Actual source code: ex8.c

petsc-dev 2014-04-23
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  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>

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

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

 70:   /* -------------------------------------------------------------------
 71:          Compute the matrix and right-hand-side vector that define
 72:          the linear system, Ax = b.
 73:      ------------------------------------------------------------------- */

 75:   /*
 76:      Assemble the matrix for the five point stencil, YET AGAIN
 77:   */
 78:   MatCreate(PETSC_COMM_WORLD,&A);
 79:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
 80:   MatSetFromOptions(A);
 81:   MatSetUp(A);
 82:   MatGetOwnershipRange(A,&Istart,&Iend);
 83:   for (Ii=Istart; Ii<Iend; Ii++) {
 84:     v = -1.0; i = Ii/n; j = Ii - i*n;
 85:     if (i>0)   {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 86:     if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 87:     if (j>0)   {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 88:     if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 89:     v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,INSERT_VALUES);
 90:   }
 91:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 92:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

 94:   /*
 95:      Create and set vectors
 96:   */
 97:   VecCreate(PETSC_COMM_WORLD,&b);
 98:   VecSetSizes(b,PETSC_DECIDE,m*n);
 99:   VecSetFromOptions(b);
100:   VecDuplicate(b,&u);
101:   VecDuplicate(b,&x);
102:   VecSet(u,one);
103:   MatMult(A,u,b);

105:   /*
106:      Create linear solver context
107:   */
108:   KSPCreate(PETSC_COMM_WORLD,&ksp);

110:   /*
111:      Set operators. Here the matrix that defines the linear system
112:      also serves as the preconditioning matrix.
113:   */
114:   KSPSetOperators(ksp,A,A);

116:   /*
117:      Set the default preconditioner for this program to be ASM
118:   */
119:   KSPGetPC(ksp,&pc);
120:   PCSetType(pc,PCASM);

122:   /* -------------------------------------------------------------------
123:                   Define the problem decomposition
124:      ------------------------------------------------------------------- */

126:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
127:        Basic method, should be sufficient for the needs of many users.
128:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

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

140:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
141:        More advanced method, setting user-defined subdomains
142:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

149:      Then call either PCASMSetLocalSubdomains() or PCASMSetTotalSubdomains()
150:      to set the subdomains for the ASM preconditioner.
151:   */

153:   if (!user_subdomains) { /* basic version */
154:     PCASMSetOverlap(pc,overlap);
155:   } else { /* advanced version */
156:     if (size != 1) SETERRQ(PETSC_COMM_WORLD,1,"PCASMCreateSubdomains2D() is currently a uniprocessor routine only!");
157:     PCASMCreateSubdomains2D(m,n,M,N,1,overlap,&Nsub,&is,&is_local);
158:     PCASMSetLocalSubdomains(pc,Nsub,is,is_local);
159:     flg  = PETSC_FALSE;
160:     PetscOptionsGetBool(NULL,"-subdomain_view",&flg,NULL);
161:     if (flg) {
162:       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);
163:       PetscPrintf(PETSC_COMM_SELF,"IS:\n");
164:       for (i=0; i<Nsub; i++) {
165:         PetscPrintf(PETSC_COMM_SELF,"  IS[%D]\n",i);
166:         ISView(is[i],PETSC_VIEWER_STDOUT_SELF);
167:       }
168:       PetscPrintf(PETSC_COMM_SELF,"IS_local:\n");
169:       for (i=0; i<Nsub; i++) {
170:         PetscPrintf(PETSC_COMM_SELF,"  IS_local[%D]\n",i);
171:         ISView(is_local[i],PETSC_VIEWER_STDOUT_SELF);
172:       }
173:     }
174:   }

176:   /* -------------------------------------------------------------------
177:                 Set the linear solvers for the subblocks
178:      ------------------------------------------------------------------- */

180:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
181:        Basic method, should be sufficient for the needs of most users.
182:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

189:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
190:         Advanced method, setting different solvers for various blocks.
191:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

197:      - Use PCASMGetSubKSP() to extract the array of KSP contexts for
198:        the local blocks.
199:      - See ex7.c for a simple example of setting different linear solvers
200:        for the individual blocks for the block Jacobi method (which is
201:        equivalent to the ASM method with zero overlap).
202:   */

204:   flg  = PETSC_FALSE;
205:   PetscOptionsGetBool(NULL,"-user_set_subdomain_solvers",&flg,NULL);
206:   if (flg) {
207:     KSP       *subksp;        /* array of KSP contexts for local subblocks */
208:     PetscInt  nlocal,first;   /* number of local subblocks, first local subblock */
209:     PC        subpc;          /* PC context for subblock */
210:     PetscBool isasm;

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

214:     /*
215:        Set runtime options
216:     */
217:     KSPSetFromOptions(ksp);

219:     /*
220:        Flag an error if PCTYPE is changed from the runtime options
221:      */
222:     PetscObjectTypeCompare((PetscObject)pc,PCASM,&isasm);
223:     if (!isasm) SETERRQ(PETSC_COMM_WORLD,1,"Cannot Change the PCTYPE when manually changing the subdomain solver settings");

225:     /*
226:        Call KSPSetUp() to set the block Jacobi data structures (including
227:        creation of an internal KSP context for each block).

229:        Note: KSPSetUp() MUST be called before PCASMGetSubKSP().
230:     */
231:     KSPSetUp(ksp);

233:     /*
234:        Extract the array of KSP contexts for the local blocks
235:     */
236:     PCASMGetSubKSP(pc,&nlocal,&first,&subksp);

238:     /*
239:        Loop over the local blocks, setting various KSP options
240:        for each block.
241:     */
242:     for (i=0; i<nlocal; i++) {
243:       KSPGetPC(subksp[i],&subpc);
244:       PCSetType(subpc,PCILU);
245:       KSPSetType(subksp[i],KSPGMRES);
246:       KSPSetTolerances(subksp[i],1.e-7,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
247:     }
248:   } else {
249:     /*
250:        Set runtime options
251:     */
252:     KSPSetFromOptions(ksp);
253:   }

255:   /* -------------------------------------------------------------------
256:                       Solve the linear system
257:      ------------------------------------------------------------------- */

259:   KSPSolve(ksp,b,x);

261:   /* -------------------------------------------------------------------
262:                       Compare result to the exact solution
263:      ------------------------------------------------------------------- */
264:   VecAXPY(x,-1.0,u);
265:   VecNorm(x,NORM_INFINITY, &e);

267:   flg  = PETSC_FALSE;
268:   PetscOptionsGetBool(NULL,"-print_error",&flg,NULL);
269:   if (flg) {
270:     PetscPrintf(PETSC_COMM_WORLD, "Infinity norm of the error: %g\n",(double) e);
271:   }

273:   /*
274:      Free work space.  All PETSc objects should be destroyed when they
275:      are no longer needed.
276:   */

278:   if (user_subdomains) {
279:     for (i=0; i<Nsub; i++) {
280:       ISDestroy(&is[i]);
281:       ISDestroy(&is_local[i]);
282:     }
283:     PetscFree(is);
284:     PetscFree(is_local);
285:   }
286:   KSPDestroy(&ksp);
287:   VecDestroy(&u);
288:   VecDestroy(&x);
289:   VecDestroy(&b);
290:   MatDestroy(&A);
291:   PetscFinalize();
292:   return 0;
293: }