xref: /petsc/src/ksp/pc/impls/bddc/bddcfetidp.c (revision 022d8d2b5c651790d2b3588a625532f536c90c5e) 
1 #include <../src/ksp/pc/impls/bddc/bddc.h>
2 #include <../src/ksp/pc/impls/bddc/bddcprivate.h>
3 
4 #undef __FUNCT__
5 #define __FUNCT__ "PCBDDCCreateFETIDPMatContext"
6 PetscErrorCode PCBDDCCreateFETIDPMatContext(PC pc, FETIDPMat_ctx *fetidpmat_ctx)
7 {
8   FETIDPMat_ctx  newctx;
9   PetscErrorCode ierr;
10 
11   PetscFunctionBegin;
12   ierr = PetscNew(&newctx);CHKERRQ(ierr);
13   /* increase the reference count for BDDC preconditioner */
14   ierr = PetscObjectReference((PetscObject)pc);CHKERRQ(ierr);
15   newctx->pc              = pc;
16   *fetidpmat_ctx          = newctx;
17   PetscFunctionReturn(0);
18 }
19 
20 #undef __FUNCT__
21 #define __FUNCT__ "PCBDDCCreateFETIDPPCContext"
22 PetscErrorCode PCBDDCCreateFETIDPPCContext(PC pc, FETIDPPC_ctx *fetidppc_ctx)
23 {
24   FETIDPPC_ctx   newctx;
25   PetscErrorCode ierr;
26 
27   PetscFunctionBegin;
28   ierr = PetscNew(&newctx);CHKERRQ(ierr);
29   /* increase the reference count for BDDC preconditioner */
30   ierr = PetscObjectReference((PetscObject)pc);CHKERRQ(ierr);
31   newctx->pc              = pc;
32   *fetidppc_ctx           = newctx;
33   PetscFunctionReturn(0);
34 }
35 
36 #undef __FUNCT__
37 #define __FUNCT__ "PCBDDCDestroyFETIDPMat"
38 PetscErrorCode PCBDDCDestroyFETIDPMat(Mat A)
39 {
40   FETIDPMat_ctx  mat_ctx;
41   PetscErrorCode ierr;
42 
43   PetscFunctionBegin;
44   ierr = MatShellGetContext(A,(void**)&mat_ctx);CHKERRQ(ierr);
45   ierr = VecDestroy(&mat_ctx->lambda_local);CHKERRQ(ierr);
46   ierr = VecDestroy(&mat_ctx->temp_solution_D);CHKERRQ(ierr);
47   ierr = VecDestroy(&mat_ctx->temp_solution_B);CHKERRQ(ierr);
48   ierr = MatDestroy(&mat_ctx->B_delta);CHKERRQ(ierr);
49   ierr = MatDestroy(&mat_ctx->B_Ddelta);CHKERRQ(ierr);
50   ierr = MatDestroy(&mat_ctx->B_BB);CHKERRQ(ierr);
51   ierr = MatDestroy(&mat_ctx->B_BI);CHKERRQ(ierr);
52   ierr = MatDestroy(&mat_ctx->Bt_BB);CHKERRQ(ierr);
53   ierr = MatDestroy(&mat_ctx->Bt_BI);CHKERRQ(ierr);
54   ierr = MatDestroy(&mat_ctx->C);CHKERRQ(ierr);
55   ierr = VecDestroy(&mat_ctx->vP);CHKERRQ(ierr);
56   ierr = VecDestroy(&mat_ctx->xPg);CHKERRQ(ierr);
57   ierr = VecDestroy(&mat_ctx->yPg);CHKERRQ(ierr);
58   ierr = VecScatterDestroy(&mat_ctx->l2g_lambda);CHKERRQ(ierr);
59   ierr = VecScatterDestroy(&mat_ctx->l2g_p);CHKERRQ(ierr);
60   ierr = VecScatterDestroy(&mat_ctx->g2g_p);CHKERRQ(ierr);
61   ierr = PCDestroy(&mat_ctx->pc);CHKERRQ(ierr); /* decrease PCBDDC reference count */
62   ierr = PetscFree(mat_ctx);CHKERRQ(ierr);
63   PetscFunctionReturn(0);
64 }
65 
66 #undef __FUNCT__
67 #define __FUNCT__ "PCBDDCDestroyFETIDPPC"
68 PetscErrorCode PCBDDCDestroyFETIDPPC(PC pc)
69 {
70   FETIDPPC_ctx   pc_ctx;
71   PetscErrorCode ierr;
72 
73   PetscFunctionBegin;
74   ierr = PCShellGetContext(pc,(void**)&pc_ctx);CHKERRQ(ierr);
75   ierr = VecDestroy(&pc_ctx->lambda_local);CHKERRQ(ierr);
76   ierr = MatDestroy(&pc_ctx->B_Ddelta);CHKERRQ(ierr);
77   ierr = VecScatterDestroy(&pc_ctx->l2g_lambda);CHKERRQ(ierr);
78   ierr = MatDestroy(&pc_ctx->S_j);CHKERRQ(ierr);
79   ierr = PCDestroy(&pc_ctx->pc);CHKERRQ(ierr); /* decrease PCBDDC reference count */
80   ierr = KSPDestroy(&pc_ctx->kP);CHKERRQ(ierr);
81   ierr = VecDestroy(&pc_ctx->xPg);CHKERRQ(ierr);
82   ierr = VecDestroy(&pc_ctx->yPg);CHKERRQ(ierr);
83   ierr = PetscFree(pc_ctx);CHKERRQ(ierr);
84   PetscFunctionReturn(0);
85 }
86 
87 #undef __FUNCT__
88 #define __FUNCT__ "PCBDDCSetupFETIDPMatContext"
89 PetscErrorCode PCBDDCSetupFETIDPMatContext(FETIDPMat_ctx fetidpmat_ctx )
90 {
91   PetscErrorCode ierr;
92   PC_IS          *pcis=(PC_IS*)fetidpmat_ctx->pc->data;
93   PC_BDDC        *pcbddc=(PC_BDDC*)fetidpmat_ctx->pc->data;
94   PCBDDCGraph    mat_graph=pcbddc->mat_graph;
95   Mat_IS         *matis  = (Mat_IS*)fetidpmat_ctx->pc->pmat->data;
96   MPI_Comm       comm;
97   Mat            ScalingMat;
98   Vec            fetidp_global;
99   IS             IS_l2g_lambda;
100   IS             subset,subset_mult,subset_n;
101   PetscBool      skip_node,fully_redundant;
102   PetscInt       i,j,k,s,n_boundary_dofs,n_global_lambda,n_vertices,partial_sum;
103   PetscInt       cum,n_local_lambda,n_lambda_for_dof,dual_size,n_neg_values,n_pos_values;
104   PetscMPIInt    rank,size,buf_size,neigh;
105   PetscScalar    scalar_value;
106   PetscInt       *vertex_indices;
107   PetscInt       *dual_dofs_boundary_indices,*aux_local_numbering_1;
108   const PetscInt *aux_global_numbering;
109   PetscInt       *aux_sums,*cols_B_delta,*l2g_indices;
110   PetscScalar    *array,*scaling_factors,*vals_B_delta;
111   PetscInt       *aux_local_numbering_2;
112   PetscLayout    llay;
113   /* For communication of scaling factors */
114   PetscInt       *ptrs_buffer,neigh_position;
115   PetscScalar    **all_factors,*send_buffer,*recv_buffer;
116   MPI_Request    *send_reqs,*recv_reqs;
117   /* tests */
118   PetscBool      test_fetidp;
119   PetscViewer    viewer;
120   /* saddlepoint */
121   ISLocalToGlobalMapping l2gmap_p;
122   PetscLayout            play;
123   IS                     gP,pP;
124   PetscInt               nPl,nPg,nPgl;
125 
126   PetscFunctionBegin;
127   ierr = PetscObjectGetComm((PetscObject)(fetidpmat_ctx->pc),&comm);CHKERRQ(ierr);
128   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
129   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
130 
131   /* saddlepoint */
132   nPl      = 0;
133   nPg      = 0;
134   nPgl     = 0;
135   gP       = NULL;
136   pP       = NULL;
137   l2gmap_p = NULL;
138   play     = NULL;
139   ierr = PetscObjectQuery((PetscObject)fetidpmat_ctx->pc,"__KSPFETIDP_pP",(PetscObject*)&pP);CHKERRQ(ierr);
140   if (pP) { /* saddle point */
141     /* subdomain pressures in global numbering */
142     ierr = PetscObjectQuery((PetscObject)fetidpmat_ctx->pc,"__KSPFETIDP_gP",(PetscObject*)&gP);CHKERRQ(ierr);
143     if (!gP) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"gP not present");
144     ierr = ISGetLocalSize(gP,&nPl);CHKERRQ(ierr);
145     ierr = VecCreate(PETSC_COMM_SELF,&fetidpmat_ctx->vP);CHKERRQ(ierr);
146     ierr = VecSetSizes(fetidpmat_ctx->vP,nPl,nPl);CHKERRQ(ierr);
147     ierr = VecSetType(fetidpmat_ctx->vP,VECSTANDARD);CHKERRQ(ierr);
148     ierr = VecSetUp(fetidpmat_ctx->vP);CHKERRQ(ierr);
149 
150     /* interface pressure matrix */
