Actual source code: ex34.c

      1: /*T
      2:    Concepts: KSP^solving a system of linear equations
      3:    Concepts: KSP^Laplacian, 3d
      4:    Processors: n
      5: T*/

      9: /*
     10: Laplacian in 3D. Modeled by the partial differential equation

     12:    div  grad u = f,  0 < x,y,z < 1,

     14: with pure Neumann boundary conditions

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

     18: The functions are cell-centered

     20: This uses multigrid to solve the linear system

     22:        Contributed by Jianming Yang <jianming-yang@uiowa.edu>
     23: */

     25: static char help[] = "Solves 3D Laplacian using multigrid.\n\n";

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

     31: extern PetscErrorCode ComputeMatrix(KSP,Mat,Mat,void*);
     32: extern PetscErrorCode ComputeRHS(KSP,Vec,void*);

     34: int main(int argc,char **argv)
     35: {
     36:   KSP            ksp;
     37:   DM             da;
     38:   PetscReal      norm;
     40:   PetscInt       i,j,k,mx,my,mz,xm,ym,zm,xs,ys,zs,d,dof;
     41:   PetscScalar    Hx,Hy,Hz;
     42:   PetscScalar    ****array;
     43:   Vec            x,b,r;
     44:   Mat            J;

     46:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
     47:   dof  = 1;
     48:   PetscOptionsGetInt(NULL,NULL,"-da_dof",&dof,NULL);
     49:   KSPCreate(PETSC_COMM_WORLD,&ksp);
     50:   DMDACreate3d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,12,12,12,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE,dof,1,0,0,0,&da);
     51:   DMSetFromOptions(da);
     52:   DMSetUp(da);
     53:   DMDASetInterpolationType(da, DMDA_Q0);

     55:   KSPSetDM(ksp,da);

     57:   KSPSetComputeRHS(ksp,ComputeRHS,NULL);
     58:   KSPSetComputeOperators(ksp,ComputeMatrix,NULL);
     59:   KSPSetFromOptions(ksp);
     60:   KSPSolve(ksp,NULL,NULL);
     61:   KSPGetSolution(ksp,&x);
     62:   KSPGetRhs(ksp,&b);
     63:   KSPGetOperators(ksp,NULL,&J);
     64:   VecDuplicate(b,&r);

     66:   MatMult(J,x,r);
     67:   VecAXPY(r,-1.0,b);
     68:   VecNorm(r,NORM_2,&norm);
     69:   PetscPrintf(PETSC_COMM_WORLD,"Residual norm %g\n",(double)norm);

     71:   DMDAGetInfo(da, 0, &mx, &my, &mz, 0,0,0,0,0,0,0,0,0);
     72:   Hx   = 1.0 / (PetscReal)(mx);
     73:   Hy   = 1.0 / (PetscReal)(my);
     74:   Hz   = 1.0 / (PetscReal)(mz);
     75:   DMDAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);
     76:   DMDAVecGetArrayDOF(da, x, &array);

     78:   for (k=zs; k<zs+zm; k++) {
     79:     for (j=ys; j<ys+ym; j++) {
     80:       for (i=xs; i<xs+xm; i++) {
     81:         for (d=0; d<dof; d++) {
     82:           array[k][j][i][d] -=
     83:             PetscCosScalar(2*PETSC_PI*(((PetscReal)i+0.5)*Hx))*
     84:             PetscCosScalar(2*PETSC_PI*(((PetscReal)j+0.5)*Hy))*
     85:             PetscCosScalar(2*PETSC_PI*(((PetscReal)k+0.5)*Hz));
     86:         }
     87:       }
     88:     }
     89:   }
     90:   DMDAVecRestoreArrayDOF(da, x, &array);
     91:   VecAssemblyBegin(x);
     92:   VecAssemblyEnd(x);

     94:   VecNorm(x,NORM_INFINITY,&norm);
     95:   PetscPrintf(PETSC_COMM_WORLD,"Error norm %g\n",(double)norm);
     96:   VecNorm(x,NORM_1,&norm);
     97:   PetscPrintf(PETSC_COMM_WORLD,"Error norm %g\n",(double)(norm/((PetscReal)(mx)*(PetscReal)(my)*(PetscReal)(mz))));
     98:   VecNorm(x,NORM_2,&norm);
     99:   PetscPrintf(PETSC_COMM_WORLD,"Error norm %g\n",(double)(norm/((PetscReal)(mx)*(PetscReal)(my)*(PetscReal)(mz))));

    101:   VecDestroy(&r);
    102:   KSPDestroy(&ksp);
    103:   DMDestroy(&da);
    104:   PetscFinalize();
    105:   return ierr;
    106: }

    108: PetscErrorCode ComputeRHS(KSP ksp,Vec b,void *ctx)
    109: {
    111:   PetscInt       d,dof,i,j,k,mx,my,mz,xm,ym,zm,xs,ys,zs;
    112:   PetscScalar    Hx,Hy,Hz;
    113:   PetscScalar    ****array;
    114:   DM             da;
    115:   MatNullSpace   nullspace;

