Actual source code: ex7.c

  1: /*$Id: ex7.c,v 1.58 2001/08/07 21:30:54 bsmith Exp $*/

  3: static char help[] = "Block Jacobi preconditioner for solving a linear system in parallel with SLES.n
  4: The code indicates then
  5: procedures for setting the particular block sizes and for using differentn
  6: linear solvers on the individual blocks.nn";

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

 13:    Recall: The block Jacobi method is equivalent to the ASM preconditioner
 14:    with zero overlap.
 15:  */

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

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

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

 49:   PetscInitialize(&argc,&args,(char *)0,help);
 50:   PetscOptionsGetInt(PETSC_NULL,"-m",&m,PETSC_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,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n,&A);
 64:   MatSetFromOptions(A);
 65:   MatGetOwnershipRange(A,&Istart,&Iend);
 66:   for (I=Istart; I<Iend; I++) {
 67:     v = -1.0; i = I/n; j = I - i*n;
 68:     if (i>0)   {J = I - n; MatSetValues(A,1,&I,1,&J,&v,ADD_VALUES);}
 69:     if (i<m-1) {J = I + n; MatSetValues(A,1,&I,1,&J,&v,ADD_VALUES);}
 70:     if (j>0)   {J = I - 1; MatSetValues(A,1,&I,1,&J,&v,ADD_VALUES);}
 71:     if (j<n-1) {J = I + 1; MatSetValues(A,1,&I,1,&J,&v,ADD_VALUES);}
 72:     v = 4.0; MatSetValues(A,1,&I,1,&I,&v,ADD_VALUES);
 73:   }
 74:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 75:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

 77:   /*
 78:      Create parallel vectors
 79:   */
 80:   VecCreate(PETSC_COMM_WORLD,&u);
 81:   VecSetSizes(u,PETSC_DECIDE,m*n);
 82:   VecSetFromOptions(u);
 83:   VecDuplicate(u,&b);
 84:   VecDuplicate(b,&x);

 86:   /*
 87:      Set exact solution; then compute right-hand-side vector.
 88:   */
 89:   VecSet(&one,u);
 90:   MatMult(A,u,b);

 92:   /*
 93:      Create linear solver context
 94:   */
 95:   SLESCreate(PETSC_COMM_WORLD,&sles);

 97:   /* 
 98:      Set operators. Here the matrix that defines the linear system
 99:      also serves as the preconditioning matrix.
100:   */
101:   SLESSetOperators(sles,A,A,DIFFERENT_NONZERO_PATTERN);

103:   /*
104:      Set default preconditioner for this program to be block Jacobi.
105:      This choice can be overridden at runtime with the option
106:         -pc_type <type>
107:   */
108:   SLESGetPC(sles,&pc);
109:   PCSetType(pc,PCBJACOBI);


112:   /* -------------------------------------------------------------------
113:                    Define the problem decomposition
114:      ------------------------------------------------------------------- */

116:   /* 
117:      Call PCBJacobiSetTotalBlocks() to set individually the size of
118:      each block in the preconditioner.  This could also be done with
119:      the runtime option
120:          -pc_bjacobi_blocks <blocks>
121:      Also, see the command PCBJacobiSetLocalBlocks() to set the
122:      local blocks.

124:       Note: The default decomposition is 1 block per processor.
125:   */
126:   PetscMalloc(m*sizeof(int),&blks);
127:   for (i=0; i<m; i++) blks[i] = n;
128:   PCBJacobiSetTotalBlocks(pc,m,blks);
129:   PetscFree(blks);


132:   /* -------------------------------------------------------------------
133:                Set the linear solvers for the subblocks
134:      ------------------------------------------------------------------- */

136:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
137:        Basic method, should be sufficient for the needs of most users.
138:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 

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

146:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
147:         Advanced method, setting different solvers for various blocks.
148:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 

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

163:        Note: SLESSetUp() MUST be called before PCBJacobiGetSubSLES().
164:     */
165:     SLESSetUp(sles,x,b);

167:     /*
168:        Extract the array of SLES contexts for the local blocks
169:     */
170:     PCBJacobiGetSubSLES(pc,&nlocal,&first,&subsles);

172:     /*
173:        Loop over the local blocks, setting various SLES options
174:        for each block.  
175:     */
176:     for (i=0; i<nlocal; i++) {
177:       SLESGetPC(subsles[i],&subpc);
178:       SLESGetKSP(subsles[i],&subksp);
179:       if (!rank) {
180:         if (i%2) {
181:           PCSetType(subpc,PCILU);
182:         } else {
183:           PCSetType(subpc,PCNONE);
184:           KSPSetType(subksp,KSPBCGS);
185:           KSPSetTolerances(subksp,1.e-6,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
186:         }
187:       } else {
188:         PCSetType(subpc,PCJACOBI);
189:         KSPSetType(subksp,KSPGMRES);
190:         KSPSetTolerances(subksp,1.e-7,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
191:       }
192:     }
193:   }

195:   /* -------------------------------------------------------------------
196:                       Solve the linear system
197:      ------------------------------------------------------------------- */

199:   /* 
200:     Set runtime options
201:   */
202:   SLESSetFromOptions(sles);

204:   /*
205:      Solve the linear system
206:   */
207:   SLESSolve(sles,b,x,&its);

209:   /*
210:      View info about the solver
211:   */
212:   PetscOptionsHasName(PETSC_NULL,"-noslesview",&flg);
213:   if (!flg) {
214:     SLESView(sles,PETSC_VIEWER_STDOUT_WORLD);
215:   }

217:   /* -------------------------------------------------------------------
218:                       Check solution and clean up
219:      ------------------------------------------------------------------- */

221:   /*
222:      Check the error
223:   */
224:   VecAXPY(&none,u,x);
225:   VecNorm(x,NORM_2,&norm);
226:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A iterations %dn",norm,its);

228:   /* 
229:      Free work space.  All PETSc objects should be destroyed when they
230:      are no longer needed.
231:   */
232:   SLESDestroy(sles);
233:   VecDestroy(u);  VecDestroy(x);
234:   VecDestroy(b);  MatDestroy(A);
235:   PetscFinalize();
236:   return 0;
237: }