Actual source code: ex26.c

petsc-3.6.4 2016-04-12
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  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 <petscdm.h>
 30: #include <petscdmda.h>

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

 46: int main(int argc,char **argv)
 47: {
 49:   PetscInt       its,n,Nx=PETSC_DECIDE,Ny=PETSC_DECIDE,nlocal;
 50:   PetscMPIInt    size;
 51:   PetscScalar    one = 1.0;
 52:   PetscInt       mx,my;
 53:   Mat            A;
 54:   GridCtx        fine_ctx;
 55:   KSP            ksp;
 56:   PetscBool      flg;

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

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

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

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

 86:   /* set values for rhs vector */
 87:   VecSet(fine_ctx.b,one);
 88:   {
 89:     PetscRandom rdm;
 90:     PetscRandomCreate(PETSC_COMM_WORLD,&rdm);
 91:     PetscRandomSetFromOptions(rdm);
 92:     VecSetRandom(fine_ctx.b,rdm);
 93:     PetscRandomDestroy(&rdm);
 94:   }

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

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

112:   PetscFinalize();
113:   return 0;
114: }

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

128:   mx    = grid->mx;            my = grid->my;
129:   hx    = one/(PetscReal)(mx-1);  hy = one/(PetscReal)(my-1);
130:   hxdhy = hx/hy;            hydhx = hy/hx;

132:   /* Get ghost points */
133:   DMDAGetCorners(grid->da,&xs,&ys,0,&xm,&ym,0);
134:   DMDAGetGhostCorners(grid->da,&Xs,&Ys,0,&Xm,&Ym,0);
135:   DMGetLocalToGlobalMapping(grid->da,&ltogm);
136:   ISLocalToGlobalMappingGetIndices(ltogm,&ltog);

138:   /* Evaluate Jacobian of function */
139:   for (j=ys; j<ys+ym; j++) {
140:     row = (j - Ys)*Xm + xs - Xs - 1;
141:     for (i=xs; i<xs+xm; i++) {
142:       row++;
143:       grow = ltog[row];
144:       if (i > 0 && i < mx-1 && j > 0 && j < my-1) {
145:         v[0] = -hxdhy; col[0] = ltog[row - Xm];
146:         v[1] = -hydhx; col[1] = ltog[row - 1];
147:         v[2] = two*(hydhx + hxdhy); col[2] = grow;
148:         v[3] = -hydhx; col[3] = ltog[row + 1];
149:         v[4] = -hxdhy; col[4] = ltog[row + Xm];
150:         MatSetValues(jac,1,&grow,5,col,v,INSERT_VALUES);
151:       } else if ((i > 0 && i < mx-1) || (j > 0 && j < my-1)) {
152:         value = .5*two*(hydhx + hxdhy);
153:         MatSetValues(jac,1,&grow,1,&grow,&value,INSERT_VALUES);
154:       } else {
155:         value = .25*two*(hydhx + hxdhy);
156:         MatSetValues(jac,1,&grow,1,&grow,&value,INSERT_VALUES);
157:       }
158:     }
159:   }
160:   ISLocalToGlobalMappingRestoreIndices(ltogm,&ltog);
161:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
162:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
163:   return 0;
164: }