xref: /petsc/src/ksp/pc/impls/is/pcis.c (revision dcf908cab9b0ea5e30ac5791f6aa2fcfe1440bec)
1 
2 #include <../src/ksp/pc/impls/is/pcis.h> /*I "petscpc.h" I*/
3 
4 static PetscErrorCode PCISSetUseStiffnessScaling_IS(PC pc, PetscBool use)
5 {
6   PC_IS *pcis = (PC_IS*)pc->data;
7 
8   PetscFunctionBegin;
9   pcis->use_stiffness_scaling = use;
10   PetscFunctionReturn(0);
11 }
12 
13 /*@
14  PCISSetUseStiffnessScaling - Tells PCIS to construct partition of unity using
15                               local matrices' diagonal.
16 
17    Not collective
18 
19    Input Parameters:
20 +  pc - the preconditioning context
21 -  use - whether or not pcis use matrix diagonal to build partition of unity.
22 
23    Level: intermediate
24 
25    Notes:
26 
27 .seealso: PCBDDC
28 @*/
29 PetscErrorCode PCISSetUseStiffnessScaling(PC pc, PetscBool use)
30 {
31   PetscErrorCode ierr;
32 
33   PetscFunctionBegin;
34   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
35   ierr = PetscTryMethod(pc,"PCISSetUseStiffnessScaling_C",(PC,PetscBool),(pc,use));CHKERRQ(ierr);
36   PetscFunctionReturn(0);
37 }
38 
39 static PetscErrorCode PCISSetSubdomainDiagonalScaling_IS(PC pc, Vec scaling_factors)
40 {
41   PetscErrorCode ierr;
42   PC_IS          *pcis = (PC_IS*)pc->data;
43 
44   PetscFunctionBegin;
45   ierr    = PetscObjectReference((PetscObject)scaling_factors);CHKERRQ(ierr);
46   ierr    = VecDestroy(&pcis->D);CHKERRQ(ierr);
47   pcis->D = scaling_factors;
48   PetscFunctionReturn(0);
49 }
50 
51 /*@
52  PCISSetSubdomainDiagonalScaling - Set diagonal scaling for PCIS.
53 
54    Not collective
55 
56    Input Parameters:
57 +  pc - the preconditioning context
58 -  scaling_factors - scaling factors for the subdomain
59 
60    Level: intermediate
61 
62    Notes:
63    Intended to use with jumping coefficients cases.
64 
65 .seealso: PCBDDC
66 @*/
67 PetscErrorCode PCISSetSubdomainDiagonalScaling(PC pc, Vec scaling_factors)
68 {
69   PetscErrorCode ierr;
70 
71   PetscFunctionBegin;
72   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
73   ierr = PetscTryMethod(pc,"PCISSetSubdomainDiagonalScaling_C",(PC,Vec),(pc,scaling_factors));CHKERRQ(ierr);
74   PetscFunctionReturn(0);
75 }
76 
77 static PetscErrorCode PCISSetSubdomainScalingFactor_IS(PC pc, PetscScalar scal)
78 {
79   PC_IS *pcis = (PC_IS*)pc->data;
80 
81   PetscFunctionBegin;
82   pcis->scaling_factor = scal;