151     ierr = PetscObjectQuery((PetscObject)fetidpmat_ctx->pc,"__KSPFETIDP_C",(PetscObject*)&fetidpmat_ctx->C);CHKERRQ(ierr);
152     if (!fetidpmat_ctx->C) { /* null pressure block, compute layout and global numbering for interface pressures */
153       IS Pg;
154 
155       ierr = ISRenumber(gP,NULL,&nPg,&Pg);CHKERRQ(ierr);
156       ierr = ISLocalToGlobalMappingCreateIS(Pg,&l2gmap_p);CHKERRQ(ierr);
157       ierr = ISDestroy(&Pg);CHKERRQ(ierr);
158       ierr = PetscLayoutCreate(comm,&play);CHKERRQ(ierr);
159       ierr = PetscLayoutSetBlockSize(play,1);CHKERRQ(ierr);
160       ierr = PetscLayoutSetSize(play,nPg);CHKERRQ(ierr);
161       ierr = ISGetLocalSize(pP,&nPgl);CHKERRQ(ierr);
162       ierr = PetscLayoutSetLocalSize(play,nPgl);CHKERRQ(ierr);
163       ierr = PetscLayoutSetUp(play);CHKERRQ(ierr);
164     } else {
165       ierr = PetscObjectReference((PetscObject)fetidpmat_ctx->C);CHKERRQ(ierr);
166       ierr = MatGetLocalToGlobalMapping(fetidpmat_ctx->C,&l2gmap_p,NULL);CHKERRQ(ierr);
167       ierr = PetscObjectReference((PetscObject)l2gmap_p);CHKERRQ(ierr);
168       ierr = MatGetSize(fetidpmat_ctx->C,&nPg,NULL);CHKERRQ(ierr);
169       ierr = MatGetLocalSize(fetidpmat_ctx->C,NULL,&nPgl);CHKERRQ(ierr);
170       ierr = MatGetLayouts(fetidpmat_ctx->C,NULL,&llay);CHKERRQ(ierr);
171       ierr = PetscLayoutReference(llay,&play);CHKERRQ(ierr);
172     }
173     ierr = VecCreateMPIWithArray(comm,1,nPgl,nPg,NULL,&fetidpmat_ctx->xPg);CHKERRQ(ierr);
174     ierr = VecCreateMPIWithArray(comm,1,nPgl,nPg,NULL,&fetidpmat_ctx->yPg);CHKERRQ(ierr);
175 
176     /* import matrices for interface pressures coupling */
177     ierr = PetscObjectQuery((PetscObject)fetidpmat_ctx->pc,"__KSPFETIDP_B_BI",(PetscObject*)&fetidpmat_ctx->B_BI);CHKERRQ(ierr);
178     if (!fetidpmat_ctx->B_BI) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"B_BI not present");
179     ierr = PetscObjectReference((PetscObject)fetidpmat_ctx->B_BI);CHKERRQ(ierr);
180 
181     ierr = PetscObjectQuery((PetscObject)fetidpmat_ctx->pc,"__KSPFETIDP_B_BB",(PetscObject*)&fetidpmat_ctx->B_BB);CHKERRQ(ierr);
182     if (!fetidpmat_ctx->B_BB) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"B_BB not present");
183     ierr = PetscObjectReference((PetscObject)fetidpmat_ctx->B_BB);CHKERRQ(ierr);
184 
185     ierr = PetscObjectQuery((PetscObject)fetidpmat_ctx->pc,"__KSPFETIDP_Bt_BI",(PetscObject*)&fetidpmat_ctx->Bt_BI);CHKERRQ(ierr);
186     if (!fetidpmat_ctx->Bt_BI) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Bt_BI not present");
187     ierr = PetscObjectReference((PetscObject)fetidpmat_ctx->Bt_BI);CHKERRQ(ierr);
188 
189     ierr = PetscObjectQuery((PetscObject)fetidpmat_ctx->pc,"__KSPFETIDP_Bt_BB",(PetscObject*)&fetidpmat_ctx->Bt_BB);CHKERRQ(ierr);
190     if (!fetidpmat_ctx->Bt_BB) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Bt_BB not present");
191     ierr = PetscObjectReference((PetscObject)fetidpmat_ctx->Bt_BB);CHKERRQ(ierr);
192   }
193 
194   /* Default type of lagrange multipliers is non-redundant */
195   fully_redundant = fetidpmat_ctx->fully_redundant;
196 
197   /* Evaluate local and global number of lagrange multipliers */
198   ierr = VecSet(pcis->vec1_N,0.0);CHKERRQ(ierr);
199   n_local_lambda = 0;
200   partial_sum = 0;
201   n_boundary_dofs = 0;
202   s = 0;
203   /* Get Vertices used to define the BDDC */
204   n_vertices = pcbddc->n_vertices;
205   vertex_indices = pcbddc->local_primal_ref_node;
206   dual_size = pcis->n_B-n_vertices;
207   ierr = PetscMalloc1(dual_size,&dual_dofs_boundary_indices);CHKERRQ(ierr);
208   ierr = PetscMalloc1(dual_size,&aux_local_numbering_1);CHKERRQ(ierr);
209   ierr = PetscMalloc1(dual_size,&aux_local_numbering_2);CHKERRQ(ierr);
210 
211   ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
212   for (i=0;i<pcis->n;i++){
213     j = mat_graph->count[i]; /* RECALL: mat_graph->count[i] does not count myself */
214     if ( j > 0 ) {
215       n_boundary_dofs++;
216     }
217     skip_node = PETSC_FALSE;
218     if ( s < n_vertices && vertex_indices[s]==i) { /* it works for a sorted set of vertices */
219       skip_node = PETSC_TRUE;
220       s++;
221     }
222     if (j < 1) {
223       skip_node = PETSC_TRUE;
224     }
225     if ( !skip_node ) {
226       if (fully_redundant) {
227         /* fully redundant set of lagrange multipliers */
228         n_lambda_for_dof = (j*(j+1))/2;
229       } else {
230         n_lambda_for_dof = j;
231       }
232       n_local_lambda += j;
233       /* needed to evaluate global number of lagrange multipliers */
234       array[i]=(1.0*n_lambda_for_dof)/(j+1.0); /* already scaled for the next global sum */
235       /* store some data needed */
236       dual_dofs_boundary_indices[partial_sum] = n_boundary_dofs-1;
237       aux_local_numbering_1[partial_sum] = i;
238       aux_local_numbering_2[partial_sum] = n_lambda_for_dof;
239       partial_sum++;
240     }
241   }
242   ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
243 
244   /* compute global ordering of lagrange multipliers and associate l2g map */
245   ierr = ISCreateGeneral(comm,partial_sum,aux_local_numbering_1,PETSC_COPY_VALUES,&subset_n);CHKERRQ(ierr);
246   ierr = ISLocalToGlobalMappingApplyIS(pcis->mapping,subset_n,&subset);CHKERRQ(ierr);
247   ierr = ISDestroy(&subset_n);CHKERRQ(ierr);
248   ierr = ISCreateGeneral(comm,partial_sum,aux_local_numbering_2,PETSC_OWN_POINTER,&subset_mult);CHKERRQ(ierr);
249   ierr = ISRenumber(subset,subset_mult,&fetidpmat_ctx->n_lambda,&subset_n);CHKERRQ(ierr);
250   ierr = ISDestroy(&subset);CHKERRQ(ierr);
251 
252 #if defined(PETSC_USE_DEBUG)
253   ierr = VecSet(pcis->vec1_global,0.0);CHKERRQ(ierr);
254   ierr = VecScatterBegin(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
255   ierr = VecScatterEnd(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
256   ierr = VecSum(pcis->vec1_global,&scalar_value);CHKERRQ(ierr);
257   i = (PetscInt)PetscRealPart(scalar_value);
258   if (i != fetidpmat_ctx->n_lambda) SETERRQ2(PETSC_COMM_WORLD,PETSC_ERR_PLIB,"Global number of multipliers mismatch! (%d!=%d)\n",fetidpmat_ctx->n_lambda,i);
259 #endif
260 
261   /* init data for scaling factors exchange */
262   partial_sum = 0;
263   ierr = PetscMalloc1(pcis->n_neigh,&ptrs_buffer);CHKERRQ(ierr);
264   ierr = PetscMalloc1(PetscMax(pcis->n_neigh-1,0),&send_reqs);CHKERRQ(ierr);
265   ierr = PetscMalloc1(PetscMax(pcis->n_neigh-1,0),&recv_reqs);CHKERRQ(ierr);
