x, Ydot, f, PETSC_FALSE));
1067: ts->dm = dmsave;
1068: PetscCall(TSGLLERestoreVecs(ts, dm, &Z, &Ydot));
1069: PetscFunctionReturn(PETSC_SUCCESS);
1070: }
1072: static PetscErrorCode SNESTSFormJacobian_GLLE(SNES snes, Vec x, Mat A, Mat B, TS ts)
1073: {
1074: TS_GLLE *gl = (TS_GLLE *)ts->data;
1075: Vec Z, Ydot;
1076: DM dm, dmsave;
1078: PetscFunctionBegin;
1079: PetscCall(SNESGetDM(snes, &dm));
1080: PetscCall(TSGLLEGetVecs(ts, dm, &Z, &Ydot));
1081: dmsave = ts->dm;
1082: ts->dm = dm;
1083: /* gl->Xdot will have already been computed in SNESTSFormFunction_GLLE */
1084: PetscCall(TSComputeIJacobian(ts, gl->stage_time, x, gl->Ydot[gl->stage], gl->scoeff / ts->time_step, A, B, PETSC_FALSE));
1085: ts->dm = dmsave;
1086: PetscCall(TSGLLERestoreVecs(ts, dm, &Z, &Ydot));
1087: PetscFunctionReturn(PETSC_SUCCESS);
1088: }
1090: static PetscErrorCode TSSetUp_GLLE(TS ts)
1091: {
1092: TS_GLLE *gl = (TS_GLLE *)ts->data;
1093: PetscInt max_r, max_s;
1094: DM dm;
1096: PetscFunctionBegin;
1097: gl->setupcalled = PETSC_TRUE;
1098: PetscCall(TSGLLEGetMaxSizes(ts, &max_r, &max_s));
1099: PetscCall(VecDuplicateVecs(ts->vec_sol, max_r, &gl->X));
1100: PetscCall(VecDuplicateVecs(ts->vec_sol, max_r, &gl->Xold));
1101: PetscCall(VecDuplicateVecs(ts->vec_sol, max_s, &gl->Ydot));
1102: PetscCall(VecDuplicateVecs(ts->vec_sol, 3, &gl->himom));
1103: PetscCall(VecDuplicate(ts->vec_sol, &gl->W));
1104: PetscCall(VecDuplicate(ts->vec_sol, &gl->Y));
1105: PetscCall(VecDuplicate(ts->vec_sol, &gl->Z));
1107: /* Default acceptance tests and adaptivity */
1108: if (!gl->Accept) PetscCall(TSGLLESetAcceptType(ts, TSGLLEACCEPT_ALWAYS));
1109: if (!gl->adapt) PetscCall(TSGLLEGetAdapt(ts, &gl->adapt));
1111: if (gl->current_scheme < 0) {
1112: PetscInt i;
1113: for (i = 0;; i++) {
1114: if (gl->schemes[i]->p == gl->start_order) break;
1115: PetscCheck(i + 1 != gl->nschemes, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "No schemes available with requested start order %" PetscInt_FMT, i);
1116: }
1117: gl->current_scheme = i;
1118: }
1119: PetscCall(TSGetDM(ts, &dm));
1120: PetscCall(DMCoarsenHookAdd(dm, DMCoarsenHook_TSGLLE, DMRestrictHook_TSGLLE, ts));
1121: PetscCall(DMSubDomainHookAdd(dm, DMSubDomainHook_TSGLLE, DMSubDomainRestrictHook_TSGLLE, ts));
1122: PetscFunctionReturn(PETSC_SUCCESS);
1123: }
1124: /*------------------------------------------------------------*/
1126: static PetscErrorCode TSSetFromOptions_GLLE(TS ts, PetscOptionItems *PetscOptionsObject)
1127: {
1128: TS_GLLE *gl = (TS_GLLE *)ts->data;
1129: char tname[256] = TSGLLE_IRKS, completef[256] = "rescale-and-modify";
1131: PetscFunctionBegin;
1132: PetscOptionsHeadBegin(PetscOptionsObject, "General Linear ODE solver options");
1133: {
1134: PetscBool flg;
1135: PetscCall(PetscOptionsFList("-ts_gl_type", "Type of GL method", "TSGLLESetType", TSGLLEList, gl->type_name[0] ? gl->type_name : tname, tname, sizeof(tname), &flg));
1136: if (flg || !gl->type_name[0]) PetscCall(TSGLLESetType(ts, tname));
1137: 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));
1138: PetscCall(PetscOptionsInt("-ts_gl_max_order", "Maximum order to try", "TSGLLESetMaxOrder", gl->max_order, &gl->max_order, NULL));
1139: PetscCall(PetscOptionsInt("-ts_gl_min_order", "Minimum order to try", "TSGLLESetMinOrder", gl->min_order, &gl->min_order, NULL));
1140: PetscCall(PetscOptionsInt("-ts_gl_start_order", "Initial order to try", "TSGLLESetMinOrder", gl->start_order, &gl->start_order, NULL));
