Date: 2022-08-02T03:14:47+00:00

Actual source code: ex29.c

      2: /*
      3: Added at the request of Marc Garbey.

      5: Inhomogeneous Laplacian in 2D. Modeled by the partial differential equation

      7:    -div \rho grad u = f,  0 < x,y < 1,

      9: with forcing function

     11:    f = e^{-x^2/\nu} e^{-y^2/\nu}

     13: with Dirichlet boundary conditions

     15:    u = f(x,y) for x = 0, x = 1, y = 0, y = 1

     17: or pure Neumman boundary conditions

     19: This uses multigrid to solve the linear system
     20: */

     22: static char help[] = "Solves 2D inhomogeneous Laplacian using multigrid.\n\n";

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

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

     31: typedef enum {DIRICHLET, NEUMANN} BCType;

     33: typedef struct {
     34:   PetscReal rho;
     35:   PetscReal nu;
     36:   BCType    bcType;
     37: } UserContext;

     39: int main(int argc,char **argv)
     40: {
     41:   KSP            ksp;
     42:   DM             da;
     43:   UserContext    user;
     44:   const char     *bcTypes[2] = {"dirichlet","neumann"};
     46:   PetscInt       bc;
     47:   Vec            b,x;
     48:   PetscBool      testsolver = PETSC_FALSE;

     50:   PetscInitialize(&argc,&argv,(char*)0,help);
     51:   KSPCreate(PETSC_COMM_WORLD,&ksp);
     52:   DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,3,3,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,&da);
     53:   DMSetFromOptions(da);
     54:   DMSetUp(da);
     55:   DMDASetUniformCoordinates(da,0,1,0,1,0,0);
     56:   DMDASetFieldName(da,0,"Pressure");

     58:   PetscOptionsBegin(PETSC_COMM_WORLD, "", "Options for the inhomogeneous Poisson equation", "DMqq");
     59:   user.rho    = 1.0;
     60:   PetscOptionsReal("-rho", "The conductivity", "ex29.c", user.rho, &user.rho, NULL);
     61:   user.nu     = 0.1;
     62:   PetscOptionsReal("-nu", "The width of the Gaussian source", "ex29.c", user.nu, &user.nu, NULL);
     63:   bc          = (PetscInt)DIRICHLET;
     64:   PetscOptionsEList("-bc_type","Type of boundary condition","ex29.c",bcTypes,2,bcTypes[0],&bc,NULL);
     65:   user.bcType = (BCType)bc;
     66:   PetscOptionsBool("-testsolver", "Run solver multiple times, useful for performance studies of solver", "ex29.c", testsolver, &testsolver, NULL);
     67:   PetscOptionsEnd();

     69:   KSPSetComputeRHS(ksp,ComputeRHS,&user);
     70:   KSPSetComputeOperators(ksp,ComputeMatrix,&user);
     71:   KSPSetDM(ksp,da);
     72:   KSPSetFromOptions(ksp);
     73:   KSPSetUp(ksp);
     74:   KSPSolve(ksp,NULL,NULL);

     76:   if (testsolver) {
     77:     KSPGetSolution(ksp,&x);
     78:     KSPGetRhs(ksp,&b);
     79:     KSPSetDMActive(ksp,PETSC_FALSE);
     80:     KSPSolve(ksp,b,x);
     81:     {
     82: #if defined(PETSC_USE_LOG)
     83:       PetscLogStage stage;
     84: #endif
     85:       PetscInt      i,n = 20;

     87:       PetscLogStageRegister("Solve only",&stage);
     88:       PetscLogStagePush(stage);
     89:       for (i=0; i<n; i++) {
     90:         KSPSolve(ksp,b,x);
     91:       }
     92:       PetscLogStagePop();
     93:     }
     94:   }

     96:   DMDestroy(&da);
     97:   KSPDestroy(&ksp);
     98:   PetscFinalize();
     99:   return 0;
    100: }

    102: PetscErrorCode ComputeRHS(KSP ksp,Vec b,void *ctx)
    103: {
    104:   UserContext    *user = (UserContext*)ctx;
    105:   PetscInt       i,j,mx,my,xm,ym,xs,ys;
    106:   PetscScalar    Hx,Hy;
    107:   PetscScalar    **array;
    108:   DM             da;

