Actual source code: gl.c
petsc-3.7.7 2017-09-25
2: #include <../src/ts/impls/implicit/gl/gl.h> /*I "petscts.h" I*/
3: #include <petscdm.h>
4: #include <petscblaslapack.h>
6: static const char *TSGLErrorDirections[] = {"FORWARD","BACKWARD","TSGLErrorDirection","TSGLERROR_",0};
7: static PetscFunctionList TSGLList;
8: static PetscFunctionList TSGLAcceptList;
9: static PetscBool TSGLPackageInitialized;
10: static PetscBool TSGLRegisterAllCalled;
12: /* This function is pure */
13: static PetscScalar Factorial(PetscInt n)
14: {
15: PetscInt i;
16: if (n < 12) { /* Can compute with 32-bit integers */
17: PetscInt f = 1;
18: for (i=2; i<=n; i++) f *= i;
19: return (PetscScalar)f;
20: } else {
21: PetscScalar f = 1.;
22: for (i=2; i<=n; i++) f *= (PetscScalar)i;
23: return f;
24: }
25: }
27: /* This function is pure */
28: static PetscScalar CPowF(PetscScalar c,PetscInt p)
29: {
30: return PetscPowRealInt(PetscRealPart(c),p)/Factorial(p);
31: }
35: static PetscErrorCode TSGLGetVecs(TS ts,DM dm,Vec *Z,Vec *Ydotstage)
36: {
37: TS_GL *gl = (TS_GL*)ts->data;
41: if (Z) {
42: if (dm && dm != ts->dm) {
43: DMGetNamedGlobalVector(dm,"TSGL_Z",Z);
44: } else *Z = gl->Z;
45: }
46: if (Ydotstage) {
47: if (dm && dm != ts->dm) {
48: DMGetNamedGlobalVector(dm,"TSGL_Ydot",Ydotstage);
49: } else *Ydotstage = gl->Ydot[gl->stage];
50: }
51: return(0);
52: }
57: static PetscErrorCode TSGLRestoreVecs(TS ts,DM dm,Vec *Z,Vec *Ydotstage)
58: {
62: if (Z) {
63: if (dm && dm != ts->dm) {
64: DMRestoreNamedGlobalVector(dm,"TSGL_Z",Z);
65: }
66: }
67: if (Ydotstage) {
69: if (dm && dm != ts->dm) {
70: DMRestoreNamedGlobalVector(dm,"TSGL_Ydot",Ydotstage);
71: }
72: }
73: return(0);
74: }
78: static PetscErrorCode DMCoarsenHook_TSGL(DM fine,DM coarse,void *ctx)
79: {
81: return(0);
82: }
86: static PetscErrorCode DMRestrictHook_TSGL(DM fine,Mat restrct,Vec rscale,Mat inject,DM coarse,void *ctx)
87: {
88: TS ts = (TS)ctx;
90: Vec Ydot,Ydot_c;
93: TSGLGetVecs(ts,fine,NULL,&Ydot);
94: TSGLGetVecs(ts,coarse,NULL,&Ydot_c);
95: MatRestrict(restrct,Ydot,Ydot_c);
96: VecPointwiseMult(Ydot_c,rscale,Ydot_c);
97: TSGLRestoreVecs(ts,fine,NULL,&Ydot);
98: TSGLRestoreVecs(ts,coarse,NULL,&Ydot_c);
99: return(0);
100: }
104: static PetscErrorCode DMSubDomainHook_TSGL(DM dm,DM subdm,void *ctx)
105: {
107: return(0);
108: }
112: static PetscErrorCode DMSubDomainRestrictHook_TSGL(DM dm,VecScatter gscat, VecScatter lscat,DM subdm,void *ctx)
113: {
114: TS ts = (TS)ctx;
116: Vec Ydot,Ydot_s;
119: TSGLGetVecs(ts,dm,NULL,&Ydot);
120: TSGLGetVecs(ts,subdm,NULL,&Ydot_s);
122: VecScatterBegin(gscat,Ydot,Ydot_s,INSERT_VALUES,SCATTER_FORWARD);
123: VecScatterEnd(gscat,Ydot,Ydot_s,INSERT_VALUES,SCATTER_FORWARD);
125: TSGLRestoreVecs(ts,dm,NULL,&Ydot);
126: TSGLRestoreVecs(ts,subdm,NULL,&Ydot_s);
127: return(0);
128: }
132: static PetscErrorCode TSGLSchemeCreate(PetscInt p,PetscInt q,PetscInt r,PetscInt s,const PetscScalar *c,
133: const PetscScalar *a,const PetscScalar *b,const PetscScalar *u,const PetscScalar *v,TSGLScheme *inscheme)
134: {
135: TSGLScheme scheme;
136: PetscInt j;
140: if (p < 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Scheme order must be positive");
141: if (r < 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"At least one item must be carried between steps");
142: if (s < 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"At least one stage is required");
144: *inscheme = 0;
145: PetscNew(&scheme);
146: scheme->p = p;
147: scheme->q = q;
148: scheme->r = r;
149: scheme->s = s;
151: PetscMalloc5(s,&scheme->c,s*s,&scheme->a,r*s,&scheme->b,r*s,&scheme->u,r*r,&scheme->v);
152: PetscMemcpy(scheme->c,c,s*sizeof(PetscScalar));
153: for (j=0; j<s*s; j++) scheme->a[j] = (PetscAbsScalar(a[j]) < 1e-12) ? 0 : a[j];
154: for (j=0; j<r*s; j++) scheme->b[j] = (PetscAbsScalar(b[j]) < 1e-12) ? 0 : b[j];
155: for (j=0; j<s*r; j++) scheme->u[j] = (PetscAbsScalar(u[j]) < 1e-12) ? 0 : u[j];
156: for (j=0; j<r*r; j++) scheme->v[j] = (PetscAbsScalar(v[j]) < 1e-12) ? 0 : v[j];
158: PetscMalloc6(r,&scheme->alpha,r,&scheme->beta,r,&scheme->gamma,3*s,&scheme->phi,3*r,&scheme->psi,r,&scheme->stage_error);
159: {
160: PetscInt i,j,k,ss=s+2;
161: PetscBLASInt m,n,one=1,*ipiv,lwork=4*((s+3)*3+3),info,ldb;
162: PetscReal rcond,*sing,*workreal;
163: PetscScalar *ImV,*H,*bmat,*workscalar,*c=scheme->c,*a=scheme->a,*b=scheme->b,*u=scheme->u,*v=scheme->v;
164: #if !defined(PETSC_MISSING_LAPACK_GELSS)
165: PetscBLASInt rank;
166: #endif
167: PetscMalloc7(PetscSqr(r),&ImV,3*s,&H,3*ss,&bmat,lwork,&workscalar,5*(3+r),&workreal,r+s,&sing,r+s,&ipiv);
169: /* column-major input */
170: for (i=0; i<r-1; i++) {
171: for (j=0; j<r-1; j++) ImV[i+j*r] = 1.0*(i==j) - v[(i+1)*r+j+1];
172: }
173: /* Build right hand side for alpha (tp - glm.B(2:end,:)*(glm.c.^(p)./factorial(p))) */
174: for (i=1; i<r; i++) {
175: scheme->alpha[i] = 1./Factorial(p+1-i);
176: for (j=0; j<s; j++) scheme->alpha[i] -= b[i*s+j]*CPowF(c[j],p);
177: }
178: PetscBLASIntCast(r-1,&m);
179: PetscBLASIntCast(r,&n);
180: PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&m,&one,ImV,&n,ipiv,scheme->alpha+1,&n,&info));
181: if (info < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Bad argument to GESV");
182: if (info > 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Bad LU factorization");
184: /* Build right hand side for beta (tp1 - glm.B(2:end,:)*(glm.c.^(p+1)./factorial(p+1)) - e.alpha) */
185: for (i=1; i<r; i++) {
186: scheme->beta[i] = 1./Factorial(p+2-i) - scheme->alpha[i];
187: for (j=0; j<s; j++) scheme->beta[i] -= b[i*s+j]*CPowF(c[j],p+1);
188: }
189: PetscStackCallBLAS("LAPACKgetrs",LAPACKgetrs_("No transpose",&m,&one,ImV,&n,ipiv,scheme->beta+1,&n,&info));
190: if (info < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Bad argument to GETRS");
191: if (info > 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Should not happen");
193: /* Build stage_error vector
194: xi = glm.c.^(p+1)/factorial(p+1) - glm.A*glm.c.^p/factorial(p) + glm.U(:,2:end)*e.alpha;
195: */
196: for (i=0; i<s; i++) {
197: scheme->stage_error[i] = CPowF(c[i],p+1);
198: for (j=0; j<s; j++) scheme->stage_error[i] -= a[i*s+j]*CPowF(c[j],p);
199: for (j=1; j<r; j++) scheme->stage_error[i] += u[i*r+j]*scheme->alpha[j];
200: }
202: /* alpha[0] (epsilon in B,J,W 2007)
203: epsilon = 1/factorial(p+1) - B(1,:)*c.^p/factorial(p) + V(1,2:end)*e.alpha;
204: */
205: scheme->alpha[0] = 1./Factorial(p+1);
206: for (j=0; j<s; j++) scheme->alpha[0] -= b[0*s+j]*CPowF(c[j],p);
207: for (j=1; j<r; j++) scheme->alpha[0] += v[0*r+j]*scheme->alpha[j];
209: /* right hand side for gamma (glm.B(2:end,:)*e.xi - e.epsilon*eye(s-1,1)) */
210: for (i=1; i<r; i++) {
211: scheme->gamma[i] = (i==1 ? -1. : 0)*scheme->alpha[0];
212: for (j=0; j<s; j++) scheme->gamma[i] += b[i*s+j]*scheme->stage_error[j];
213: }
214: PetscStackCallBLAS("LAPACKgetrs",LAPACKgetrs_("No transpose",&m,&one,ImV,&n,ipiv,scheme->gamma+1,&n,&info));
215: if (info < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Bad argument to GETRS");
216: if (info > 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Should not happen");
218: /* beta[0] (rho in B,J,W 2007)
219: e.rho = 1/factorial(p+2) - glm.B(1,:)*glm.c.^(p+1)/factorial(p+1) ...