83   PetscFunctionReturn(0);
84 }
85 
86 /*@
87  PCISSetSubdomainScalingFactor - Set scaling factor for PCIS.
88 
89    Not collective
90 
91    Input Parameters:
92 +  pc - the preconditioning context
93 -  scal - scaling factor for the subdomain
94 
95    Level: intermediate
96 
97    Notes:
98    Intended to use with jumping coefficients cases.
99 
100 .seealso: PCBDDC
101 @*/
102 PetscErrorCode PCISSetSubdomainScalingFactor(PC pc, PetscScalar scal)
103 {
104   PetscErrorCode ierr;
105 
106   PetscFunctionBegin;
107   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
108   ierr = PetscTryMethod(pc,"PCISSetSubdomainScalingFactor_C",(PC,PetscScalar),(pc,scal));CHKERRQ(ierr);
109   PetscFunctionReturn(0);
110 }
111 
112 
113 /* -------------------------------------------------------------------------- */
114 /*
115    PCISSetUp -
116 */
117 PetscErrorCode  PCISSetUp(PC pc, PetscBool computematrices, PetscBool computesolvers)
118 {
119   PC_IS          *pcis  = (PC_IS*)(pc->data);
120   Mat_IS         *matis;
121   MatReuse       reuse;
122   PetscErrorCode ierr;
123   PetscBool      flg,issbaij;
124 
125   PetscFunctionBegin;
126   ierr = PetscObjectTypeCompare((PetscObject)pc->pmat,MATIS,&flg);CHKERRQ(ierr);
127   if (!flg) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONG,"Preconditioner type of Neumann Neumman requires matrix of type MATIS");
128   matis = (Mat_IS*)pc->pmat->data;
129 
130   /* first time creation, get info on substructuring */
131   if (!pc->setupcalled) {
132     PetscInt    n_I;
133     PetscInt    *idx_I_local,*idx_B_local,*idx_I_global,*idx_B_global;
134     PetscBT     bt;
135     PetscInt    i,j;
136 
137     /* get info on mapping */
138     ierr = PetscObjectReference((PetscObject)pc->pmat->rmap->mapping);CHKERRQ(ierr);
139     ierr = ISLocalToGlobalMappingDestroy(&pcis->mapping);CHKERRQ(ierr);
140     pcis->mapping = pc->pmat->rmap->mapping;
141     ierr = ISLocalToGlobalMappingGetSize(pcis->mapping,&pcis->n);CHKERRQ(ierr);
142     ierr = ISLocalToGlobalMappingGetInfo(pcis->mapping,&(pcis->n_neigh),&(pcis->neigh),&(pcis->n_shared),&(pcis->shared));CHKERRQ(ierr);
143 
144     /* Identifying interior and interface nodes, in local numbering */
145     ierr = PetscBTCreate(pcis->n,&bt);CHKERRQ(ierr);
146     for (i=0;i<pcis->n_neigh;i++)
147       for (j=0;j<pcis->n_shared[i];j++) {
148           ierr = PetscBTSet(bt,pcis->shared[i][j]);CHKERRQ(ierr);
149       }
150 
151     /* Creating local and global index sets for interior and inteface nodes. */
152     ierr = PetscMalloc1(pcis->n,&idx_I_local);CHKERRQ(ierr);
153     ierr = PetscMalloc1(pcis->n,&idx_B_local);CHKERRQ(ierr);
154     for (i=0, pcis->n_B=0, n_I=0; i<pcis->n; i++) {
155       if (!PetscBTLookup(bt,i)) {
156         idx_I_local[n_I] = i;
157         n_I++;
158       } else {
159         idx_B_local[pcis->n_B] = i;
160         pcis->n_B++;
161       }
162     }
163 
164     /* Getting the global numbering */
165     idx_B_global = idx_I_local + n_I; /* Just avoiding allocating extra memory, since we have vacant space */
166     idx_I_global = idx_B_local + pcis->n_B;
167     ierr         = ISLocalToGlobalMappingApply(pcis->mapping,pcis->n_B,idx_B_local,idx_B_global);CHKERRQ(ierr);
