Actual source code: ex8.c


  2: static char help[] = "Illustrates use of the preconditioner ASM.\n\
  3: The Additive Schwarz Method for solving a linear system in parallel with KSP.  The\n\
  4: code indicates the procedure for setting user-defined subdomains.  Input\n\
  5: parameters include:\n\
  6:   -user_set_subdomain_solvers:  User explicitly sets subdomain solvers\n\
  7:   -user_set_subdomains:  Activate user-defined subdomains\n\n";

  9: /*
 10:    Note:  This example focuses on setting the subdomains for the ASM
 11:    preconditioner for a problem on a 2D rectangular grid.  See ex1.c
 12:    and ex2.c for more detailed comments on the basic usage of KSP
 13:    (including working with matrices and vectors).

 15:    The ASM preconditioner is fully parallel, but currently the routine
 16:    PCASMCreateSubdomains2D(), which is used in this example to demonstrate
 17:    user-defined subdomains (activated via -user_set_subdomains), is
 18:    uniprocessor only.

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

 25: /*T
 26:    Concepts: KSP^Additive Schwarz Method (ASM) with user-defined subdomains
 27:    Processors: n
 28: T*/

 30: /*
 31:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
 32:   automatically includes:
 33:      petscsys.h       - base PETSc routines   petscvec.h - vectors
 34:      petscmat.h - matrices
 35:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
 36:      petscviewer.h - viewers               petscpc.h  - preconditioners
 37: */
 38: #include <petscksp.h>

 40: int main(int argc,char **args)
 41: {
 42:   Vec            x,b,u;                 /* approx solution, RHS, exact solution */
 43:   Mat            A;                       /* linear system matrix */
 44:   KSP            ksp;                    /* linear solver context */
 45:   PC             pc;                      /* PC context */
 46:   IS             *is,*is_local;           /* array of index sets that define the subdomains */
 47:   PetscInt       overlap = 1;             /* width of subdomain overlap */
 48:   PetscInt       Nsub;                    /* number of subdomains */
 49:   PetscInt       m = 15,n = 17;          /* mesh dimensions in x- and y- directions */
 50:   PetscInt       M = 2,N = 1;            /* number of subdomains in x- and y- directions */
 51:   PetscInt       i,j,Ii,J,Istart,Iend;
 52:   PetscMPIInt    size;
 53:   PetscBool      flg;
 54:   PetscBool      user_subdomains = PETSC_FALSE;
 55:   PetscScalar    v, one = 1.0;
 56:   PetscReal      e;

 58:   PetscInitialize(&argc,&args,(char*)0,help);
 59:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
 60:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
 61:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 62:   PetscOptionsGetInt(NULL,NULL,"-Mdomains",&M,NULL);
 63:   PetscOptionsGetInt(NULL,NULL,"-Ndomains",&N,NULL);
 64:   PetscOptionsGetInt(NULL,NULL,"-overlap",&overlap,NULL);
 65:   PetscOptionsGetBool(NULL,NULL,"-user_set_subdomains",&user_subdomains,NULL);

 67:   /* -------------------------------------------------------------------
 68:          Compute the matrix and right-hand-side vector that define
 69:          the linear system, Ax = b.
 70:      ------------------------------------------------------------------- */

 72:   /*
 73:      Assemble the matrix for the five point stencil, YET AGAIN
 74:   */
 75:   MatCreate(PETSC_COMM_WORLD,&A);
 76:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
 77:   MatSetFromOptions(A);
 78:   MatSetUp(A);
 79:   MatGetOwnershipRange(A,&Istart,&Iend);
 80:   for (Ii=Istart; Ii<Iend; Ii++) {
 81:     v = -1.0; i = Ii/n; j = Ii - i*n;
 82:     if (i>0)   {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 83:     if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 84:     if (j>0)   {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 85:     if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 86:     v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,INSERT_VALUES);
 87:   }
 88:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 89:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

 91:   /*
 92:      Create and set vectors
 93:   */
 94:   MatCreateVecs(A,&u,&b);
 95:   VecDuplicate(u,&x);
 96:   VecSet(u,one);
 97:   MatMult(A,u,b);

 99:   /*
100:      Create linear solver context
101:   */
102:   KSPCreate(PETSC_COMM_WORLD,&ksp);

104:   /*
105:      Set operators. Here the matrix that defines the linear system
106:      also serves as the preconditioning matrix.
107:   */
108:   KSPSetOperators(ksp,A,A);

110:   /*
111:      Set the default preconditioner for this program to be ASM
112:   */
113:   KSPGetPC(ksp,&pc);
114:   PCSetType(pc,PCASM);

116:   /* -------------------------------------------------------------------
117:                   Define the problem decomposition
118:      ------------------------------------------------------------------- */

120:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
121:        Basic method, should be sufficient for the needs of many users.
122:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

124:      Set the overlap, using the default PETSc decomposition via
125:          PCASMSetOverlap(pc,overlap);
126:      Could instead use the option -pc_asm_overlap <ovl>

128:      Set the total number of blocks via -pc_asm_blocks <blks>
129:      Note:  The ASM default is to use 1 block per processor.  To
130:      experiment on a single processor with various overlaps, you
131:      must specify use of multiple blocks!
132:   */

134:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
135:        More advanced method, setting user-defined subdomains
136:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

138:      Firstly, create index sets that define the subdomains.  The utility
139:      routine PCASMCreateSubdomains2D() is a simple example (that currently
140:      supports 1 processor only!).  More generally, the user should write
141:      a custom routine for a particular problem geometry.

