Actual source code: ex29.c

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

      7: /*
      8: Added at the request of Marc Garbey.

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

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

     14: with forcing function

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

     18: with Dirichlet boundary conditions

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

     22: or pure Neumman boundary conditions

     24: This uses multigrid to solve the linear system
     25: */

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

     29:  #include petscda.h
     30:  #include petscksp.h
     31:  #include petscmg.h
     32:  #include petscdmmg.h

     38: typedef enum {DIRICHLET, NEUMANN} BCType;

     40: typedef struct {
     41:   PetscScalar   nu;
     42:   BCType        bcType;
     43: } UserContext;

     47: int main(int argc,char **argv)
     48: {
     49:   DMMG           *dmmg;
     50:   DA             da;
     51:   UserContext    user;
     52:   PetscReal      norm;
     53:   PetscScalar    mone = -1.0;
     54:   const char     *bcTypes[2] = {"dirichlet","neumann"};
     56:   PetscInt       l,bc;

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

     60:   DMMGCreate(PETSC_COMM_WORLD,3,PETSC_NULL,&dmmg);
     61:   DACreate2d(PETSC_COMM_WORLD,DA_NONPERIODIC,DA_STENCIL_STAR,-3,-3,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,&da);
     62:   DMMGSetDM(dmmg,(DM)da);
     63:   DADestroy(da);
     64:   for (l = 0; l < DMMGGetLevels(dmmg); l++) {
     65:     DMMGSetUser(dmmg,l,&user);
     66:   }

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

     76:   DMMGSetKSP(dmmg,ComputeRHS,ComputeJacobian);
     77:   if (user.bcType == NEUMANN) {
     78:     DMMGSetNullSpace(dmmg,PETSC_TRUE,0,PETSC_NULL);
     79:   }

     81:   DMMGSolve(dmmg);

     83:   MatMult(DMMGGetJ(dmmg),DMMGGetx(dmmg),DMMGGetr(dmmg));
     84:   VecAXPY(DMMGGetr(dmmg),mone,DMMGGetRHS(dmmg));
     85:   VecNorm(DMMGGetr(dmmg),NORM_2,&norm);
     86:   /* PetscPrintf(PETSC_COMM_WORLD,"Residual norm %g\n",norm); */
     87:   VecAssemblyBegin(DMMGGetx(dmmg));
     88:   VecAssemblyEnd(DMMGGetx(dmmg));
     89:   VecView_VTK(DMMGGetRHS(dmmg), "rhs.vtk", bcTypes[user.bcType]);
     90:   VecView_VTK(DMMGGetx(dmmg), "solution.vtk", bcTypes[user.bcType]);

     92:   DMMGDestroy(dmmg);
     93:   PetscFinalize();

     95:   return 0;
     96: }

    100: PetscErrorCode ComputeRHS(DMMG dmmg, Vec b)
    101: {
    102:   DA             da = (DA)dmmg->dm;
    103:   UserContext    *user = (UserContext *) dmmg->user;
    105:   PetscInt       i,j,mx,my,xm,ym,xs,ys;
    106:   PetscScalar    Hx,Hy;
    107:   PetscScalar    **array;

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

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

    129:     KSPGetNullSpace(dmmg->ksp,&nullspace);
    130:     MatNullSpaceRemove(nullspace,b,PETSC_NULL);
    131:   }
    132:   return(0);
    133: }

    135:
    138: PetscErrorCode ComputeRho(PetscInt i, PetscInt j, PetscInt mx, PetscInt my, PetscScalar *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 = 100.0;
    143:   } else {
    144:     *rho = 1.0;
    145:   }
    146:   return(0);
    147: }

    151: PetscErrorCode ComputeJacobian(DMMG dmmg, Mat jac)
    152: {
    153:   DA             da = (DA) dmmg->dm;
    154:   UserContext    *user = (UserContext *) dmmg->user;
    156:   PetscInt       i,j,mx,my,xm,ym,xs,ys,num;
    157:   PetscScalar    v[5],Hx,Hy,HydHx,HxdHy,rho;
    158:   MatStencil     row, col[5];

    161:   DAGetInfo(da,0,&mx,&my,0,0,0,0,0,0,0,0);
    162:   Hx    = 1.0 / (PetscReal)(mx-1);
    163:   Hy    = 1.0 / (PetscReal)(my-1);
    164:   HxdHy = Hx/Hy;
    165:   HydHx = Hy/Hx;
    166:   DAGetCorners(da,&xs,&ys,0,&xm,&ym,0);
    167:   for (j=ys; j<ys+ym; j++){
    168:     for(i=xs; i<xs+xm; i++){
    169:       row.i = i; row.j = j;
    170:       if (i==0 || j==0 || i==mx-1 || j==my-1) {
    171:        ComputeRho(i, j, mx, my, &rho);
    172:        if (user->bcType == DIRICHLET) {
    173:            v[0] = 2.0*rho*(HxdHy + HydHx);
    174:           MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);
    175:         } else if (user->bcType == NEUMANN) {
    176:           num = 0;
    177:           if (j!=0) {
    178:             v[num] = -rho*HxdHy;              col[num].i = i;   col[num].j = j-1;
    179:             num++;
    180:           }
    181:           if (i!=0) {
    182:             v[num] = -rho*HydHx;              col[num].i = i-1; col[num].j = j;
    183:             num++;
    184:           }
    185:           if (i!=mx-1) {
    186:             v[num] = -rho*HydHx;              col[num].i = i+1; col[num].j = j;
    187:             num++;
    188:           }
    189:           if (j!=my-1) {
    190:             v[num] = -rho*HxdHy;              col[num].i = i;   col[num].j = j+1;
    191:             num++;
    192:           }
    193:           v[num]   = (num/2.0)*rho*(HxdHy + HydHx); col[num].i = i;   col[num].j = j;
    194:           num++;
    195:           MatSetValuesStencil(jac,1,&row,num,col,v,INSERT_VALUES);
    196:         }
    197:       } else {
    198:         v[0] = -rho*HxdHy;              col[0].i = i;   col[0].j = j-1;
    199:         v[1] = -rho*HydHx;              col[1].i = i-1; col[1].j = j;
    200:         v[2] = 2.0*rho*(HxdHy + HydHx); col[2].i = i;   col[2].j = j;
    201:         v[3] = -rho*HydHx;              col[3].i = i+1; col[3].j = j;
    202:         v[4] = -rho*HxdHy;              col[4].i = i;   col[4].j = j+1;
    203:         MatSetValuesStencil(jac,1,&row,5,col,v,INSERT_VALUES);
    204:       }
    205:     }
    206:   }
    207:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
    208:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
    209:   return(0);
    210: }