266   ierr = PetscMalloc1(pcis->n,&all_factors);CHKERRQ(ierr);
267   if (pcis->n_neigh > 0) ptrs_buffer[0]=0;
268   for (i=1;i<pcis->n_neigh;i++) {
269     partial_sum += pcis->n_shared[i];
270     ptrs_buffer[i] = ptrs_buffer[i-1]+pcis->n_shared[i];
271   }
272   ierr = PetscMalloc1(partial_sum,&send_buffer);CHKERRQ(ierr);
273   ierr = PetscMalloc1(partial_sum,&recv_buffer);CHKERRQ(ierr);
274   ierr = PetscMalloc1(partial_sum,&all_factors[0]);CHKERRQ(ierr);
275   for (i=0;i<pcis->n-1;i++) {
276     j = mat_graph->count[i];
277     all_factors[i+1]=all_factors[i]+j;
278   }
279   /* scatter B scaling to N vec */
280   ierr = VecScatterBegin(pcis->N_to_B,pcis->D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
281   ierr = VecScatterEnd(pcis->N_to_B,pcis->D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
282   /* communications */
283   ierr = VecGetArrayRead(pcis->vec1_N,(const PetscScalar**)&array);CHKERRQ(ierr);
284   for (i=1;i<pcis->n_neigh;i++) {
285     for (j=0;j<pcis->n_shared[i];j++) {
286       send_buffer[ptrs_buffer[i-1]+j]=array[pcis->shared[i][j]];
287     }
288     ierr = PetscMPIIntCast(ptrs_buffer[i]-ptrs_buffer[i-1],&buf_size);CHKERRQ(ierr);
289     ierr = PetscMPIIntCast(pcis->neigh[i],&neigh);CHKERRQ(ierr);
290     ierr = MPI_Isend(&send_buffer[ptrs_buffer[i-1]],buf_size,MPIU_SCALAR,neigh,0,comm,&send_reqs[i-1]);CHKERRQ(ierr);
291     ierr = MPI_Irecv(&recv_buffer[ptrs_buffer[i-1]],buf_size,MPIU_SCALAR,neigh,0,comm,&recv_reqs[i-1]);CHKERRQ(ierr);
292   }
293   ierr = VecRestoreArrayRead(pcis->vec1_N,(const PetscScalar**)&array);CHKERRQ(ierr);
294   if (pcis->n_neigh > 0) {
295     ierr = MPI_Waitall(pcis->n_neigh-1,recv_reqs,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
296   }
297   /* put values in correct places */
298   for (i=1;i<pcis->n_neigh;i++) {
299     for (j=0;j<pcis->n_shared[i];j++) {
300       k = pcis->shared[i][j];
301       neigh_position = 0;
302       while(mat_graph->neighbours_set[k][neigh_position] != pcis->neigh[i]) {neigh_position++;}
303       all_factors[k][neigh_position]=recv_buffer[ptrs_buffer[i-1]+j];
304     }
305   }
306   if (pcis->n_neigh > 0) {
307     ierr = MPI_Waitall(pcis->n_neigh-1,send_reqs,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
308   }
309   ierr = PetscFree(send_reqs);CHKERRQ(ierr);
310   ierr = PetscFree(recv_reqs);CHKERRQ(ierr);
311   ierr = PetscFree(send_buffer);CHKERRQ(ierr);
312   ierr = PetscFree(recv_buffer);CHKERRQ(ierr);
313   ierr = PetscFree(ptrs_buffer);CHKERRQ(ierr);
314 
315   /* Compute B and B_delta (local actions) */
316   ierr = PetscMalloc1(pcis->n_neigh,&aux_sums);CHKERRQ(ierr);
317   ierr = PetscMalloc1(n_local_lambda,&l2g_indices);CHKERRQ(ierr);
318   ierr = PetscMalloc1(n_local_lambda,&vals_B_delta);CHKERRQ(ierr);
319   ierr = PetscMalloc1(n_local_lambda,&cols_B_delta);CHKERRQ(ierr);
320   ierr = PetscMalloc1(n_local_lambda,&scaling_factors);CHKERRQ(ierr);
321   ierr = ISGetIndices(subset_n,&aux_global_numbering);CHKERRQ(ierr);
322   partial_sum=0;
323   cum = 0;
324   for (i=0;i<dual_size;i++) {
325     n_global_lambda = aux_global_numbering[cum];
326     j = mat_graph->count[aux_local_numbering_1[i]];
327     aux_sums[0]=0;
328     for (s=1;s<j;s++) {
329       aux_sums[s]=aux_sums[s-1]+j-s+1;
330     }
331     array = all_factors[aux_local_numbering_1[i]];
332     n_neg_values = 0;
333     while(n_neg_values < j && mat_graph->neighbours_set[aux_local_numbering_1[i]][n_neg_values] < rank) {n_neg_values++;}
334     n_pos_values = j - n_neg_values;
335     if (fully_redundant) {
336       for (s=0;s<n_neg_values;s++) {
337         l2g_indices    [partial_sum+s]=aux_sums[s]+n_neg_values-s-1+n_global_lambda;
338         cols_B_delta   [partial_sum+s]=dual_dofs_boundary_indices[i];
339         vals_B_delta   [partial_sum+s]=-1.0;
340         scaling_factors[partial_sum+s]=array[s];
341       }
342       for (s=0;s<n_pos_values;s++) {
343         l2g_indices    [partial_sum+s+n_neg_values]=aux_sums[n_neg_values]+s+n_global_lambda;
344         cols_B_delta   [partial_sum+s+n_neg_values]=dual_dofs_boundary_indices[i];
345         vals_B_delta   [partial_sum+s+n_neg_values]=1.0;
346         scaling_factors[partial_sum+s+n_neg_values]=array[s+n_neg_values];
347       }
348       partial_sum += j;
349     } else {
350       /* l2g_indices and default cols and vals of B_delta */
351       for (s=0;s<j;s++) {
352         l2g_indices    [partial_sum+s]=n_global_lambda+s;
353         cols_B_delta   [partial_sum+s]=dual_dofs_boundary_indices[i];
354         vals_B_delta   [partial_sum+s]=0.0;
355       }
356       /* B_delta */
357       if ( n_neg_values > 0 ) { /* there's a rank next to me to the left */
358         vals_B_delta   [partial_sum+n_neg_values-1]=-1.0;
359       }
360       if ( n_neg_values < j ) { /* there's a rank next to me to the right */
361         vals_B_delta   [partial_sum+n_neg_values]=1.0;
362       }
363       /* scaling as in Klawonn-Widlund 1999*/
364       for (s=0;s<n_neg_values;s++) {
365         scalar_value = 0.0;
366         for (k=0;k<s+1;k++) {
367           scalar_value += array[k];
368         }
369         scaling_factors[partial_sum+s] = -scalar_value;
370       }
371       for (s=0;s<n_pos_values;s++) {
372         scalar_value = 0.0;
373         for (k=s+n_neg_values;k<j;k++) {
374           scalar_value += array[k];
375         }
376         scaling_factors[partial_sum+s+n_neg_values] = scalar_value;
377       }
378       partial_sum += j;
379     }
380     cum += aux_local_numbering_2[i];
381   }
382   ierr = ISRestoreIndices(subset_n,&aux_global_numbering);CHKERRQ(ierr);
383   ierr = ISDestroy(&subset_mult);CHKERRQ(ierr);
384   ierr = ISDestroy(&subset_n);CHKERRQ(ierr);
385   ierr = PetscFree(aux_sums);CHKERRQ(ierr);
386   ierr = PetscFree(aux_local_numbering_1);CHKERRQ(ierr);
387   ierr = PetscFree(dual_dofs_boundary_indices);CHKERRQ(ierr);
388   ierr = PetscFree(all_factors[0]);CHKERRQ(ierr);
389   ierr = PetscFree(all_factors);CHKERRQ(ierr);
390 
391   /* Create local part of B_delta */
392   ierr = MatCreate(PETSC_COMM_SELF,&fetidpmat_ctx->B_delta);CHKERRQ(ierr);
393   ierr = MatSetSizes(fetidpmat_ctx->B_delta,n_local_lambda,pcis->n_B,n_local_lambda,pcis->n_B);CHKERRQ(ierr);
394   ierr = MatSetType(fetidpmat_ctx->B_delta,MATSEQAIJ);CHKERRQ(ierr);
