xref: /petsc/src/ksp/pc/impls/bddc/bddcnullspace.c (revision 29b3c8a1c1d29fc05018f23f4f087a3ebe1dff6f) 
1 #include <../src/ksp/pc/impls/bddc/bddc.h>
2 #include <../src/ksp/pc/impls/bddc/bddcprivate.h>
3 #include <../src/mat/impls/dense/seq/dense.h>
4 
5 /* E + small_solve */
6 static PetscErrorCode PCBDDCNullSpaceCorrPreSolve(KSP ksp,Vec y,Vec x, void* ctx)
7 {
8   NullSpaceCorrection_ctx corr_ctx = (NullSpaceCorrection_ctx)ctx;
9   Mat                     K;
10   PetscErrorCode          ierr;
11 
12   PetscFunctionBegin;
13   ierr = PetscLogEventBegin(corr_ctx->evapply,ksp,0,0,0);CHKERRQ(ierr);
14   ierr = MatMultTranspose(corr_ctx->basis_mat,y,corr_ctx->sw[0]);CHKERRQ(ierr);
15   ierr = MatMultTranspose(corr_ctx->inv_smat,corr_ctx->sw[0],corr_ctx->sw[1]);CHKERRQ(ierr);
16   ierr = VecScale(corr_ctx->sw[1],-1.0);CHKERRQ(ierr);
17   ierr = MatMult(corr_ctx->basis_mat,corr_ctx->sw[1],corr_ctx->fw[0]);CHKERRQ(ierr);
18   ierr = VecScale(corr_ctx->sw[1],-1.0);CHKERRQ(ierr);
19   ierr = KSPGetOperators(ksp,&K,NULL);CHKERRQ(ierr);
20   ierr = MatMultAdd(K,corr_ctx->fw[0],y,y);CHKERRQ(ierr);
21   ierr = PetscLogEventEnd(corr_ctx->evapply,ksp,0,0,0);CHKERRQ(ierr);
22   PetscFunctionReturn(0);
23 }
24 
25 /* E^t + small */
26 static PetscErrorCode PCBDDCNullSpaceCorrPostSolve(KSP ksp,Vec y,Vec x, void* ctx)
27 {
28   NullSpaceCorrection_ctx corr_ctx = (NullSpaceCorrection_ctx)ctx;
29   PetscErrorCode          ierr;
30   Mat                     K;
31 
32   PetscFunctionBegin;
33   ierr = PetscLogEventBegin(corr_ctx->evapply,ksp,0,0,0);CHKERRQ(ierr);
34   ierr = KSPGetOperators(ksp,&K,NULL);CHKERRQ(ierr);
35   ierr = MatMultTranspose(K,x,corr_ctx->fw[0]);CHKERRQ(ierr);
36   ierr = MatMultTranspose(corr_ctx->basis_mat,corr_ctx->fw[0],corr_ctx->sw[0]);CHKERRQ(ierr);
37   ierr = VecScale(corr_ctx->sw[0],-1.0);CHKERRQ(ierr);
38   ierr = MatMult(corr_ctx->inv_smat,corr_ctx->sw[0],corr_ctx->sw[2]);CHKERRQ(ierr);
39   ierr = MatMultAdd(corr_ctx->basis_mat,corr_ctx->sw[2],x,corr_ctx->fw[0]);CHKERRQ(ierr);
40   ierr = VecScale(corr_ctx->fw[0],corr_ctx->scale);CHKERRQ(ierr);
41   /* Sum contributions from approximate solver and projected system */
42   ierr = MatMultAdd(corr_ctx->basis_mat,corr_ctx->sw[1],corr_ctx->fw[0],x);CHKERRQ(ierr);
43   ierr = PetscLogEventEnd(corr_ctx->evapply,ksp,0,0,0);CHKERRQ(ierr);
44   PetscFunctionReturn(0);
45 }
46 
47 static PetscErrorCode PCBDDCNullSpaceCorrDestroy(void * ctx)
48 {
49   NullSpaceCorrection_ctx corr_ctx = (NullSpaceCorrection_ctx)ctx;
50   PetscErrorCode          ierr;
51 
52   PetscFunctionBegin;
53   ierr = VecDestroyVecs(3,&corr_ctx->sw);CHKERRQ(ierr);
54   ierr = VecDestroyVecs(1,&corr_ctx->fw);CHKERRQ(ierr);
55   ierr = MatDestroy(&corr_ctx->basis_mat);CHKERRQ(ierr);
56   ierr = MatDestroy(&corr_ctx->inv_smat);CHKERRQ(ierr);
57   ierr = PetscFree(corr_ctx);CHKERRQ(ierr);
58   PetscFunctionReturn(0);
59 }
60 