168     ierr         = ISLocalToGlobalMappingApply(pcis->mapping,n_I,idx_I_local,idx_I_global);CHKERRQ(ierr);
169 
170     /* Creating the index sets */
171     ierr = ISCreateGeneral(PETSC_COMM_SELF,pcis->n_B,idx_B_local,PETSC_COPY_VALUES, &pcis->is_B_local);CHKERRQ(ierr);
172     ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pc),pcis->n_B,idx_B_global,PETSC_COPY_VALUES,&pcis->is_B_global);CHKERRQ(ierr);
173     ierr = ISCreateGeneral(PETSC_COMM_SELF,n_I,idx_I_local,PETSC_COPY_VALUES, &pcis->is_I_local);CHKERRQ(ierr);
174     ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pc),n_I,idx_I_global,PETSC_COPY_VALUES,&pcis->is_I_global);CHKERRQ(ierr);
175 
176     /* Freeing memory */
177     ierr = PetscFree(idx_B_local);CHKERRQ(ierr);
178     ierr = PetscFree(idx_I_local);CHKERRQ(ierr);
179     ierr = PetscBTDestroy(&bt);CHKERRQ(ierr);
180 
181     /* Creating work vectors and arrays */
182     ierr = VecDuplicate(matis->x,&pcis->vec1_N);CHKERRQ(ierr);
183     ierr = VecDuplicate(pcis->vec1_N,&pcis->vec2_N);CHKERRQ(ierr);
184     ierr = VecCreate(PETSC_COMM_SELF,&pcis->vec1_D);CHKERRQ(ierr);
185     ierr = VecSetSizes(pcis->vec1_D,pcis->n-pcis->n_B,PETSC_DECIDE);CHKERRQ(ierr);
186     ierr = VecSetType(pcis->vec1_D,((PetscObject)pcis->vec1_N)->type_name);CHKERRQ(ierr);
187     ierr = VecDuplicate(pcis->vec1_D,&pcis->vec2_D);CHKERRQ(ierr);
188     ierr = VecDuplicate(pcis->vec1_D,&pcis->vec3_D);CHKERRQ(ierr);
189     ierr = VecDuplicate(pcis->vec1_D,&pcis->vec4_D);CHKERRQ(ierr);
190     ierr = VecCreate(PETSC_COMM_SELF,&pcis->vec1_B);CHKERRQ(ierr);
191     ierr = VecSetSizes(pcis->vec1_B,pcis->n_B,PETSC_DECIDE);CHKERRQ(ierr);
192     ierr = VecSetType(pcis->vec1_B,((PetscObject)pcis->vec1_N)->type_name);CHKERRQ(ierr);
193     ierr = VecDuplicate(pcis->vec1_B,&pcis->vec2_B);CHKERRQ(ierr);
194     ierr = VecDuplicate(pcis->vec1_B,&pcis->vec3_B);CHKERRQ(ierr);
195     ierr = MatCreateVecs(pc->pmat,&pcis->vec1_global,0);CHKERRQ(ierr);
196     ierr = PetscMalloc1(pcis->n,&pcis->work_N);CHKERRQ(ierr);
197     /* scaling vector */
198     if (!pcis->D) { /* it can happen that the user passed in a scaling vector via PCISSetSubdomainDiagonalScaling */
199       ierr = VecDuplicate(pcis->vec1_B,&pcis->D);CHKERRQ(ierr);
200       ierr = VecSet(pcis->D,pcis->scaling_factor);CHKERRQ(ierr);
201     }
202 
203     /* Creating the scatter contexts */
204     ierr = VecScatterCreate(pcis->vec1_N,pcis->is_I_local,pcis->vec1_D,(IS)0,&pcis->N_to_D);CHKERRQ(ierr);
205     ierr = VecScatterCreate(pcis->vec1_global,pcis->is_I_global,pcis->vec1_D,(IS)0,&pcis->global_to_D);CHKERRQ(ierr);
206     ierr = VecScatterCreate(pcis->vec1_N,pcis->is_B_local,pcis->vec1_B,(IS)0,&pcis->N_to_B);CHKERRQ(ierr);
207     ierr = VecScatterCreate(pcis->vec1_global,pcis->is_B_global,pcis->vec1_B,(IS)0,&pcis->global_to_B);CHKERRQ(ierr);
208 
209     /* map from boundary to local */
210     ierr = ISLocalToGlobalMappingCreateIS(pcis->is_B_local,&pcis->BtoNmap);CHKERRQ(ierr);
211   }
212 
213   /*
214     Extracting the blocks A_II, A_BI, A_IB and A_BB from A. If the numbering
215     is such that interior nodes come first than the interface ones, we have
216 
217         [ A_II | A_IB ]
218     A = [------+------]
219         [ A_BI | A_BB ]
220   */
221   if (computematrices) {
222     reuse = MAT_INITIAL_MATRIX;
