Actual source code: bcgsl.c
petsc-3.12.0 2019-09-29
1: /*
2: * Implementation of BiCGstab(L) the paper by D.R. Fokkema,
3: * "Enhanced implementation of BiCGStab(L) for solving linear systems
4: * of equations". This uses tricky delayed updating ideas to prevent
5: * round-off buildup.
6: *
7: * This has not been completely cleaned up into PETSc style.
8: *
9: * All the BLAS and LAPACK calls below should be removed and replaced with
10: * loops and the macros for block solvers converted from LINPACK; there is no way
11: * calls to BLAS/LAPACK make sense for size 2, 3, 4, etc.
12: */
13: #include <petsc/private/kspimpl.h>
14: #include <../src/ksp/ksp/impls/bcgsl/bcgslimpl.h>
15: #include <petscblaslapack.h>
18: static PetscErrorCode KSPSolve_BCGSL(KSP ksp)
19: {
20: KSP_BCGSL *bcgsl = (KSP_BCGSL*) ksp->data;
21: PetscScalar alpha, beta, omega, sigma;
22: PetscScalar rho0, rho1;
23: PetscReal kappa0, kappaA, kappa1;
24: PetscReal ghat;
25: PetscReal zeta, zeta0, rnmax_computed, rnmax_true, nrm0;
26: PetscBool bUpdateX;
27: PetscInt maxit;
28: PetscInt h, i, j, k, vi, ell;
29: PetscBLASInt ldMZ,bierr;
30: PetscScalar utb;
31: PetscReal max_s, pinv_tol;
35: /* set up temporary vectors */
36: vi = 0;
37: ell = bcgsl->ell;
38: bcgsl->vB = ksp->work[vi]; vi++;
39: bcgsl->vRt = ksp->work[vi]; vi++;
40: bcgsl->vTm = ksp->work[vi]; vi++;
41: bcgsl->vvR = ksp->work+vi; vi += ell+1;
42: bcgsl->vvU = ksp->work+vi; vi += ell+1;
43: bcgsl->vXr = ksp->work[vi]; vi++;
44: PetscBLASIntCast(ell+1,&ldMZ);
46: /* Prime the iterative solver */
47: KSPInitialResidual(ksp, VX, VTM, VB, VVR[0], ksp->vec_rhs);
48: VecNorm(VVR[0], NORM_2, &zeta0);
49: KSPCheckNorm(ksp,zeta0);
50: rnmax_computed = zeta0;
51: rnmax_true = zeta0;
53: (*ksp->converged)(ksp, 0, zeta0, &ksp->reason, ksp->cnvP);
54: if (ksp->reason) {
55: PetscObjectSAWsTakeAccess((PetscObject)ksp);
56: ksp->its = 0;
57: ksp->rnorm = zeta0;
58: PetscObjectSAWsGrantAccess((PetscObject)ksp);
59: return(0);
60: }
62: VecSet(VVU[0],0.0);
63: alpha = 0.;
64: rho0 = omega = 1;
66: if (bcgsl->delta>0.0) {
67: VecCopy(VX, VXR);
68: VecSet(VX,0.0);
69: VecCopy(VVR[0], VB);
70: } else {
71: VecCopy(ksp->vec_rhs, VB);
72: }
74: /* Life goes on */
75: VecCopy(VVR[0], VRT);
76: zeta = zeta0;
78: KSPGetTolerances(ksp, NULL, NULL, NULL, &maxit);
80: for (k=0; k<maxit; k += bcgsl->ell) {
81: ksp->its = k;
82: ksp->rnorm = zeta;
84: KSPLogResidualHistory(ksp, zeta);
85: KSPMonitor(ksp, ksp->its, zeta);