1141: PetscCall(PetscOptionsEnum("-ts_gl_error_direction", "Which direction to look when estimating error", "TSGLLESetErrorDirection", TSGLLEErrorDirections, (PetscEnum)gl->error_direction, (PetscEnum *)&gl->error_direction, NULL));
1142: PetscCall(PetscOptionsBool("-ts_gl_extrapolate", "Extrapolate stage solution from previous solution (sometimes unstable)", "TSGLLESetExtrapolate", gl->extrapolate, &gl->extrapolate, NULL));
1143: PetscCall(PetscOptionsReal("-ts_gl_atol", "Absolute tolerance", "TSGLLESetTolerances", gl->wrms_atol, &gl->wrms_atol, NULL));
1144: PetscCall(PetscOptionsReal("-ts_gl_rtol", "Relative tolerance", "TSGLLESetTolerances", gl->wrms_rtol, &gl->wrms_rtol, NULL));
1145: PetscCall(PetscOptionsString("-ts_gl_complete", "Method to use for completing the step", "none", completef, completef, sizeof(completef), &flg));
1146: if (flg) {
1147: PetscBool match1, match2;
1148: PetscCall(PetscStrcmp(completef, "rescale", &match1));
1149: PetscCall(PetscStrcmp(completef, "rescale-and-modify", &match2));
1150: if (match1) gl->CompleteStep = TSGLLECompleteStep_Rescale;
1151: else if (match2) gl->CompleteStep = TSGLLECompleteStep_RescaleAndModify;
1152: else SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_ARG_UNKNOWN_TYPE, "%s", completef);
1153: }
1154: {
1155: char type[256] = TSGLLEACCEPT_ALWAYS;
1156: 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));
1157: if (flg || !gl->accept_name[0]) PetscCall(TSGLLESetAcceptType(ts, type));
1158: }
1159: {
1160: TSGLLEAdapt adapt;
1161: PetscCall(TSGLLEGetAdapt(ts, &adapt));
1162: PetscCall(TSGLLEAdaptSetFromOptions(adapt, PetscOptionsObject));
1163: }
1164: }
1165: PetscOptionsHeadEnd();
1166: PetscFunctionReturn(PETSC_SUCCESS);
1167: }
1169: static PetscErrorCode TSView_GLLE(TS ts, PetscViewer viewer)
1170: {
1171: TS_GLLE *gl = (TS_GLLE *)ts->data;
1172: PetscInt i;
1173: PetscBool iascii, details;
1175: PetscFunctionBegin;
1176: PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
1177: if (iascii) {
1178: 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));
1179: PetscCall(PetscViewerASCIIPrintf(viewer, " Error estimation: %s\n", TSGLLEErrorDirections[gl->error_direction]));
1180: PetscCall(PetscViewerASCIIPrintf(viewer, " Extrapolation: %s\n", gl->extrapolate ? "yes" : "no"));
1181: PetscCall(PetscViewerASCIIPrintf(viewer, " Acceptance test: %s\n", gl->accept_name[0] ? gl->accept_name : "(not yet set)"));
1182: PetscCall(PetscViewerASCIIPushTab(viewer));
1183: PetscCall(TSGLLEAdaptView(gl->adapt, viewer));
1184: PetscCall(PetscViewerASCIIPopTab(viewer));
1185: PetscCall(PetscViewerASCIIPrintf(viewer, " type: %s\n", gl->type_name[0] ? gl->type_name : "(not yet set)"));
1186: PetscCall(PetscViewerASCIIPrintf(viewer, "Schemes within family (%" PetscInt_FMT "):\n", gl->nschemes));
1187: details = PETSC_FALSE;
1188: PetscCall(PetscOptionsGetBool(((PetscObject)ts)->options, ((PetscObject)ts)->prefix, "-ts_gl_view_detailed", &details, NULL));
1189: PetscCall(PetscViewerASCIIPushTab(viewer));
1190: for (i = 0; i < gl->nschemes; i++) PetscCall(TSGLLESchemeView(gl->schemes[i], details, viewer));
1191: if (gl->View) PetscCall((*gl->View)(gl, viewer));
1192: PetscCall(PetscViewerASCIIPopTab(viewer));
1193: }
1194: PetscFunctionReturn(PETSC_SUCCESS);
1195: }
1197: /*@C
1198: TSGLLERegister - adds a `TSGLLE` implementation
1200: Not Collective, No Fortran Support
1202: Input Parameters:
1203: + sname - name of user-defined general linear scheme
1204: - function - routine to create method context
1206: Level: advanced
1208: Note:
1209: `TSGLLERegister()` may be called multiple times to add several user-defined families.