223     if (pcis->reusesubmatrices && pc->setupcalled) {
224       if (pc->flag == SAME_NONZERO_PATTERN) {
225         reuse = MAT_REUSE_MATRIX;
226       } else {
227         reuse = MAT_INITIAL_MATRIX;
228       }
229     }
230     if (reuse == MAT_INITIAL_MATRIX) {
231       ierr = MatDestroy(&pcis->A_II);CHKERRQ(ierr);
232       ierr = MatDestroy(&pcis->A_IB);CHKERRQ(ierr);
233       ierr = MatDestroy(&pcis->A_BI);CHKERRQ(ierr);
234       ierr = MatDestroy(&pcis->A_BB);CHKERRQ(ierr);
235     }
236 
237     ierr = MatCreateSubMatrix(matis->A,pcis->is_I_local,pcis->is_I_local,reuse,&pcis->A_II);CHKERRQ(ierr);
238     ierr = MatCreateSubMatrix(matis->A,pcis->is_B_local,pcis->is_B_local,reuse,&pcis->A_BB);CHKERRQ(ierr);
239     ierr = PetscObjectTypeCompare((PetscObject)matis->A,MATSEQSBAIJ,&issbaij);CHKERRQ(ierr);
240     if (!issbaij) {
241       ierr = MatCreateSubMatrix(matis->A,pcis->is_I_local,pcis->is_B_local,reuse,&pcis->A_IB);CHKERRQ(ierr);
242       ierr = MatCreateSubMatrix(matis->A,pcis->is_B_local,pcis->is_I_local,reuse,&pcis->A_BI);CHKERRQ(ierr);
243     } else {
244       Mat newmat;
245 
246       ierr = MatConvert(matis->A,MATSEQBAIJ,MAT_INITIAL_MATRIX,&newmat);CHKERRQ(ierr);
247       ierr = MatCreateSubMatrix(newmat,pcis->is_I_local,pcis->is_B_local,reuse,&pcis->A_IB);CHKERRQ(ierr);
248       ierr = MatCreateSubMatrix(newmat,pcis->is_B_local,pcis->is_I_local,reuse,&pcis->A_BI);CHKERRQ(ierr);
249       ierr = MatDestroy(&newmat);CHKERRQ(ierr);
250     }
251   }
252 
253   /* Creating scaling vector D */
254   ierr = PetscOptionsGetBool(((PetscObject)pc)->options,((PetscObject)pc)->prefix,"-pc_is_use_stiffness_scaling",&pcis->use_stiffness_scaling,NULL);CHKERRQ(ierr);
255   if (pcis->use_stiffness_scaling) {
256     PetscScalar *a;
257     PetscInt    i,n;
258 
259     if (pcis->A_BB) {
260       ierr = MatGetDiagonal(pcis->A_BB,pcis->D);CHKERRQ(ierr);
261     } else {
262       ierr = MatGetDiagonal(matis->A,pcis->vec1_N);CHKERRQ(ierr);
263       ierr = VecScatterBegin(pcis->N_to_D,pcis->vec1_N,pcis->D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
264       ierr = VecScatterEnd(pcis->N_to_D,pcis->vec1_N,pcis->D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
265     }
266     ierr = VecGetLocalSize(pcis->D,&n);CHKERRQ(ierr);
267     ierr = VecGetArray(pcis->D,&a);CHKERRQ(ierr);
268     for (i=0;i<n;i++) if (PetscAbsScalar(a[i])<PETSC_SMALL) a[i] = 1.0;
269     ierr = VecRestoreArray(pcis->D,&a);CHKERRQ(ierr);
270   }
271   ierr = VecScatterBegin(pcis->N_to_B,matis->counter,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
272   ierr = VecScatterEnd(pcis->N_to_B,matis->counter,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
273   ierr = VecPointwiseDivide(pcis->D,pcis->D,pcis->vec1_B);CHKERRQ(ierr);
274 
275   /* See historical note 01, at the bottom of this file. */
276 
277   /* Creating the KSP contexts for the local Dirichlet and Neumann problems */
278   if (computesolvers) {
279     PC pc_ctx;
280 
281     pcis->pure_neumann = matis->pure_neumann;
282     /* Dirichlet */
283     ierr = KSPCreate(PETSC_COMM_SELF,&pcis->ksp_D);CHKERRQ(ierr);
284     ierr = KSPSetErrorIfNotConverged(pcis->ksp_D,pc->erroriffailure);CHKERRQ(ierr);
285     ierr = PetscObjectIncrementTabLevel((PetscObject)pcis->ksp_D,(PetscObject)pc,1);CHKERRQ(ierr);