87: (*ksp->converged)(ksp, k, zeta, &ksp->reason, ksp->cnvP);
88: if (ksp->reason < 0) return(0);
89: else if (ksp->reason) break;
91: /* BiCG part */
92: rho0 = -omega*rho0;
93: nrm0 = zeta;
94: for (j=0; j<bcgsl->ell; j++) {
95: /* rho1 <- r_j' * r_tilde */
96: VecDot(VVR[j], VRT, &rho1);
97: KSPCheckDot(ksp,rho1);
98: if (rho1 == 0.0) {
99: ksp->reason = KSP_DIVERGED_BREAKDOWN_BICG;
100: return(0);
101: }
102: beta = alpha*(rho1/rho0);
103: rho0 = rho1;
104: for (i=0; i<=j; i++) {
105: /* u_i <- r_i - beta*u_i */
106: VecAYPX(VVU[i], -beta, VVR[i]);
107: }
108: /* u_{j+1} <- inv(K)*A*u_j */
109: KSP_PCApplyBAorAB(ksp, VVU[j], VVU[j+1], VTM);
111: VecDot(VVU[j+1], VRT, &sigma);
112: KSPCheckDot(ksp,sigma);
113: if (sigma == 0.0) {
114: ksp->reason = KSP_DIVERGED_BREAKDOWN_BICG;
115: return(0);
116: }
117: alpha = rho1/sigma;
119: /* x <- x + alpha*u_0 */
120: VecAXPY(VX, alpha, VVU[0]);
122: for (i=0; i<=j; i++) {
123: /* r_i <- r_i - alpha*u_{i+1} */
124: VecAXPY(VVR[i], -alpha, VVU[i+1]);
125: }
127: /* r_{j+1} <- inv(K)*A*r_j */
128: KSP_PCApplyBAorAB(ksp, VVR[j], VVR[j+1], VTM);
130: VecNorm(VVR[0], NORM_2, &nrm0);
131: KSPCheckNorm(ksp,nrm0);
132: if (bcgsl->delta>0.0) {
133: if (rnmax_computed<nrm0) rnmax_computed = nrm0;
134: if (rnmax_true<nrm0) rnmax_true = nrm0;
135: }
137: /* NEW: check for early exit */
138: (*ksp->converged)(ksp, k+j, nrm0, &ksp->reason, ksp->cnvP);
139: if (ksp->reason) {
140: PetscObjectSAWsTakeAccess((PetscObject)ksp);
142: ksp->its = k+j;
143: ksp->rnorm = nrm0;
145: PetscObjectSAWsGrantAccess((PetscObject)ksp);
146: if (ksp->reason < 0) return(0);
147: }
148: }
150: /* Polynomial part */
151: for (i = 0; i <= bcgsl->ell; ++i) {
152: VecMDot(VVR[i], i+1, VVR, &MZa[i*ldMZ]);
153: }
154: /* Symmetrize MZa */
155: for (i = 0; i <= bcgsl->ell; ++i) {
156: for (j = i+1; j <= bcgsl->ell; ++j) {
157: MZa[i*ldMZ+j] = MZa[j*ldMZ+i] = PetscConj(MZa[j*ldMZ+i]);
158: }
159: }
160: /* Copy MZa to MZb */
161: PetscArraycpy(MZb,MZa,ldMZ*ldMZ);
163: if (!bcgsl->bConvex || bcgsl->ell==1) {
164: PetscBLASInt ione = 1,bell;
165: PetscBLASIntCast(bcgsl->ell,&bell);
167: AY0c[0] = -1;
168: if (bcgsl->pinv) {
169: #if defined(PETSC_MISSING_LAPACK_GESVD)
170: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GESVD - Lapack routine is unavailable.");
171: #else
172: # if defined(PETSC_USE_COMPLEX)