220: + glm.V(1,2:end)*e.beta;% - e.epsilon;
221: % Note: The paper (B,J,W 2007) includes the last term in their definition
222: * */
223: scheme->beta[0] = 1./Factorial(p+2);
224: for (j=0; j<s; j++) scheme->beta[0] -= b[0*s+j]*CPowF(c[j],p+1);
225: for (j=1; j<r; j++) scheme->beta[0] += v[0*r+j]*scheme->beta[j];
227: /* gamma[0] (sigma in B,J,W 2007)
228: * e.sigma = glm.B(1,:)*e.xi + glm.V(1,2:end)*e.gamma;
229: * */
230: scheme->gamma[0] = 0.0;
231: for (j=0; j<s; j++) scheme->gamma[0] += b[0*s+j]*scheme->stage_error[j];
232: for (j=1; j<r; j++) scheme->gamma[0] += v[0*s+j]*scheme->gamma[j];
234: /* Assemble H
235: * % Determine the error estimators phi
236: H = [[cpow(glm.c,p) + C*e.alpha] [cpow(glm.c,p+1) + C*e.beta] ...
237: [e.xi - C*(e.gamma + 0*e.epsilon*eye(s-1,1))]]';
238: % Paper has formula above without the 0, but that term must be left
239: % out to satisfy the conditions they propose and to make the
240: % example schemes work
241: e.H = H;
242: e.phi = (H \ [1 0 0;1 1 0;0 0 -1])';
243: e.psi = -e.phi*C;
244: * */
245: for (j=0; j<s; j++) {
246: H[0+j*3] = CPowF(c[j],p);
247: H[1+j*3] = CPowF(c[j],p+1);
248: H[2+j*3] = scheme->stage_error[j];
249: for (k=1; k<r; k++) {
250: H[0+j*3] += CPowF(c[j],k-1)*scheme->alpha[k];
251: H[1+j*3] += CPowF(c[j],k-1)*scheme->beta[k];
252: H[2+j*3] -= CPowF(c[j],k-1)*scheme->gamma[k];
253: }
254: }
255: bmat[0+0*ss] = 1.; bmat[0+1*ss] = 0.; bmat[0+2*ss] = 0.;
256: bmat[1+0*ss] = 1.; bmat[1+1*ss] = 1.; bmat[1+2*ss] = 0.;
257: bmat[2+0*ss] = 0.; bmat[2+1*ss] = 0.; bmat[2+2*ss] = -1.;
258: m = 3;
259: PetscBLASIntCast(s,&n);
260: PetscBLASIntCast(ss,&ldb);
261: rcond = 1e-12;
262: #if defined(PETSC_MISSING_LAPACK_GELSS)
263: /* ESSL does not have this routine */
264: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GELSS - Lapack routine is unavailable\nNot able to run GL time stepping.");
265: #else
266: #if defined(PETSC_USE_COMPLEX)
267: /* ZGELSS( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, WORK, LWORK, RWORK, INFO) */
268: PetscStackCallBLAS("LAPACKgelss",LAPACKgelss_(&m,&n,&m,H,&m,bmat,&ldb,sing,&rcond,&rank,workscalar,&lwork,workreal,&info));
269: #else
270: /* DGELSS( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, WORK, LWORK, INFO) */
271: PetscStackCallBLAS("LAPACKgelss",LAPACKgelss_(&m,&n,&m,H,&m,bmat,&ldb,sing,&rcond,&rank,workscalar,&lwork,&info));
272: #endif
273: if (info < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Bad argument to GELSS");
274: if (info > 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"SVD failed to converge");
275: #endif
277: for (j=0; j<3; j++) {
278: for (k=0; k<s; k++) scheme->phi[k+j*s] = bmat[k+j*ss];
279: }
281: /* the other part of the error estimator, psi in B,J,W 2007 */
282: scheme->psi[0*r+0] = 0.;
283: scheme->psi[1*r+0] = 0.;
284: scheme->psi[2*r+0] = 0.;
285: for (j=1; j<r; j++) {
286: scheme->psi[0*r+j] = 0.;
287: scheme->psi[1*r+j] = 0.;
288: scheme->psi[2*r+j] = 0.;
289: for (k=0; k<s; k++) {
290: scheme->psi[0*r+j] -= CPowF(c[k],j-1)*scheme->phi[0*s+k];
291: scheme->psi[1*r+j] -= CPowF(c[k],j-1)*scheme->phi[1*s+k];
292: scheme->psi[2*r+j] -= CPowF(c[k],j-1)*scheme->phi[2*s+k];
293: }
294: }
295: PetscFree7(ImV,H,bmat,workscalar,workreal,sing,ipiv);
296: }
297: /* Check which properties are satisfied */
298: scheme->stiffly_accurate = PETSC_TRUE;
299: if (scheme->c[s-1] != 1.) scheme->stiffly_accurate = PETSC_FALSE;
300: for (j=0; j<s; j++) if (a[(s-1)*s+j] != b[j]) scheme->stiffly_accurate = PETSC_FALSE;
301: for (j=0; j<r; j++) if (u[(s-1)*r+j] != v[j]) scheme->stiffly_accurate = PETSC_FALSE;
302: scheme->fsal = scheme->stiffly_accurate; /* FSAL is stronger */
303: for (j=0; j<s-1; j++) if (r>1 && b[1*s+j] != 0.) scheme->fsal = PETSC_FALSE;
304: if (b[1*s+r-1] != 1.) scheme->fsal = PETSC_FALSE;
305: for (j=0; j<r; j++) if (r>1 && v[1*r+j] != 0.) scheme->fsal = PETSC_FALSE;
307: *inscheme = scheme;
308: return(0);
309: }
313: static PetscErrorCode TSGLSchemeDestroy(TSGLScheme sc)
314: {
318: PetscFree5(sc->c,sc->a,sc->b,sc->u,sc->v);
319: PetscFree6(sc->alpha,sc->beta,sc->gamma,sc->phi,sc->psi,sc->stage_error);
320: PetscFree(sc);
321: return(0);
322: }
326: static PetscErrorCode TSGLDestroy_Default(TS_GL *gl)
327: {
329: PetscInt i;
332: for (i=0; i<gl->nschemes; i++) {
333: if (gl->schemes[i]) {TSGLSchemeDestroy(gl->schemes[i]);}
334: }
335: PetscFree(gl->schemes);
336: gl->nschemes = 0;
337: PetscMemzero(gl->type_name,sizeof(gl->type_name));
338: return(0);
339: }
343: static PetscErrorCode TSGLViewTable_Private(PetscViewer viewer,PetscInt m,PetscInt n,const PetscScalar a[],const char name[])
344: {
346: PetscBool iascii;
347: PetscInt i,j;
350: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
351: if (iascii) {
352: PetscViewerASCIIPrintf(viewer,"%30s = [",name);
353: for (i=0; i<m; i++) {
354: if (i) {PetscViewerASCIIPrintf(viewer,"%30s [","");}
355: PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);
356: for (j=0; j<n; j++) {
357: PetscViewerASCIIPrintf(viewer," %12.8g",PetscRealPart(a[i*n+j]));
358: }
359: PetscViewerASCIIPrintf(viewer,"]\n");
360: PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);
361: }
362: }
363: return(0);
364: }
369: static PetscErrorCode TSGLSchemeView(TSGLScheme sc,PetscBool view_details,PetscViewer viewer)
370: {
372: PetscBool iascii;
375: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
376: if (iascii) {
377: PetscViewerASCIIPrintf(viewer,"GL scheme p,q,r,s = %d,%d,%d,%d\n",sc->p,sc->q,sc->r,sc->s);
378: PetscViewerASCIIPushTab(viewer);
379: PetscViewerASCIIPrintf(viewer,"Stiffly accurate: %s, FSAL: %s\n",sc->stiffly_accurate ? "yes" : "no",sc->fsal ? "yes" : "no");
380: PetscViewerASCIIPrintf(viewer,"Leading error constants: %10.3e %10.3e %10.3e\n",
381: PetscRealPart(sc->alpha[0]),PetscRealPart(sc->beta[0]),PetscRealPart(sc->gamma[0]));
382: TSGLViewTable_Private(viewer,1,sc->s,sc->c,"Abscissas c");
383: if (view_details) {
384: TSGLViewTable_Private(viewer,sc->s,sc->s,sc->a,"A");
385: TSGLViewTable_Private(viewer,sc->r,sc->s,sc->b,"B");
386: TSGLViewTable_Private(viewer,sc->s,sc->r,sc->u,"U");
387: TSGLViewTable_Private(viewer,sc->r,sc->r,sc->v,"V");
389: TSGLViewTable_Private(viewer,3,sc->s,sc->phi,"Error estimate phi");
390: TSGLViewTable_Private(viewer,3,sc->r,sc->psi,"Error estimate psi");
391: TSGLViewTable_Private(viewer,1,sc->r,sc->alpha,"Modify alpha");
392: TSGLViewTable_Private(viewer,1,sc->r,sc->beta,"Modify beta");
393: TSGLViewTable_Private(viewer,1,sc->r,sc->gamma,"Modify gamma");
394: TSGLViewTable_Private(viewer,1,sc->s,sc->stage_error,"Stage error xi");