395   ierr = MatSeqAIJSetPreallocation(fetidpmat_ctx->B_delta,1,NULL);CHKERRQ(ierr);
396   ierr = MatSetOption(fetidpmat_ctx->B_delta,MAT_IGNORE_ZERO_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
397   for (i=0;i<n_local_lambda;i++) {
398     ierr = MatSetValue(fetidpmat_ctx->B_delta,i,cols_B_delta[i],vals_B_delta[i],INSERT_VALUES);CHKERRQ(ierr);
399   }
400   ierr = PetscFree(vals_B_delta);CHKERRQ(ierr);
401   ierr = MatAssemblyBegin(fetidpmat_ctx->B_delta,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
402   ierr = MatAssemblyEnd  (fetidpmat_ctx->B_delta,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
403 
404   if (fully_redundant) {
405     ierr = MatCreate(PETSC_COMM_SELF,&ScalingMat);CHKERRQ(ierr);
406     ierr = MatSetSizes(ScalingMat,n_local_lambda,n_local_lambda,n_local_lambda,n_local_lambda);CHKERRQ(ierr);
407     ierr = MatSetType(ScalingMat,MATSEQAIJ);CHKERRQ(ierr);
408     ierr = MatSeqAIJSetPreallocation(ScalingMat,1,NULL);CHKERRQ(ierr);
409     for (i=0;i<n_local_lambda;i++) {
410       ierr = MatSetValue(ScalingMat,i,i,scaling_factors[i],INSERT_VALUES);CHKERRQ(ierr);
411     }
412     ierr = MatAssemblyBegin(ScalingMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
413     ierr = MatAssemblyEnd  (ScalingMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
414     ierr = MatMatMult(ScalingMat,fetidpmat_ctx->B_delta,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&fetidpmat_ctx->B_Ddelta);CHKERRQ(ierr);
415     ierr = MatDestroy(&ScalingMat);CHKERRQ(ierr);
416   } else {
417     ierr = MatCreate(PETSC_COMM_SELF,&fetidpmat_ctx->B_Ddelta);CHKERRQ(ierr);
418     ierr = MatSetSizes(fetidpmat_ctx->B_Ddelta,n_local_lambda,pcis->n_B,n_local_lambda,pcis->n_B);CHKERRQ(ierr);
419     ierr = MatSetType(fetidpmat_ctx->B_Ddelta,MATSEQAIJ);CHKERRQ(ierr);
420     ierr = MatSeqAIJSetPreallocation(fetidpmat_ctx->B_Ddelta,1,NULL);CHKERRQ(ierr);
421     for (i=0;i<n_local_lambda;i++) {
422       ierr = MatSetValue(fetidpmat_ctx->B_Ddelta,i,cols_B_delta[i],scaling_factors[i],INSERT_VALUES);CHKERRQ(ierr);
423     }
424     ierr = MatAssemblyBegin(fetidpmat_ctx->B_Ddelta,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
425     ierr = MatAssemblyEnd  (fetidpmat_ctx->B_Ddelta,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
426   }
427   ierr = PetscFree(scaling_factors);CHKERRQ(ierr);
428   ierr = PetscFree(cols_B_delta);CHKERRQ(ierr);
429 
430   /* Layout of multipliers */
431   ierr = PetscLayoutCreate(comm,&llay);CHKERRQ(ierr);
432   ierr = PetscLayoutSetBlockSize(llay,1);CHKERRQ(ierr);
433   ierr = PetscLayoutSetSize(llay,fetidpmat_ctx->n_lambda);CHKERRQ(ierr);
434   ierr = PetscLayoutSetUp(llay);CHKERRQ(ierr);
435   ierr = PetscLayoutGetLocalSize(llay,&fetidpmat_ctx->n);CHKERRQ(ierr);
436 
437   /* fetidpmat sizes */
438   fetidpmat_ctx->n += nPgl;
439   fetidpmat_ctx->N  = fetidpmat_ctx->n_lambda+nPg;
440 
441   /* Local work vector of multipliers */
442   ierr = VecCreate(PETSC_COMM_SELF,&fetidpmat_ctx->lambda_local);CHKERRQ(ierr);
443   ierr = VecSetSizes(fetidpmat_ctx->lambda_local,n_local_lambda,n_local_lambda);CHKERRQ(ierr);
444   ierr = VecSetType(fetidpmat_ctx->lambda_local,VECSEQ);CHKERRQ(ierr);
445 
446   /* Global vector for FETI-DP linear system */
447   ierr = VecCreate(comm,&fetidp_global);CHKERRQ(ierr);
448   ierr = VecSetSizes(fetidp_global,fetidpmat_ctx->n,fetidpmat_ctx->N);CHKERRQ(ierr);
449   ierr = VecSetType(fetidp_global,VECMPI);CHKERRQ(ierr);
450   ierr = VecSetUp(fetidp_global);CHKERRQ(ierr);
451 
452   /* Decide layout for fetidp dofs: if it is a saddle point problem
453      pressure is ordered first in the local part of the global vector
454      of the FETI-DP linear system */
455   if (nPg) {
456     IS             IS_l2g_p,ais;
457     PetscLayout    alay;
458     const PetscInt *idxs,*pranges,*aranges,*lranges;
459     PetscInt       *l2g_indices_p,rst;
460 
461     ierr = PetscMalloc1(nPl,&l2g_indices_p);CHKERRQ(ierr);
462     ierr = VecGetLayout(fetidp_global,&alay);CHKERRQ(ierr);
463     ierr = PetscLayoutGetRanges(alay,&aranges);CHKERRQ(ierr);
464     ierr = PetscLayoutGetRanges(play,&pranges);CHKERRQ(ierr);
465     ierr = PetscLayoutGetRanges(llay,&lranges);CHKERRQ(ierr);
466     ierr = ISLocalToGlobalMappingGetIndices(l2gmap_p,&idxs);CHKERRQ(ierr);
467     /* shift local to global indices for pressure */
468     for (i=0;i<nPl;i++) {
469       PetscInt owner;
470 
471       ierr = PetscLayoutFindOwner(play,idxs[i],&owner);CHKERRQ(ierr);
472       l2g_indices_p[i] = idxs[i]-pranges[owner]+aranges[owner];
473     }
474     ierr = ISLocalToGlobalMappingRestoreIndices(l2gmap_p,&idxs);CHKERRQ(ierr);
475     ierr = ISCreateGeneral(comm,nPl,l2g_indices_p,PETSC_OWN_POINTER,&IS_l2g_p);CHKERRQ(ierr);
476 
477     /* local to global scatter for interface pressure */
478     ierr = VecScatterCreate(fetidpmat_ctx->vP,NULL,fetidp_global,IS_l2g_p,&fetidpmat_ctx->l2g_p);CHKERRQ(ierr);
479     ierr = ISDestroy(&IS_l2g_p);CHKERRQ(ierr);
480 
481     /* shift local to global indices for multipliers */
482     for (i=0;i<n_local_lambda;i++) {
483       PetscInt owner,ps;
484 
485       ierr = PetscLayoutFindOwner(llay,l2g_indices[i],&owner);CHKERRQ(ierr);
486       ps = pranges[owner+1]-pranges[owner];
487       l2g_indices[i] = l2g_indices[i]-lranges[owner]+aranges[owner]+ps;
488     }
489 
490     /* scatter from alldofs to interface pressures global fetidp vector */
491     ierr = PetscLayoutGetRange(alay,&rst,NULL);CHKERRQ(ierr);
492     ierr = ISCreateStride(comm,nPgl,rst,1,&ais);CHKERRQ(ierr);
493     ierr = VecScatterCreate(pcis->vec1_global,pP,fetidp_global,ais,&fetidpmat_ctx->g2g_p);CHKERRQ(ierr);
494     ierr = ISDestroy(&ais);CHKERRQ(ierr);
495   }
496   ierr = PetscLayoutDestroy(&llay);CHKERRQ(ierr);
497   ierr = PetscLayoutDestroy(&play);CHKERRQ(ierr);
498   ierr = ISCreateGeneral(comm,n_local_lambda,l2g_indices,PETSC_OWN_POINTER,&IS_l2g_lambda);CHKERRQ(ierr);
499   /* scatter from local to global multipliers */
500   ierr = VecScatterCreate(fetidpmat_ctx->lambda_local,NULL,fetidp_global,IS_l2g_lambda,&fetidpmat_ctx->l2g_lambda);CHKERRQ(ierr);
501   ierr = ISDestroy(&IS_l2g_lambda);CHKERRQ(ierr);
502   ierr = ISLocalToGlobalMappingDestroy(&l2gmap_p);CHKERRQ(ierr);
503 
504   /* Create some vectors needed by fetidp */
505   ierr = VecDuplicate(pcis->vec1_B,&fetidpmat_ctx->temp_solution_B);CHKERRQ(ierr);
