Actual source code: ex7.c

petsc-3.4.4 2014-03-13
  2: static char help[] = "Block Jacobi preconditioner for solving a linear system in parallel with KSP.\n\
  3: The code indicates the\n\
  4: procedures for setting the particular block sizes and for using different\n\
  5: linear solvers on the individual blocks.\n\n";

  7: /*
  8:    Note:  This example focuses on ways to customize the block Jacobi
  9:    preconditioner. See ex1.c and ex2.c for more detailed comments on
 10:    the basic usage of KSP (including working with matrices and vectors).

 12:    Recall: The block Jacobi method is equivalent to the ASM preconditioner
 13:    with zero overlap.
 14:  */

 16: /*T
 17:    Concepts: KSP^customizing the block Jacobi preconditioner
 18:    Processors: n
 19: T*/

 21: /*
 22:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
 23:   automatically includes:
 24:      petscsys.h       - base PETSc routines   petscvec.h - vectors
 25:      petscmat.h - matrices
 26:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
 27:      petscviewer.h - viewers               petscpc.h  - preconditioners
 28: */
 29: #include <petscksp.h>

 33: int main(int argc,char **args)
 34: {
 35:   Vec            x,b,u;      /* approx solution, RHS, exact solution */
 36:   Mat            A;            /* linear system matrix */
 37:   KSP            ksp;         /* KSP context */
 38:   KSP            *subksp;     /* array of local KSP contexts on this processor */
 39:   PC             pc;           /* PC context */
 40:   PC             subpc;        /* PC context for subdomain */
 41:   PetscReal      norm;         /* norm of solution error */
 43:   PetscInt       i,j,Ii,J,*blks,m = 8,n;
 44:   PetscMPIInt    rank,size;
 45:   PetscInt       its,nlocal,first,Istart,Iend;
 46:   PetscScalar    v,one = 1.0,none = -1.0;
 47:   PetscBool      isbjacobi,flg = PETSC_FALSE;

 49:   PetscInitialize(&argc,&args,(char*)0,help);
 50:   PetscOptionsGetInt(NULL,"-m",&m,NULL);
 51:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
 52:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
 53:   n    = m+2;

 55:   /* -------------------------------------------------------------------
 56:          Compute the matrix and right-hand-side vector that define
 57:          the linear system, Ax = b.
 58:      ------------------------------------------------------------------- */

 60:   /*
 61:      Create and assemble parallel matrix
 62:   */
 63:   MatCreate(PETSC_COMM_WORLD,&A);
 64:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
 65:   MatSetFromOptions(A);
 66:   MatMPIAIJSetPreallocation(A,5,NULL,5,NULL);
 67:   MatSeqAIJSetPreallocation(A,5,NULL);
 68:   MatGetOwnershipRange(A,&Istart,&Iend);
 69:   for (Ii=Istart; Ii<Iend; Ii++) {
 70:     v = -1.0; i = Ii/n; j = Ii - i*n;
 71:     if (i>0)   {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
 72:     if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
 73:     if (j>0)   {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
 74:     if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
 75:     v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,ADD_VALUES);
 76:   }
 77:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 78:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

 80:   /*
 81:      Create parallel vectors
 82:   */
 83:   VecCreate(PETSC_COMM_WORLD,&u);
 84:   VecSetSizes(u,PETSC_DECIDE,m*n);
 85:   VecSetFromOptions(u);
 86:   VecDuplicate(u,&b);
 87:   VecDuplicate(b,&x);

 89:   /*
 90:      Set exact solution; then compute right-hand-side vector.
 91:   */
 92:   VecSet(u,one);
 93:   MatMult(A,u,b);

 95:   /*
 96:      Create linear solver context
 97:   */
 98:   KSPCreate(PETSC_COMM_WORLD,&ksp);

100:   /*
101:      Set operators. Here the matrix that defines the linear system
102:      also serves as the preconditioning matrix.
103:   */
104:   KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN);

106:   /*
107:      Set default preconditioner for this program to be block Jacobi.
108:      This choice can be overridden at runtime with the option
109:         -pc_type <type>
110:   */
111:   KSPGetPC(ksp,&pc);
112:   PCSetType(pc,PCBJACOBI);


115:   /* -------------------------------------------------------------------
116:                    Define the problem decomposition
117:      ------------------------------------------------------------------- */

119:   /*
120:      Call PCBJacobiSetTotalBlocks() to set individually the size of
121:      each block in the preconditioner.  This could also be done with
122:      the runtime option
123:          -pc_bjacobi_blocks <blocks>
124:      Also, see the command PCBJacobiSetLocalBlocks() to set the
125:      local blocks.