395: }
396: PetscViewerASCIIPopTab(viewer);
397: } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Viewer type %s not supported",((PetscObject)viewer)->type_name);
398: return(0);
399: }
403: static PetscErrorCode TSGLEstimateHigherMoments_Default(TSGLScheme sc,PetscReal h,Vec Ydot[],Vec Xold[],Vec hm[])
404: {
406: PetscInt i;
409: if (sc->r > 64 || sc->s > 64) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Ridiculous number of stages or items passed between stages");
410: /* build error vectors*/
411: for (i=0; i<3; i++) {
412: PetscScalar phih[64];
413: PetscInt j;
414: for (j=0; j<sc->s; j++) phih[j] = sc->phi[i*sc->s+j]*h;
415: VecZeroEntries(hm[i]);
416: VecMAXPY(hm[i],sc->s,phih,Ydot);
417: VecMAXPY(hm[i],sc->r,&sc->psi[i*sc->r],Xold);
418: }
419: return(0);
420: }
424: static PetscErrorCode TSGLCompleteStep_Rescale(TSGLScheme sc,PetscReal h,TSGLScheme next_sc,PetscReal next_h,Vec Ydot[],Vec Xold[],Vec X[])
425: {
427: PetscScalar brow[32],vrow[32];
428: PetscInt i,j,r,s;
431: /* Build the new solution from (X,Ydot) */
432: r = sc->r;
433: s = sc->s;
434: for (i=0; i<r; i++) {
435: VecZeroEntries(X[i]);
436: for (j=0; j<s; j++) brow[j] = h*sc->b[i*s+j];
437: VecMAXPY(X[i],s,brow,Ydot);
438: for (j=0; j<r; j++) vrow[j] = sc->v[i*r+j];
439: VecMAXPY(X[i],r,vrow,Xold);
440: }
441: return(0);
442: }
446: static PetscErrorCode TSGLCompleteStep_RescaleAndModify(TSGLScheme sc,PetscReal h,TSGLScheme next_sc,PetscReal next_h,Vec Ydot[],Vec Xold[],Vec X[])
447: {
449: PetscScalar brow[32],vrow[32];
450: PetscReal ratio;
451: PetscInt i,j,p,r,s;
454: /* Build the new solution from (X,Ydot) */
455: p = sc->p;
456: r = sc->r;
457: s = sc->s;
458: ratio = next_h/h;
459: for (i=0; i<r; i++) {
460: VecZeroEntries(X[i]);
461: for (j=0; j<s; j++) {
462: brow[j] = h*(PetscPowRealInt(ratio,i)*sc->b[i*s+j]
463: + (PetscPowRealInt(ratio,i) - PetscPowRealInt(ratio,p+1))*(+ sc->alpha[i]*sc->phi[0*s+j])
464: + (PetscPowRealInt(ratio,i) - PetscPowRealInt(ratio,p+2))*(+ sc->beta [i]*sc->phi[1*s+j]
465: + sc->gamma[i]*sc->phi[2*s+j]));
466: }
467: VecMAXPY(X[i],s,brow,Ydot);
468: for (j=0; j<r; j++) {
469: vrow[j] = (PetscPowRealInt(ratio,i)*sc->v[i*r+j]
470: + (PetscPowRealInt(ratio,i) - PetscPowRealInt(ratio,p+1))*(+ sc->alpha[i]*sc->psi[0*r+j])
471: + (PetscPowRealInt(ratio,i) - PetscPowRealInt(ratio,p+2))*(+ sc->beta [i]*sc->psi[1*r+j]
472: + sc->gamma[i]*sc->psi[2*r+j]));
473: }
474: VecMAXPY(X[i],r,vrow,Xold);
475: }
476: if (r < next_sc->r) {
477: if (r+1 != next_sc->r) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Cannot accommodate jump in r greater than 1");
478: VecZeroEntries(X[r]);
479: for (j=0; j<s; j++) brow[j] = h*PetscPowRealInt(ratio,p+1)*sc->phi[0*s+j];
480: VecMAXPY(X[r],s,brow,Ydot);
481: for (j=0; j<r; j++) vrow[j] = PetscPowRealInt(ratio,p+1)*sc->psi[0*r+j];
482: VecMAXPY(X[r],r,vrow,Xold);
483: }
484: return(0);
485: }
489: static PetscErrorCode TSGLCreate_IRKS(TS ts)
490: {
491: TS_GL *gl = (TS_GL*)ts->data;
495: gl->Destroy = TSGLDestroy_Default;
496: gl->EstimateHigherMoments = TSGLEstimateHigherMoments_Default;
497: gl->CompleteStep = TSGLCompleteStep_RescaleAndModify;
498: PetscMalloc1(10,&gl->schemes);
499: gl->nschemes = 0;
501: {
502: /* p=1,q=1, r=s=2, A- and L-stable with error estimates of order 2 and 3
503: * Listed in Butcher & Podhaisky 2006. On error estimation in general linear methods for stiff ODE.
504: * irks(0.3,0,[.3,1],[1],1)
505: * Note: can be made to have classical order (not stage order) 2 by replacing 0.3 with 1-sqrt(1/2)
506: * but doing so would sacrifice the error estimator.
507: */
508: const PetscScalar c[2] = {3./10., 1.};
509: const PetscScalar a[2][2] = {{3./10., 0}, {7./10., 3./10.}};
510: const PetscScalar b[2][2] = {{7./10., 3./10.}, {0,1}};
511: const PetscScalar u[2][2] = {{1,0},{1,0}};
512: const PetscScalar v[2][2] = {{1,0},{0,0}};
513: TSGLSchemeCreate(1,1,2,2,c,*a,*b,*u,*v,&gl->schemes[gl->nschemes++]);
514: }
516: {
517: /* p=q=2, r=s=3: irks(4/9,0,[1:3]/3,[0.33852],1) */
518: /* http://www.math.auckland.ac.nz/~hpod/atlas/i2a.html */
519: const PetscScalar c[3] = {1./3., 2./3., 1}
520: ,a[3][3] = {{4./9. ,0 , 0},
521: {1.03750643704090e+00 , 4./9., 0},
522: {7.67024779410304e-01 , -3.81140216918943e-01, 4./9.}}
523: ,b[3][3] = {{0.767024779410304, -0.381140216918943, 4./9.},
524: {0.000000000000000, 0.000000000000000, 1.000000000000000},
525: {-2.075048385225385, 0.621728385225383, 1.277197204924873}}
526: ,u[3][3] = {{1.0000000000000000, -0.1111111111111109, -0.0925925925925922},
527: {1.0000000000000000, -0.8152842148186744, -0.4199095530877056},
528: {1.0000000000000000, 0.1696709930641948, 0.0539741070314165}}
529: ,v[3][3] = {{1.0000000000000000, 0.1696709930641948, 0.0539741070314165},
530: {0.000000000000000, 0.000000000000000, 0.000000000000000},
531: {0.000000000000000, 0.176122795075129, 0.000000000000000}};
532: TSGLSchemeCreate(2,2,3,3,c,*a,*b,*u,*v,&gl->schemes[gl->nschemes++]);
533: }
534: {
535: /* p=q=3, r=s=4: irks(9/40,0,[1:4]/4,[0.3312 1.0050],[0.49541 1;1 0]) */
536: const PetscScalar c[4] = {0.25,0.5,0.75,1.0}
537: ,a[4][4] = {{9./40. , 0, 0, 0},
538: {2.11286958887701e-01 , 9./40. , 0, 0},
539: {9.46338294287584e-01 , -3.42942861246094e-01, 9./40. , 0},
540: {0.521490453970721 , -0.662474225622980, 0.490476425459734, 9./40. }}
541: ,b[4][4] = {{0.521490453970721 , -0.662474225622980, 0.490476425459734, 9./40. },
542: {0.000000000000000 , 0.000000000000000, 0.000000000000000, 1.000000000000000},
543: {-0.084677029310348 , 1.390757514776085, -1.568157386206001, 2.023192696767826},
544: {0.465383797936408 , 1.478273530625148, -1.930836081010182, 1.644872111193354}}
545: ,u[4][4] = {{1.00000000000000000 , 0.02500000000001035, -0.02499999999999053, -0.00442708333332865},
546: {1.00000000000000000 , 0.06371304111232945, -0.04032173972189845, -0.01389438413189452},
547: {1.00000000000000000 , -0.07839543304147778, 0.04738685705116663, 0.02032603595928376},
548: {1.00000000000000000 , 0.42550734619251651, 0.10800718022400080, -0.01726712647760034}}
549: ,v[4][4] = {{1.00000000000000000 , 0.42550734619251651, 0.10800718022400080, -0.01726712647760034},
550: {0.000000000000000 , 0.000000000000000, 0.000000000000000, 0.000000000000000},
551: {0.000000000000000 , -1.761115796027561, -0.521284157173780, 0.258249384305463},
552: {0.000000000000000 , -1.657693358744728, -1.052227765232394, 0.521284157173780}};
553: TSGLSchemeCreate(3,3,4,4,c,*a,*b,*u,*v,&gl->schemes[gl->nschemes++]);
554: }
555: {
556: /* p=q=4, r=s=5:
557: irks(3/11,0,[1:5]/5, [0.1715 -0.1238 0.6617],...