    118:   KSPGetDM(ksp,&da);
    119:   DMDAGetInfo(da, 0, &mx, &my, &mz, 0,0,0,&dof,0,0,0,0,0);
    120:   Hx   = 1.0 / (PetscReal)(mx);
    121:   Hy   = 1.0 / (PetscReal)(my);
    122:   Hz   = 1.0 / (PetscReal)(mz);
    123:   DMDAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);
    124:   DMDAVecGetArrayDOF(da, b, &array);
    125:   for (k=zs; k<zs+zm; k++) {
    126:     for (j=ys; j<ys+ym; j++) {
    127:       for (i=xs; i<xs+xm; i++) {
    128:         for (d=0; d<dof; d++) {
    129:           array[k][j][i][d] = 12 * PETSC_PI * PETSC_PI
    130:                            * PetscCosScalar(2*PETSC_PI*(((PetscReal)i+0.5)*Hx))
    131:                            * PetscCosScalar(2*PETSC_PI*(((PetscReal)j+0.5)*Hy))
    132:                            * PetscCosScalar(2*PETSC_PI*(((PetscReal)k+0.5)*Hz))
    133:                            * Hx * Hy * Hz;
    134:         }
    135:       }
    136:     }
    137:   }
    138:   DMDAVecRestoreArrayDOF(da, b, &array);
    139:   VecAssemblyBegin(b);
    140:   VecAssemblyEnd(b);

    142:   /* force right hand side to be consistent for singular matrix */
    143:   /* note this is really a hack, normally the model would provide you with a consistent right handside */

    145:   MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
    146:   MatNullSpaceRemove(nullspace,b);
    147:   MatNullSpaceDestroy(&nullspace);
    148:   return(0);
    149: }

    152: PetscErrorCode ComputeMatrix(KSP ksp, Mat J,Mat jac, void *ctx)
    153: {
    155:   PetscInt       dof,i,j,k,d,mx,my,mz,xm,ym,zm,xs,ys,zs,num, numi, numj, numk;
    156:   PetscScalar    v[7],Hx,Hy,Hz,HyHzdHx,HxHzdHy,HxHydHz;
    157:   MatStencil     row, col[7];
    158:   DM             da;
    159:   MatNullSpace   nullspace;
    160:   PetscBool      dump_mat = PETSC_FALSE, check_matis = PETSC_FALSE;

    163:   KSPGetDM(ksp,&da);
    164:   DMDAGetInfo(da,0,&mx,&my,&mz,0,0,0,&dof,0,0,0,0,0);
    165:   Hx      = 1.0 / (PetscReal)(mx);
    166:   Hy      = 1.0 / (PetscReal)(my);
    167:   Hz      = 1.0 / (PetscReal)(mz);
    168:   HyHzdHx = Hy*Hz/Hx;
    169:   HxHzdHy = Hx*Hz/Hy;
    170:   HxHydHz = Hx*Hy/Hz;
    171:   DMDAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);
    172:   for (k=zs; k<zs+zm; k++) {
    173:     for (j=ys; j<ys+ym; j++) {
    174:       for (i=xs; i<xs+xm; i++) {
    175:         for (d=0; d<dof; d++) {
    176:           row.i = i; row.j = j; row.k = k; row.c = d;
    177:           if (i==0 || j==0 || k==0 || i==mx-1 || j==my-1 || k==mz-1) {
    178:             num = 0; numi=0; numj=0; numk=0;
    179:             if (k!=0) {
    180:               v[num]     = -HxHydHz;
    181:               col[num].i = i;
    182:               col[num].j = j;
    183:               col[num].k = k-1;
    184:               col[num].c = d;
    185:               num++; numk++;
    186:             }
    187:             if (j!=0) {
    188:               v[num]     = -HxHzdHy;
    189:               col[num].i = i;
    190:               col[num].j = j-1;
    191:               col[num].k = k;
    192:               col[num].c = d;
    193:               num++; numj++;
    194:               }
    195:             if (i!=0) {
    196:               v[num]     = -HyHzdHx;
    197:               col[num].i = i-1;
    198:               col[num].j = j;
    199:               col[num].k = k;
    200:               col[num].c = d;
    201:               num++; numi++;
    202:             }
    203:             if (i!=mx-1) {
    204:               v[num]     = -HyHzdHx;
    205:               col[num].i = i+1;
    206:               col[num].j = j;
    207:               col[num].k = k;
    208:               col[num].c = d;
    209:               num++; numi++;
    210:             }
    211:             if (j!=my-1) {
    212:               v[num]     = -HxHzdHy;
    213:               col[num].i = i;
    214:               col[num].j = j+1;
    215:               col[num].k = k;
    216:               col[num].c = d;
    217:               num++; numj++;
    218:             }
    219:             if (k!=mz-1) {
    220:               v[num]     = -HxHydHz;
    221:               col[num].i = i;
    222:               col[num].j = j;
    223:               col[num].k = k+1;
    224:               col[num].c = d;
    225:               num++; numk++;
    226:             }
    227:             v[num]     = (PetscReal)(numk)*HxHydHz + (PetscReal)(numj)*HxHzdHy + (PetscReal)(numi)*HyHzdHx;
    228:             col[num].i = i;   col[num].j = j;   col[num].k = k; col[num].c = d;
    229:             num++;
    230:             MatSetValuesStencil(jac,1,&row,num,col,v,INSERT_VALUES);
    231:           } else {
    232:             v[0] = -HxHydHz;                          col[0].i = i;   col[0].j = j;   col[0].k = k-1; col[0].c = d;
    233:             v[1] = -HxHzdHy;                          col[1].i = i;   col[1].j = j-1; col[1].k = k;   col[1].c = d;
    234:             v[2] = -HyHzdHx;                          col[2].i = i-1; col[2].j = j;   col[2].k = k;   col[2].c = d;
    235:             v[3] = 2.0*(HyHzdHx + HxHzdHy + HxHydHz); col[3].i = i;   col[3].j = j;   col[3].k = k;   col[3].c = d;
    236:             v[4] = -HyHzdHx;                          col[4].i = i+1; col[4].j = j;   col[4].k = k;   col[4].c = d;
    237:             v[5] = -HxHzdHy;                          col[5].i = i;   col[5].j = j+1; col[5].k = k;   col[5].c = d;
    238:             v[6] = -HxHydHz;                          col[6].i = i;   col[6].j = j;   col[6].k = k+1; col[6].c = d;
    239:             MatSetValuesStencil(jac,1,&row,7,col,v,INSERT_VALUES);
    240:           }
    241:         }
    242:       }
    243:     }
    244:   }
    245:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
    246:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
    247:   PetscOptionsGetBool(NULL,NULL,"-dump_mat",&dump_mat,NULL);
    248:   if (dump_mat) {
    249:     Mat JJ;