61 PetscErrorCode PCBDDCNullSpaceAssembleCorrection(PC pc, PetscBool isdir, PetscBool needscaling)
62 {
63   PC_BDDC                  *pcbddc = (PC_BDDC*)pc->data;
64   MatNullSpace             NullSpace = NULL;
65   KSP                      local_ksp;
66   NullSpaceCorrection_ctx  shell_ctx;
67   Mat                      local_mat,local_pmat,dmat,Kbasis_mat;
68   Vec                      v;
69   PetscContainer           c;
70   PetscInt                 basis_size;
71   IS                       zerorows;
72   PetscErrorCode           ierr;
73 
74   PetscFunctionBegin;
75   if (isdir) local_ksp = pcbddc->ksp_D; /* Dirichlet solver */
76   else local_ksp = pcbddc->ksp_R; /* Neumann solver */
77   ierr = KSPGetOperators(local_ksp,&local_mat,&local_pmat);CHKERRQ(ierr);
78   ierr = MatGetNearNullSpace(local_pmat,&NullSpace);CHKERRQ(ierr);
79   if (!NullSpace) {
80     if (pcbddc->dbg_flag) {
81       ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d doesn't have local (near) nullspace: no need for correction in %s solver \n",PetscGlobalRank,isdir ? "Dirichlet" : "Neumann");CHKERRQ(ierr);
82     }
83     PetscFunctionReturn(0);
84   }
85   ierr = PetscObjectQuery((PetscObject)NullSpace,"_PBDDC_Null_dmat",(PetscObject*)&dmat);CHKERRQ(ierr);
86   if (!dmat) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Missing dense matrix");CHKERRQ(ierr);
87   ierr = PetscLogEventBegin(PC_BDDC_ApproxSetUp[pcbddc->current_level],pc,0,0,0);CHKERRQ(ierr);
88 
89   ierr = PetscNew(&shell_ctx);CHKERRQ(ierr);
90   shell_ctx->scale = 1.0;
91   ierr = PetscObjectReference((PetscObject)dmat);CHKERRQ(ierr);
92   shell_ctx->basis_mat = dmat;
93   ierr = MatGetSize(dmat,NULL,&basis_size);CHKERRQ(ierr);
94   shell_ctx->evapply = PC_BDDC_ApproxApply[pcbddc->current_level];
95 
96   /* explicit construct (Phi^T K Phi)^-1 */
97   ierr = MatMatMult(local_mat,shell_ctx->basis_mat,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&Kbasis_mat);CHKERRQ(ierr);
98   ierr = MatTransposeMatMult(Kbasis_mat,shell_ctx->basis_mat,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&shell_ctx->inv_smat);CHKERRQ(ierr);
99   ierr = MatDestroy(&Kbasis_mat);CHKERRQ(ierr);
100   ierr = MatFindZeroRows(shell_ctx->inv_smat,&zerorows);CHKERRQ(ierr);
101   if (zerorows) { /* linearly dependent basis */
102     const PetscInt *idxs;
103     PetscInt       i,nz;
104 
105     ierr = ISGetLocalSize(zerorows,&nz);CHKERRQ(ierr);
106     ierr = ISGetIndices(zerorows,&idxs);CHKERRQ(ierr);
107     for (i=0;i<nz;i++) {
108       ierr = MatSetValue(shell_ctx->inv_smat,idxs[i],idxs[i],1.0,INSERT_VALUES);CHKERRQ(ierr);
109     }
110     ierr = ISRestoreIndices(zerorows,&idxs);CHKERRQ(ierr);
111     ierr = MatAssemblyBegin(shell_ctx->inv_smat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
112     ierr = MatAssemblyEnd(shell_ctx->inv_smat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
113   }
