Date: 2013-07-02T14:48:48+00:00

Actual source code: ex32.c
petsc-3.4.2 2013-07-02

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

      7: /*
      8: Laplacian in 2D. Modeled by the partial differential equation

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

     12: with forcing function

     14:    f = e^{-(1 - x)^2/\nu} e^{-(1 - y)^2/\nu}

     16: with pure Neumann boundary conditions

     18: The functions are cell-centered

     20: This uses multigrid to solve the linear system

     22:        Contributed by Andrei Draganescu <aidraga@sandia.gov>

     24: Note the nice multigrid convergence despite the fact it is only using
     25: peicewise constant interpolation/restriction. This is because cell-centered multigrid
     26: does not need the same rule:

     28:     polynomial degree(interpolation) + polynomial degree(restriction) + 2 > degree of PDE

     30: that vertex based multigrid needs.
     31: */

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

     35: #include <petscdmda.h>
     36: #include <petscksp.h>

     38: extern PetscErrorCode ComputeMatrix(KSP,Mat,Mat,MatStructure*,void*);
     39: extern PetscErrorCode ComputeRHS(KSP,Vec,void*);

     41: typedef enum {DIRICHLET, NEUMANN} BCType;

     43: typedef struct {
     44:   PetscScalar nu;
     45:   BCType      bcType;
     46: } UserContext;

     50: int main(int argc,char **argv)
     51: {
     52:   KSP            ksp;
     53:   DM             da;
     54:   UserContext    user;
     55:   const char     *bcTypes[2] = {"dirichlet","neumann"};
     57:   PetscInt       bc;

     59:   PetscInitialize(&argc,&argv,(char*)0,help);

     61:   KSPCreate(PETSC_COMM_WORLD,&ksp);
     62:   DMDACreate2d(PETSC_COMM_WORLD, DMDA_BOUNDARY_NONE, DMDA_BOUNDARY_NONE,DMDA_STENCIL_STAR,12,12,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,&da);
     63:   DMDASetInterpolationType(da, DMDA_Q0);

     65:   KSPSetDM(ksp,da);

     68:   PetscOptionsBegin(PETSC_COMM_WORLD, "", "Options for the inhomogeneous Poisson equation", "DM");
     69:   user.nu     = 0.1;
     70:   PetscOptionsScalar("-nu", "The width of the Gaussian source", "ex29.c", 0.1, &user.nu, NULL);
     71:   bc          = (PetscInt)NEUMANN;
     72:   PetscOptionsEList("-bc_type","Type of boundary condition","ex29.c",bcTypes,2,bcTypes[0],&bc,NULL);
     73:   user.bcType = (BCType)bc;
     74:   PetscOptionsEnd();

     76:   KSPSetComputeRHS(ksp,ComputeRHS,&user);
     77:   KSPSetComputeOperators(ksp,ComputeMatrix,&user);
     78:   KSPSetFromOptions(ksp);

     80:   KSPSolve(ksp,NULL,NULL);

     82:   KSPDestroy(&ksp);
     83:   DMDestroy(&da);
     84:   PetscFinalize();
     85:   return 0;
     86: }

     90: PetscErrorCode ComputeRHS(KSP ksp,Vec b,void *ctx)
     91: {
     92:   UserContext    *user = (UserContext*)ctx;
     94:   PetscInt       i,j,mx,my,xm,ym,xs,ys;
     95:   PetscScalar    Hx,Hy;
     96:   PetscScalar    **array;
     97:   DM             da;

    100:   KSPGetDM(ksp,&da);
    101:   DMDAGetInfo(da, 0, &mx, &my, 0,0,0,0,0,0,0,0,0,0);
    102:   Hx   = 1.0 / (PetscReal)(mx);
    103:   Hy   = 1.0 / (PetscReal)(my);
    104:   DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);
    105:   DMDAVecGetArray(da, b, &array);
    106:   for (j=ys; j<ys+ym; j++) {
    107:     for (i=xs; i<xs+xm; i++) {
    108:       array[j][i] = PetscExpScalar(-(((PetscReal)i+0.5)*Hx)*(((PetscReal)i+0.5)*Hx)/user->nu)*PetscExpScalar(-(((PetscReal)j+0.5)*Hy)*(((PetscReal)j+0.5)*Hy)/user->nu)*Hx*Hy;
    109:     }
    110:   }
    111:   DMDAVecRestoreArray(da, b, &array);
    112:   VecAssemblyBegin(b);
    113:   VecAssemblyEnd(b);