173: PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("A","A",&bell,&bell,&MZa[1+ldMZ],&ldMZ,bcgsl->s,bcgsl->u,&bell,bcgsl->v,&bell,bcgsl->work,&bcgsl->lwork,bcgsl->realwork,&bierr));
174: # else
175: PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("A","A",&bell,&bell,&MZa[1+ldMZ],&ldMZ,bcgsl->s,bcgsl->u,&bell,bcgsl->v,&bell,bcgsl->work,&bcgsl->lwork,&bierr));
176: # endif
177: #endif
178: if (bierr!=0) {
179: ksp->reason = KSP_DIVERGED_BREAKDOWN;
180: return(0);
181: }
182: /* Apply pseudo-inverse */
183: max_s = bcgsl->s[0];
184: for (i=1; i<bell; i++) {
185: if (bcgsl->s[i] > max_s) {
186: max_s = bcgsl->s[i];
187: }
188: }
189: /* tolerance is hardwired to bell*max(s)*PETSC_MACHINE_EPSILON */
190: pinv_tol = bell*max_s*PETSC_MACHINE_EPSILON;
191: PetscArrayzero(&AY0c[1],bell);
192: for (i=0; i<bell; i++) {
193: if (bcgsl->s[i] >= pinv_tol) {
194: utb=0.;
195: for (j=0; j<bell; j++) {
196: utb += MZb[1+j]*bcgsl->u[i*bell+j];
197: }
199: for (j=0; j<bell; j++) {
200: AY0c[1+j] += utb/bcgsl->s[i]*bcgsl->v[j*bell+i];
201: }
202: }
203: }
204: } else {
205: #if defined(PETSC_MISSING_LAPACK_POTRF)
206: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"POTRF - Lapack routine is unavailable.");
207: #else
208: PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("Lower", &bell, &MZa[1+ldMZ], &ldMZ, &bierr));
209: #endif
210: if (bierr!=0) {
211: ksp->reason = KSP_DIVERGED_BREAKDOWN;
212: return(0);
213: }
214: PetscArraycpy(&AY0c[1],&MZb[1],bcgsl->ell);
215: PetscStackCallBLAS("LAPACKpotrs",LAPACKpotrs_("Lower", &bell, &ione, &MZa[1+ldMZ], &ldMZ, &AY0c[1], &ldMZ, &bierr));
216: }
217: } else {
218: PetscBLASInt ione = 1;
219: PetscScalar aone = 1.0, azero = 0.0;
220: PetscBLASInt neqs;
221: PetscBLASIntCast(bcgsl->ell-1,&neqs);
223: #if defined(PETSC_MISSING_LAPACK_POTRF)
224: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"POTRF - Lapack routine is unavailable.");
225: #else
226: PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("Lower", &neqs, &MZa[1+ldMZ], &ldMZ, &bierr));
227: #endif
228: if (bierr!=0) {
229: ksp->reason = KSP_DIVERGED_BREAKDOWN;
230: return(0);
231: }
232: PetscArraycpy(&AY0c[1],&MZb[1],bcgsl->ell-1);
233: PetscStackCallBLAS("LAPACKpotrs",LAPACKpotrs_("Lower", &neqs, &ione, &MZa[1+ldMZ], &ldMZ, &AY0c[1], &ldMZ, &bierr));
234: AY0c[0] = -1;
235: AY0c[bcgsl->ell] = 0.;
237: PetscArraycpy(&AYlc[1],&MZb[1+ldMZ*(bcgsl->ell)],bcgsl->ell-1);
238: PetscStackCallBLAS("LAPACKpotrs",LAPACKpotrs_("Lower", &neqs, &ione, &MZa[1+ldMZ], &ldMZ, &AYlc[1], &ldMZ, &bierr));