1211: Example Usage:
1212: .vb
1213: TSGLLERegister("my_scheme", MySchemeCreate);
1214: .ve
1216: Then, your scheme can be chosen with the procedural interface via
1217: $ TSGLLESetType(ts, "my_scheme")
1218: or at runtime via the option
1219: $ -ts_gl_type my_scheme
1221: .seealso: [](ch_ts), `TSGLLE`, `TSGLLEType`, `TSGLLERegisterAll()`
1222: @*/
1223: PetscErrorCode TSGLLERegister(const char sname[], PetscErrorCode (*function)(TS))
1224: {
1225: PetscFunctionBegin;
1226: PetscCall(TSGLLEInitializePackage());
1227: PetscCall(PetscFunctionListAdd(&TSGLLEList, sname, function));
1228: PetscFunctionReturn(PETSC_SUCCESS);
1229: }
1231: /*@C
1232: TSGLLEAcceptRegister - adds a `TSGLLE` acceptance scheme
1234: Not Collective
1236: Input Parameters:
1237: + sname - name of user-defined acceptance scheme
1238: - function - routine to create method context, see `TSGLLEAcceptFn` for the calling sequence
1240: Level: advanced
1242: Note:
1243: `TSGLLEAcceptRegister()` may be called multiple times to add several user-defined families.
1245: Example Usage:
1246: .vb
1247: TSGLLEAcceptRegister("my_scheme", MySchemeCreate);
1248: .ve
1250: Then, your scheme can be chosen with the procedural interface via
1251: .vb
1252: TSGLLESetAcceptType(ts, "my_scheme")
1253: .ve
1254: or at runtime via the option `-ts_gl_accept_type my_scheme`
1256: .seealso: [](ch_ts), `TSGLLE`, `TSGLLEType`, `TSGLLERegisterAll()`, `TSGLLEAcceptFn`
1257: @*/
1258: PetscErrorCode TSGLLEAcceptRegister(const char sname[], TSGLLEAcceptFn *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 {cite}`butcher_2007` {cite}`butcher2016numerical`
1325: Options Database Keys:
1326: + -ts_gl_type <type> - the class of general linear method (irks)
1327: . -ts_gl_rtol <tol> - relative error
1328: . -ts_gl_atol <tol> - absolute error
1329: . -ts_gl_min_order <p> - minimum order method to consider (default=1)
1330: . -ts_gl_max_order <p> - maximum order method to consider (default=3)
1331: . -ts_gl_start_order <p> - order of starting method (default=1)
1332: . -ts_gl_complete <method> - method to use for completing the step (rescale-and-modify or rescale)
1333: - -ts_adapt_type <method> - adaptive controller to use (none step both)
1335: Level: beginner
1337: Notes:
1338: These methods contain Runge-Kutta and multistep schemes as special cases. These special cases
1339: have some fundamental limitations. For example, diagonally implicit Runge-Kutta cannot have
1340: stage order greater than 1 which limits their applicability to very stiff systems.
1341: Meanwhile, multistep methods cannot be A-stable for order greater than 2 and BDF are not
1342: 0-stable for order greater than 6. GL methods can be A- and L-stable with arbitrarily high
1343: stage order and reliable error estimates for both 1 and 2 orders higher to facilitate
1344: adaptive step sizes and adaptive order schemes. All this is possible while preserving a
1345: singly diagonally implicit structure.
1347: This integrator can be applied to DAE.
