Actual source code: ex62.c

petsc-master 2019-11-11
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  1: static char help[] = "Illustrates use of PCGASM.\n\
  2: The Generalized Additive Schwarz Method for solving a linear system in parallel with KSP.  The\n\
  3: code indicates the procedure for setting user-defined subdomains.\n\
  4: See section 'ex62' below for command-line options.\n\
  5: Without -user_set_subdomains, the general PCGASM options are meaningful:\n\
  6:   -pc_gasm_total_subdomains\n\
  7:   -pc_gasm_print_subdomains\n\
  8: \n";

 10: /*
 11:    Note:  This example focuses on setting the subdomains for the GASM
 12:    preconditioner for a problem on a 2D rectangular grid.  See ex1.c
 13:    and ex2.c for more detailed comments on the basic usage of KSP
 14:    (including working with matrices and vectors).

 16:    The GASM preconditioner is fully parallel.  The user-space routine
 17:    CreateSubdomains2D that computes the domain decomposition is also parallel
 18:    and attempts to generate both subdomains straddling processors and multiple
 19:    domains per processor.


 22:    This matrix in this linear system arises from the discretized Laplacian,
 23:    and thus is not very interesting in terms of experimenting with variants
 24:    of the GASM preconditioner.
 25: */

 27: /*T
 28:    Concepts: KSP^Additive Schwarz Method (GASM) with user-defined subdomains
 29:    Processors: n
 30: T*/



 34: /*
 35:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
 36:   automatically includes:
 37:      petscsys.h    - base PETSc routines   petscvec.h - vectors
 38:      petscmat.h    - matrices
 39:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
 40:      petscviewer.h - viewers               petscpc.h  - preconditioners
 41: */
 42:  #include <petscksp.h>

 44: PetscErrorCode AssembleMatrix(Mat,PetscInt m,PetscInt n);

 46: int main(int argc,char **args)
 47: {
 48:   Vec            x,b,u;                  /* approx solution, RHS, exact solution */
 49:   Mat            A;                      /* linear system matrix */
 50:   KSP            ksp;                    /* linear solver context */
 51:   PC             pc;                     /* PC context */
 52:   IS             *inneris,*outeris;      /* array of index sets that define the subdomains */
 53:   PetscInt       overlap;                /* width of subdomain overlap */
 54:   PetscInt       Nsub;                   /* number of subdomains */
 55:   PetscInt       m,n;                    /* mesh dimensions in x- and y- directions */
 56:   PetscInt       M,N;                    /* number of subdomains in x- and y- directions */
 58:   PetscMPIInt    size;
 59:   PetscBool      flg=PETSC_FALSE;
 60:   PetscBool      user_set_subdomains=PETSC_FALSE;
 61:   PetscReal      one,e;

 63:   PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
 64:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
 65:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"ex62","PCGASM");
 66:   m = 15;
 67:   PetscOptionsInt("-M", "Number of mesh points in the x-direction","PCGASMCreateSubdomains2D",m,&m,NULL);
 68:   n = 17;
 69:   PetscOptionsInt("-N","Number of mesh points in the y-direction","PCGASMCreateSubdomains2D",n,&n,NULL);
 70:   user_set_subdomains = PETSC_FALSE;
 71:   PetscOptionsBool("-user_set_subdomains","Use the user-specified 2D tiling of mesh by subdomains","PCGASMCreateSubdomains2D",user_set_subdomains,&user_set_subdomains,NULL);
 72:   M = 2;
 73:   PetscOptionsInt("-Mdomains","Number of subdomain tiles in the x-direction","PCGASMSetSubdomains2D",M,&M,NULL);
 74:   N = 1;
 75:   PetscOptionsInt("-Ndomains","Number of subdomain tiles in the y-direction","PCGASMSetSubdomains2D",N,&N,NULL);
 76:   overlap = 1;
 77:   PetscOptionsInt("-overlap","Size of tile overlap.","PCGASMSetSubdomains2D",overlap,&overlap,NULL);
 78:   PetscOptionsEnd();