506   ierr = VecDuplicate(pcis->vec1_D,&fetidpmat_ctx->temp_solution_D);CHKERRQ(ierr);
507 
508   test_fetidp = PETSC_FALSE;
509   ierr = PetscOptionsGetBool(NULL,NULL,"-fetidp_check",&test_fetidp,NULL);CHKERRQ(ierr);
510 
511   if (test_fetidp && !pcbddc->use_deluxe_scaling) {
512     Vec       test_vec,test_vec_p = NULL;
513     PetscReal real_value;
514 
515     ierr = PetscViewerASCIIGetStdout(comm,&viewer);CHKERRQ(ierr);
516     ierr = PetscViewerASCIIPushSynchronized(viewer);CHKERRQ(ierr);
517     ierr = PetscViewerASCIIPrintf(viewer,"----------FETI_DP SIZES--------------\n");CHKERRQ(ierr);
518     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%04d]: Sizes %D %D %D %D %D\n",rank,fetidpmat_ctx->n,fetidpmat_ctx->N,nPgl,nPg,nPl);CHKERRQ(ierr);
519     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
520     ierr = PetscViewerASCIIPrintf(viewer,"----------FETI_DP TESTS--------------\n");CHKERRQ(ierr);
521     ierr = PetscViewerASCIIPrintf(viewer,"All tests should return zero!\n");CHKERRQ(ierr);
522     ierr = PetscViewerASCIIPrintf(viewer,"FETIDP MAT context in the ");CHKERRQ(ierr);
523     if (fully_redundant) {
524       ierr = PetscViewerASCIIPrintf(viewer,"fully redundant case for lagrange multipliers.\n");CHKERRQ(ierr);
525     } else {
526       ierr = PetscViewerASCIIPrintf(viewer,"Non-fully redundant case for lagrange multiplier.\n");CHKERRQ(ierr);
527     }
528     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
529 
530     /******************************************************************/
531     /* TEST A/B: Test numbering of global fetidp dofs             */
532     /******************************************************************/
533 
534     ierr = VecDuplicate(fetidpmat_ctx->lambda_local,&test_vec);CHKERRQ(ierr);
535     ierr = VecSet(fetidp_global,1.0);CHKERRQ(ierr);
536     ierr = VecSet(test_vec,1.);CHKERRQ(ierr);
537     ierr = VecScatterBegin(fetidpmat_ctx->l2g_lambda,fetidp_global,fetidpmat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
538     ierr = VecScatterEnd(fetidpmat_ctx->l2g_lambda,fetidp_global,fetidpmat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
539     if (fetidpmat_ctx->l2g_p) {
540       ierr = VecDuplicate(fetidpmat_ctx->vP,&test_vec_p);CHKERRQ(ierr);
541       ierr = VecSet(test_vec_p,1.);CHKERRQ(ierr);
542       ierr = VecScatterBegin(fetidpmat_ctx->l2g_p,fetidp_global,fetidpmat_ctx->vP,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
543       ierr = VecScatterEnd(fetidpmat_ctx->l2g_p,fetidp_global,fetidpmat_ctx->vP,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
544     }
545     scalar_value = -1.0;
546     ierr = VecAXPY(test_vec,scalar_value,fetidpmat_ctx->lambda_local);CHKERRQ(ierr);
547     ierr = VecNorm(test_vec,NORM_INFINITY,&real_value);CHKERRQ(ierr);
548     ierr = VecDestroy(&test_vec);CHKERRQ(ierr);
549     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"A[%04d]: CHECK glob to loc: % 1.14e\n",rank,real_value);CHKERRQ(ierr);
550     if (fetidpmat_ctx->l2g_p) {
551       ierr = VecAXPY(test_vec_p,scalar_value,fetidpmat_ctx->vP);CHKERRQ(ierr);
552       ierr = VecNorm(test_vec_p,NORM_INFINITY,&real_value);CHKERRQ(ierr);
553       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"A[%04d]: CHECK glob to loc (p): % 1.14e\n",rank,real_value);CHKERRQ(ierr);
554     }
555     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
556     if (fully_redundant) {
557       ierr = VecSet(fetidp_global,0.0);CHKERRQ(ierr);
558       ierr = VecSet(fetidpmat_ctx->lambda_local,0.5);CHKERRQ(ierr);
559       ierr = VecScatterBegin(fetidpmat_ctx->l2g_lambda,fetidpmat_ctx->lambda_local,fetidp_global,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
560       ierr = VecScatterEnd(fetidpmat_ctx->l2g_lambda,fetidpmat_ctx->lambda_local,fetidp_global,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
561       ierr = VecSum(fetidp_global,&scalar_value);CHKERRQ(ierr);
562       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"B[%04d]: CHECK loc to glob: % 1.14e\n",rank,PetscRealPart(scalar_value)-fetidpmat_ctx->n_lambda);CHKERRQ(ierr);
563       ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
564     }
565     if (fetidpmat_ctx->l2g_p) {
566       ierr = VecSet(pcis->vec1_N,1.0);CHKERRQ(ierr);
567       ierr = VecSet(pcis->vec1_global,0.0);CHKERRQ(ierr);
568       ierr = VecScatterBegin(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
569       ierr = VecScatterEnd(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
570 
571       ierr = VecSet(fetidp_global,0.0);CHKERRQ(ierr);
572       ierr = VecSet(fetidpmat_ctx->vP,-1.0);CHKERRQ(ierr);
573       ierr = VecScatterBegin(fetidpmat_ctx->l2g_p,fetidpmat_ctx->vP,fetidp_global,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
574       ierr = VecScatterEnd(fetidpmat_ctx->l2g_p,fetidpmat_ctx->vP,fetidp_global,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
575       ierr = VecScatterBegin(fetidpmat_ctx->g2g_p,fetidp_global,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
576       ierr = VecScatterEnd(fetidpmat_ctx->g2g_p,fetidp_global,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
577       ierr = VecScatterBegin(fetidpmat_ctx->g2g_p,pcis->vec1_global,fetidp_global,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
578       ierr = VecScatterEnd(fetidpmat_ctx->g2g_p,pcis->vec1_global,fetidp_global,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
579       ierr = VecSum(fetidp_global,&scalar_value);CHKERRQ(ierr);
580       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"B[%04d]: CHECK loc to glob (p): % 1.14e\n",rank,PetscRealPart(scalar_value));CHKERRQ(ierr);
581     }
582     /******************************************************************/
583     /* TEST C: It should holds B_delta*w=0, w\in\widehat{W}           */
584     /* This is the meaning of the B matrix                            */
585     /******************************************************************/
586 
587     ierr = VecSetRandom(pcis->vec1_N,NULL);CHKERRQ(ierr);
588     ierr = VecSet(pcis->vec1_global,0.0);CHKERRQ(ierr);
589     ierr = VecScatterBegin(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
590     ierr = VecScatterEnd(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
591     ierr = VecScatterBegin(matis->rctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
592     ierr = VecScatterEnd(matis->rctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
