Actual source code: ex26.c
petsc-3.4.2 2013-07-02

      1: static char help[] ="Solvers Laplacian with multigrid, bad way.\n\
      2:   -mx <xg>, where <xg> = number of grid points in the x-direction\n\
      3:   -my <yg>, where <yg> = number of grid points in the y-direction\n\
      4:   -Nx <npx>, where <npx> = number of processors in the x-direction\n\
      5:   -Ny <npy>, where <npy> = number of processors in the y-direction\n\n";

      7: /*  Modified from ~src/ksp/examples/tests/ex19.c. Used for testing ML 6.2 interface.

      9:     This problem is modeled by
     10:     the partial differential equation

     12:             -Laplacian u  = g,  0 < x,y < 1,

     14:     with boundary conditions

     16:              u = 0  for  x = 0, x = 1, y = 0, y = 1.

     18:     A finite difference approximation with the usual 5-point stencil
     19:     is used to discretize the boundary value problem to obtain a nonlinear
     20:     system of equations.

     22:     Usage: ./ex26 -ksp_monitor_short -pc_type ml
     23:            -mg_coarse_ksp_max_it 10
     24:            -mg_levels_1_ksp_max_it 10 -mg_levels_2_ksp_max_it 10
     25:            -mg_fine_ksp_max_it 10
     26: */

     28: #include <petscksp.h>
     29: #include <petscdmda.h>

     31: /* User-defined application contexts */
     32: typedef struct {
     33:   PetscInt mx,my;              /* number grid points in x and y direction */
     34:   Vec      localX,localF;      /* local vectors with ghost region */
     35:   DM       da;
     36:   Vec      x,b,r;              /* global vectors */
     37:   Mat      J;                  /* Jacobian on grid */
     38:   Mat      A,P,R;
     39:   KSP      ksp;
     40: } GridCtx;
     41: extern int FormJacobian_Grid(GridCtx*,Mat*);

     45: int main(int argc,char **argv)
     46: {
     48:   PetscInt       its,n,Nx=PETSC_DECIDE,Ny=PETSC_DECIDE,nlocal;
     49:   PetscMPIInt    size;
     50:   PetscScalar    one = 1.0;
     51:   PetscInt       mx,my;
     52:   Mat            A;
     53:   GridCtx        fine_ctx;
     54:   KSP            ksp;
     55:   PetscBool      flg;

     57:   PetscInitialize(&argc,&argv,(char*)0,help);
     58:   /* set up discretization matrix for fine grid */
     59:   fine_ctx.mx = 9; fine_ctx.my = 9;
     60:   PetscOptionsGetInt(NULL,"-mx",&mx,&flg);
     61:   if (flg) fine_ctx.mx = mx;
     62:   PetscOptionsGetInt(NULL,"-my",&my,&flg);
     63:   if (flg) fine_ctx.my = my;
     64:   PetscPrintf(PETSC_COMM_WORLD,"Fine grid size %D by %D\n",fine_ctx.mx,fine_ctx.my);
     65:   n    = fine_ctx.mx*fine_ctx.my;

     67:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
     68:   PetscOptionsGetInt(NULL,"-Nx",&Nx,NULL);
     69:   PetscOptionsGetInt(NULL,"-Ny",&Ny,NULL);

     71:   /* Set up distributed array for fine grid */
     72:   DMDACreate2d(PETSC_COMM_WORLD, DMDA_BOUNDARY_NONE, DMDA_BOUNDARY_NONE,DMDA_STENCIL_STAR,fine_ctx.mx,
     73:                       fine_ctx.my,Nx,Ny,1,1,NULL,NULL,&fine_ctx.da);
     74:   DMCreateGlobalVector(fine_ctx.da,&fine_ctx.x);
     75:   VecDuplicate(fine_ctx.x,&fine_ctx.b);
     76:   VecGetLocalSize(fine_ctx.x,&nlocal);
     77:   DMCreateLocalVector(fine_ctx.da,&fine_ctx.localX);
     78:   VecDuplicate(fine_ctx.localX,&fine_ctx.localF);
     79:   MatCreateAIJ(PETSC_COMM_WORLD,nlocal,nlocal,n,n,5,NULL,3,NULL,&A);
     80:   FormJacobian_Grid(&fine_ctx,&A);