    251:     MatComputeOperator(jac,MATAIJ,&JJ);
    252:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_MATLAB);
    253:     MatView(JJ,PETSC_VIEWER_STDOUT_WORLD);
    254:     MatDestroy(&JJ);
    255:   }
    256:   MatViewFromOptions(jac,NULL,"-view_mat");
    257:   PetscOptionsGetBool(NULL,NULL,"-check_matis",&check_matis,NULL);
    258:   if (check_matis) {
    259:     void      (*f)(void);
    260:     Mat       J2;
    261:     MatType   jtype;
    262:     PetscReal nrm;

    264:     MatGetType(jac,&jtype);
    265:     MatConvert(jac,MATIS,MAT_INITIAL_MATRIX,&J2);
    266:     MatViewFromOptions(J2,NULL,"-view_conv");
    267:     MatConvert(J2,jtype,MAT_INPLACE_MATRIX,&J2);
    268:     MatGetOperation(jac,MATOP_VIEW,&f);
    269:     MatSetOperation(J2,MATOP_VIEW,f);
    270:     MatSetDM(J2,da);
    271:     MatViewFromOptions(J2,NULL,"-view_conv_assembled");
    272:     MatAXPY(J2,-1.,jac,DIFFERENT_NONZERO_PATTERN);
    273:     MatNorm(J2,NORM_FROBENIUS,&nrm);
    274:     PetscPrintf(PETSC_COMM_WORLD,"Error MATIS %g\n",(double)nrm);
    275:     MatViewFromOptions(J2,NULL,"-view_conv_err");
    276:     MatDestroy(&J2);
    277:   }
    278:   MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
    279:   MatSetNullSpace(J,nullspace);
    280:   MatNullSpaceDestroy(&nullspace);
    281:   return(0);
    282: }

    286: /*TEST

    288:    build:
    289:       requires: !complex !single

    291:    test:
    292:       args: -pc_type mg -pc_mg_type full -ksp_type fgmres -ksp_monitor_short -pc_mg_levels 3 -mg_coarse_pc_factor_shift_type nonzero -ksp_view

    294:    test:
    295:       suffix: 2
    296:       nsize: 2
    297:       args: -ksp_monitor_short -da_grid_x 50 -da_grid_y 50 -pc_type ksp -ksp_ksp_type cg -ksp_pc_type bjacobi -ksp_ksp_rtol 1e-1 -ksp_ksp_monitor -ksp_type pipefgmres -ksp_gmres_restart 5

    299:    test:
    300:       suffix: hyprestruct
    301:       nsize: 3
    302:       requires: hypre
    303:       args: -ksp_type gmres -pc_type pfmg -dm_mat_type hyprestruct -ksp_monitor -da_refine 3

    305: TEST*/