143:      Then call either PCASMSetLocalSubdomains() or PCASMSetTotalSubdomains()
144:      to set the subdomains for the ASM preconditioner.
145:   */

147:   if (!user_subdomains) { /* basic version */
148:     PCASMSetOverlap(pc,overlap);
149:   } else { /* advanced version */
151:     PCASMCreateSubdomains2D(m,n,M,N,1,overlap,&Nsub,&is,&is_local);
152:     PCASMSetLocalSubdomains(pc,Nsub,is,is_local);
153:     flg  = PETSC_FALSE;
154:     PetscOptionsGetBool(NULL,NULL,"-subdomain_view",&flg,NULL);
155:     if (flg) {
156:       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);
157:       PetscPrintf(PETSC_COMM_SELF,"IS:\n");
158:       for (i=0; i<Nsub; i++) {
159:         PetscPrintf(PETSC_COMM_SELF,"  IS[%D]\n",i);
160:         ISView(is[i],PETSC_VIEWER_STDOUT_SELF);
161:       }
162:       PetscPrintf(PETSC_COMM_SELF,"IS_local:\n");
163:       for (i=0; i<Nsub; i++) {
164:         PetscPrintf(PETSC_COMM_SELF,"  IS_local[%D]\n",i);
165:         ISView(is_local[i],PETSC_VIEWER_STDOUT_SELF);
166:       }
167:     }
168:   }

170:   /* -------------------------------------------------------------------
171:                 Set the linear solvers for the subblocks
172:      ------------------------------------------------------------------- */

174:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
175:        Basic method, should be sufficient for the needs of most users.
176:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

183:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
184:         Advanced method, setting different solvers for various blocks.
185:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

191:      - Use PCASMGetSubKSP() to extract the array of KSP contexts for
192:        the local blocks.
193:      - See ex7.c for a simple example of setting different linear solvers
194:        for the individual blocks for the block Jacobi method (which is
195:        equivalent to the ASM method with zero overlap).
196:   */

198:   flg  = PETSC_FALSE;
199:   PetscOptionsGetBool(NULL,NULL,"-user_set_subdomain_solvers",&flg,NULL);
200:   if (flg) {
201:     KSP       *subksp;        /* array of KSP contexts for local subblocks */
202:     PetscInt  nlocal,first;   /* number of local subblocks, first local subblock */
203:     PC        subpc;          /* PC context for subblock */
204:     PetscBool isasm;

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

208:     /*
209:        Set runtime options
210:     */
211:     KSPSetFromOptions(ksp);

213:     /*
214:        Flag an error if PCTYPE is changed from the runtime options
215:      */
216:     PetscObjectTypeCompare((PetscObject)pc,PCASM,&isasm);

219:     /*
220:        Call KSPSetUp() to set the block Jacobi data structures (including
221:        creation of an internal KSP context for each block).

223:        Note: KSPSetUp() MUST be called before PCASMGetSubKSP().
224:     */
225:     KSPSetUp(ksp);

227:     /*
228:        Extract the array of KSP contexts for the local blocks
229:     */
230:     PCASMGetSubKSP(pc,&nlocal,&first,&subksp);

232:     /*
233:        Loop over the local blocks, setting various KSP options
234:        for each block.
235:     */
236:     for (i=0; i<nlocal; i++) {
237:       KSPGetPC(subksp[i],&subpc);
238:       PCSetType(subpc,PCILU);
239:       KSPSetType(subksp[i],KSPGMRES);
240:       KSPSetTolerances(subksp[i],1.e-7,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
241:     }
242:   } else {
243:     /*
244:        Set runtime options
245:     */
246:     KSPSetFromOptions(ksp);
247:   }

249:   /* -------------------------------------------------------------------
250:                       Solve the linear system
251:      ------------------------------------------------------------------- */

253:   KSPSolve(ksp,b,x);

255:   /* -------------------------------------------------------------------
256:                       Compare result to the exact solution
257:      ------------------------------------------------------------------- */
258:   VecAXPY(x,-1.0,u);
259:   VecNorm(x,NORM_INFINITY, &e);

261:   flg  = PETSC_FALSE;
262:   PetscOptionsGetBool(NULL,NULL,"-print_error",&flg,NULL);
263:   if (flg) {
264:     PetscPrintf(PETSC_COMM_WORLD, "Infinity norm of the error: %g\n",(double) e);
265:   }

267:   /*
268:      Free work space.  All PETSc objects should be destroyed when they
269:      are no longer needed.
270:   */

272:   if (user_subdomains) {
273:     for (i=0; i<Nsub; i++) {
274:       ISDestroy(&is[i]);
275:       ISDestroy(&is_local[i]);
276:     }
277:     PetscFree(is);
278:     PetscFree(is_local);
279:   }
280:   KSPDestroy(&ksp);
281:   VecDestroy(&u);
282:   VecDestroy(&x);
283:   VecDestroy(&b);
284:   MatDestroy(&A);
285:   PetscFinalize();
286:   return 0;
287: }

289: /*TEST

291:    test:
292:       suffix: 1
293:       args: -print_error

295: TEST*/