286     ierr = KSPSetOperators(pcis->ksp_D,pcis->A_II,pcis->A_II);CHKERRQ(ierr);
287     ierr = KSPSetOptionsPrefix(pcis->ksp_D,"is_localD_");CHKERRQ(ierr);
288     ierr = KSPGetPC(pcis->ksp_D,&pc_ctx);CHKERRQ(ierr);
289     ierr = PCSetType(pc_ctx,PCLU);CHKERRQ(ierr);
290     ierr = KSPSetType(pcis->ksp_D,KSPPREONLY);CHKERRQ(ierr);
291     ierr = KSPSetFromOptions(pcis->ksp_D);CHKERRQ(ierr);
292     /* the vectors in the following line are dummy arguments, just telling the KSP the vector size. Values are not used */
293     ierr = KSPSetUp(pcis->ksp_D);CHKERRQ(ierr);
294     /* Neumann */
295     ierr = KSPCreate(PETSC_COMM_SELF,&pcis->ksp_N);CHKERRQ(ierr);
296     ierr = KSPSetErrorIfNotConverged(pcis->ksp_N,pc->erroriffailure);CHKERRQ(ierr);
297     ierr = PetscObjectIncrementTabLevel((PetscObject)pcis->ksp_N,(PetscObject)pc,1);CHKERRQ(ierr);
298     ierr = KSPSetOperators(pcis->ksp_N,matis->A,matis->A);CHKERRQ(ierr);
299     ierr = KSPSetOptionsPrefix(pcis->ksp_N,"is_localN_");CHKERRQ(ierr);
300     ierr = KSPGetPC(pcis->ksp_N,&pc_ctx);CHKERRQ(ierr);
301     ierr = PCSetType(pc_ctx,PCLU);CHKERRQ(ierr);
302     ierr = KSPSetType(pcis->ksp_N,KSPPREONLY);CHKERRQ(ierr);
303     ierr = KSPSetFromOptions(pcis->ksp_N);CHKERRQ(ierr);
304     {
305       PetscBool damp_fixed                    = PETSC_FALSE,
306                 remove_nullspace_fixed        = PETSC_FALSE,
307                 set_damping_factor_floating   = PETSC_FALSE,
308                 not_damp_floating             = PETSC_FALSE,
309                 not_remove_nullspace_floating = PETSC_FALSE;
310       PetscReal fixed_factor,
311                 floating_factor;
312 
313       ierr = PetscOptionsGetReal(((PetscObject)pc_ctx)->options,((PetscObject)pc_ctx)->prefix,"-pc_is_damp_fixed",&fixed_factor,&damp_fixed);CHKERRQ(ierr);
314       if (!damp_fixed) fixed_factor = 0.0;
315       ierr = PetscOptionsGetBool(((PetscObject)pc_ctx)->options,((PetscObject)pc_ctx)->prefix,"-pc_is_damp_fixed",&damp_fixed,NULL);CHKERRQ(ierr);
316 
317       ierr = PetscOptionsGetBool(((PetscObject)pc_ctx)->options,((PetscObject)pc_ctx)->prefix,"-pc_is_remove_nullspace_fixed",&remove_nullspace_fixed,NULL);CHKERRQ(ierr);
318 
319       ierr = PetscOptionsGetReal(((PetscObject)pc_ctx)->options,((PetscObject)pc_ctx)->prefix,"-pc_is_set_damping_factor_floating",
320                               &floating_factor,&set_damping_factor_floating);CHKERRQ(ierr);
321       if (!set_damping_factor_floating) floating_factor = 0.0;
322       ierr = PetscOptionsGetBool(((PetscObject)pc_ctx)->options,((PetscObject)pc_ctx)->prefix,"-pc_is_set_damping_factor_floating",&set_damping_factor_floating,NULL);CHKERRQ(ierr);
323       if (!set_damping_factor_floating) floating_factor = 1.e-12;
324 
325       ierr = PetscOptionsGetBool(((PetscObject)pc_ctx)->options,((PetscObject)pc_ctx)->prefix,"-pc_is_not_damp_floating",&not_damp_floating,NULL);CHKERRQ(ierr);
326 
327       ierr = PetscOptionsGetBool(((PetscObject)pc_ctx)->options,((PetscObject)pc_ctx)->prefix,"-pc_is_not_remove_nullspace_floating",&not_remove_nullspace_floating,NULL);CHKERRQ(ierr);
328 
329       if (pcis->pure_neumann) {  /* floating subdomain */
330         if (!(not_damp_floating)) {