240: AYlc[0] = 0.;
241: AYlc[bcgsl->ell] = -1;
243: PetscStackCallBLAS("BLASgemv",BLASgemv_("NoTr", &ldMZ, &ldMZ, &aone, MZb, &ldMZ, AY0c, &ione, &azero, AYtc, &ione));
245: kappa0 = PetscRealPart(BLASdot_(&ldMZ, AY0c, &ione, AYtc, &ione));
247: /* round-off can cause negative kappa's */
248: if (kappa0<0) kappa0 = -kappa0;
249: kappa0 = PetscSqrtReal(kappa0);
251: kappaA = PetscRealPart(BLASdot_(&ldMZ, AYlc, &ione, AYtc, &ione));
253: PetscStackCallBLAS("BLASgemv",BLASgemv_("noTr", &ldMZ, &ldMZ, &aone, MZb, &ldMZ, AYlc, &ione, &azero, AYtc, &ione));
255: kappa1 = PetscRealPart(BLASdot_(&ldMZ, AYlc, &ione, AYtc, &ione));
257: if (kappa1<0) kappa1 = -kappa1;
258: kappa1 = PetscSqrtReal(kappa1);
260: if (kappa0!=0.0 && kappa1!=0.0) {
261: if (kappaA<0.7*kappa0*kappa1) {
262: ghat = (kappaA<0.0) ? -0.7*kappa0/kappa1 : 0.7*kappa0/kappa1;
263: } else {
264: ghat = kappaA/(kappa1*kappa1);
265: }
266: for (i=0; i<=bcgsl->ell; i++) {
267: AY0c[i] = AY0c[i] - ghat* AYlc[i];
268: }
269: }
270: }
272: omega = AY0c[bcgsl->ell];
273: for (h=bcgsl->ell; h>0 && omega==0.0; h--) omega = AY0c[h];
274: if (omega==0.0) {
275: ksp->reason = KSP_DIVERGED_BREAKDOWN;
276: return(0);
277: }
280: VecMAXPY(VX, bcgsl->ell,AY0c+1, VVR);
281: for (i=1; i<=bcgsl->ell; i++) AY0c[i] *= -1.0;
282: VecMAXPY(VVU[0], bcgsl->ell,AY0c+1, VVU+1);
283: VecMAXPY(VVR[0], bcgsl->ell,AY0c+1, VVR+1);
284: for (i=1; i<=bcgsl->ell; i++) AY0c[i] *= -1.0;
285: VecNorm(VVR[0], NORM_2, &zeta);
286: KSPCheckNorm(ksp,zeta);
288: /* Accurate Update */
289: if (bcgsl->delta>0.0) {
290: if (rnmax_computed<zeta) rnmax_computed = zeta;
291: if (rnmax_true<zeta) rnmax_true = zeta;
293: bUpdateX = (PetscBool) (zeta<bcgsl->delta*zeta0 && zeta0<=rnmax_computed);
294: if ((zeta<bcgsl->delta*rnmax_true && zeta0<=rnmax_true) || bUpdateX) {
295: /* r0 <- b-inv(K)*A*X */
296: KSP_PCApplyBAorAB(ksp, VX, VVR[0], VTM);
297: VecAYPX(VVR[0], -1.0, VB);
298: rnmax_true = zeta;
300: if (bUpdateX) {
301: VecAXPY(VXR,1.0,VX);
302: VecSet(VX,0.0);
303: VecCopy(VVR[0], VB);
304: rnmax_computed = zeta;
305: }
306: }
307: }
308: }
309: if (bcgsl->delta>0.0) {
310: VecAXPY(VX,1.0,VXR);
311: }
313: (*ksp->converged)(ksp, k, zeta, &ksp->reason, ksp->cnvP);
314: if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
315: return(0);
316: }
318: /*@
319: KSPBCGSLSetXRes - Sets the parameter governing when
320: exact residuals will be used instead of computed residuals.
