Date: 2022-03-04T17:39:13+00:00

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*/

      7: /*
      8: Laplacian in 3D. Modeled by the partial differential equation

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

     12: with pure Neumann boundary conditions

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

     16: The functions are cell-centered

     18: This uses multigrid to solve the linear system

     20:        Contributed by Jianming Yang <jianming-yang@uiowa.edu>
     21: */

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

     25: #include <petscdm.h>
     26: #include <petscdmda.h>
     27: #include <petscksp.h>

     29: extern PetscErrorCode ComputeMatrix(KSP,Mat,Mat,void*);
     30: extern PetscErrorCode ComputeRHS(KSP,Vec,void*);

     32: int main(int argc,char **argv)
     33: {
     34:   KSP            ksp;
     35:   DM             da;
     36:   PetscReal      norm;
     38:   PetscInt       i,j,k,mx,my,mz,xm,ym,zm,xs,ys,zs,d,dof;
     39:   PetscScalar    Hx,Hy,Hz;
     40:   PetscScalar    ****array;
     41:   Vec            x,b,r;
     42:   Mat            J;

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

     53:   KSPSetDM(ksp,da);

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

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

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

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

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

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

    106: PetscErrorCode ComputeRHS(KSP ksp,Vec b,void *ctx)
    107: {
    109:   PetscInt       d,dof,i,j,k,mx,my,mz,xm,ym,zm,xs,ys,zs;
    110:   PetscScalar    Hx,Hy,Hz;
    111:   PetscScalar    ****array;
    112:   DM             da;
    113:   MatNullSpace   nullspace;

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

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

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

    149: PetscErrorCode ComputeMatrix(KSP ksp, Mat J,Mat jac, void *ctx)
    150: {
    152:   PetscInt       dof,i,j,k,d,mx,my,mz,xm,ym,zm,xs,ys,zs,num, numi, numj, numk;
    153:   PetscScalar    v[7],Hx,Hy,Hz,HyHzdHx,HxHzdHy,HxHydHz;
    154:   MatStencil     row, col[7];
    155:   DM             da;
    156:   MatNullSpace   nullspace;
    157:   PetscBool      dump_mat = PETSC_FALSE, check_matis = PETSC_FALSE;

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

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

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

    281: /*TEST

    283:    build:
    284:       requires: !complex !single

    286:    test:
    287:       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

    289:    test:
    290:       suffix: 2
    291:       nsize: 2
    292:       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

    294:    test:
    295:       suffix: hyprestruct
    296:       nsize: 3
    297:       requires: hypre !defined(PETSC_HAVE_HYPRE_DEVICE)
    298:       args: -ksp_type gmres -pc_type pfmg -dm_mat_type hyprestruct -ksp_monitor -da_refine 3

    300: TEST*/