1349: Diagonally implicit general linear (DIGL) methods are a generalization of diagonally implicit
1350: Runge-Kutta (DIRK). They are represented by the tableau
1352: .vb
1353: A | U
1354: -------
1355: B | V
1356: .ve
1358: combined with a vector c of abscissa. "Diagonally implicit" means that $A$ is lower
1359: triangular. A step of the general method reads
1361: $$
1362: \begin{align*}
1363: [ Y ] = [A U] [ Y' ] \\
1364: [X^k] = [B V] [X^{k-1}]
1365: \end{align*}
1366: $$
1368: where Y is the multivector of stage values, $Y'$ is the multivector of stage derivatives, $X^k$
1369: is the Nordsieck vector of the solution at step $k$. The Nordsieck vector consists of the first
1370: $r$ moments of the solution, given by
1372: $$
1373: X = [x_0,x_1,...,x_{r-1}] = [x, h x', h^2 x'', ..., h^{r-1} x^{(r-1)} ]
1374: $$
1376: If $A$ is lower triangular, we can solve the stages $(Y, Y')$ sequentially
1378: $$
1379: y_i = h \sum_{j=0}^{s-1} (a_{ij} y'_j) + \sum_{j=0}^{r-1} u_{ij} x_j, \, \, i=0,...,{s-1}
1380: $$
1382: and then construct the pieces to carry to the next step
1384: $$
1385: xx_i = h \sum_{j=0}^{s-1} b_{ij} y'_j + \sum_{j=0}^{r-1} v_{ij} x_j, \, \, i=0,...,{r-1}
1386: $$
1388: Note that when the equations are cast in implicit form, we are using the stage equation to
1389: define $y'_i$ in terms of $y_i$ and known stuff ($y_j$ for $j<i$ and $x_j$ for all $j$).
1391: Error estimation
1393: At present, the most attractive GL methods for stiff problems are singly diagonally implicit
1394: schemes which posses Inherent Runge-Kutta Stability (`TSIRKS`). These methods have $r=s$, the
1395: number of items passed between steps is equal to the number of stages. The order and
1396: stage-order are one less than the number of stages. We use the error estimates in the 2007
1397: paper which provide the following estimates
1399: $$
1400: \begin{align*}
1401: h^{p+1} X^{(p+1)} = \phi_0^T Y' + [0 \psi_0^T] Xold \\
1402: h^{p+2} X^{(p+2)} = \phi_1^T Y' + [0 \psi_1^T] Xold \\
1403: h^{p+2} (dx'/dx) X^{(p+1)} = \phi_2^T Y' + [0 \psi_2^T] Xold
1404: \end{align*}
1405: $$
1407: These estimates are accurate to $ O(h^{p+3})$.
1409: Changing the step size
1411: Uses the generalized "rescale and modify" scheme, see equation (4.5) of {cite}`butcher_2007`.
1413: .seealso: [](ch_ts), `TSCreate()`, `TS`, `TSSetType()`, `TSType`
1414: M*/
1415: PETSC_EXTERN PetscErrorCode TSCreate_GLLE(TS ts)
1416: {
1417: TS_GLLE *gl;
1419: PetscFunctionBegin;
1420: PetscCall(TSGLLEInitializePackage());
1422: PetscCall(PetscNew(&gl));
1423: ts->data = (void *)gl;
1425: ts->ops->reset = TSReset_GLLE;
1426: ts->ops->destroy = TSDestroy_GLLE;
1427: ts->ops->view = TSView_GLLE;
1428: ts->ops->setup = TSSetUp_GLLE;
1429: ts->ops->solve = TSSolve_GLLE;
1430: ts->ops->setfromoptions = TSSetFromOptions_GLLE;
1431: ts->ops->snesfunction = SNESTSFormFunction_GLLE;
1432: ts->ops->snesjacobian = SNESTSFormJacobian_GLLE;
1434: ts->usessnes = PETSC_TRUE;
1436: gl->max_step_rejections = 1;
1437: gl->min_order = 1;
1438: gl->max_order = 3;
1439: gl->start_order = 1;
1440: gl->current_scheme = -1;
1441: gl->extrapolate = PETSC_FALSE;
1443: gl->wrms_atol = 1e-8;
1444: gl->wrms_rtol = 1e-5;
1446: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSGLLESetType_C", &TSGLLESetType_GLLE));
1447: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSGLLESetAcceptType_C", &TSGLLESetAcceptType_GLLE));
1448: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSGLLEGetAdapt_C", &TSGLLEGetAdapt_GLLE));
1449: PetscFunctionReturn(PETSC_SUCCESS);
1450: }