Actual source code: ex62.c

petsc-3.7.7 2017-09-25
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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*/

 32: /*
 33:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
 34:   automatically includes:
 35:      petscsys.h    - base PETSc routines   petscvec.h - vectors
 36:      petscmat.h    - matrices
 37:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
 38:      petscviewer.h - viewers               petscpc.h  - preconditioners
 39: */
 40: #include <petscksp.h>

 42: 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);
 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:   AssembleMatrix(A,m,n);

 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:   one  = 1.0;
103:   VecSet(u,one);
104:   MatMult(A,u,b);

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

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

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

123:   /* -------------------------------------------------------------------
124:                   Define the problem decomposition
125:      ------------------------------------------------------------------- */

127:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
128:        Basic method, should be sufficient for the needs of many users.
129:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

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

141:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
142:        More advanced method, setting user-defined subdomains
143:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

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

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

179:   /* -------------------------------------------------------------------
180:                 Set the linear solvers for the subblocks
181:      ------------------------------------------------------------------- */

183:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
184:        Basic method, should be sufficient for the needs of most users.
185:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

192:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
193:         Advanced method, setting different solvers for various blocks.
194:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

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

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

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

217:     /*
218:        Set runtime options
219:     */
220:     KSPSetFromOptions(ksp);

222:     /*
223:        Flag an error if PCTYPE is changed from the runtime options
224:      */
225:     PetscObjectTypeCompare((PetscObject)pc,PCGASM,&isasm);
226:     if (!isasm) SETERRQ(PETSC_COMM_WORLD,1,"Cannot Change the PCTYPE when manually changing the subdomain solver settings");

228:     /*
229:        Call KSPSetUp() to set the block Jacobi data structures (including
230:        creation of an internal KSP context for each block).

232:        Note: KSPSetUp() MUST be called before PCGASMGetSubKSP().
233:     */
234:     KSPSetUp(ksp);

236:     /*
237:        Extract the array of KSP contexts for the local blocks
238:     */
239:     PCGASMGetSubKSP(pc,&nlocal,&first,&subksp);

241:     /*
242:        Loop over the local blocks, setting various KSP options
243:        for each block.
244:     */
245:     for (i=0; i<nlocal; i++) {
246:       KSPGetPC(subksp[i],&subpc);
247:       PCSetType(subpc,PCILU);
248:       KSPSetType(subksp[i],KSPGMRES);
249:       KSPSetTolerances(subksp[i],1.e-7,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
250:     }
251:   } else {
252:     /*
253:        Set runtime options
254:     */
255:     KSPSetFromOptions(ksp);
256:   }

258:   /* -------------------------------------------------------------------
259:                       Solve the linear system
260:      ------------------------------------------------------------------- */

262:   KSPSolve(ksp,b,x);

264:   /* -------------------------------------------------------------------
265:         Assemble the matrix again to test repeated setup and solves.
266:      ------------------------------------------------------------------- */

268:   AssembleMatrix(A,m,n);
269:   KSPSolve(ksp,b,x);

271:   /* -------------------------------------------------------------------
272:                       Compare result to the exact solution
273:      ------------------------------------------------------------------- */
274:   VecAXPY(x,-1.0,u);
275:   VecNorm(x,NORM_INFINITY, &e);

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

283:   /*
284:      Free work space.  All PETSc objects should be destroyed when they
285:      are no longer needed.
286:   */

288:   KSPDestroy(&ksp);
289:   VecDestroy(&u);
290:   VecDestroy(&x);
291:   VecDestroy(&b);
292:   MatDestroy(&A);
293:   PetscFinalize();
294:   return 0;
295: }

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: }