Actual source code: ex46.c

petsc-master 2014-12-19
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  2: static char help[] = "Solves a linear system in parallel with KSP and DM.\n\
  3: Compare this to ex2 which solves the same problem without a DM.\n\n";

  5: /*T
  6:    Concepts: KSP^basic parallel example;
  7:    Concepts: KSP^Laplacian, 2d
  8:    Concepts: DM^using distributed arrays;
  9:    Concepts: Laplacian, 2d
 10:    Processors: n
 11: T*/

 13: /*
 14:   Include "petscdmda.h" so that we can use distributed arrays (DMDAs).
 15:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
 16:   automatically includes:
 17:      petscsys.h       - base PETSc routines   petscvec.h - vectors
 18:      petscmat.h - matrices
 19:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
 20:      petscviewer.h - viewers               petscpc.h  - preconditioners
 21: */
 22: #include <petscdm.h>
 23: #include <petscdmda.h>
 24: #include <petscksp.h>

 28: int main(int argc,char **argv)
 29: {
 30:   DM             da;            /* distributed array */
 31:   Vec            x,b,u;         /* approx solution, RHS, exact solution */
 32:   Mat            A;             /* linear system matrix */
 33:   KSP            ksp;           /* linear solver context */
 34:   PetscRandom    rctx;          /* random number generator context */
 35:   PetscReal      norm;          /* norm of solution error */
 36:   PetscInt       i,j,its;
 38:   PetscBool      flg = PETSC_FALSE;
 39:   PetscLogStage  stage;
 40:   DMDALocalInfo  info;

 42:   PetscInitialize(&argc,&argv,(char*)0,help);

 44:   /*
 45:      Create distributed array to handle parallel distribution.
 46:      The problem size will default to 8 by 7, but this can be
 47:      changed using -da_grid_x M -da_grid_y N
 48:   */
 49:   DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,-8,-7,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);

 51:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 52:          Compute the matrix and right-hand-side vector that define
 53:          the linear system, Ax = b.
 54:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 55:   /*
 56:      Create parallel matrix preallocated according to the DMDA, format AIJ by default.
 57:      To use symmetric storage, run with -dm_mat_type sbaij -mat_ignore_lower_triangular
 58:   */
 59:   DMCreateMatrix(da,&A);

 61:   /*
 62:      Set matrix elements for the 2-D, five-point stencil in parallel.
 63:       - Each processor needs to insert only elements that it owns
 64:         locally (but any non-local elements will be sent to the
 65:         appropriate processor during matrix assembly).
 66:       - Rows and columns are specified by the stencil
 67:       - Entries are normalized for a domain [0,1]x[0,1]
 68:    */
 69:   PetscLogStageRegister("Assembly", &stage);
 70:   PetscLogStagePush(stage);
 71:   DMDAGetLocalInfo(da,&info);
 72:   for (j=info.ys; j<info.ys+info.ym; j++) {
 73:     for (i=info.xs; i<info.xs+info.xm; i++) {
 74:       PetscReal   hx  = 1./info.mx,hy = 1./info.my;
 75:       MatStencil  row = {0},col[5] = {{0}};
 76:       PetscScalar v[5];
 77:       PetscInt    ncols = 0;
 78:       row.j        = j; row.i = i;
 79:       col[ncols].j = j; col[ncols].i = i; v[ncols++] = 2*(hx/hy + hy/hx);
 80:       /* boundaries */
 81:       if (i>0)         {col[ncols].j = j;   col[ncols].i = i-1; v[ncols++] = -hy/hx;}
 82:       if (i<info.mx-1) {col[ncols].j = j;   col[ncols].i = i+1; v[ncols++] = -hy/hx;}
 83:       if (j>0)         {col[ncols].j = j-1; col[ncols].i = i;   v[ncols++] = -hx/hy;}
 84:       if (j<info.my-1) {col[ncols].j = j+1; col[ncols].i = i;   v[ncols++] = -hx/hy;}
 85:       MatSetValuesStencil(A,1,&row,ncols,col,v,INSERT_VALUES);
 86:     }
 87:   }

 89:   /*
 90:      Assemble matrix, using the 2-step process:
 91:        MatAssemblyBegin(), MatAssemblyEnd()
 92:      Computations can be done while messages are in transition
 93:      by placing code between these two statements.
 94:   */
 95:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 96:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
 97:   PetscLogStagePop();

 99:   /*
100:      Create parallel vectors compatible with the DMDA.
101:   */
102:   DMCreateGlobalVector(da,&u);
103:   VecDuplicate(u,&b);
104:   VecDuplicate(u,&x);

106:   /*
107:      Set exact solution; then compute right-hand-side vector.
108:      By default we use an exact solution of a vector with all
109:      elements of 1.0;  Alternatively, using the runtime option
110:      -random_sol forms a solution vector with random components.
111:   */
112:   PetscOptionsGetBool(NULL,"-random_exact_sol",&flg,NULL);
113:   if (flg) {
114:     PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
115:     PetscRandomSetFromOptions(rctx);
116:     VecSetRandom(u,rctx);
117:     PetscRandomDestroy(&rctx);
118:   } else {
119:     VecSet(u,1.);
120:   }
121:   MatMult(A,u,b);

123:   /*
124:      View the exact solution vector if desired
125:   */
126:   flg  = PETSC_FALSE;
127:   PetscOptionsGetBool(NULL,"-view_exact_sol",&flg,NULL);
128:   if (flg) {VecView(u,PETSC_VIEWER_STDOUT_WORLD);}

130:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
131:                 Create the linear solver and set various options
132:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

134:   /*
135:      Create linear solver context
136:   */
137:   KSPCreate(PETSC_COMM_WORLD,&ksp);

139:   /*
140:      Set operators. Here the matrix that defines the linear system
141:      also serves as the preconditioning matrix.
142:   */
143:   KSPSetOperators(ksp,A,A);

145:   /*
146:     Set runtime options, e.g.,
147:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
148:     These options will override those specified above as long as
149:     KSPSetFromOptions() is called _after_ any other customization
150:     routines.
151:   */
152:   KSPSetFromOptions(ksp);

154:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
155:                       Solve the linear system
156:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

158:   KSPSolve(ksp,b,x);

160:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
161:                       Check solution and clean up
162:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

164:   /*
165:      Check the error
166:   */
167:   VecAXPY(x,-1.,u);
168:   VecNorm(x,NORM_2,&norm);
169:   KSPGetIterationNumber(ksp,&its);

171:   /*
172:      Print convergence information.  PetscPrintf() produces a single
173:      print statement from all processes that share a communicator.
174:      An alternative is PetscFPrintf(), which prints to a file.
175:   */
176:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g iterations %D\n",(double)norm,its);

178:   /*
179:      Free work space.  All PETSc objects should be destroyed when they
180:      are no longer needed.
181:   */
182:   KSPDestroy(&ksp);
183:   VecDestroy(&u);
184:   VecDestroy(&x);
185:   VecDestroy(&b);
186:   MatDestroy(&A);
187:   DMDestroy(&da);

189:   /*
190:      Always call PetscFinalize() before exiting a program.  This routine
191:        - finalizes the PETSc libraries as well as MPI
192:        - provides summary and diagnostic information if certain runtime
193:          options are chosen (e.g., -log_summary).
194:   */
195:   PetscFinalize();
196:   return 0;
197: }