558: [ -0.0812 0.4079 1.0000
559: 1.0000 0 0
560: 0.8270 1.0000 0])
561: */
562: const PetscScalar c[5] = {0.2,0.4,0.6,0.8,1.0}
563: ,a[5][5] = {{2.72727272727352e-01 , 0.00000000000000e+00, 0.00000000000000e+00 , 0.00000000000000e+00 , 0.00000000000000e+00},
564: {-1.03980153733431e-01, 2.72727272727405e-01, 0.00000000000000e+00, 0.00000000000000e+00 , 0.00000000000000e+00},
565: {-1.58615400341492e+00, 7.44168951881122e-01, 2.72727272727309e-01, 0.00000000000000e+00 , 0.00000000000000e+00},
566: {-8.73658042865628e-01, 5.37884671894595e-01, -1.63298538799523e-01, 2.72727272726996e-01 , 0.00000000000000e+00},
567: {2.95489397443992e-01 , -1.18481693910097e+00 , -6.68029812659953e-01 , 1.00716687860943e+00 , 2.72727272727288e-01}}
568: ,b[5][5] = {{2.95489397443992e-01 , -1.18481693910097e+00 , -6.68029812659953e-01 , 1.00716687860943e+00 , 2.72727272727288e-01},
569: {0.00000000000000e+00 , 1.11022302462516e-16 , -2.22044604925031e-16 , 0.00000000000000e+00 , 1.00000000000000e+00},
570: {-4.05882503986005e+00, -4.00924006567769e+00, -1.38930610972481e+00, 4.45223930308488e+00 , 6.32331093108427e-01},
571: {8.35690179937017e+00 , -2.26640927349732e+00 , 6.86647884973826e+00 , -5.22595158025740e+00 , 4.50893068837431e+00},
572: {1.27656267027479e+01 , 2.80882153840821e+00 , 8.91173096522890e+00 , -1.07936444078906e+01 , 4.82534148988854e+00}}
573: ,u[5][5] = {{1.00000000000000e+00 , -7.27272727273551e-02 , -3.45454545454419e-02 , -4.12121212119565e-03 ,-2.96969696964014e-04},
574: {1.00000000000000e+00 , 2.31252881006154e-01 , -8.29487834416481e-03 , -9.07191207681020e-03 ,-1.70378403743473e-03},
575: {1.00000000000000e+00 , 1.16925777880663e+00 , 3.59268562942635e-02 , -4.09013451730615e-02 ,-1.02411119670164e-02},
576: {1.00000000000000e+00 , 1.02634463704356e+00 , 1.59375044913405e-01 , 1.89673015035370e-03 ,-4.89987231897569e-03},
577: {1.00000000000000e+00 , 1.27746320298021e+00 , 2.37186008132728e-01 , -8.28694373940065e-02 ,-5.34396510196430e-02}}
578: ,v[5][5] = {{1.00000000000000e+00 , 1.27746320298021e+00 , 2.37186008132728e-01 , -8.28694373940065e-02 ,-5.34396510196430e-02},
579: {0.00000000000000e+00 , -1.77635683940025e-15 , -1.99840144432528e-15 , -9.99200722162641e-16 ,-3.33066907387547e-16},
580: {0.00000000000000e+00 , 4.37280081906924e+00 , 5.49221645016377e-02 , -8.88913177394943e-02 , 1.12879077989154e-01},
581: {0.00000000000000e+00 , -1.22399504837280e+01 , -5.21287338448645e+00 , -8.03952325565291e-01 , 4.60298678047147e-01},
582: {0.00000000000000e+00 , -1.85178762883829e+01 , -5.21411849862624e+00 , -1.04283436528809e+00 , 7.49030161063651e-01}};
583: TSGLSchemeCreate(4,4,5,5,c,*a,*b,*u,*v,&gl->schemes[gl->nschemes++]);
584: }
585: {
586: /* p=q=5, r=s=6;
587: irks(1/3,0,[1:6]/6,...
588: [-0.0489 0.4228 -0.8814 0.9021],...
589: [-0.3474 -0.6617 0.6294 0.2129
590: 0.0044 -0.4256 -0.1427 -0.8936
591: -0.8267 0.4821 0.1371 -0.2557
592: -0.4426 -0.3855 -0.7514 0.3014])
593: */
594: const PetscScalar c[6] = {1./6, 2./6, 3./6, 4./6, 5./6, 1.}
595: ,a[6][6] = {{ 3.33333333333940e-01, 0 , 0 , 0 , 0 , 0 },
596: { -8.64423857333350e-02, 3.33333333332888e-01, 0 , 0 , 0 , 0 },
597: { -2.16850174258252e+00, -2.23619072028839e+00, 3.33333333335204e-01, 0 , 0 , 0 },
598: { -4.73160970138997e+00, -3.89265344629268e+00, -2.76318716520933e-01, 3.33333333335759e-01, 0 , 0 },
599: { -6.75187540297338e+00, -7.90756533769377e+00, 7.90245051802259e-01, -4.48352364517632e-01, 3.33333333328483e-01, 0 },
600: { -4.26488287921548e+00, -1.19320395589302e+01, 3.38924509887755e+00, -2.23969848002481e+00, 6.62807710124007e-01, 3.33333333335440e-01}}
601: ,b[6][6] = {{ -4.26488287921548e+00, -1.19320395589302e+01, 3.38924509887755e+00, -2.23969848002481e+00, 6.62807710124007e-01, 3.33333333335440e-01},
602: { -8.88178419700125e-16, 4.44089209850063e-16, -1.54737334057131e-15, -8.88178419700125e-16, 0.00000000000000e+00, 1.00000000000001e+00},
603: { -2.87780425770651e+01, -1.13520448264971e+01, 2.62002318943161e+01, 2.56943874812797e+01, -3.06702268304488e+01, 6.68067773510103e+00},
604: { 5.47971245256474e+01, 6.80366875868284e+01, -6.50952588861999e+01, -8.28643975339097e+01, 8.17416943896414e+01, -1.17819043489036e+01},
605: { -2.33332114788869e+02, 6.12942539462634e+01, -4.91850135865944e+01, 1.82716844135480e+02, -1.29788173979395e+02, 3.09968095651099e+01},
606: { -1.72049132343751e+02, 8.60194713593999e+00, 7.98154219170200e-01, 1.50371386053218e+02, -1.18515423962066e+02, 2.50898277784663e+01}}
607: ,u[6][6] = {{ 1.00000000000000e+00, -1.66666666666870e-01, -4.16666666664335e-02, -3.85802469124815e-03, -2.25051440302250e-04, -9.64506172339142e-06},
608: { 1.00000000000000e+00, 8.64423857327162e-02, -4.11484912671353e-02, -1.11450903217645e-02, -1.47651050487126e-03, -1.34395070766826e-04},
609: { 1.00000000000000e+00, 4.57135912953434e+00, 1.06514719719137e+00, 1.33517564218007e-01, 1.11365952968659e-02, 6.12382756769504e-04},
610: { 1.00000000000000e+00, 9.23391519753404e+00, 2.22431212392095e+00, 2.91823807741891e-01, 2.52058456411084e-02, 1.22800542949647e-03},
611: { 1.00000000000000e+00, 1.48175480533865e+01, 3.73439117461835e+00, 5.14648336541804e-01, 4.76430038853402e-02, 2.56798515502156e-03},
612: { 1.00000000000000e+00, 1.50512347758335e+01, 4.10099701165164e+00, 5.66039141003603e-01, 3.91213893800891e-02, -2.99136269067853e-03}}
613: ,v[6][6] = {{ 1.00000000000000e+00, 1.50512347758335e+01, 4.10099701165164e+00, 5.66039141003603e-01, 3.91213893800891e-02, -2.99136269067853e-03},
614: { 0.00000000000000e+00, -4.88498130835069e-15, -6.43929354282591e-15, -3.55271367880050e-15, -1.22124532708767e-15, -3.12250225675825e-16},
615: { 0.00000000000000e+00, 1.22250171233141e+01, -1.77150760606169e+00, 3.54516769879390e-01, 6.22298845883398e-01, 2.31647447450276e-01},
616: { 0.00000000000000e+00, -4.48339457331040e+01, -3.57363126641880e-01, 5.18750173123425e-01, 6.55727990241799e-02, 1.63175368287079e-01},
617: { 0.00000000000000e+00, 1.37297394708005e+02, -1.60145272991317e+00, -5.05319555199441e+00, 1.55328940390990e-01, 9.16629423682464e-01},
618: { 0.00000000000000e+00, 1.05703241119022e+02, -1.16610260983038e+00, -2.99767252773859e+00, -1.13472315553890e-01, 1.09742849254729e+00}};
619: TSGLSchemeCreate(5,5,6,6,c,*a,*b,*u,*v,&gl->schemes[gl->nschemes++]);
620: }
621: return(0);
622: }
626: /*@C
627: TSGLSetType - sets the class of general linear method to use for time-stepping
629: Collective on TS
631: Input Parameters:
632: + ts - the TS context
633: - type - a method
635: Options Database Key:
636: . -ts_gl_type <type> - sets the method, use -help for a list of available method (e.g. irks)
638: Notes:
639: See "petsc/include/petscts.h" for available methods (for instance)
640: . TSGL_IRKS - Diagonally implicit methods with inherent Runge-Kutta stability (for stiff problems)
642: Normally, it is best to use the TSSetFromOptions() command and
643: then set the TSGL type from the options database rather than by using
644: this routine. Using the options database provides the user with
645: maximum flexibility in evaluating the many different solvers.