 80:   /* -------------------------------------------------------------------
 81:          Compute the matrix and right-hand-side vector that define
 82:          the linear system, Ax = b.
 83:      ------------------------------------------------------------------- */

 85:   /*
 86:      Assemble the matrix for the five point stencil, YET AGAIN
 87:   */
 88:   MatCreate(PETSC_COMM_WORLD,&A);
 89:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
 90:   MatSetFromOptions(A);
 91:   MatSetUp(A);
 92:   MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);
 93:   MatSetOption(A, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_FALSE);
 94:   AssembleMatrix(A,m,n);

 96:   /*
 97:      Create and set vectors
 98:   */
 99:   VecCreate(PETSC_COMM_WORLD,&b);
100:   VecSetSizes(b,PETSC_DECIDE,m*n);
101:   VecSetFromOptions(b);
102:   VecDuplicate(b,&u);
103:   VecDuplicate(b,&x);
104:   one  = 1.0;
105:   VecSet(u,one);
106:   MatMult(A,u,b);

108:   /*
109:      Create linear solver context
110:   */
111:   KSPCreate(PETSC_COMM_WORLD,&ksp);

113:   /*
114:      Set operators. Here the matrix that defines the linear system
115:      also serves as the preconditioning matrix.
116:   */
117:   KSPSetOperators(ksp,A,A);

119:   /*
120:      Set the default preconditioner for this program to be GASM
121:   */
122:   KSPGetPC(ksp,&pc);
123:   PCSetType(pc,PCGASM);

125:   /* -------------------------------------------------------------------
126:                   Define the problem decomposition
127:      ------------------------------------------------------------------- */

129:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
130:        Basic method, should be sufficient for the needs of many users.
131:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

133:      Set the overlap, using the default PETSc decomposition via
134:          PCGASMSetOverlap(pc,overlap);
135:      Could instead use the option -pc_gasm_overlap <ovl>

137:      Set the total number of blocks via -pc_gasm_blocks <blks>
138:      Note:  The GASM default is to use 1 block per processor.  To
139:      experiment on a single processor with various overlaps, you
140:      must specify use of multiple blocks!
141:   */

143:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
144:        More advanced method, setting user-defined subdomains
145:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

147:      Firstly, create index sets that define the subdomains.  The utility
148:      routine PCGASMCreateSubdomains2D() is a simple example, which partitions
149:      the 2D grid into MxN subdomains with an optional overlap.
150:      More generally, the user should write a custom routine for a particular
151:      problem geometry.

153:      Then call PCGASMSetLocalSubdomains() with resulting index sets
154:      to set the subdomains for the GASM preconditioner.
155:   */

157:   if (user_set_subdomains) { /* user-control version */
158:     PCGASMCreateSubdomains2D(pc, m,n,M,N,1,overlap,&Nsub,&inneris,&outeris);
159:     PCGASMSetSubdomains(pc,Nsub,inneris,outeris);
160:     PCGASMDestroySubdomains(Nsub,&inneris,&outeris);
161:     flg  = PETSC_FALSE;
162:     PetscOptionsGetBool(NULL,NULL,"-subdomain_view",&flg,NULL);
163:     if (flg) {
164:       PetscInt i;
165:       PetscPrintf(PETSC_COMM_SELF,"Nmesh points: %D x %D; subdomain partition: %D x %D; overlap: %D; Nsub: %D\n",m,n,M,N,overlap,Nsub);
166:       PetscPrintf(PETSC_COMM_SELF,"Outer IS:\n");
167:       for (i=0; i<Nsub; i++) {
168:         PetscPrintf(PETSC_COMM_SELF,"  outer IS[%D]\n",i);
169:         ISView(outeris[i],PETSC_VIEWER_STDOUT_SELF);
170:       }
171:       PetscPrintf(PETSC_COMM_SELF,"Inner IS:\n");
172:       for (i=0; i<Nsub; i++) {
173:         PetscPrintf(PETSC_COMM_SELF,"  inner IS[%D]\n",i);
174:         ISView(inneris[i],PETSC_VIEWER_STDOUT_SELF);
175:       }
176:     }
177:   } else { /* basic setup */
178:     KSPSetFromOptions(ksp);
179:   }