127:       Note: The default decomposition is 1 block per processor.
128:   */
129:   PetscMalloc(m*sizeof(PetscInt),&blks);
130:   for (i=0; i<m; i++) blks[i] = n;
131:   PCBJacobiSetTotalBlocks(pc,m,blks);
132:   PetscFree(blks);


135:   /* -------------------------------------------------------------------
136:                Set the linear solvers for the subblocks
137:      ------------------------------------------------------------------- */

139:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
140:        Basic method, should be sufficient for the needs of most users.
141:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

143:      By default, the block Jacobi method uses the same solver on each
144:      block of the problem.  To set the same solver options on all blocks,
145:      use the prefix -sub before the usual PC and KSP options, e.g.,
146:           -sub_pc_type <pc> -sub_ksp_type <ksp> -sub_ksp_rtol 1.e-4
147:   */

149:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
150:         Advanced method, setting different solvers for various blocks.
151:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

153:      Note that each block's KSP context is completely independent of
154:      the others, and the full range of uniprocessor KSP options is
155:      available for each block. The following section of code is intended
156:      to be a simple illustration of setting different linear solvers for
157:      the individual blocks.  These choices are obviously not recommended
158:      for solving this particular problem.
159:   */
160:   PetscObjectTypeCompare((PetscObject)pc,PCBJACOBI,&isbjacobi);
161:   if (isbjacobi) {
162:     /*
163:        Call KSPSetUp() to set the block Jacobi data structures (including
164:        creation of an internal KSP context for each block).

166:        Note: KSPSetUp() MUST be called before PCBJacobiGetSubKSP().
167:     */
168:     KSPSetUp(ksp);

170:     /*
171:        Extract the array of KSP contexts for the local blocks
172:     */
173:     PCBJacobiGetSubKSP(pc,&nlocal,&first,&subksp);

175:     /*
176:        Loop over the local blocks, setting various KSP options
177:        for each block.
178:     */
179:     for (i=0; i<nlocal; i++) {
180:       KSPGetPC(subksp[i],&subpc);
181:       if (!rank) {
182:         if (i%2) {
183:           PCSetType(subpc,PCILU);
184:         } else {
185:           PCSetType(subpc,PCNONE);
186:           KSPSetType(subksp[i],KSPBCGS);
187:           KSPSetTolerances(subksp[i],1.e-6,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
188:         }
189:       } else {
190:         PCSetType(subpc,PCJACOBI);
191:         KSPSetType(subksp[i],KSPGMRES);
192:         KSPSetTolerances(subksp[i],1.e-7,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
193:       }
194:     }
195:   }

197:   /* -------------------------------------------------------------------
198:                       Solve the linear system
199:      ------------------------------------------------------------------- */

201:   /*
202:     Set runtime options
203:   */
204:   KSPSetFromOptions(ksp);

206:   /*
207:      Solve the linear system
208:   */
209:   KSPSolve(ksp,b,x);

211:   /*
212:      View info about the solver
213:   */
214:   PetscOptionsGetBool(NULL,"-nokspview",&flg,NULL);
215:   if (!flg) {
216:     KSPView(ksp,PETSC_VIEWER_STDOUT_WORLD);
217:   }

219:   /* -------------------------------------------------------------------
220:                       Check solution and clean up
221:      ------------------------------------------------------------------- */

223:   /*
224:      Check the error
225:   */
226:   VecAXPY(x,none,u);
227:   VecNorm(x,NORM_2,&norm);
228:   KSPGetIterationNumber(ksp,&its);
229:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %G iterations %D\n",norm,its);

231:   /*
232:      Free work space.  All PETSc objects should be destroyed when they
233:      are no longer needed.
234:   */
235:   KSPDestroy(&ksp);
236:   VecDestroy(&u);  VecDestroy(&x);
237:   VecDestroy(&b);  MatDestroy(&A);
238:   PetscFinalize();
239:   return 0;
240: }