    111:   KSPGetDM(ksp,&da);
    112:   DMDAGetInfo(da, 0, &mx, &my, 0,0,0,0,0,0,0,0,0,0);
    113:   Hx   = 1.0 / (PetscReal)(mx-1);
    114:   Hy   = 1.0 / (PetscReal)(my-1);
    115:   DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);
    116:   DMDAVecGetArray(da, b, &array);
    117:   for (j=ys; j<ys+ym; j++) {
    118:     for (i=xs; i<xs+xm; i++) {
    119:       array[j][i] = PetscExpScalar(-((PetscReal)i*Hx)*((PetscReal)i*Hx)/user->nu)*PetscExpScalar(-((PetscReal)j*Hy)*((PetscReal)j*Hy)/user->nu)*Hx*Hy;
    120:     }
    121:   }
    122:   DMDAVecRestoreArray(da, b, &array);
    123:   VecAssemblyBegin(b);
    124:   VecAssemblyEnd(b);

    126:   /* force right hand side to be consistent for singular matrix */
    127:   /* note this is really a hack, normally the model would provide you with a consistent right handside */
    128:   if (user->bcType == NEUMANN) {
    129:     MatNullSpace nullspace;

    131:     MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
    132:     MatNullSpaceRemove(nullspace,b);
    133:     MatNullSpaceDestroy(&nullspace);
    134:   }
    135:   return 0;
    136: }

    138: PetscErrorCode ComputeRho(PetscInt i, PetscInt j, PetscInt mx, PetscInt my, PetscReal centerRho, PetscReal *rho)
    139: {
    141:   if ((i > mx/3.0) && (i < 2.0*mx/3.0) && (j > my/3.0) && (j < 2.0*my/3.0)) {
    142:     *rho = centerRho;
    143:   } else {
    144:     *rho = 1.0;
    145:   }
    146:   return 0;
    147: }

    149: PetscErrorCode ComputeMatrix(KSP ksp,Mat J,Mat jac,void *ctx)
    150: {
    151:   UserContext    *user = (UserContext*)ctx;
    152:   PetscReal      centerRho;
    153:   PetscInt       i,j,mx,my,xm,ym,xs,ys;
    154:   PetscScalar    v[5];
    155:   PetscReal      Hx,Hy,HydHx,HxdHy,rho;
    156:   MatStencil     row, col[5];
    157:   DM             da;
    158:   PetscBool      check_matis = PETSC_FALSE;

    161:   KSPGetDM(ksp,&da);
    162:   centerRho = user->rho;
    163:   DMDAGetInfo(da,0,&mx,&my,0,0,0,0,0,0,0,0,0,0);
    164:   Hx        = 1.0 / (PetscReal)(mx-1);
    165:   Hy        = 1.0 / (PetscReal)(my-1);
    166:   HxdHy     = Hx/Hy;
    167:   HydHx     = Hy/Hx;
    168:   DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);
    169:   for (j=ys; j<ys+ym; j++) {
    170:     for (i=xs; i<xs+xm; i++) {
    171:       row.i = i; row.j = j;
    172:       ComputeRho(i, j, mx, my, centerRho, &rho);
    173:       if (i==0 || j==0 || i==mx-1 || j==my-1) {
    174:         if (user->bcType == DIRICHLET) {
    175:           v[0] = 2.0*rho*(HxdHy + HydHx);
    176:           MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);
    177:         } else if (user->bcType == NEUMANN) {
    178:           PetscInt numx = 0, numy = 0, num = 0;
    179:           if (j!=0) {
    180:             v[num] = -rho*HxdHy;              col[num].i = i;   col[num].j = j-1;
    181:             numy++; num++;
    182:           }
    183:           if (i!=0) {
    184:             v[num] = -rho*HydHx;              col[num].i = i-1; col[num].j = j;
    185:             numx++; num++;
    186:           }
    187:           if (i!=mx-1) {
    188:             v[num] = -rho*HydHx;              col[num].i = i+1; col[num].j = j;
    189:             numx++; num++;
    190:           }
    191:           if (j!=my-1) {
    192:             v[num] = -rho*HxdHy;              col[num].i = i;   col[num].j = j+1;
    193:             numy++; num++;
    194:           }
    195:           v[num] = numx*rho*HydHx + numy*rho*HxdHy; col[num].i = i;   col[num].j = j;
    196:           num++;
    197:           MatSetValuesStencil(jac,1,&row,num,col,v,INSERT_VALUES);
    198:         }
    199:       } else {
    200:         v[0] = -rho*HxdHy;              col[0].i = i;   col[0].j = j-1;
    201:         v[1] = -rho*HydHx;              col[1].i = i-1; col[1].j = j;
    202:         v[2] = 2.0*rho*(HxdHy + HydHx); col[2].i = i;   col[2].j = j;
    203:         v[3] = -rho*HydHx;              col[3].i = i+1; col[3].j = j;
    204:         v[4] = -rho*HxdHy;              col[4].i = i;   col[4].j = j+1;
    205:         MatSetValuesStencil(jac,1,&row,5,col,v,INSERT_VALUES);
    206:       }
    207:     }
    208:   }
    209:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
    210:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
    211:   MatViewFromOptions(jac,NULL,"-view_mat");
    212:   PetscOptionsGetBool(NULL,NULL,"-check_matis",&check_matis,NULL);
    213:   if (check_matis) {
    214:     void      (*f)(void);
    215:     Mat       J2;
    216:     MatType   jtype;
    217:     PetscReal nrm;

