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: }