593     ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
594     ierr = VecScatterEnd(pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
595     /* Action of B_delta */
596     ierr = MatMult(fetidpmat_ctx->B_delta,pcis->vec1_B,fetidpmat_ctx->lambda_local);CHKERRQ(ierr);
597     ierr = VecSet(fetidp_global,0.0);CHKERRQ(ierr);
598     ierr = VecScatterBegin(fetidpmat_ctx->l2g_lambda,fetidpmat_ctx->lambda_local,fetidp_global,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
599     ierr = VecScatterEnd(fetidpmat_ctx->l2g_lambda,fetidpmat_ctx->lambda_local,fetidp_global,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
600     ierr = VecNorm(fetidp_global,NORM_INFINITY,&real_value);CHKERRQ(ierr);
601     ierr = PetscViewerASCIIPrintf(viewer,"C[coll]: CHECK infty norm of B_delta*w (w continuous): % 1.14e\n",real_value);CHKERRQ(ierr);
602     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
603 
604     /******************************************************************/
605     /* TEST D: It should holds E_Dw = w - P_Dw w\in\widetilde{W}     */
606     /* E_D = R_D^TR                                                   */
607     /* P_D = B_{D,delta}^T B_{delta}                                  */
608     /* eq.44 Mandel Tezaur and Dohrmann 2005                          */
609     /******************************************************************/
610 
611     /* compute a random vector in \widetilde{W} */
612     ierr = VecSetRandom(pcis->vec1_N,NULL);CHKERRQ(ierr);
613     scalar_value = 0.0;  /* set zero at vertices */
614     ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
615     for (i=0;i<n_vertices;i++) { array[vertex_indices[i]]=scalar_value; }
616     ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
617     /* store w for final comparison */
618     ierr = VecDuplicate(pcis->vec1_B,&test_vec);CHKERRQ(ierr);
619     ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_N,test_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
620     ierr = VecScatterEnd(pcis->N_to_B,pcis->vec1_N,test_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
621 
622     /* Jump operator P_D : results stored in pcis->vec1_B */
623 
624     ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
625     ierr = VecScatterEnd(pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
626     /* Action of B_delta */
627     ierr = MatMult(fetidpmat_ctx->B_delta,pcis->vec1_B,fetidpmat_ctx->lambda_local);CHKERRQ(ierr);
628     ierr = VecSet(fetidp_global,0.0);CHKERRQ(ierr);
629     ierr = VecScatterBegin(fetidpmat_ctx->l2g_lambda,fetidpmat_ctx->lambda_local,fetidp_global,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
630     ierr = VecScatterEnd(fetidpmat_ctx->l2g_lambda,fetidpmat_ctx->lambda_local,fetidp_global,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
631     /* Action of B_Ddelta^T */
632     ierr = VecScatterBegin(fetidpmat_ctx->l2g_lambda,fetidp_global,fetidpmat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
633     ierr = VecScatterEnd(fetidpmat_ctx->l2g_lambda,fetidp_global,fetidpmat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
634     ierr = MatMultTranspose(fetidpmat_ctx->B_Ddelta,fetidpmat_ctx->lambda_local,pcis->vec1_B);CHKERRQ(ierr);
635 
636     /* Average operator E_D : results stored in pcis->vec2_B */
637     ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_N,pcis->vec2_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
638     ierr = VecScatterEnd(pcis->N_to_B,pcis->vec1_N,pcis->vec2_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
639     ierr = PCBDDCScalingExtension(fetidpmat_ctx->pc,pcis->vec2_B,pcis->vec1_global);CHKERRQ(ierr);
640     ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_global,pcis->vec2_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
641     ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_global,pcis->vec2_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
642 
643     /* test E_D=I-P_D */
644     scalar_value = 1.0;
645     ierr = VecAXPY(pcis->vec1_B,scalar_value,pcis->vec2_B);CHKERRQ(ierr);
646     scalar_value = -1.0;
647     ierr = VecAXPY(pcis->vec1_B,scalar_value,test_vec);CHKERRQ(ierr);
648     ierr = VecNorm(pcis->vec1_B,NORM_INFINITY,&real_value);CHKERRQ(ierr);
649     ierr = VecDestroy(&test_vec);CHKERRQ(ierr);
650     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"D[%04d] CHECK infty norm of E_D + P_D - I: % 1.14e\n",rank,real_value);CHKERRQ(ierr);
651     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
652 
653     /******************************************************************/
654     /* TEST E: It should holds R_D^TP_Dw=0 w\in\widetilde{W}          */
655     /* eq.48 Mandel Tezaur and Dohrmann 2005                          */
656     /******************************************************************/
657 
658     ierr = VecSetRandom(pcis->vec1_N,NULL);CHKERRQ(ierr);
659     ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
660     scalar_value = 0.0;  /* set zero at vertices */
661     for (i=0;i<n_vertices;i++) { array[vertex_indices[i]]=scalar_value; }
662     ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
663 
664     /* Jump operator P_D : results stored in pcis->vec1_B */
665 
666     ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
667     ierr = VecScatterEnd(pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
668     /* Action of B_delta */
669     ierr = MatMult(fetidpmat_ctx->B_delta,pcis->vec1_B,fetidpmat_ctx->lambda_local);CHKERRQ(ierr);
670     ierr = VecSet(fetidp_global,0.0);CHKERRQ(ierr);
671     ierr = VecScatterBegin(fetidpmat_ctx->l2g_lambda,fetidpmat_ctx->lambda_local,fetidp_global,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
672     ierr = VecScatterEnd(fetidpmat_ctx->l2g_lambda,fetidpmat_ctx->lambda_local,fetidp_global,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
673     /* Action of B_Ddelta^T */
674     ierr = VecScatterBegin(fetidpmat_ctx->l2g_lambda,fetidp_global,fetidpmat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
675     ierr = VecScatterEnd(fetidpmat_ctx->l2g_lambda,fetidp_global,fetidpmat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
676     ierr = MatMultTranspose(fetidpmat_ctx->B_Ddelta,fetidpmat_ctx->lambda_local,pcis->vec1_B);CHKERRQ(ierr);
677     /* scaling */