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

    120:     MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
    121:     MatNullSpaceRemove(nullspace,b,NULL);
    122:     MatNullSpaceDestroy(&nullspace);
    123:   }
    124:   return(0);
    125: }

    130: PetscErrorCode ComputeMatrix(KSP ksp, Mat J,Mat jac,MatStructure *str, void *ctx)
    131: {
    132:   UserContext    *user = (UserContext*)ctx;
    134:   PetscInt       i,j,mx,my,xm,ym,xs,ys,num, numi, numj;
    135:   PetscScalar    v[5],Hx,Hy,HydHx,HxdHy;
    136:   MatStencil     row, col[5];
    137:   DM             da;

    140:   KSPGetDM(ksp,&da);
    141:   DMDAGetInfo(da,0,&mx,&my,0,0,0,0,0,0,0,0,0,0);
    142:   Hx    = 1.0 / (PetscReal)(mx);
    143:   Hy    = 1.0 / (PetscReal)(my);
    144:   HxdHy = Hx/Hy;
    145:   HydHx = Hy/Hx;
    146:   DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);
    147:   for (j=ys; j<ys+ym; j++) {
    148:     for (i=xs; i<xs+xm; i++) {
    149:       row.i = i; row.j = j;
    150:       if (i==0 || j==0 || i==mx-1 || j==my-1) {
    151:         if (user->bcType == DIRICHLET) {
    152:           v[0] = 2.0*(HxdHy + HydHx);
    153:           MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);
    154:           SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Dirichlet boundary conditions not supported !\n");
    155:         } else if (user->bcType == NEUMANN) {
    156:           num = 0; numi=0; numj=0;
    157:           if (j!=0) {
    158:             v[num] = -HxdHy;
    159:             col[num].i = i;
    160:             col[num].j = j-1;
    161:             num++; numj++;
    162:           }
    163:           if (i!=0) {
    164:             v[num]     = -HydHx;
    165:             col[num].i = i-1;
    166:             col[num].j = j;
    167:             num++; numi++;
    168:           }
    169:           if (i!=mx-1) {
    170:             v[num]     = -HydHx;
    171:             col[num].i = i+1;
    172:             col[num].j = j;
    173:             num++; numi++;
    174:           }
    175:           if (j!=my-1) {
    176:             v[num]     = -HxdHy;
    177:             col[num].i = i;
    178:             col[num].j = j+1;
    179:             num++; numj++;
    180:           }
    181:           v[num] = (PetscReal)(numj)*HxdHy + (PetscReal)(numi)*HydHx; col[num].i = i;   col[num].j = j;
    182:           num++;
    183:           MatSetValuesStencil(jac,1,&row,num,col,v,INSERT_VALUES);
    184:         }
    185:       } else {
    186:         v[0] = -HxdHy;              col[0].i = i;   col[0].j = j-1;
    187:         v[1] = -HydHx;              col[1].i = i-1; col[1].j = j;
    188:         v[2] = 2.0*(HxdHy + HydHx); col[2].i = i;   col[2].j = j;
    189:         v[3] = -HydHx;              col[3].i = i+1; col[3].j = j;
    190:         v[4] = -HxdHy;              col[4].i = i;   col[4].j = j+1;
    191:         MatSetValuesStencil(jac,1,&row,5,col,v,INSERT_VALUES);
    192:       }
    193:     }
    194:   }
    195:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
    196:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
    197:   if (user->bcType == NEUMANN) {
    198:     MatNullSpace nullspace;

    200:     MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
    201:     MatSetNullSpace(jac,nullspace);
    202:     MatNullSpaceDestroy(&nullspace);
    203:   }
    204:   return(0);
    205: }