331           ierr = PCFactorSetShiftType(pc_ctx,MAT_SHIFT_NONZERO);CHKERRQ(ierr);
332           ierr = PCFactorSetShiftAmount(pc_ctx,floating_factor);CHKERRQ(ierr);
333         }
334         if (!(not_remove_nullspace_floating)) {
335           MatNullSpace nullsp;
336           ierr = MatNullSpaceCreate(PETSC_COMM_SELF,PETSC_TRUE,0,NULL,&nullsp);CHKERRQ(ierr);
337           ierr = MatSetNullSpace(matis->A,nullsp);CHKERRQ(ierr);
338           ierr = MatNullSpaceDestroy(&nullsp);CHKERRQ(ierr);
339         }
340       } else {  /* fixed subdomain */
341         if (damp_fixed) {
342           ierr = PCFactorSetShiftType(pc_ctx,MAT_SHIFT_NONZERO);CHKERRQ(ierr);
343           ierr = PCFactorSetShiftAmount(pc_ctx,floating_factor);CHKERRQ(ierr);
344         }
345         if (remove_nullspace_fixed) {
346           MatNullSpace nullsp;
347           ierr = MatNullSpaceCreate(PETSC_COMM_SELF,PETSC_TRUE,0,NULL,&nullsp);CHKERRQ(ierr);
348           ierr = MatSetNullSpace(matis->A,nullsp);CHKERRQ(ierr);
349           ierr = MatNullSpaceDestroy(&nullsp);CHKERRQ(ierr);
350         }
351       }
352     }
353     /* the vectors in the following line are dummy arguments, just telling the KSP the vector size. Values are not used */
354     ierr = KSPSetUp(pcis->ksp_N);CHKERRQ(ierr);
355   }
356   PetscFunctionReturn(0);
357 }
358 
359 /* -------------------------------------------------------------------------- */
360 /*
361    PCISDestroy -
362 */
363 PetscErrorCode  PCISDestroy(PC pc)
364 {
365   PC_IS          *pcis = (PC_IS*)(pc->data);
366   PetscErrorCode ierr;
367 
368   PetscFunctionBegin;
369   ierr = ISDestroy(&pcis->is_B_local);CHKERRQ(ierr);
370   ierr = ISDestroy(&pcis->is_I_local);CHKERRQ(ierr);
371   ierr = ISDestroy(&pcis->is_B_global);CHKERRQ(ierr);
372   ierr = ISDestroy(&pcis->is_I_global);CHKERRQ(ierr);
373   ierr = MatDestroy(&pcis->A_II);CHKERRQ(ierr);
374   ierr = MatDestroy(&pcis->A_IB);CHKERRQ(ierr);
375   ierr = MatDestroy(&pcis->A_BI);CHKERRQ(ierr);
376   ierr = MatDestroy(&pcis->A_BB);CHKERRQ(ierr);
377   ierr = VecDestroy(&pcis->D);CHKERRQ(ierr);
378   ierr = KSPDestroy(&pcis->ksp_N);CHKERRQ(ierr);
379   ierr = KSPDestroy(&pcis->ksp_D);CHKERRQ(ierr);
380   ierr = VecDestroy(&pcis->vec1_N);CHKERRQ(ierr);
381   ierr = VecDestroy(&pcis->vec2_N);CHKERRQ(ierr);
382   ierr = VecDestroy(&pcis->vec1_D);CHKERRQ(ierr);
383   ierr = VecDestroy(&pcis->vec2_D);CHKERRQ(ierr);
384   ierr = VecDestroy(&pcis->vec3_D);CHKERRQ(ierr);
385   ierr = VecDestroy(&pcis->vec4_D);CHKERRQ(ierr);
386   ierr = VecDestroy(&pcis->vec1_B);CHKERRQ(ierr);
387   ierr = VecDestroy(&pcis->vec2_B);CHKERRQ(ierr);
388   ierr = VecDestroy(&pcis->vec3_B);CHKERRQ(ierr);
389   ierr = VecDestroy(&pcis->vec1_global);CHKERRQ(ierr);
390   ierr = VecScatterDestroy(&pcis->global_to_D);CHKERRQ(ierr);
391   ierr = VecScatterDestroy(&pcis->N_to_B);CHKERRQ(ierr);
392   ierr = VecScatterDestroy(&pcis->N_to_D);CHKERRQ(ierr);
393   ierr = VecScatterDestroy(&pcis->global_to_B);CHKERRQ(ierr);
394   ierr = PetscFree(pcis->work_N);CHKERRQ(ierr);
395   if (pcis->n_neigh > -1) {
396     ierr = ISLocalToGlobalMappingRestoreInfo(pcis->mapping,&(pcis->n_neigh),&(pcis->neigh),&(pcis->n_shared),&(pcis->shared));CHKERRQ(ierr);
397   }
398   ierr = ISLocalToGlobalMappingDestroy(&pcis->mapping);CHKERRQ(ierr);