678     ierr = PCBDDCScalingExtension(fetidpmat_ctx->pc,pcis->vec1_B,pcis->vec1_global);CHKERRQ(ierr);
679     ierr = VecNorm(pcis->vec1_global,NORM_INFINITY,&real_value);CHKERRQ(ierr);
680     ierr = PetscViewerASCIIPrintf(viewer,"E[coll]: CHECK infty norm of R^T_D P_D: % 1.14e\n",real_value);CHKERRQ(ierr);
681     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
682 
683     if (!fully_redundant) {
684       /******************************************************************/
685       /* TEST F: It should holds B_{delta}B^T_{D,delta}=I               */
686       /* Corollary thm 14 Mandel Tezaur and Dohrmann 2005               */
687       /******************************************************************/
688       ierr = VecDuplicate(fetidp_global,&test_vec);CHKERRQ(ierr);
689       ierr = VecSetRandom(fetidp_global,NULL);CHKERRQ(ierr);
690       if (fetidpmat_ctx->l2g_p) {
691         ierr = VecSet(fetidpmat_ctx->vP,0.);CHKERRQ(ierr);
692         ierr = VecScatterBegin(fetidpmat_ctx->l2g_p,fetidpmat_ctx->vP,fetidp_global,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
693         ierr = VecScatterEnd(fetidpmat_ctx->l2g_p,fetidpmat_ctx->vP,fetidp_global,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
694       }
695       /* Action of B_Ddelta^T */
696       ierr = VecScatterBegin(fetidpmat_ctx->l2g_lambda,fetidp_global,fetidpmat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
697       ierr = VecScatterEnd(fetidpmat_ctx->l2g_lambda,fetidp_global,fetidpmat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
698       ierr = MatMultTranspose(fetidpmat_ctx->B_Ddelta,fetidpmat_ctx->lambda_local,pcis->vec1_B);CHKERRQ(ierr);
699       /* Action of B_delta */
700       ierr = MatMult(fetidpmat_ctx->B_delta,pcis->vec1_B,fetidpmat_ctx->lambda_local);CHKERRQ(ierr);
701       ierr = VecSet(test_vec,0.0);CHKERRQ(ierr);
702       ierr = VecScatterBegin(fetidpmat_ctx->l2g_lambda,fetidpmat_ctx->lambda_local,test_vec,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
703       ierr = VecScatterEnd(fetidpmat_ctx->l2g_lambda,fetidpmat_ctx->lambda_local,test_vec,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
704       scalar_value = -1.0;
705       ierr = VecAXPY(fetidp_global,scalar_value,test_vec);CHKERRQ(ierr);
706       ierr = VecNorm(fetidp_global,NORM_INFINITY,&real_value);CHKERRQ(ierr);
707       ierr = PetscViewerASCIIPrintf(viewer,"E[coll]: CHECK infty norm of P^T_D - I: % 1.14e\n",real_value);CHKERRQ(ierr);
708       ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
709       ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
710       ierr = VecDestroy(&test_vec);CHKERRQ(ierr);
711     }
712     ierr = VecDestroy(&test_vec_p);CHKERRQ(ierr);
713   }
714   /* final cleanup */
715   ierr = VecDestroy(&fetidp_global);CHKERRQ(ierr);
716   PetscFunctionReturn(0);
717 }
718 
719 #undef __FUNCT__
720 #define __FUNCT__ "PCBDDCSetupFETIDPPCContext"
721 PetscErrorCode PCBDDCSetupFETIDPPCContext(Mat fetimat, FETIDPPC_ctx fetidppc_ctx)
722 {
723   FETIDPMat_ctx  mat_ctx;
724   PC_IS          *pcis;
725   PetscBool      lumped = PETSC_FALSE;
726   PetscErrorCode ierr;
727 
728   PetscFunctionBegin;
729   ierr = MatShellGetContext(fetimat,(void**)&mat_ctx);CHKERRQ(ierr);
730   /* get references from objects created when setting up feti mat context */
731   ierr = PetscObjectReference((PetscObject)mat_ctx->lambda_local);CHKERRQ(ierr);
732   fetidppc_ctx->lambda_local = mat_ctx->lambda_local;
733   ierr = PetscObjectReference((PetscObject)mat_ctx->B_Ddelta);CHKERRQ(ierr);
734   fetidppc_ctx->B_Ddelta = mat_ctx->B_Ddelta;
735   ierr = PetscObjectReference((PetscObject)mat_ctx->l2g_lambda);CHKERRQ(ierr);
736   fetidppc_ctx->l2g_lambda = mat_ctx->l2g_lambda;
737   /* create preconditioner */
738   pcis = (PC_IS*)fetidppc_ctx->pc->data;
739   /* Dirichlet preconditioner */
740   ierr = PetscOptionsGetBool(NULL,NULL,"-fetidp_lumped",&lumped,NULL);CHKERRQ(ierr);
741   if (!lumped) {
742     ierr = MatCreateSchurComplement(pcis->A_II,pcis->A_II,pcis->A_IB,pcis->A_BI,pcis->A_BB,&fetidppc_ctx->S_j);CHKERRQ(ierr);
743     ierr = MatSchurComplementSetKSP(fetidppc_ctx->S_j,pcis->ksp_D);CHKERRQ(ierr);
744   } else {
745     ierr = PetscObjectReference((PetscObject)pcis->A_BB);CHKERRQ(ierr);
746     fetidppc_ctx->S_j = pcis->A_BB;
747   }
748   /* saddle-point */
749   if (mat_ctx->xPg) {
750     Mat PAmat = NULL,PPmat = NULL;
751 
752     ierr = PetscObjectReference((PetscObject)mat_ctx->xPg);CHKERRQ(ierr);
753     fetidppc_ctx->xPg = mat_ctx->xPg;
754     ierr = PetscObjectReference((PetscObject)mat_ctx->yPg);CHKERRQ(ierr);
755     fetidppc_ctx->yPg = mat_ctx->yPg;
756     ierr = PetscObjectQuery((PetscObject)fetidppc_ctx->pc,"__KSPFETIDP_PPmat",(PetscObject*)&PPmat);CHKERRQ(ierr);
757     ierr = PetscObjectQuery((PetscObject)fetidppc_ctx->pc,"__KSPFETIDP_PAmat",(PetscObject*)&PAmat);CHKERRQ(ierr);
758     ierr = KSPCreate(PetscObjectComm((PetscObject)fetidppc_ctx->pc),&fetidppc_ctx->kP);CHKERRQ(ierr);
759     ierr = KSPSetOperators(fetidppc_ctx->kP,PAmat,PPmat);CHKERRQ(ierr);
760     ierr = KSPSetOptionsPrefix(fetidppc_ctx->kP,"fetidp_pmass_");CHKERRQ(ierr);
761     ierr = KSPSetFromOptions(fetidppc_ctx->kP);CHKERRQ(ierr);
762   }
763   PetscFunctionReturn(0);
764 }
765 
766 #undef __FUNCT__
767 #define __FUNCT__ "FETIDPMatMult"
768 PetscErrorCode FETIDPMatMult(Mat fetimat, Vec x, Vec y)
769 {
770   FETIDPMat_ctx  mat_ctx;
771   PC_BDDC        *pcbddc;
772   PC_IS          *pcis;
773   PetscErrorCode ierr;
774 
775   PetscFunctionBegin;
776   ierr = MatShellGetContext(fetimat,(void**)&mat_ctx);CHKERRQ(ierr);
777   pcis = (PC_IS*)mat_ctx->pc->data;
778   pcbddc = (PC_BDDC*)mat_ctx->pc->data;
779   /* Application of B_delta^T */
780   ierr = VecSet(pcis->vec1_B,0.);CHKERRQ(ierr);
781   ierr = VecScatterBegin(mat_ctx->l2g_lambda,x,mat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
782   ierr = VecScatterEnd(mat_ctx->l2g_lambda,x,mat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
783   ierr = MatMultTranspose(mat_ctx->B_delta,mat_ctx->lambda_local,pcis->vec1_B);CHKERRQ(ierr);
784 
785   /* Add contribution from saddle point */
786   if (mat_ctx->l2g_p) {
787     ierr = VecScatterBegin(mat_ctx->l2g_p,x,mat_ctx->vP,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
788     ierr = VecScatterEnd(mat_ctx->l2g_p,x,mat_ctx->vP,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