    214: PetscErrorCode VecView_VTK(Vec x, const char filename[], const char bcName[])
    215: {
    216:   MPI_Comm           comm;
    217:   DA                 da;
    218:   Vec                coords;
    219:   PetscViewer        viewer;
    220:   PetscScalar       *array, *values;
    221:   PetscInt           n, N, maxn, mx, my, dof;
    222:   PetscInt           i, p;
    223:   MPI_Status         status;
    224:   PetscMPIInt        rank, size, tag;
    225:   PetscErrorCode     ierr;

    228:   PetscObjectGetComm((PetscObject) x, &comm);
    229:   PetscViewerASCIIOpen(comm, filename, &viewer);

    231:   VecGetSize(x, &N);
    232:   VecGetLocalSize(x, &n);
    233:   PetscObjectQuery((PetscObject) x, "DA", (PetscObject *) &da);
    234:   if (!da) SETERRQ(PETSC_ERR_ARG_WRONG,"Vector not generated from a DA");

    236:   DAGetInfo(da, 0, &mx, &my, 0,0,0,0, &dof,0,0,0);

    238:   PetscViewerASCIIPrintf(viewer, "# vtk DataFile Version 2.0\n");
    239:   PetscViewerASCIIPrintf(viewer, "Inhomogeneous Poisson Equation with %s boundary conditions\n", bcName);
    240:   PetscViewerASCIIPrintf(viewer, "ASCII\n");
    241:   /* get coordinates of nodes */
    242:   DAGetCoordinates(da, &coords);
    243:   if (!coords) {
    244:     DASetUniformCoordinates(da, 0.0, 1.0, 0.0, 1.0, 0.0, 0.0);
    245:     DAGetCoordinates(da, &coords);
    246:   }
    247:   PetscViewerASCIIPrintf(viewer, "DATASET RECTILINEAR_GRID\n");
    248:   PetscViewerASCIIPrintf(viewer, "DIMENSIONS %d %d %d\n", mx, my, 1);
    249:   VecGetArray(coords, &array);
    250:   PetscViewerASCIIPrintf(viewer, "X_COORDINATES %d double\n", mx);
    251:   for(i = 0; i < mx; i++) {
    252:     PetscViewerASCIIPrintf(viewer, "%g ", PetscRealPart(array[i*2]));
    253:   }
    254:   PetscViewerASCIIPrintf(viewer, "\n");
    255:   PetscViewerASCIIPrintf(viewer, "Y_COORDINATES %d double\n", my);
    256:   for(i = 0; i < my; i++) {
    257:     PetscViewerASCIIPrintf(viewer, "%g ", PetscRealPart(array[i*mx*2+1]));
    258:   }
    259:   PetscViewerASCIIPrintf(viewer, "\n");
    260:   PetscViewerASCIIPrintf(viewer, "Z_COORDINATES %d double\n", 1);
    261:   PetscViewerASCIIPrintf(viewer, "%g\n", 0.0);
    262:   VecRestoreArray(coords, &array);
    263:   PetscViewerASCIIPrintf(viewer, "POINT_DATA %d\n", N);
    264:   PetscViewerASCIIPrintf(viewer, "SCALARS scalars double %d\n", dof);
    265:   PetscViewerASCIIPrintf(viewer, "LOOKUP_TABLE default\n");
    266:   VecGetArray(x, &array);
    267:   /* Determine maximum message to arrive */
    268:   MPI_Comm_rank(comm, &rank);
    269:   MPI_Comm_size(comm, &size);
    270:   MPI_Reduce(&n, &maxn, 1, MPIU_INT, MPI_MAX, 0, comm);
    271:   tag  = ((PetscObject) viewer)->tag;
    272:   if (!rank) {
    273:     PetscMalloc((maxn+1) * sizeof(PetscScalar), &values);
    274:     for(i = 0; i < n; i++) {
    275:       PetscViewerASCIIPrintf(viewer, "%g\n", PetscRealPart(array[i]));
    276:     }
    277:     for(p = 1; p < size; p++) {
    278:       MPI_Recv(values, (PetscMPIInt) n, MPIU_SCALAR, p, tag, comm, &status);
    279:       MPI_Get_count(&status, MPIU_SCALAR, &n);
    280:       for(i = 0; i < n; i++) {
    281:         PetscViewerASCIIPrintf(viewer, "%g\n", PetscRealPart(array[i]));
    282:       }
    283:     }
    284:     PetscFree(values);
    285:   } else {
    286:     MPI_Send(array, n, MPIU_SCALAR, 0, tag, comm);
    287:   }
    288:   VecRestoreArray(x, &array);
    289:   PetscViewerFlush(viewer);
    290:   PetscViewerDestroy(viewer);
    291:   return(0);
    292: }