646: The TSGLSetType() routine is provided for those situations where it
647: is necessary to set the timestepping solver independently of the
648: command line or options database. This might be the case, for example,
649: when the choice of solver changes during the execution of the
650: program, and the user's application is taking responsibility for
651: choosing the appropriate method.
653: Level: intermediate
655: .keywords: TS, TSGL, set, type
656: @*/
657: PetscErrorCode TSGLSetType(TS ts,TSGLType type)
658: {
664: PetscTryMethod(ts,"TSGLSetType_C",(TS,TSGLType),(ts,type));
665: return(0);
666: }
670: /*@C
671: TSGLSetAcceptType - sets the acceptance test
673: Time integrators that need to control error must have the option to reject a time step based on local error
674: estimates. This function allows different schemes to be set.
676: Logically Collective on TS
678: Input Parameters:
679: + ts - the TS context
680: - type - the type
682: Options Database Key:
683: . -ts_gl_accept_type <type> - sets the method used to determine whether to accept or reject a step
685: Level: intermediate
687: .seealso: TS, TSGL, TSGLAcceptRegister(), TSGLAdapt, set type
688: @*/
689: PetscErrorCode TSGLSetAcceptType(TS ts,TSGLAcceptType type)
690: {
696: PetscTryMethod(ts,"TSGLSetAcceptType_C",(TS,TSGLAcceptType),(ts,type));
697: return(0);
698: }
702: /*@C
703: TSGLGetAdapt - gets the TSGLAdapt object from the TS
705: Not Collective
707: Input Parameter:
708: . ts - the TS context
710: Output Parameter:
711: . adapt - the TSGLAdapt context
713: Notes:
714: This allows the user set options on the TSGLAdapt object. Usually it is better to do this using the options
715: database, so this function is rarely needed.
717: Level: advanced
719: .seealso: TSGLAdapt, TSGLAdaptRegister()
720: @*/
721: PetscErrorCode TSGLGetAdapt(TS ts,TSGLAdapt *adapt)
722: {
728: PetscUseMethod(ts,"TSGLGetAdapt_C",(TS,TSGLAdapt*),(ts,adapt));
729: return(0);
730: }
734: static PetscErrorCode TSGLAccept_Always(TS ts,PetscReal tleft,PetscReal h,const PetscReal enorms[],PetscBool *accept)
735: {
737: *accept = PETSC_TRUE;
738: return(0);
739: }
743: static PetscErrorCode TSGLUpdateWRMS(TS ts)
744: {
745: TS_GL *gl = (TS_GL*)ts->data;
747: PetscScalar *x,*w;
748: PetscInt n,i;
751: VecGetArray(gl->X[0],&x);
752: VecGetArray(gl->W,&w);
753: VecGetLocalSize(gl->W,&n);
754: for (i=0; i<n; i++) w[i] = 1./(gl->wrms_atol + gl->wrms_rtol*PetscAbsScalar(x[i]));
755: VecRestoreArray(gl->X[0],&x);
756: VecRestoreArray(gl->W,&w);
757: return(0);
758: }
762: static PetscErrorCode TSGLVecNormWRMS(TS ts,Vec X,PetscReal *nrm)
763: {
764: TS_GL *gl = (TS_GL*)ts->data;
766: PetscScalar *x,*w;
767: PetscReal sum = 0.0,gsum;
768: PetscInt n,N,i;
771: VecGetArray(X,&x);
772: VecGetArray(gl->W,&w);
773: VecGetLocalSize(gl->W,&n);
774: for (i=0; i<n; i++) sum += PetscAbsScalar(PetscSqr(x[i]*w[i]));
775: VecRestoreArray(X,&x);
776: VecRestoreArray(gl->W,&w);
777: MPIU_Allreduce(&sum,&gsum,1,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)ts));
778: VecGetSize(gl->W,&N);
779: *nrm = PetscSqrtReal(gsum/(1.*N));
780: return(0);
781: }
785: static PetscErrorCode TSGLSetType_GL(TS ts,TSGLType type)
786: {
787: PetscErrorCode ierr,(*r)(TS);
788: PetscBool same;
789: TS_GL *gl = (TS_GL*)ts->data;
792: if (gl->type_name[0]) {
793: PetscStrcmp(gl->type_name,type,&same);
794: if (same) return(0);
795: (*gl->Destroy)(gl);
796: }
798: PetscFunctionListFind(TSGLList,type,&r);
799: if (!r) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_UNKNOWN_TYPE,"Unknown TSGL type \"%s\" given",type);
800: (*r)(ts);
801: PetscStrcpy(gl->type_name,type);
802: return(0);
803: }
807: static PetscErrorCode TSGLSetAcceptType_GL(TS ts,TSGLAcceptType type)
808: {
809: PetscErrorCode ierr;
810: TSGLAcceptFunction r;
811: TS_GL *gl = (TS_GL*)ts->data;
814: PetscFunctionListFind(TSGLAcceptList,type,&r);
815: if (!r) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_UNKNOWN_TYPE,"Unknown TSGLAccept type \"%s\" given",type);
816: gl->Accept = r;
817: PetscStrncpy(gl->accept_name,type,sizeof(gl->accept_name));
818: return(0);
819: }
823: static PetscErrorCode TSGLGetAdapt_GL(TS ts,TSGLAdapt *adapt)
824: {
826: TS_GL *gl = (TS_GL*)ts->data;
829: if (!gl->adapt) {
830: TSGLAdaptCreate(PetscObjectComm((PetscObject)ts),&gl->adapt);
831: PetscObjectIncrementTabLevel((PetscObject)gl->adapt,(PetscObject)ts,1);
832: PetscLogObjectParent((PetscObject)ts,(PetscObject)gl->adapt);
833: }
834: *adapt = gl->adapt;
835: return(0);
836: }
840: static PetscErrorCode TSGLChooseNextScheme(TS ts,PetscReal h,const PetscReal hmnorm[],PetscInt *next_scheme,PetscReal *next_h,PetscBool *finish)
841: {
843: TS_GL *gl = (TS_GL*)ts->data;
844: PetscInt i,n,cur_p,cur,next_sc,candidates[64],orders[64];
845: PetscReal errors[64],costs[64],tleft;
848: cur = -1;
849: cur_p = gl->schemes[gl->current_scheme]->p;
850: tleft = ts->max_time - (ts->ptime + ts->time_step);
851: for (i=0,n=0; i<gl->nschemes; i++) {
852: TSGLScheme sc = gl->schemes[i];
853: if (sc->p < gl->min_order || gl->max_order < sc->p) continue;
854: if (sc->p == cur_p - 1) errors[n] = PetscAbsScalar(sc->alpha[0])*hmnorm[0];
855: else if (sc->p == cur_p) errors[n] = PetscAbsScalar(sc->alpha[0])*hmnorm[1];
856: else if (sc->p == cur_p+1) errors[n] = PetscAbsScalar(sc->alpha[0])*(hmnorm[2]+hmnorm[3]);
857: else continue;
858: candidates[n] = i;
859: orders[n] = PetscMin(sc->p,sc->q); /* order of global truncation error */
860: costs[n] = sc->s; /* estimate the cost as the number of stages */
861: if (i == gl->current_scheme) cur = n;
862: n++;
863: }
864: if (cur < 0 || gl->nschemes <= cur) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Current scheme not found in scheme list");
865: TSGLAdaptChoose(gl->adapt,n,orders,errors,costs,cur,h,tleft,&next_sc,next_h,finish);
866: *next_scheme = candidates[next_sc];
867: PetscInfo7(ts,"Adapt chose scheme %d (%d,%d,%d,%d) with step size %6.2e, finish=%d\n",*next_scheme,gl->schemes[*next_scheme]->p,gl->schemes[*next_scheme]->q,gl->schemes[*next_scheme]->r,gl->schemes[*next_scheme]->s,*next_h,*finish);
868: return(0);
869: }
873: static PetscErrorCode TSGLGetMaxSizes(TS ts,PetscInt *max_r,PetscInt *max_s)
874: {
875: TS_GL *gl = (TS_GL*)ts->data;
878: *max_r = gl->schemes[gl->nschemes-1]->r;
879: *max_s = gl->schemes[gl->nschemes-1]->s;
880: return(0);
881: }
885: static PetscErrorCode TSSolve_GL(TS ts)
886: {
887: TS_GL *gl = (TS_GL*)ts->data;
888: PetscInt i,k,its,lits,max_r,max_s;
889: PetscBool final_step,finish;
890: SNESConvergedReason snesreason;
891: PetscErrorCode ierr;
894: TSMonitor(ts,ts->steps,ts->ptime,ts->vec_sol);
896: TSGLGetMaxSizes(ts,&max_r,&max_s);
897: VecCopy(ts->vec_sol,gl->X[0]);
898: for (i=1; i<max_r; i++) {
899: VecZeroEntries(gl->X[i]);
900: }
901: TSGLUpdateWRMS(ts);
903: if (0) {
904: /* Find consistent initial data for DAE */
905: gl->stage_time = ts->ptime + ts->time_step;
906: gl->scoeff = 1.;
907: gl->stage = 0;
909: VecCopy(ts->vec_sol,gl->Z);
910: VecCopy(ts->vec_sol,gl->Y);
911: SNESSolve(ts->snes,NULL,gl->Y);
912: SNESGetIterationNumber(ts->snes,&its);
913: SNESGetLinearSolveIterations(ts->snes,&lits);
914: SNESGetConvergedReason(ts->snes,&snesreason);
916: ts->snes_its += its; ts->ksp_its += lits;
917: if (snesreason < 0 && ts->max_snes_failures > 0 && ++ts->num_snes_failures >= ts->max_snes_failures) {
918: ts->reason = TS_DIVERGED_NONLINEAR_SOLVE;
919: PetscInfo2(ts,"Step=%D, nonlinear solve solve failures %D greater than current TS allowed, stopping solve\n",ts->steps,ts->num_snes_failures);
920: return(0);
921: }
922: }
924: if (gl->current_scheme < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"A starting scheme has not been provided");
926: for (k=0,final_step=PETSC_FALSE,finish=PETSC_FALSE; k<ts->max_steps && !finish; k++) {
927: PetscInt j,r,s,next_scheme = 0,rejections;
928: PetscReal h,hmnorm[4],enorm[3],next_h;
929: PetscBool accept;
930: const PetscScalar *c,*a,*u;
931: Vec *X,*Ydot,Y;
932: TSGLScheme scheme = gl->schemes[gl->current_scheme];
934: r = scheme->r; s = scheme->s;
935: c = scheme->c;
936: a = scheme->a; u = scheme->u;
937: h = ts->time_step;
938: X = gl->X; Ydot = gl->Ydot; Y = gl->Y;
940: if (ts->ptime > ts->max_time) break;
942: /*
943: We only call PreStep at the start of each STEP, not each STAGE. This is because it is
944: possible to fail (have to restart a step) after multiple stages.