114 
115   ierr = MatLUFactor(shell_ctx->inv_smat,NULL,NULL,NULL);CHKERRQ(ierr);
116   ierr = MatSeqDenseInvertFactors_Private(shell_ctx->inv_smat);CHKERRQ(ierr);
117   if (zerorows) { /* linearly dependent basis */
118     const PetscInt *idxs;
119     PetscInt       i,nz;
120 
121     ierr = ISGetLocalSize(zerorows,&nz);CHKERRQ(ierr);
122     ierr = ISGetIndices(zerorows,&idxs);CHKERRQ(ierr);
123     for (i=0;i<nz;i++) {
124       ierr = MatSetValue(shell_ctx->inv_smat,idxs[i],idxs[i],0.0,INSERT_VALUES);CHKERRQ(ierr);
125     }
126     ierr = ISRestoreIndices(zerorows,&idxs);CHKERRQ(ierr);
127     ierr = MatAssemblyBegin(shell_ctx->inv_smat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
128     ierr = MatAssemblyEnd(shell_ctx->inv_smat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
129   }
130   ierr = ISDestroy(&zerorows);CHKERRQ(ierr);
131 
132   /* Create work vectors in shell context */
133   ierr = MatCreateVecs(shell_ctx->inv_smat,&v,NULL);CHKERRQ(ierr);
134   ierr = KSPCreateVecs(local_ksp,1,&shell_ctx->fw,0,NULL);CHKERRQ(ierr);
135   ierr = VecDuplicateVecs(v,3,&shell_ctx->sw);CHKERRQ(ierr);
136   ierr = VecDestroy(&v);CHKERRQ(ierr);
137 
138   /* add special pre/post solve to KSP (see [1], eq. 48) */
139   ierr = KSPSetPreSolve(local_ksp,PCBDDCNullSpaceCorrPreSolve,shell_ctx);CHKERRQ(ierr);
140   ierr = KSPSetPostSolve(local_ksp,PCBDDCNullSpaceCorrPostSolve,shell_ctx);CHKERRQ(ierr);
141   ierr = PetscContainerCreate(PetscObjectComm((PetscObject)local_ksp),&c);CHKERRQ(ierr);
142   ierr = PetscContainerSetPointer(c,shell_ctx);CHKERRQ(ierr);
143   ierr = PetscContainerSetUserDestroy(c,PCBDDCNullSpaceCorrDestroy);CHKERRQ(ierr);
144   ierr = PetscObjectCompose((PetscObject)local_ksp,"_PCBDDC_Null_PrePost_ctx",(PetscObject)c);CHKERRQ(ierr);
145   ierr = PetscContainerDestroy(&c);CHKERRQ(ierr);
146 
147   /* Create ksp object suitable for extreme eigenvalues' estimation */
148   if (needscaling || pcbddc->dbg_flag) {
149     KSP         check_ksp;
150     PC          local_pc;
151     Vec         work1,work2;
152     const char* prefix;
153     PetscReal   test_err,lambda_min,lambda_max;
154     PetscInt    k,maxit;
155 
156     ierr = VecDuplicate(shell_ctx->fw[0],&work1);CHKERRQ(ierr);
157     ierr = VecDuplicate(shell_ctx->fw[0],&work2);CHKERRQ(ierr);
158     ierr = KSPCreate(PETSC_COMM_SELF,&check_ksp);CHKERRQ(ierr);
159     if (local_mat->spd) {
160       ierr = KSPSetType(check_ksp,KSPCG);CHKERRQ(ierr);
161     }
162     ierr = PetscObjectIncrementTabLevel((PetscObject)check_ksp,(PetscObject)local_ksp,0);CHKERRQ(ierr);
163     ierr = KSPGetOptionsPrefix(local_ksp,&prefix);CHKERRQ(ierr);
164     ierr = KSPSetOptionsPrefix(check_ksp,prefix);CHKERRQ(ierr);
165     ierr = KSPAppendOptionsPrefix(check_ksp,"approximate_scale_");CHKERRQ(ierr);
166     ierr = KSPSetErrorIfNotConverged(check_ksp,PETSC_FALSE);CHKERRQ(ierr);