     82:   /* create linear solver */
     83:   KSPCreate(PETSC_COMM_WORLD,&ksp);

     85:   /* set values for rhs vector */
     86:   VecSet(fine_ctx.b,one);
     87:   {
     88:     PetscRandom rdm;
     89:     PetscRandomCreate(PETSC_COMM_WORLD,&rdm);
     90:     PetscRandomSetFromOptions(rdm);
     91:     VecSetRandom(fine_ctx.b,rdm);
     92:     PetscRandomDestroy(&rdm);
     93:   }

     95:   /* set options, then solve system */
     96:   KSPSetFromOptions(ksp); /* calls PCSetFromOptions_ML if 'pc_type=ml' */
     97:   KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN);
     98:   KSPSolve(ksp,fine_ctx.b,fine_ctx.x);
     99:   KSPGetIterationNumber(ksp,&its);
    100:   PetscPrintf(PETSC_COMM_WORLD,"Number of iterations = %D\n",its);

    102:   /* free data structures */
    103:   VecDestroy(&fine_ctx.x);
    104:   VecDestroy(&fine_ctx.b);
    105:   DMDestroy(&fine_ctx.da);
    106:   VecDestroy(&fine_ctx.localX);
    107:   VecDestroy(&fine_ctx.localF);
    108:   MatDestroy(&A);
    109:   KSPDestroy(&ksp);

    111:   PetscFinalize();
    112:   return 0;
    113: }

    117: int FormJacobian_Grid(GridCtx *grid,Mat *J)
    118: {
    119:   Mat            jac = *J;
    121:   PetscInt       i,j,row,mx,my,xs,ys,xm,ym,Xs,Ys,Xm,Ym,col[5];
    122:   PetscInt       nloc,*ltog,grow;
    123:   PetscScalar    two = 2.0,one = 1.0,v[5],hx,hy,hxdhy,hydhx,value;

    125:   mx    = grid->mx;            my = grid->my;
    126:   hx    = one/(PetscReal)(mx-1);  hy = one/(PetscReal)(my-1);
    127:   hxdhy = hx/hy;            hydhx = hy/hx;

    129:   /* Get ghost points */
    130:   DMDAGetCorners(grid->da,&xs,&ys,0,&xm,&ym,0);
    131:   DMDAGetGhostCorners(grid->da,&Xs,&Ys,0,&Xm,&Ym,0);
    132:   DMDAGetGlobalIndices(grid->da,&nloc,&ltog);

    134:   /* Evaluate Jacobian of function */
    135:   for (j=ys; j<ys+ym; j++) {
    136:     row = (j - Ys)*Xm + xs - Xs - 1;
    137:     for (i=xs; i<xs+xm; i++) {
    138:       row++;
    139:       grow = ltog[row];
    140:       if (i > 0 && i < mx-1 && j > 0 && j < my-1) {
    141:         v[0] = -hxdhy; col[0] = ltog[row - Xm];
    142:         v[1] = -hydhx; col[1] = ltog[row - 1];
    143:         v[2] = two*(hydhx + hxdhy); col[2] = grow;
    144:         v[3] = -hydhx; col[3] = ltog[row + 1];
    145:         v[4] = -hxdhy; col[4] = ltog[row + Xm];
    146:         MatSetValues(jac,1,&grow,5,col,v,INSERT_VALUES);
    147:       } else if ((i > 0 && i < mx-1) || (j > 0 && j < my-1)) {
    148:         value = .5*two*(hydhx + hxdhy);
    149:         MatSetValues(jac,1,&grow,1,&grow,&value,INSERT_VALUES);
    150:       } else {
    151:         value = .25*two*(hydhx + hxdhy);
    152:         MatSetValues(jac,1,&grow,1,&grow,&value,INSERT_VALUES);
    153:       }
    154:     }
    155:   }
    156:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
    157:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
    158:   return 0;
    159: }