322: Logically Collective on ksp
324: Input Parameters:
325: + ksp - iterative context obtained from KSPCreate
326: - delta - computed residuals are used alone when delta is not positive
328: Options Database Keys:
330: . -ksp_bcgsl_xres delta
332: Level: intermediate
334: .seealso: KSPBCGSLSetEll(), KSPBCGSLSetPol(), KSP
335: @*/
336: PetscErrorCode KSPBCGSLSetXRes(KSP ksp, PetscReal delta)
337: {
338: KSP_BCGSL *bcgsl = (KSP_BCGSL*)ksp->data;
343: if (ksp->setupstage) {
344: if ((delta<=0 && bcgsl->delta>0) || (delta>0 && bcgsl->delta<=0)) {
345: VecDestroyVecs(ksp->nwork,&ksp->work);
346: PetscFree5(AY0c,AYlc,AYtc,MZa,MZb);
347: PetscFree4(bcgsl->work,bcgsl->s,bcgsl->u,bcgsl->v);
348: ksp->setupstage = KSP_SETUP_NEW;
349: }
350: }
351: bcgsl->delta = delta;
352: return(0);
353: }
355: /*@
356: KSPBCGSLSetUsePseudoinverse - Use pseudoinverse (via SVD) to solve polynomial part of update
358: Logically Collective on ksp
360: Input Parameters:
361: + ksp - iterative context obtained from KSPCreate
362: - use_pinv - set to PETSC_TRUE when using pseudoinverse
364: Options Database Keys:
366: . -ksp_bcgsl_pinv - use pseudoinverse
368: Level: intermediate
370: .seealso: KSPBCGSLSetEll(), KSP
371: @*/
372: PetscErrorCode KSPBCGSLSetUsePseudoinverse(KSP ksp,PetscBool use_pinv)
373: {
374: KSP_BCGSL *bcgsl = (KSP_BCGSL*)ksp->data;
377: bcgsl->pinv = use_pinv;
378: return(0);
379: }
381: /*@
382: KSPBCGSLSetPol - Sets the type of polynomial part will
383: be used in the BiCGSTab(L) solver.
385: Logically Collective on ksp
387: Input Parameters:
388: + ksp - iterative context obtained from KSPCreate
389: - uMROR - set to PETSC_TRUE when the polynomial is a convex combination of an MR and an OR step.
391: Options Database Keys:
393: + -ksp_bcgsl_cxpoly - use enhanced polynomial
394: - -ksp_bcgsl_mrpoly - use standard polynomial
396: Level: intermediate
398: .seealso: KSP, KSPBCGSL, KSPCreate(), KSPSetType()
399: @*/
400: PetscErrorCode KSPBCGSLSetPol(KSP ksp, PetscBool uMROR)
401: {
402: KSP_BCGSL *bcgsl = (KSP_BCGSL*)ksp->data;
408: if (!ksp->setupstage) bcgsl->bConvex = uMROR;
409: else if (bcgsl->bConvex != uMROR) {
410: /* free the data structures,
411: then create them again
412: */
413: VecDestroyVecs(ksp->nwork,&ksp->work);
414: PetscFree5(AY0c,AYlc,AYtc,MZa,MZb);
415: PetscFree4(bcgsl->work,bcgsl->s,bcgsl->u,bcgsl->v);
417: bcgsl->bConvex = uMROR;
418: ksp->setupstage = KSP_SETUP_NEW;
419: }
420: return(0);
421: }
423: /*@
424: KSPBCGSLSetEll - Sets the number of search directions in BiCGStab(L).
426: Logically Collective on ksp
428: Input Parameters:
429: + ksp - iterative context obtained from KSPCreate
430: - ell - number of search directions
432: Options Database Keys:
434: . -ksp_bcgsl_ell ell
436: Level: intermediate
438: Notes:
439: For large ell it is common for the polynomial update problem to become singular (due to happy breakdown for smallish
440: test problems, but also for larger problems). Consequently, by default, the system is solved by pseudoinverse, which
441: allows the iteration to complete successfully. See KSPBCGSLSetUsePseudoinverse() to switch to a conventional solve.