167     ierr = KSPSetOperators(check_ksp,local_mat,local_pmat);CHKERRQ(ierr);
168     ierr = KSPSetComputeSingularValues(check_ksp,PETSC_TRUE);CHKERRQ(ierr);
169     ierr = KSPSetPreSolve(check_ksp,PCBDDCNullSpaceCorrPreSolve,shell_ctx);CHKERRQ(ierr);
170     ierr = KSPSetPostSolve(check_ksp,PCBDDCNullSpaceCorrPostSolve,shell_ctx);CHKERRQ(ierr);
171     ierr = KSPSetTolerances(check_ksp,PETSC_SMALL,PETSC_SMALL,PETSC_DEFAULT,PETSC_DEFAULT);CHKERRQ(ierr);
172     ierr = KSPSetFromOptions(check_ksp);CHKERRQ(ierr);
173     /* setup with default maxit, then set maxit to min(10,any_set_from_command_line) (bug in computing eigenvalues when chaning the number of iterations */
174     ierr = KSPSetUp(check_ksp);CHKERRQ(ierr);
175     ierr = KSPGetPC(local_ksp,&local_pc);CHKERRQ(ierr);
176     ierr = KSPSetPC(check_ksp,local_pc);CHKERRQ(ierr);
177     ierr = KSPGetTolerances(check_ksp,NULL,NULL,NULL,&maxit);CHKERRQ(ierr);
178     ierr = KSPSetTolerances(check_ksp,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,PetscMin(10,maxit));CHKERRQ(ierr);
179     ierr = VecSetRandom(work2,NULL);CHKERRQ(ierr);
180     ierr = MatMult(local_mat,work2,work1);CHKERRQ(ierr);
181     ierr = KSPSolve(check_ksp,work1,work1);CHKERRQ(ierr);
182     ierr = KSPCheckSolve(check_ksp,pc,work1);CHKERRQ(ierr);
183     ierr = VecAXPY(work1,-1.,work2);CHKERRQ(ierr);
184     ierr = VecNorm(work1,NORM_INFINITY,&test_err);CHKERRQ(ierr);
185     ierr = KSPComputeExtremeSingularValues(check_ksp,&lambda_max,&lambda_min);CHKERRQ(ierr);
186     ierr = KSPGetIterationNumber(check_ksp,&k);CHKERRQ(ierr);
187     if (pcbddc->dbg_flag) {
188       if (isdir) {
189         ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d infinity error for Dirichlet adapted solver (no scale) %1.14e (it %D, eigs %1.6e %1.6e)\n",PetscGlobalRank,test_err,k,lambda_min,lambda_max);CHKERRQ(ierr);
190       } else {
191         ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d infinity error for Neumann adapted solver (no scale) %1.14e (it %D, eigs %1.6e %1.6e)\n",PetscGlobalRank,test_err,k,lambda_min,lambda_max);CHKERRQ(ierr);
192       }
193     }
194     if (needscaling) shell_ctx->scale = 1.0/lambda_max;
195 
196     if (needscaling && pcbddc->dbg_flag) { /* test for scaling factor */
197       PC new_pc;
198 
199       ierr = VecSetRandom(work2,NULL);CHKERRQ(ierr);
200       ierr = MatMult(local_mat,work2,work1);CHKERRQ(ierr);
201       ierr = PCCreate(PetscObjectComm((PetscObject)check_ksp),&new_pc);CHKERRQ(ierr);
202       ierr = PCSetType(new_pc,PCKSP);CHKERRQ(ierr);
203       ierr = PCSetOperators(new_pc,local_mat,local_pmat);CHKERRQ(ierr);
204       ierr = PCKSPSetKSP(new_pc,local_ksp);CHKERRQ(ierr);
205       ierr = KSPSetPC(check_ksp,new_pc);CHKERRQ(ierr);
206       ierr = PCDestroy(&new_pc);CHKERRQ(ierr);
207       ierr = KSPSetTolerances(check_ksp,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,maxit);CHKERRQ(ierr);