945: */
946: TSPreStep(ts);
948: rejections = 0;
949: while (1) {
950: for (i=0; i<s; i++) {
951: PetscScalar shift;
952: gl->scoeff = 1./PetscRealPart(a[i*s+i]);
953: shift = gl->scoeff/ts->time_step;
954: gl->stage = i;
955: gl->stage_time = ts->ptime + PetscRealPart(c[i])*h;
957: /*
958: * Stage equation: Y = h A Y' + U X
959: * We assume that A is lower-triangular so that we can solve the stages (Y,Y') sequentially
960: * Build the affine vector z_i = -[1/(h a_ii)](h sum_j a_ij y'_j + sum_j u_ij x_j)
961: * Then y'_i = z + 1/(h a_ii) y_i
962: */
963: VecZeroEntries(gl->Z);
964: for (j=0; j<r; j++) {
965: VecAXPY(gl->Z,-shift*u[i*r+j],X[j]);
966: }
967: for (j=0; j<i; j++) {
968: VecAXPY(gl->Z,-shift*h*a[i*s+j],Ydot[j]);
969: }
970: /* Note: Z is used within function evaluation, Ydot = Z + shift*Y */
972: /* Compute an estimate of Y to start Newton iteration */
973: if (gl->extrapolate) {
974: if (i==0) {
975: /* Linear extrapolation on the first stage */
976: VecWAXPY(Y,c[i]*h,X[1],X[0]);
977: } else {
978: /* Linear extrapolation from the last stage */
979: VecAXPY(Y,(c[i]-c[i-1])*h,Ydot[i-1]);
980: }
981: } else if (i==0) { /* Directly use solution from the last step, otherwise reuse the last stage (do nothing) */
982: VecCopy(X[0],Y);
983: }
985: /* Solve this stage (Ydot[i] is computed during function evaluation) */
986: SNESSolve(ts->snes,NULL,Y);
987: SNESGetIterationNumber(ts->snes,&its);
988: SNESGetLinearSolveIterations(ts->snes,&lits);
989: SNESGetConvergedReason(ts->snes,&snesreason);
990: ts->snes_its += its; ts->ksp_its += lits;
991: if (snesreason < 0 && ts->max_snes_failures > 0 && ++ts->num_snes_failures >= ts->max_snes_failures) {
992: ts->reason = TS_DIVERGED_NONLINEAR_SOLVE;
993: PetscInfo2(ts,"Step=%D, nonlinear solve solve failures %D greater than current TS allowed, stopping solve\n",ts->steps,ts->num_snes_failures);
994: return(0);
995: }
996: }
998: gl->stage_time = ts->ptime + ts->time_step;
1000: (*gl->EstimateHigherMoments)(scheme,h,Ydot,gl->X,gl->himom);
1001: /* hmnorm[i] = h^{p+i}x^{(p+i)} with i=0,1,2; hmnorm[3] = h^{p+2}(dx'/dx) x^{(p+1)} */
1002: for (i=0; i<3; i++) {
1003: TSGLVecNormWRMS(ts,gl->himom[i],&hmnorm[i+1]);
1004: }
1005: enorm[0] = PetscRealPart(scheme->alpha[0])*hmnorm[1];
1006: enorm[1] = PetscRealPart(scheme->beta[0]) *hmnorm[2];
1007: enorm[2] = PetscRealPart(scheme->gamma[0])*hmnorm[3];
1008: (*gl->Accept)(ts,ts->max_time-gl->stage_time,h,enorm,&accept);
1009: if (accept) goto accepted;
1010: rejections++;
1011: PetscInfo3(ts,"Step %D (t=%g) not accepted, rejections=%D\n",k,gl->stage_time,rejections);
1012: if (rejections > gl->max_step_rejections) break;
1013: /*
1014: There are lots of reasons why a step might be rejected, including solvers not converging and other factors that
1015: TSGLChooseNextScheme does not support. Additionally, the error estimates may be very screwed up, so I'm not
1016: convinced that it's safe to just compute a new error estimate using the same interface as the current adaptor
1017: (the adaptor interface probably has to change). Here we make an arbitrary and naive choice. This assumes that
1018: steps were written in Nordsieck form. The "correct" method would be to re-complete the previous time step with
1019: the correct "next" step size. It is unclear to me whether the present ad-hoc method of rescaling X is stable.
1020: */
1021: h *= 0.5;
1022: for (i=1; i<scheme->r; i++) {
1023: VecScale(X[i],PetscPowRealInt(0.5,i));
1024: }
1025: }
1026: SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_CONV_FAILED,"Time step %D (t=%g) not accepted after %D failures\n",k,gl->stage_time,rejections);
1028: accepted:
1029: /* This term is not error, but it *would* be the leading term for a lower order method */
1030: TSGLVecNormWRMS(ts,gl->X[scheme->r-1],&hmnorm[0]);
1031: /* Correct scaling so that these are equivalent to norms of the Nordsieck vectors */
1033: PetscInfo4(ts,"Last moment norm %10.2e, estimated error norms %10.2e %10.2e %10.2e\n",hmnorm[0],enorm[0],enorm[1],enorm[2]);
1034: if (!final_step) {
1035: TSGLChooseNextScheme(ts,h,hmnorm,&next_scheme,&next_h,&final_step);
1036: } else {
1037: /* Dummy values to complete the current step in a consistent manner */
1038: next_scheme = gl->current_scheme;
1039: next_h = h;
1040: finish = PETSC_TRUE;
1041: }
1043: X = gl->Xold;
1044: gl->Xold = gl->X;
1045: gl->X = X;
1046: (*gl->CompleteStep)(scheme,h,gl->schemes[next_scheme],next_h,Ydot,gl->Xold,gl->X);
1048: TSGLUpdateWRMS(ts);
1050: /* Post the solution for the user, we could avoid this copy with a small bit of cleverness */
1051: VecCopy(gl->X[0],ts->vec_sol);
1052: ts->ptime += h;
1053: ts->steps++;
1054: ts->total_steps++;
1056: TSPostStep(ts);
1057: TSMonitor(ts,ts->steps,ts->ptime,ts->vec_sol);
1059: gl->current_scheme = next_scheme;
1060: ts->time_step = next_h;
1061: }
1062: return(0);
1063: }
1065: /*------------------------------------------------------------*/
1069: static PetscErrorCode TSReset_GL(TS ts)
1070: {
1071: TS_GL *gl = (TS_GL*)ts->data;
1072: PetscInt max_r,max_s;
1076: if (gl->setupcalled) {
1077: TSGLGetMaxSizes(ts,&max_r,&max_s);
1078: VecDestroyVecs(max_r,&gl->Xold);
1079: VecDestroyVecs(max_r,&gl->X);
1080: VecDestroyVecs(max_s,&gl->Ydot);
1081: VecDestroyVecs(3,&gl->himom);
1082: VecDestroy(&gl->W);
1083: VecDestroy(&gl->Y);
1084: VecDestroy(&gl->Z);
1085: }
1086: gl->setupcalled = PETSC_FALSE;
1087: return(0);
1088: }
1092: static PetscErrorCode TSDestroy_GL(TS ts)
1093: {
1094: TS_GL *gl = (TS_GL*)ts->data;
1098: TSReset_GL(ts);
1099: if (gl->adapt) {TSGLAdaptDestroy(&gl->adapt);}
1100: if (gl->Destroy) {(*gl->Destroy)(gl);}
1101: PetscFree(ts->data);
1102: PetscObjectComposeFunction((PetscObject)ts,"TSGLSetType_C",NULL);
1103: PetscObjectComposeFunction((PetscObject)ts,"TSGLSetAcceptType_C",NULL);
1104: PetscObjectComposeFunction((PetscObject)ts,"TSGLGetAdapt_C",NULL);
1105: return(0);
1106: }
1108: /*
1109: This defines the nonlinear equation that is to be solved with SNES
1110: g(x) = f(t,x,z+shift*x) = 0
1111: */
1114: static PetscErrorCode SNESTSFormFunction_GL(SNES snes,Vec x,Vec f,TS ts)
1115: {
1116: TS_GL *gl = (TS_GL*)ts->data;
1118: Vec Z,Ydot;
1119: DM dm,dmsave;
1122: SNESGetDM(snes,&dm);
1123: TSGLGetVecs(ts,dm,&Z,&Ydot);
1124: VecWAXPY(Ydot,gl->scoeff/ts->time_step,x,Z);
1125: dmsave = ts->dm;
1126: ts->dm = dm;
1127: TSComputeIFunction(ts,gl->stage_time,x,Ydot,f,PETSC_FALSE);
1128: ts->dm = dmsave;