399   ierr = ISLocalToGlobalMappingDestroy(&pcis->BtoNmap);CHKERRQ(ierr);
400   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCISSetUseStiffnessScaling_C",NULL);CHKERRQ(ierr);
401   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCISSetSubdomainScalingFactor_C",NULL);CHKERRQ(ierr);
402   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCISSetSubdomainDiagonalScaling_C",NULL);CHKERRQ(ierr);
403   PetscFunctionReturn(0);
404 }
405 
406 /* -------------------------------------------------------------------------- */
407 /*
408    PCISCreate -
409 */
410 PetscErrorCode  PCISCreate(PC pc)
411 {
412   PC_IS          *pcis = (PC_IS*)(pc->data);
413   PetscErrorCode ierr;
414 
415   PetscFunctionBegin;
416   pcis->n_neigh          = -1;
417   pcis->scaling_factor   = 1.0;
418   pcis->reusesubmatrices = PETSC_TRUE;
419   /* composing functions */
420   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCISSetUseStiffnessScaling_C",PCISSetUseStiffnessScaling_IS);CHKERRQ(ierr);
421   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCISSetSubdomainScalingFactor_C",PCISSetSubdomainScalingFactor_IS);CHKERRQ(ierr);
422   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCISSetSubdomainDiagonalScaling_C",PCISSetSubdomainDiagonalScaling_IS);CHKERRQ(ierr);
423   PetscFunctionReturn(0);
424 }
425 
426 /* -------------------------------------------------------------------------- */
427 /*
428    PCISApplySchur -
429 
430    Input parameters:
431 .  pc - preconditioner context
432 .  v - vector to which the Schur complement is to be applied (it is NOT modified inside this function, UNLESS vec2_B is null)
433 
434    Output parameters:
435 .  vec1_B - result of Schur complement applied to chunk
436 .  vec2_B - garbage (used as work space), or null (and v is used as workspace)
437 .  vec1_D - garbage (used as work space)
438 .  vec2_D - garbage (used as work space)
439 
440 */
441 PetscErrorCode  PCISApplySchur(PC pc, Vec v, Vec vec1_B, Vec vec2_B, Vec vec1_D, Vec vec2_D)
442 {
443   PetscErrorCode ierr;
444   PC_IS          *pcis = (PC_IS*)(pc->data);
445 
446   PetscFunctionBegin;
447   if (!vec2_B) vec2_B = v;
448 
449   ierr = MatMult(pcis->A_BB,v,vec1_B);CHKERRQ(ierr);
450   ierr = MatMult(pcis->A_IB,v,vec1_D);CHKERRQ(ierr);
451   ierr = KSPSolve(pcis->ksp_D,vec1_D,vec2_D);CHKERRQ(ierr);
452   ierr = MatMult(pcis->A_BI,vec2_D,vec2_B);CHKERRQ(ierr);
453   ierr = VecAXPY(vec1_B,-1.0,vec2_B);CHKERRQ(ierr);
454   PetscFunctionReturn(0);
455 }
456 
457 /* -------------------------------------------------------------------------- */
458 /*
459    PCISScatterArrayNToVecB - Scatters interface node values from a big array (of all local nodes, interior or interface,
460    including ghosts) into an interface vector, when in SCATTER_FORWARD mode, or vice-versa, when in SCATTER_REVERSE
461    mode.
462 
463    Input parameters:
464 .  pc - preconditioner context
465 .  array_N - [when in SCATTER_FORWARD mode] Array to be scattered into the vector
466 .  v_B - [when in SCATTER_REVERSE mode] Vector to be scattered into the array
467 
468    Output parameter:
469 .  array_N - [when in SCATTER_REVERSE mode] Array to receive the scattered vector
470 .  v_B - [when in SCATTER_FORWARD mode] Vector to receive the scattered array