208       ierr = KSPSetPreSolve(check_ksp,NULL,NULL);CHKERRQ(ierr);
209       ierr = KSPSetPostSolve(check_ksp,NULL,NULL);CHKERRQ(ierr);
210       ierr = KSPSolve(check_ksp,work1,work1);CHKERRQ(ierr);
211       ierr = KSPCheckSolve(check_ksp,pc,work1);CHKERRQ(ierr);
212       ierr = VecAXPY(work1,-1.,work2);CHKERRQ(ierr);
213       ierr = VecNorm(work1,NORM_INFINITY,&test_err);CHKERRQ(ierr);
214       ierr = KSPComputeExtremeSingularValues(check_ksp,&lambda_max,&lambda_min);CHKERRQ(ierr);
215       ierr = KSPGetIterationNumber(check_ksp,&k);CHKERRQ(ierr);
216       if (pcbddc->dbg_flag) {
217         if (isdir) {
218           ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d infinity error for Dirichlet adapted solver (scale %g) %1.14e (it %D, eigs %1.6e %1.6e)\n",PetscGlobalRank,(double)PetscRealPart(shell_ctx->scale),test_err,k,lambda_min,lambda_max);CHKERRQ(ierr);
219         } else {
220           ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d infinity error for Neumann adapted solver (scale %g) %1.14e (it %D, eigs %1.6e %1.6e)\n",PetscGlobalRank,(double)PetscRealPart(shell_ctx->scale),test_err,k,lambda_min,lambda_max);CHKERRQ(ierr);
221         }
222       }
223     }
224     ierr = KSPDestroy(&check_ksp);CHKERRQ(ierr);
225     ierr = VecDestroy(&work1);CHKERRQ(ierr);
226     ierr = VecDestroy(&work2);CHKERRQ(ierr);
227   }
228   ierr = PetscLogEventEnd(PC_BDDC_ApproxSetUp[pcbddc->current_level],pc,0,0,0);CHKERRQ(ierr);
229 
230   if (pcbddc->dbg_flag) {
231     Vec       work1,work2,work3;
232     PetscReal test_err;
233 
234     /* check nullspace basis is solved exactly */
235     ierr = VecDuplicate(shell_ctx->fw[0],&work1);CHKERRQ(ierr);
236     ierr = VecDuplicate(shell_ctx->fw[0],&work2);CHKERRQ(ierr);
237     ierr = VecDuplicate(shell_ctx->fw[0],&work3);CHKERRQ(ierr);
238     ierr = VecSetRandom(shell_ctx->sw[0],NULL);CHKERRQ(ierr);
239     ierr = MatMult(shell_ctx->basis_mat,shell_ctx->sw[0],work1);CHKERRQ(ierr);
240     ierr = VecCopy(work1,work2);CHKERRQ(ierr);
241     ierr = MatMult(local_mat,work1,work3);CHKERRQ(ierr);
242     ierr = KSPSolve(local_ksp,work3,work1);CHKERRQ(ierr);
243     ierr = VecAXPY(work1,-1.,work2);CHKERRQ(ierr);
244     ierr = VecNorm(work1,NORM_INFINITY,&test_err);CHKERRQ(ierr);
245     if (isdir) {
246       ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d infinity error for Dirichlet nullspace correction solver: %1.14e\n",PetscGlobalRank,test_err);CHKERRQ(ierr);
247     } else {
248       ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d infinity error for Neumann nullspace correction solver: %1.14e\n",PetscGlobalRank,test_err);CHKERRQ(ierr);
249     }
250     ierr = VecDestroy(&work1);CHKERRQ(ierr);
251     ierr = VecDestroy(&work2);CHKERRQ(ierr);
252     ierr = VecDestroy(&work3);CHKERRQ(ierr);
253   }
254   PetscFunctionReturn(0);
255 }
256