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:      petsc.h       - base PETSc routines   petscvec.h - vectors
 34:      petscsys.h    - system routines       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;                     /* 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:   PetscTruth     flg;
 57:   PetscTruth     user_subdomains;         /* flag - 1 indicates user-defined subdomains */
 58:   PetscScalar    v, one = 1.0;

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

 69:   /* -------------------------------------------------------------------
 70:          Compute the matrix and right-hand-side vector that define
 71:          the linear system, Ax = b.
 72:      ------------------------------------------------------------------- */

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

 92:   /* 
 93:      Create and set vectors 
 94:   */
 95:   VecCreate(PETSC_COMM_WORLD,&b);
 96:   VecSetSizes(b,PETSC_DECIDE,m*n);
 97:   VecSetFromOptions(b);
 98:   VecDuplicate(b,&u);
 99:   VecDuplicate(b,&x);
100:   VecSet(u,one);
101:   MatMult(A,u,b);

103:   /* 
104:      Create linear solver context 
105:   */
106:   KSPCreate(PETSC_COMM_WORLD,&ksp);

108:   /* 
109:      Set operators. Here the matrix that defines the linear system
110:      also serves as the preconditioning matrix.
111:   */
112:   KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN);

114:   /* 
115:      Set the default preconditioner for this program to be ASM
116:   */
117:   KSPGetPC(ksp,&pc);
118:   PCSetType(pc,PCASM);

120:   /* -------------------------------------------------------------------
121:                   Define the problem decomposition
122:      ------------------------------------------------------------------- */

124:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
125:        Basic method, should be sufficient for the needs of many users.
126:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 

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

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

138:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
139:        More advanced method, setting user-defined subdomains
140:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 

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

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

151:   if (!user_subdomains) { /* basic version */
152:     PCASMSetOverlap(pc,overlap);
153:   } else { /* advanced version */
154:     if (size != 1) SETERRQ(1,"PCASMCreateSubdomains() is currently a uniprocessor routine only!");
155:     PCASMCreateSubdomains2D(m,n,M,N,1,overlap,&Nsub,&is);
156:     PCASMSetLocalSubdomains(pc,Nsub,is);
157:   }

159:   /* -------------------------------------------------------------------
160:                 Set the linear solvers for the subblocks
161:      ------------------------------------------------------------------- */

163:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
164:        Basic method, should be sufficient for the needs of most users.
165:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 

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

172:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
173:         Advanced method, setting different solvers for various blocks.
174:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 

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

180:      - Use PCASMGetSubKSP() to extract the array of KSP contexts for
181:        the local blocks.
182:      - See ex7.c for a simple example of setting different linear solvers
183:        for the individual blocks for the block Jacobi method (which is
184:        equivalent to the ASM method with zero overlap).
185:   */

187:   PetscOptionsHasName(PETSC_NULL,"-user_set_subdomain_solvers",&flg);
188:   if (flg) {
189:     KSP        *subksp;       /* array of KSP contexts for local subblocks */
190:     PetscInt   nlocal,first;  /* number of local subblocks, first local subblock */
191:     PC         subpc;          /* PC context for subblock */
192:     PetscTruth isasm;

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

196:     /* 
197:        Set runtime options
198:     */
199:     KSPSetFromOptions(ksp);

201:     /* 
202:        Flag an error if PCTYPE is changed from the runtime options
203:      */
204:     PetscTypeCompare((PetscObject)pc,PCASM,&isasm);
205:     if (isasm) {
206:       SETERRQ(1,"Cannot Change the PCTYPE when manually changing the subdomain solver settings");
207:     }
208:     /* 
209:        Call KSPSetUp() to set the block Jacobi data structures (including
210:        creation of an internal KSP context for each block).

212:        Note: KSPSetUp() MUST be called before PCASMGetSubKSP().
213:     */
214:     KSPSetUp(ksp);

216:     /*
217:        Extract the array of KSP contexts for the local blocks
218:     */
219:     PCASMGetSubKSP(pc,&nlocal,&first,&subksp);

221:     /*
222:        Loop over the local blocks, setting various KSP options
223:        for each block.  
224:     */
225:     for (i=0; i<nlocal; i++) {
226:       KSPGetPC(subksp[i],&subpc);
227:       PCSetType(subpc,PCILU);
228:       KSPSetType(subksp[i],KSPGMRES);
229:       KSPSetTolerances(subksp[i],1.e-7,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
230:     }
231:   } else {
232:     /* 
233:        Set runtime options
234:     */
235:     KSPSetFromOptions(ksp);
236:   }

238:   /* -------------------------------------------------------------------
239:                       Solve the linear system
240:      ------------------------------------------------------------------- */

242:   KSPSolve(ksp,b,x);

244:   /* 
245:      Free work space.  All PETSc objects should be destroyed when they
246:      are no longer needed.
247:   */

249:   if (user_subdomains) {
250:     for (i=0; i<Nsub; i++) {
251:       ISDestroy(is[i]);
252:     }
253:     PetscFree(is);
254:   }
255:   KSPDestroy(ksp);
256:   VecDestroy(u);
257:   VecDestroy(x);
258:   VecDestroy(b);
259:   MatDestroy(A);
260:   PetscFinalize();
261:   return 0;
262: }