1129: TSGLRestoreVecs(ts,dm,&Z,&Ydot);
1130: return(0);
1131: }
1135: static PetscErrorCode SNESTSFormJacobian_GL(SNES snes,Vec x,Mat A,Mat B,TS ts)
1136: {
1137: TS_GL *gl = (TS_GL*)ts->data;
1139: Vec Z,Ydot;
1140: DM dm,dmsave;
1143: SNESGetDM(snes,&dm);
1144: TSGLGetVecs(ts,dm,&Z,&Ydot);
1145: dmsave = ts->dm;
1146: ts->dm = dm;
1147: /* gl->Xdot will have already been computed in SNESTSFormFunction_GL */
1148: TSComputeIJacobian(ts,gl->stage_time,x,gl->Ydot[gl->stage],gl->scoeff/ts->time_step,A,B,PETSC_FALSE);
1149: ts->dm = dmsave;
1150: TSGLRestoreVecs(ts,dm,&Z,&Ydot);
1151: return(0);
1152: }
1157: static PetscErrorCode TSSetUp_GL(TS ts)
1158: {
1159: TS_GL *gl = (TS_GL*)ts->data;
1160: PetscInt max_r,max_s;
1162: DM dm;
1165: gl->setupcalled = PETSC_TRUE;
1166: TSGLGetMaxSizes(ts,&max_r,&max_s);
1167: VecDuplicateVecs(ts->vec_sol,max_r,&gl->X);
1168: VecDuplicateVecs(ts->vec_sol,max_r,&gl->Xold);
1169: VecDuplicateVecs(ts->vec_sol,max_s,&gl->Ydot);
1170: VecDuplicateVecs(ts->vec_sol,3,&gl->himom);
1171: VecDuplicate(ts->vec_sol,&gl->W);
1172: VecDuplicate(ts->vec_sol,&gl->Y);
1173: VecDuplicate(ts->vec_sol,&gl->Z);
1175: /* Default acceptance tests and adaptivity */
1176: if (!gl->Accept) {TSGLSetAcceptType(ts,TSGLACCEPT_ALWAYS);}
1177: if (!gl->adapt) {TSGLGetAdapt(ts,&gl->adapt);}
1179: if (gl->current_scheme < 0) {
1180: PetscInt i;
1181: for (i=0;; i++) {
1182: if (gl->schemes[i]->p == gl->start_order) break;
1183: if (i+1 == gl->nschemes) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"No schemes available with requested start order %d",i);
1184: }
1185: gl->current_scheme = i;
1186: }
1187: TSGetDM(ts,&dm);
1188: if (dm) {
1189: DMCoarsenHookAdd(dm,DMCoarsenHook_TSGL,DMRestrictHook_TSGL,ts);
1190: DMSubDomainHookAdd(dm,DMSubDomainHook_TSGL,DMSubDomainRestrictHook_TSGL,ts);
1191: }
1192: return(0);
1193: }
1194: /*------------------------------------------------------------*/
1198: static PetscErrorCode TSSetFromOptions_GL(PetscOptionItems *PetscOptionsObject,TS ts)
1199: {
1200: TS_GL *gl = (TS_GL*)ts->data;
1201: char tname[256] = TSGL_IRKS,completef[256] = "rescale-and-modify";
1205: PetscOptionsHead(PetscOptionsObject,"General Linear ODE solver options");
1206: {
1207: PetscBool flg;
1208: PetscOptionsFList("-ts_gl_type","Type of GL method","TSGLSetType",TSGLList,gl->type_name[0] ? gl->type_name : tname,tname,sizeof(tname),&flg);
1209: if (flg || !gl->type_name[0]) {
1210: TSGLSetType(ts,tname);
1211: }
1212: PetscOptionsInt("-ts_gl_max_step_rejections","Maximum number of times to attempt a step","None",gl->max_step_rejections,&gl->max_step_rejections,NULL);
1213: PetscOptionsInt("-ts_gl_max_order","Maximum order to try","TSGLSetMaxOrder",gl->max_order,&gl->max_order,NULL);
1214: PetscOptionsInt("-ts_gl_min_order","Minimum order to try","TSGLSetMinOrder",gl->min_order,&gl->min_order,NULL);
1215: PetscOptionsInt("-ts_gl_start_order","Initial order to try","TSGLSetMinOrder",gl->start_order,&gl->start_order,NULL);
1216: PetscOptionsEnum("-ts_gl_error_direction","Which direction to look when estimating error","TSGLSetErrorDirection",TSGLErrorDirections,(PetscEnum)gl->error_direction,(PetscEnum*)&gl->error_direction,NULL);
1217: PetscOptionsBool("-ts_gl_extrapolate","Extrapolate stage solution from previous solution (sometimes unstable)","TSGLSetExtrapolate",gl->extrapolate,&gl->extrapolate,NULL);
1218: PetscOptionsReal("-ts_gl_atol","Absolute tolerance","TSGLSetTolerances",gl->wrms_atol,&gl->wrms_atol,NULL);
1219: PetscOptionsReal("-ts_gl_rtol","Relative tolerance","TSGLSetTolerances",gl->wrms_rtol,&gl->wrms_rtol,NULL);
1220: PetscOptionsString("-ts_gl_complete","Method to use for completing the step","none",completef,completef,sizeof(completef),&flg);
1221: if (flg) {
1222: PetscBool match1,match2;
1223: PetscStrcmp(completef,"rescale",&match1);
1224: PetscStrcmp(completef,"rescale-and-modify",&match2);
1225: if (match1) gl->CompleteStep = TSGLCompleteStep_Rescale;
1226: else if (match2) gl->CompleteStep = TSGLCompleteStep_RescaleAndModify;
1227: else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_UNKNOWN_TYPE,"%s",completef);
1228: }
1229: {
1230: char type[256] = TSGLACCEPT_ALWAYS;
1231: PetscOptionsFList("-ts_gl_accept_type","Method to use for determining whether to accept a step","TSGLSetAcceptType",TSGLAcceptList,gl->accept_name[0] ? gl->accept_name : type,type,sizeof(type),&flg);
1232: if (flg || !gl->accept_name[0]) {
1233: TSGLSetAcceptType(ts,type);
1234: }
1235: }
1236: {
1237: TSGLAdapt adapt;
1238: TSGLGetAdapt(ts,&adapt);
1239: TSGLAdaptSetFromOptions(PetscOptionsObject,adapt);
1240: }
1241: }
1242: PetscOptionsTail();
1243: return(0);
1244: }
1248: static PetscErrorCode TSView_GL(TS ts,PetscViewer viewer)
1249: {
1250: TS_GL *gl = (TS_GL*)ts->data;
1251: PetscInt i;
1252: PetscBool iascii,details;
1256: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
1257: if (iascii) {
1258: PetscViewerASCIIPrintf(viewer," min order %D, max order %D, current order %D\n",gl->min_order,gl->max_order,gl->schemes[gl->current_scheme]->p);
1259: PetscViewerASCIIPrintf(viewer," Error estimation: %s\n",TSGLErrorDirections[gl->error_direction]);
1260: PetscViewerASCIIPrintf(viewer," Extrapolation: %s\n",gl->extrapolate ? "yes" : "no");
1261: PetscViewerASCIIPrintf(viewer," Acceptance test: %s\n",gl->accept_name[0] ? gl->accept_name : "(not yet set)");
1262: PetscViewerASCIIPushTab(viewer);
1263: TSGLAdaptView(gl->adapt,viewer);
1264: PetscViewerASCIIPopTab(viewer);
1265: PetscViewerASCIIPrintf(viewer," type: %s\n",gl->type_name[0] ? gl->type_name : "(not yet set)");
1266: PetscViewerASCIIPrintf(viewer,"Schemes within family (%d):\n",gl->nschemes);
1267: details = PETSC_FALSE;
1268: PetscOptionsGetBool(((PetscObject)ts)->options,((PetscObject)ts)->prefix,"-ts_gl_view_detailed",&details,NULL);
1269: PetscViewerASCIIPushTab(viewer);
1270: for (i=0; i<gl->nschemes; i++) {
1271: TSGLSchemeView(gl->schemes[i],details,viewer);
1272: }
1273: if (gl->View) {
1274: (*gl->View)(gl,viewer);
1275: }
1276: PetscViewerASCIIPopTab(viewer);
1277: }
1278: SNESView(ts->snes,viewer);
1279: return(0);
1280: }
1284: /*@C
1285: TSGLRegister - adds a TSGL implementation
1287: Not Collective
1289: Input Parameters:
1290: + name_scheme - name of user-defined general linear scheme
1291: - routine_create - routine to create method context
1293: Notes:
1294: TSGLRegister() may be called multiple times to add several user-defined families.