443: .seealso: KSPBCGSLSetUsePseudoinverse(), KSP, KSPBCGSL
444: @*/
445: PetscErrorCode KSPBCGSLSetEll(KSP ksp, PetscInt ell)
446: {
447: KSP_BCGSL *bcgsl = (KSP_BCGSL*)ksp->data;
451: if (ell < 1) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE, "KSPBCGSLSetEll: second argument must be positive");
454: if (!ksp->setupstage) bcgsl->ell = ell;
455: else if (bcgsl->ell != ell) {
456: /* free the data structures, then create them again */
457: VecDestroyVecs(ksp->nwork,&ksp->work);
458: PetscFree5(AY0c,AYlc,AYtc,MZa,MZb);
459: PetscFree4(bcgsl->work,bcgsl->s,bcgsl->u,bcgsl->v);
461: bcgsl->ell = ell;
462: ksp->setupstage = KSP_SETUP_NEW;
463: }
464: return(0);
465: }
467: PetscErrorCode KSPView_BCGSL(KSP ksp, PetscViewer viewer)
468: {
469: KSP_BCGSL *bcgsl = (KSP_BCGSL*)ksp->data;
471: PetscBool isascii;
474: PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii);
476: if (isascii) {
477: PetscViewerASCIIPrintf(viewer, " Ell = %D\n", bcgsl->ell);
478: PetscViewerASCIIPrintf(viewer, " Delta = %lg\n", bcgsl->delta);
479: }
480: return(0);
481: }
483: PetscErrorCode KSPSetFromOptions_BCGSL(PetscOptionItems *PetscOptionsObject,KSP ksp)
484: {
485: KSP_BCGSL *bcgsl = (KSP_BCGSL*)ksp->data;
487: PetscInt this_ell;
488: PetscReal delta;
489: PetscBool flga = PETSC_FALSE, flg;
492: /* PetscOptionsBegin/End are called in KSPSetFromOptions. They
493: don't need to be called here.
494: */
495: PetscOptionsHead(PetscOptionsObject,"KSP BiCGStab(L) Options");
497: /* Set number of search directions */
498: PetscOptionsInt("-ksp_bcgsl_ell","Number of Krylov search directions","KSPBCGSLSetEll",bcgsl->ell,&this_ell,&flg);
499: if (flg) {
500: KSPBCGSLSetEll(ksp, this_ell);
501: }
503: /* Set polynomial type */
504: PetscOptionsBool("-ksp_bcgsl_cxpoly", "Polynomial part of BiCGStabL is MinRes + OR", "KSPBCGSLSetPol", flga,&flga,NULL);
505: if (flga) {
506: KSPBCGSLSetPol(ksp, PETSC_TRUE);
507: } else {
508: flg = PETSC_FALSE;
509: PetscOptionsBool("-ksp_bcgsl_mrpoly", "Polynomial part of BiCGStabL is MinRes", "KSPBCGSLSetPol", flg,&flg,NULL);
510: KSPBCGSLSetPol(ksp, PETSC_FALSE);
511: }
513: /* Will computed residual be refreshed? */
514: PetscOptionsReal("-ksp_bcgsl_xres", "Threshold used to decide when to refresh computed residuals", "KSPBCGSLSetXRes", bcgsl->delta, &delta, &flg);
515: if (flg) {
516: KSPBCGSLSetXRes(ksp, delta);
517: }
519: /* Use pseudoinverse? */
520: flg = bcgsl->pinv;
521: PetscOptionsBool("-ksp_bcgsl_pinv", "Polynomial correction via pseudoinverse", "KSPBCGSLSetUsePseudoinverse",flg,&flg,NULL);
522: KSPBCGSLSetUsePseudoinverse(ksp,flg);
523: PetscOptionsTail();
524: return(0);
525: }
527: PetscErrorCode KSPSetUp_BCGSL(KSP ksp)
528: {
529: KSP_BCGSL *bcgsl = (KSP_BCGSL*)ksp->data;
530: PetscInt ell = bcgsl->ell,ldMZ = ell+1;
534: KSPSetWorkVecs(ksp, 6+2*ell);
535: PetscMalloc5(ldMZ,&AY0c,ldMZ,&AYlc,ldMZ,&AYtc,ldMZ*ldMZ,&MZa,ldMZ*ldMZ,&MZb);
536: PetscBLASIntCast(5*ell,&bcgsl->lwork);
537: PetscMalloc5(bcgsl->lwork,&bcgsl->work,ell,&bcgsl->s,ell*ell,&bcgsl->u,ell*ell,&bcgsl->v,5*ell,&bcgsl->realwork);
538: return(0);
539: }
541: PetscErrorCode KSPReset_BCGSL(KSP ksp)
542: {
543: KSP_BCGSL *bcgsl = (KSP_BCGSL*)ksp->data;
547: VecDestroyVecs(ksp->nwork,&ksp->work);
548: PetscFree5(AY0c,AYlc,AYtc,MZa,MZb);
549: PetscFree5(bcgsl->work,bcgsl->s,bcgsl->u,bcgsl->v,bcgsl->realwork);
550: return(0);
551: }
553: PetscErrorCode KSPDestroy_BCGSL(KSP ksp)
554: {
558: KSPReset_BCGSL(ksp);
559: KSPDestroyDefault(ksp);
560: return(0);
561: }
563: /*MC
564: KSPBCGSL - Implements a slight variant of the Enhanced
565: BiCGStab(L) algorithm in (3) and (2). The variation
566: concerns cases when either kappa0**2 or kappa1**2 is
567: negative due to round-off. Kappa0 has also been pulled
568: out of the denominator in the formula for ghat.