789     if (pcbddc->switch_static) {
790       ierr = MatMult(mat_ctx->Bt_BI,mat_ctx->vP,pcis->vec1_D);CHKERRQ(ierr);
791     }
792     ierr = MatMultAdd(mat_ctx->Bt_BB,mat_ctx->vP,pcis->vec1_B,pcis->vec1_B);CHKERRQ(ierr);
793   } else {
794     if (pcbddc->switch_static) {
795       ierr = VecSet(pcis->vec1_D,0.0);CHKERRQ(ierr);
796     }
797   }
798   /* Application of \widetilde{S}^-1 */
799   ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
800   ierr = PCBDDCApplyInterfacePreconditioner(mat_ctx->pc,PETSC_FALSE);CHKERRQ(ierr);
801   ierr = PetscMemzero(pcbddc->benign_p0,pcbddc->benign_n*sizeof(PetscScalar));CHKERRQ(ierr);
802   ierr = VecSet(y,0.0);CHKERRQ(ierr);
803   /* Application of B_delta */
804   ierr = MatMult(mat_ctx->B_delta,pcis->vec1_B,mat_ctx->lambda_local);CHKERRQ(ierr);
805   /* Contribution from boundary pressures */
806   if (mat_ctx->C) {
807     const PetscScalar *lx;
808     PetscScalar       *ly;
809 
810     /* pressures ordered first in x and y */
811     ierr = VecGetArrayRead(x,&lx);CHKERRQ(ierr);
812     ierr = VecGetArray(y,&ly);CHKERRQ(ierr);
813     ierr = VecPlaceArray(mat_ctx->xPg,lx);CHKERRQ(ierr);
814     ierr = VecPlaceArray(mat_ctx->yPg,ly);CHKERRQ(ierr);
815     ierr = MatMult(mat_ctx->C,mat_ctx->xPg,mat_ctx->yPg);CHKERRQ(ierr);
816     ierr = VecResetArray(mat_ctx->xPg);CHKERRQ(ierr);
817     ierr = VecResetArray(mat_ctx->yPg);CHKERRQ(ierr);
818     ierr = VecRestoreArrayRead(x,&lx);CHKERRQ(ierr);
819     ierr = VecRestoreArray(y,&ly);CHKERRQ(ierr);
820   }
821   /* Add contribution from saddle point */
822   if (mat_ctx->l2g_p) {
823     ierr = MatMult(mat_ctx->B_BB,pcis->vec1_B,mat_ctx->vP);CHKERRQ(ierr);
824     if (pcbddc->switch_static) {
825       ierr = MatMultAdd(mat_ctx->B_BI,pcis->vec1_D,mat_ctx->vP,mat_ctx->vP);CHKERRQ(ierr);
826     }
827     ierr = VecScatterBegin(mat_ctx->l2g_p,mat_ctx->vP,y,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
828     ierr = VecScatterEnd(mat_ctx->l2g_p,mat_ctx->vP,y,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
829   }
830   ierr = VecScatterBegin(mat_ctx->l2g_lambda,mat_ctx->lambda_local,y,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
831   ierr = VecScatterEnd(mat_ctx->l2g_lambda,mat_ctx->lambda_local,y,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
832   PetscFunctionReturn(0);
833 }
834 
835 #undef __FUNCT__
836 #define __FUNCT__ "FETIDPMatMultTranspose"
837 PetscErrorCode FETIDPMatMultTranspose(Mat fetimat, Vec x, Vec y)
838 {
839   FETIDPMat_ctx  mat_ctx;
840   PC_IS          *pcis;
841   PetscErrorCode ierr;
842 
843   PetscFunctionBegin;
844   ierr = MatShellGetContext(fetimat,(void**)&mat_ctx);CHKERRQ(ierr);
845   pcis = (PC_IS*)mat_ctx->pc->data;
846   /* Application of B_delta^T */
847   ierr = VecScatterBegin(mat_ctx->l2g_lambda,x,mat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
848   ierr = VecScatterEnd(mat_ctx->l2g_lambda,x,mat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
849   ierr = MatMultTranspose(mat_ctx->B_delta,mat_ctx->lambda_local,pcis->vec1_B);CHKERRQ(ierr);
850   /* Application of \widetilde{S}^-1 */
851   ierr = VecSet(pcis->vec1_D,0.0);CHKERRQ(ierr);
852   ierr = PCBDDCApplyInterfacePreconditioner(mat_ctx->pc,PETSC_TRUE);CHKERRQ(ierr);
853   /* Application of B_delta */
854   ierr = MatMult(mat_ctx->B_delta,pcis->vec1_B,mat_ctx->lambda_local);CHKERRQ(ierr);
855   ierr = VecSet(y,0.0);CHKERRQ(ierr);
856   ierr = VecScatterBegin(mat_ctx->l2g_lambda,mat_ctx->lambda_local,y,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
857   ierr = VecScatterEnd(mat_ctx->l2g_lambda,mat_ctx->lambda_local,y,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
858   PetscFunctionReturn(0);
859 }
860 
861 #undef __FUNCT__
862 #define __FUNCT__ "FETIDPPCApply"
863 PetscErrorCode FETIDPPCApply(PC fetipc, Vec x, Vec y)
864 {
865   FETIDPPC_ctx   pc_ctx;
866   PC_IS          *pcis;
867   PetscErrorCode ierr;
868 
869   PetscFunctionBegin;
870   ierr = PCShellGetContext(fetipc,(void**)&pc_ctx);CHKERRQ(ierr);
871   pcis = (PC_IS*)pc_ctx->pc->data;
872   /* Application of B_Ddelta^T */
873   ierr = VecScatterBegin(pc_ctx->l2g_lambda,x,pc_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
874   ierr = VecScatterEnd(pc_ctx->l2g_lambda,x,pc_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
875   ierr = VecSet(pcis->vec2_B,0.0);CHKERRQ(ierr);
876   ierr = MatMultTranspose(pc_ctx->B_Ddelta,pc_ctx->lambda_local,pcis->vec2_B);CHKERRQ(ierr);
877   /* Application of local Schur complement */
878   ierr = MatMult(pc_ctx->S_j,pcis->vec2_B,pcis->vec1_B);CHKERRQ(ierr);
879   /* Application of B_Ddelta */
880   ierr = MatMult(pc_ctx->B_Ddelta,pcis->vec1_B,pc_ctx->lambda_local);CHKERRQ(ierr);
881   ierr = VecSet(y,0.0);CHKERRQ(ierr);
882   ierr = VecScatterBegin(pc_ctx->l2g_lambda,pc_ctx->lambda_local,y,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
883   ierr = VecScatterEnd(pc_ctx->l2g_lambda,pc_ctx->lambda_local,y,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
884   PetscFunctionReturn(0);
885 }
886 
887 #undef __FUNCT__
888 #define __FUNCT__ "FETIDPPCApplyTranspose"
889 PetscErrorCode FETIDPPCApplyTranspose(PC fetipc, Vec x, Vec y)
890 {
891   FETIDPPC_ctx   pc_ctx;
892   PC_IS          *pcis;
893   PetscErrorCode ierr;
894 
895   PetscFunctionBegin;
896   ierr = PCShellGetContext(fetipc,(void**)&pc_ctx);CHKERRQ(ierr);
897   pcis = (PC_IS*)pc_ctx->pc->data;
898   /* Application of B_Ddelta^T */
899   ierr = VecScatterBegin(pc_ctx->l2g_lambda,x,pc_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
900   ierr = VecScatterEnd(pc_ctx->l2g_lambda,x,pc_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
901   ierr = VecSet(pcis->vec2_B,0.0);CHKERRQ(ierr);
902   ierr = MatMultTranspose(pc_ctx->B_Ddelta,pc_ctx->lambda_local,pcis->vec2_B);CHKERRQ(ierr);
903   /* Application of local Schur complement */
904   ierr = MatMultTranspose(pc_ctx->S_j,pcis->vec2_B,pcis->vec1_B);CHKERRQ(ierr);
905   /* Application of B_Ddelta */
906   ierr = MatMult(pc_ctx->B_Ddelta,pcis->vec1_B,pc_ctx->lambda_local);CHKERRQ(ierr);
907   ierr = VecSet(y,0.0);CHKERRQ(ierr);
908   ierr = VecScatterBegin(pc_ctx->l2g_lambda,pc_ctx->lambda_local,y,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
909   ierr = VecScatterEnd(pc_ctx->l2g_lambda,pc_ctx->lambda_local,y,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
910   PetscFunctionReturn(0);
911 }
912