1296: Sample usage:
1297: .vb
1298: TSGLRegister("my_scheme",MySchemeCreate);
1299: .ve
1301: Then, your scheme can be chosen with the procedural interface via
1302: $ TSGLSetType(ts,"my_scheme")
1303: or at runtime via the option
1304: $ -ts_gl_type my_scheme
1306: Level: advanced
1308: .keywords: TSGL, register
1310: .seealso: TSGLRegisterAll()
1311: @*/
1312: PetscErrorCode TSGLRegister(const char sname[],PetscErrorCode (*function)(TS))
1313: {
1317: PetscFunctionListAdd(&TSGLList,sname,function);
1318: return(0);
1319: }
1323: /*@C
1324: TSGLAcceptRegister - adds a TSGL acceptance scheme
1326: Not Collective
1328: Input Parameters:
1329: + name_scheme - name of user-defined acceptance scheme
1330: - routine_create - routine to create method context
1332: Notes:
1333: TSGLAcceptRegister() may be called multiple times to add several user-defined families.
1335: Sample usage:
1336: .vb
1337: TSGLAcceptRegister("my_scheme",MySchemeCreate);
1338: .ve
1340: Then, your scheme can be chosen with the procedural interface via
1341: $ TSGLSetAcceptType(ts,"my_scheme")
1342: or at runtime via the option
1343: $ -ts_gl_accept_type my_scheme
1345: Level: advanced
1347: .keywords: TSGL, TSGLAcceptType, register
1349: .seealso: TSGLRegisterAll()
1350: @*/
1351: PetscErrorCode TSGLAcceptRegister(const char sname[],TSGLAcceptFunction function)
1352: {
1356: PetscFunctionListAdd(&TSGLAcceptList,sname,function);
1357: return(0);
1358: }
1362: /*@C
1363: TSGLRegisterAll - Registers all of the general linear methods in TSGL
1365: Not Collective
1367: Level: advanced
1369: .keywords: TS, TSGL, register, all
1371: .seealso: TSGLRegisterDestroy()
1372: @*/
1373: PetscErrorCode TSGLRegisterAll(void)
1374: {
1378: if (TSGLRegisterAllCalled) return(0);
1379: TSGLRegisterAllCalled = PETSC_TRUE;
1381: TSGLRegister(TSGL_IRKS, TSGLCreate_IRKS);
1382: TSGLAcceptRegister(TSGLACCEPT_ALWAYS,TSGLAccept_Always);
1383: return(0);
1384: }
1388: /*@C
1389: TSGLInitializePackage - This function initializes everything in the TSGL package. It is called
1390: from PetscDLLibraryRegister() when using dynamic libraries, and on the first call to TSCreate_GL()
1391: when using static libraries.
1393: Level: developer
1395: .keywords: TS, TSGL, initialize, package
1396: .seealso: PetscInitialize()
1397: @*/
1398: PetscErrorCode TSGLInitializePackage(void)
1399: {
1403: if (TSGLPackageInitialized) return(0);
1404: TSGLPackageInitialized = PETSC_TRUE;
1405: TSGLRegisterAll();
1406: PetscRegisterFinalize(TSGLFinalizePackage);
1407: return(0);
1408: }
1412: /*@C
1413: TSGLFinalizePackage - This function destroys everything in the TSGL package. It is
1414: called from PetscFinalize().
1416: Level: developer
1418: .keywords: Petsc, destroy, package
1419: .seealso: PetscFinalize()
1420: @*/
1421: PetscErrorCode TSGLFinalizePackage(void)
1422: {
1426: PetscFunctionListDestroy(&TSGLList);
1427: PetscFunctionListDestroy(&TSGLAcceptList);
1428: TSGLPackageInitialized = PETSC_FALSE;
1429: TSGLRegisterAllCalled = PETSC_FALSE;
1430: return(0);
1431: }
1433: /* ------------------------------------------------------------ */
1434: /*MC
1435: TSGL - DAE solver using implicit General Linear methods
1437: These methods contain Runge-Kutta and multistep schemes as special cases. These special cases have some fundamental
1438: limitations. For example, diagonally implicit Runge-Kutta cannot have stage order greater than 1 which limits their
1439: applicability to very stiff systems. Meanwhile, multistep methods cannot be A-stable for order greater than 2 and BDF
1440: are not 0-stable for order greater than 6. GL methods can be A- and L-stable with arbitrarily high stage order and
1441: reliable error estimates for both 1 and 2 orders higher to facilitate adaptive step sizes and adaptive order schemes.
1442: All this is possible while preserving a singly diagonally implicit structure.
1444: Options database keys:
1445: + -ts_gl_type <type> - the class of general linear method (irks)
1446: . -ts_gl_rtol <tol> - relative error
1447: . -ts_gl_atol <tol> - absolute error
1448: . -ts_gl_min_order <p> - minimum order method to consider (default=1)
1449: . -ts_gl_max_order <p> - maximum order method to consider (default=3)
1450: . -ts_gl_start_order <p> - order of starting method (default=1)
1451: . -ts_gl_complete <method> - method to use for completing the step (rescale-and-modify or rescale)
1452: - -ts_adapt_type <method> - adaptive controller to use (none step both)
1454: Notes:
1455: This integrator can be applied to DAE.
1457: Diagonally implicit general linear (DIGL) methods are a generalization of diagonally implicit Runge-Kutta (DIRK).
1458: They are represented by the tableau
1460: .vb
1461: A | U
1462: -------
1463: B | V
1464: .ve
1466: combined with a vector c of abscissa. "Diagonally implicit" means that A is lower triangular.
1467: A step of the general method reads
1469: .vb
1470: [ Y ] = [A U] [ Y' ]
1471: [X^k] = [B V] [X^{k-1}]
1472: .ve
1474: where Y is the multivector of stage values, Y' is the multivector of stage derivatives, X^k is the Nordsieck vector of
1475: the solution at step k. The Nordsieck vector consists of the first r moments of the solution, given by
1477: .vb
1478: X = [x_0,x_1,...,x_{r-1}] = [x, h x', h^2 x'', ..., h^{r-1} x^{(r-1)} ]
1479: .ve
1481: If A is lower triangular, we can solve the stages (Y,Y') sequentially
1483: .vb
1484: 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}
1485: .ve
1487: and then construct the pieces to carry to the next step
1489: .vb
1490: 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}
1491: .ve
1493: Note that when the equations are cast in implicit form, we are using the stage equation to define y'_i
1494: in terms of y_i and known stuff (y_j for j<i and x_j for all j).
1497: Error estimation
1499: At present, the most attractive GL methods for stiff problems are singly diagonally implicit schemes which posses
1500: Inherent Runge-Kutta Stability (IRKS). These methods have r=s, the number of items passed between steps is equal to
1501: the number of stages. The order and stage-order are one less than the number of stages. We use the error estimates
1502: in the 2007 paper which provide the following estimates
1504: .vb
1505: h^{p+1} X^{(p+1)} = phi_0^T Y' + [0 psi_0^T] Xold
1506: h^{p+2} X^{(p+2)} = phi_1^T Y' + [0 psi_1^T] Xold
1507: h^{p+2} (dx'/dx) X^{(p+1)} = phi_2^T Y' + [0 psi_2^T] Xold
1508: .ve
1510: These estimates are accurate to O(h^{p+3}).
1512: Changing the step size
1514: We use the generalized "rescale and modify" scheme, see equation (4.5) of the 2007 paper.
1516: Level: beginner
1518: References:
1519: + 1. - John Butcher and Z. Jackieweicz and W. Wright, On error propagation in general linear methods for
1520: ordinary differential equations, Journal of Complexity, Vol 23, 2007.
1521: - 2. - John Butcher, Numerical methods for ordinary differential equations, second edition, Wiley, 2009.
1523: .seealso: TSCreate(), TS, TSSetType()
1525: M*/
1528: PETSC_EXTERN PetscErrorCode TSCreate_GL(TS ts)
1529: {
1530: TS_GL *gl;
1534: TSGLInitializePackage();
1536: PetscNewLog(ts,&gl);
1537: ts->data = (void*)gl;
1539: ts->ops->reset = TSReset_GL;
1540: ts->ops->destroy = TSDestroy_GL;
1541: ts->ops->view = TSView_GL;
1542: ts->ops->setup = TSSetUp_GL;
1543: ts->ops->solve = TSSolve_GL;
1544: ts->ops->setfromoptions = TSSetFromOptions_GL;
1545: ts->ops->snesfunction = SNESTSFormFunction_GL;
1546: ts->ops->snesjacobian = SNESTSFormJacobian_GL;
1548: gl->max_step_rejections = 1;
1549: gl->min_order = 1;
1550: gl->max_order = 3;
1551: gl->start_order = 1;
1552: gl->current_scheme = -1;
1553: gl->extrapolate = PETSC_FALSE;
1555: gl->wrms_atol = 1e-8;
1556: gl->wrms_rtol = 1e-5;
1558: PetscObjectComposeFunction((PetscObject)ts,"TSGLSetType_C", &TSGLSetType_GL);
1559: PetscObjectComposeFunction((PetscObject)ts,"TSGLSetAcceptType_C",&TSGLSetAcceptType_GL);
1560: PetscObjectComposeFunction((PetscObject)ts,"TSGLGetAdapt_C", &TSGLGetAdapt_GL);
1561: return(0);
1562: }