181:   /* -------------------------------------------------------------------
182:                 Set the linear solvers for the subblocks
183:      ------------------------------------------------------------------- */

185:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
186:        Basic method, should be sufficient for the needs of most users.
187:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

189:      By default, the GASM preconditioner uses the same solver on each
190:      block of the problem.  To set the same solver options on all blocks,
191:      use the prefix -sub before the usual PC and KSP options, e.g.,
192:           -sub_pc_type <pc> -sub_ksp_type <ksp> -sub_ksp_rtol 1.e-4

194:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
195:         Advanced method, setting different solvers for various blocks.
196:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

198:      Note that each block's KSP context is completely independent of
199:      the others, and the full range of uniprocessor KSP options is
200:      available for each block.

202:      - Use PCGASMGetSubKSP() to extract the array of KSP contexts for
203:        the local blocks.
204:      - See ex7.c for a simple example of setting different linear solvers
205:        for the individual blocks for the block Jacobi method (which is
206:        equivalent to the GASM method with zero overlap).
207:   */

209:   flg  = PETSC_FALSE;
210:   PetscOptionsGetBool(NULL,NULL,"-user_set_subdomain_solvers",&flg,NULL);
211:   if (flg) {
212:     KSP       *subksp;        /* array of KSP contexts for local subblocks */
213:     PetscInt  i,nlocal,first;   /* number of local subblocks, first local subblock */
214:     PC        subpc;          /* PC context for subblock */
215:     PetscBool isasm;

217:     PetscPrintf(PETSC_COMM_WORLD,"User explicitly sets subdomain solvers.\n");

219:     /*
220:        Set runtime options
221:     */
222:     KSPSetFromOptions(ksp);

224:     /*
225:        Flag an error if PCTYPE is changed from the runtime options
226:      */
227:     PetscObjectTypeCompare((PetscObject)pc,PCGASM,&isasm);
228:     if (!isasm) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Cannot Change the PCTYPE when manually changing the subdomain solver settings");

230:     /*
231:        Call KSPSetUp() to set the block Jacobi data structures (including
232:        creation of an internal KSP context for each block).

234:        Note: KSPSetUp() MUST be called before PCGASMGetSubKSP().
235:     */
236:     KSPSetUp(ksp);

238:     /*
239:        Extract the array of KSP contexts for the local blocks
240:     */
241:     PCGASMGetSubKSP(pc,&nlocal,&first,&subksp);

243:     /*
244:        Loop over the local blocks, setting various KSP options
245:        for each block.
246:     */
247:     for (i=0; i<nlocal; i++) {
248:       KSPGetPC(subksp[i],&subpc);
249:       PCSetType(subpc,PCILU);
250:       KSPSetType(subksp[i],KSPGMRES);
251:       KSPSetTolerances(subksp[i],1.e-7,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
252:     }
253:   } else {
254:     /*
255:        Set runtime options
256:     */
257:     KSPSetFromOptions(ksp);
258:   }

260:   /* -------------------------------------------------------------------
261:                       Solve the linear system
262:      ------------------------------------------------------------------- */

264:   KSPSolve(ksp,b,x);

266:   /* -------------------------------------------------------------------
267:         Assemble the matrix again to test repeated setup and solves.
268:      ------------------------------------------------------------------- */

270:   AssembleMatrix(A,m,n);
271:   KSPSolve(ksp,b,x);

273:   /* -------------------------------------------------------------------
274:                       Compare result to the exact solution
275:      ------------------------------------------------------------------- */
276:   VecAXPY(x,-1.0,u);
277:   VecNorm(x,NORM_INFINITY, &e);