471 
472    Notes:
473    The entries in the array that do not correspond to interface nodes remain unaltered.
474 */
475 PetscErrorCode  PCISScatterArrayNToVecB(PetscScalar *array_N, Vec v_B, InsertMode imode, ScatterMode smode, PC pc)
476 {
477   PetscInt       i;
478   const PetscInt *idex;
479   PetscErrorCode ierr;
480   PetscScalar    *array_B;
481   PC_IS          *pcis = (PC_IS*)(pc->data);
482 
483   PetscFunctionBegin;
484   ierr = VecGetArray(v_B,&array_B);CHKERRQ(ierr);
485   ierr = ISGetIndices(pcis->is_B_local,&idex);CHKERRQ(ierr);
486 
487   if (smode == SCATTER_FORWARD) {
488     if (imode == INSERT_VALUES) {
489       for (i=0; i<pcis->n_B; i++) array_B[i] = array_N[idex[i]];
490     } else {  /* ADD_VALUES */
491       for (i=0; i<pcis->n_B; i++) array_B[i] += array_N[idex[i]];
492     }
493   } else {  /* SCATTER_REVERSE */
494     if (imode == INSERT_VALUES) {
495       for (i=0; i<pcis->n_B; i++) array_N[idex[i]] = array_B[i];
496     } else {  /* ADD_VALUES */
497       for (i=0; i<pcis->n_B; i++) array_N[idex[i]] += array_B[i];
498     }
499   }
500   ierr = ISRestoreIndices(pcis->is_B_local,&idex);CHKERRQ(ierr);
501   ierr = VecRestoreArray(v_B,&array_B);CHKERRQ(ierr);
502   PetscFunctionReturn(0);
503 }
504 
505 /* -------------------------------------------------------------------------- */
506 /*
507    PCISApplyInvSchur - Solves the Neumann problem related to applying the inverse of the Schur complement.
508    More precisely, solves the problem:
509                                         [ A_II  A_IB ] [ . ]   [ 0 ]
510                                         [            ] [   ] = [   ]
511                                         [ A_BI  A_BB ] [ x ]   [ b ]
512 
513    Input parameters:
514 .  pc - preconditioner context
515 .  b - vector of local interface nodes (including ghosts)
516 
517    Output parameters:
518 .  x - vector of local interface nodes (including ghosts); returns the application of the inverse of the Schur
519        complement to b
520 .  vec1_N - vector of local nodes (interior and interface, including ghosts); returns garbage (used as work space)
521 .  vec2_N - vector of local nodes (interior and interface, including ghosts); returns garbage (used as work space)
522 
523 */
524 PetscErrorCode  PCISApplyInvSchur(PC pc, Vec b, Vec x, Vec vec1_N, Vec vec2_N)
525 {
526   PetscErrorCode ierr;
527   PC_IS          *pcis = (PC_IS*)(pc->data);
528 
529   PetscFunctionBegin;
530   /*
531     Neumann solvers.
532     Applying the inverse of the local Schur complement, i.e, solving a Neumann
533     Problem with zero at the interior nodes of the RHS and extracting the interface
534     part of the solution. inverse Schur complement is applied to b and the result
535     is stored in x.
536   */
537   /* Setting the RHS vec1_N */
538   ierr = VecSet(vec1_N,0.0);CHKERRQ(ierr);
539   ierr = VecScatterBegin(pcis->N_to_B,b,vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
540   ierr = VecScatterEnd  (pcis->N_to_B,b,vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
541   /* Checking for consistency of the RHS */
542   {
543     PetscBool flg = PETSC_FALSE;
544     ierr = PetscOptionsGetBool(NULL,NULL,"-pc_is_check_consistency",&flg,NULL);CHKERRQ(ierr);
545     if (flg) {
546       PetscScalar average;
547       PetscViewer viewer;
548       ierr = PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject)pc),&viewer);CHKERRQ(ierr);
549 
550       ierr    = VecSum(vec1_N,&average);CHKERRQ(ierr);
551       average = average / ((PetscReal)pcis->n);
552       ierr    = PetscViewerASCIIPushSynchronized(viewer);CHKERRQ(ierr);
553       if (pcis->pure_neumann) {
554         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Subdomain %04d is floating. Average = % 1.14e\n",PetscGlobalRank,PetscAbsScalar(average));CHKERRQ(ierr);
555       } else {
556         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Subdomain %04d is fixed.    Average = % 1.14e\n",PetscGlobalRank,PetscAbsScalar(average));CHKERRQ(ierr);
557       }
558       ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
559       ierr = PetscViewerASCIIPopSynchronized(viewer);CHKERRQ(ierr);
560     }
561   }
562   /* Solving the system for vec2_N */
563   ierr = KSPSolve(pcis->ksp_N,vec1_N,vec2_N);CHKERRQ(ierr);
564   /* Extracting the local interface vector out of the solution */
565   ierr = VecScatterBegin(pcis->N_to_B,vec2_N,x,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
566   ierr = VecScatterEnd  (pcis->N_to_B,vec2_N,x,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
567   PetscFunctionReturn(0);
568 }
569