    219:     MatGetType(jac,&jtype);
    220:     MatConvert(jac,MATIS,MAT_INITIAL_MATRIX,&J2);
    221:     MatViewFromOptions(J2,NULL,"-view_conv");
    222:     MatConvert(J2,jtype,MAT_INPLACE_MATRIX,&J2);
    223:     MatGetOperation(jac,MATOP_VIEW,&f);
    224:     MatSetOperation(J2,MATOP_VIEW,f);
    225:     MatSetDM(J2,da);
    226:     MatViewFromOptions(J2,NULL,"-view_conv_assembled");
    227:     MatAXPY(J2,-1.,jac,DIFFERENT_NONZERO_PATTERN);
    228:     MatNorm(J2,NORM_FROBENIUS,&nrm);
    229:     PetscPrintf(PETSC_COMM_WORLD,"Error MATIS %g\n",(double)nrm);
    230:     MatViewFromOptions(J2,NULL,"-view_conv_err");
    231:     MatDestroy(&J2);
    232:   }
    233:   if (user->bcType == NEUMANN) {
    234:     MatNullSpace nullspace;

    236:     MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
    237:     MatSetNullSpace(J,nullspace);
    238:     MatNullSpaceDestroy(&nullspace);
    239:   }
    240:   return 0;
    241: }

    243: /*TEST

    245:    test:
    246:       args: -pc_type mg -pc_mg_type full -ksp_type fgmres -ksp_monitor_short -da_refine 8 -ksp_rtol 1.e-3

    248:    test:
    249:       suffix: 2
    250:       args: -bc_type neumann -pc_type mg -pc_mg_type full -ksp_type fgmres -ksp_monitor_short -da_refine 8 -mg_coarse_pc_factor_shift_type nonzero
    251:       requires: !single

    253:    test:
    254:       suffix: telescope
    255:       nsize: 4
    256:       args: -ksp_monitor_short -da_grid_x 257 -da_grid_y 257 -pc_type mg -pc_mg_galerkin pmat -pc_mg_levels 4 -ksp_type richardson -mg_levels_ksp_type chebyshev -mg_levels_pc_type jacobi -mg_coarse_pc_type telescope -mg_coarse_pc_telescope_ignore_kspcomputeoperators -mg_coarse_telescope_pc_type mg -mg_coarse_telescope_pc_mg_galerkin pmat -mg_coarse_telescope_pc_mg_levels 3 -mg_coarse_telescope_mg_levels_ksp_type chebyshev -mg_coarse_telescope_mg_levels_pc_type jacobi -mg_coarse_pc_telescope_reduction_factor 4

    258:    test:
    259:       suffix: 3
    260:       args: -ksp_view -da_refine 2 -pc_type mg -pc_mg_distinct_smoothup -mg_levels_up_pc_type jacobi

    262:    test:
    263:       suffix: 4
    264:       args: -ksp_view -da_refine 2 -pc_type mg -pc_mg_distinct_smoothup -mg_levels_up_ksp_max_it 3 -mg_levels_ksp_max_it 4

    266:    test:
    267:       suffix: 5
    268:       nsize: 2
    269:       requires: hypre !complex
    270:       args: -pc_type mg  -da_refine 2 -ksp_monitor  -matptap_via hypre -pc_mg_galerkin both

    272:    test:
    273:       suffix: 6
    274:       args: -pc_type svd -pc_svd_monitor ::all

    276: TEST*/