570: References:
571: + 1. - G.L.G. Sleijpen, H.A. van der Vorst, "An overview of
572: approaches for the stable computation of hybrid BiCG
573: methods", Applied Numerical Mathematics: Transactions
574: f IMACS, 19(3), 1996.
575: . 2. - G.L.G. Sleijpen, H.A. van der Vorst, D.R. Fokkema,
576: "BiCGStab(L) and other hybrid BiCG methods",
577: Numerical Algorithms, 7, 1994.
578: - 3. - D.R. Fokkema, "Enhanced implementation of BiCGStab(L)
579: for solving linear systems of equations", preprint
580: from www.citeseer.com.
582: Contributed by: Joel M. Malard, email jm.malard@pnl.gov
584: Options Database Keys:
585: + -ksp_bcgsl_ell <ell> Number of Krylov search directions, defaults to 2 -- KSPBCGSLSetEll()
586: . -ksp_bcgsl_cxpol - Use a convex function of the MinRes and OR polynomials after the BiCG step instead of default MinRes -- KSPBCGSLSetPol()
587: . -ksp_bcgsl_mrpoly - Use the default MinRes polynomial after the BiCG step -- KSPBCGSLSetPol()
588: . -ksp_bcgsl_xres <res> Threshold used to decide when to refresh computed residuals -- KSPBCGSLSetXRes()
589: - -ksp_bcgsl_pinv <true/false> - (de)activate use of pseudoinverse -- KSPBCGSLSetUsePseudoinverse()
591: Level: beginner
593: .seealso: KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPFGMRES, KSPBCGS, KSPSetPCSide(), KSPBCGSLSetEll(), KSPBCGSLSetXRes()
595: M*/
596: PETSC_EXTERN PetscErrorCode KSPCreate_BCGSL(KSP ksp)
597: {
599: KSP_BCGSL *bcgsl;
602: /* allocate BiCGStab(L) context */
603: PetscNewLog(ksp,&bcgsl);
604: ksp->data = (void*)bcgsl;
606: KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
607: KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_RIGHT,2);
609: ksp->ops->setup = KSPSetUp_BCGSL;
610: ksp->ops->solve = KSPSolve_BCGSL;
611: ksp->ops->reset = KSPReset_BCGSL;
612: ksp->ops->destroy = KSPDestroy_BCGSL;
613: ksp->ops->buildsolution = KSPBuildSolutionDefault;
614: ksp->ops->buildresidual = KSPBuildResidualDefault;
615: ksp->ops->setfromoptions = KSPSetFromOptions_BCGSL;
616: ksp->ops->view = KSPView_BCGSL;
618: /* Let the user redefine the number of directions vectors */
619: bcgsl->ell = 2;
621: /*Choose between a single MR step or an averaged MR/OR */
622: bcgsl->bConvex = PETSC_FALSE;
624: bcgsl->pinv = PETSC_TRUE; /* Use the reliable method by default */
626: /* Set the threshold for when exact residuals will be used */
627: bcgsl->delta = 0.0;
628: return(0);
629: }