279:   flg  = PETSC_FALSE;
280:   PetscOptionsGetBool(NULL,NULL,"-print_error",&flg,NULL);
281:   if (flg) {
282:     PetscPrintf(PETSC_COMM_WORLD, "Infinity norm of the error: %g\n", (double)e);
283:   }

285:   /*
286:      Free work space.  All PETSc objects should be destroyed when they
287:      are no longer needed.
288:   */

290:   KSPDestroy(&ksp);
291:   VecDestroy(&u);
292:   VecDestroy(&x);
293:   VecDestroy(&b);
294:   MatDestroy(&A);
295:   PetscFinalize();
296:   return ierr;
297: }

299: PetscErrorCode AssembleMatrix(Mat A,PetscInt m,PetscInt n)
300: {
302:   PetscInt       i,j,Ii,J,Istart,Iend;
303:   PetscScalar    v;

306:   MatGetOwnershipRange(A,&Istart,&Iend);
307:   for (Ii=Istart; Ii<Iend; Ii++) {
308:     v = -1.0; i = Ii/n; j = Ii - i*n;
309:     if (i>0)   {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
310:     if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
311:     if (j>0)   {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
312:     if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
313:     v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,INSERT_VALUES);
314:   }
315:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
316:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

318:   return(0);
319: }


322: /*TEST

324:    test:
325:       suffix: 2D_1
326:       args: -M 7 -N 9 -user_set_subdomains -Mdomains 1 -Ndomains 3 -overlap 1 -print_error -pc_gasm_print_subdomains

328:    test:
329:       suffix: 2D_2
330:       nsize: 2
331:       args: -M 7 -N 9 -user_set_subdomains -Mdomains 1 -Ndomains 3 -overlap 1 -print_error -pc_gasm_print_subdomains

333:    test:
334:       suffix: 2D_3
335:       nsize: 3
336:       args: -M 7 -N 9 -user_set_subdomains -Mdomains 1 -Ndomains 3 -overlap 1 -print_error -pc_gasm_print_subdomains

338:    test:
339:       suffix: hp
340:       nsize: 4
341:       requires: superlu_dist
342:       args: -M 7 -N 9 -pc_gasm_overlap 1 -sub_pc_type lu -sub_pc_factor_mat_solver_type superlu_dist -ksp_monitor -print_error -pc_gasm_total_subdomains 2 -pc_gasm_use_hierachical_partitioning 1
343:       output_file: output/ex62.out
344:       TODO: bug, triggers New nonzero at (0,15) caused a malloc in MatCreateSubMatrices_MPIAIJ_SingleIS_Local

346:    test:
347:       suffix: superlu_dist_1
348:       requires: superlu_dist
349:       args: -M 7 -N 9 -print_error -pc_gasm_total_subdomains 1 -pc_gasm_print_subdomains -sub_pc_type lu -sub_pc_factor_mat_solver_type superlu_dist

351:    test:
352:       suffix: superlu_dist_2
353:       nsize: 2
354:       requires: superlu_dist
355:       args: -M 7 -N 9 -print_error -pc_gasm_total_subdomains 1 -pc_gasm_print_subdomains -sub_pc_type lu -sub_pc_factor_mat_solver_type superlu_dist

357:    test:
358:       suffix: superlu_dist_3
359:       nsize: 3
360:       requires: superlu_dist
361:       args: -M 7 -N 9 -print_error -pc_gasm_total_subdomains 2 -pc_gasm_print_subdomains -sub_pc_type lu -sub_pc_factor_mat_solver_type superlu_dist

363:    test:
364:       suffix: superlu_dist_4
365:       nsize: 4
366:       requires: superlu_dist
367:       args: -M 7 -N 9 -print_error -pc_gasm_total_subdomains 2 -pc_gasm_print_subdomains -sub_pc_type lu -sub_pc_factor_mat_solver_type superlu_dist

369: TEST*/