1: /*   DMDA/KSP solving a system of linear equations.
  2:      Poisson equation in 2D:

  4:      div(grad p) = f,  0 < x,y < 1
  5:      with
  6:        forcing function f = -cos(m*pi*x)*cos(n*pi*y),
  7:        Periodic boundary conditions
  8:          p(x=0) = p(x=1)
  9:        Neuman boundary conditions
 10:          dp/dy = 0 for y = 0, y = 1.

 12:        This example uses the DM_BOUNDARY_MIRROR to implement the Neumann boundary conditions, see the manual pages for DMBoundaryType

 14:        Compare to ex50.c
 15: */

 17: static char help[] = "Solves 2D Poisson equation,\n\
 18:                       using mirrored boundaries to implement Neumann boundary conditions,\n\
 19:                       using multigrid.\n\n";

 21:  #include <petscdm.h>
 22:  #include <petscdmda.h>
 23:  #include <petscksp.h>
 24:  #include <petscsys.h>
 25:  #include <petscvec.h>

 27: extern PetscErrorCode ComputeJacobian(KSP,Mat,Mat,void*);
 28: extern PetscErrorCode ComputeRHS(KSP,Vec,void*);

 30: typedef struct {
 31:   PetscScalar uu, tt;
 32: } UserContext;

 34: int main(int argc,char **argv)
 35: {
 36:   KSP            ksp;
 37:   DM             da;
 38:   UserContext    user;

 41:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
 42:   KSPCreate(PETSC_COMM_WORLD,&ksp);
 43:   DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_PERIODIC, DM_BOUNDARY_MIRROR,DMDA_STENCIL_STAR,11,11,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);
 44:   DMSetFromOptions(da);
 45:   DMSetUp(da);
 46:   KSPSetDM(ksp,(DM)da);
 47:   DMSetApplicationContext(da,&user);

 49:   user.uu     = 1.0;
 50:   user.tt     = 1.0;

 52:   KSPSetComputeRHS(ksp,ComputeRHS,&user);
 53:   KSPSetComputeOperators(ksp,ComputeJacobian,&user);
 54:   KSPSetFromOptions(ksp);
 55:   KSPSolve(ksp,NULL,NULL);

 57:   DMDestroy(&da);
 58:   KSPDestroy(&ksp);
 59:   PetscFinalize();
 60:   return ierr;
 61: }

 63: PetscErrorCode ComputeRHS(KSP ksp,Vec b,void *ctx)
 64: {
 65:   UserContext    *user = (UserContext*)ctx;
 67:   PetscInt       i,j,M,N,xm,ym,xs,ys;
 68:   PetscScalar    Hx,Hy,pi,uu,tt;
 69:   PetscScalar    **array;
 70:   DM             da;
 71:   MatNullSpace   nullspace;

 74:   KSPGetDM(ksp,&da);
 75:   DMDAGetInfo(da, 0, &M, &N, 0,0,0,0,0,0,0,0,0,0);
 76:   uu   = user->uu; tt = user->tt;
 77:   pi   = 4*PetscAtanReal(1.0);
 78:   Hx   = 1.0/(PetscReal)(M);
 79:   Hy   = 1.0/(PetscReal)(N);

 81:   DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0); /* Fine grid */
 82:   DMDAVecGetArray(da, b, &array);
 83:   for (j=ys; j<ys+ym; j++) {
 84:     for (i=xs; i<xs+xm; i++) {
 85:       array[j][i] = -PetscCosScalar(uu*pi*((PetscReal)i+0.5)*Hx)*PetscCosScalar(tt*pi*((PetscReal)j+0.5)*Hy)*Hx*Hy;
 86:     }
 87:   }
 88:   DMDAVecRestoreArray(da, b, &array);
 89:   VecAssemblyBegin(b);
 90:   VecAssemblyEnd(b);

 92:   /* force right hand side to be consistent for singular matrix */
 93:   /* note this is really a hack, normally the model would provide you with a consistent right handside */
 94:   MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
 95:   MatNullSpaceRemove(nullspace,b);
 96:   MatNullSpaceDestroy(&nullspace);
 97:   return(0);
 98: }

100: PetscErrorCode ComputeJacobian(KSP ksp,Mat J, Mat jac,void *ctx)
101: {
103:   PetscInt       i, j, M, N, xm, ym, xs, ys;
104:   PetscScalar    v[5], Hx, Hy, HydHx, HxdHy;
105:   MatStencil     row, col[5];
106:   DM             da;
107:   MatNullSpace   nullspace;

110:   KSPGetDM(ksp,&da);
111:   DMDAGetInfo(da,0,&M,&N,0,0,0,0,0,0,0,0,0,0);
112:   Hx    = 1.0 / (PetscReal)(M);
113:   Hy    = 1.0 / (PetscReal)(N);
114:   HxdHy = Hx/Hy;
115:   HydHx = Hy/Hx;
116:   DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);
117:   for (j=ys; j<ys+ym; j++) {
118:     for (i=xs; i<xs+xm; i++) {
119:       row.i = i; row.j = j;
120:       v[0] = -HxdHy;              col[0].i = i;   col[0].j = j-1;
121:       v[1] = -HydHx;              col[1].i = i-1; col[1].j = j;
122:       v[2] = 2.0*(HxdHy + HydHx); col[2].i = i;   col[2].j = j;
123:       v[3] = -HydHx;              col[3].i = i+1; col[3].j = j;
124:       v[4] = -HxdHy;              col[4].i = i;   col[4].j = j+1;
125:       MatSetValuesStencil(jac,1,&row,5,col,v,ADD_VALUES);
126:     }
127:   }
128:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
129:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);

131:   MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
132:   MatSetNullSpace(J,nullspace);
133:   MatNullSpaceDestroy(&nullspace);
134:   return(0);
135: }



139: /*TEST

141:    build:
142:       requires: !complex !single

144:    test:
145:       args: -pc_type mg -pc_mg_type full -ksp_monitor_short -da_refine 3 -mg_coarse_pc_type svd -ksp_view

147:    test:
148:       suffix: 2
149:       nsize: 4
150:       args: -pc_type mg -pc_mg_type full -ksp_monitor_short -da_refine 3 -mg_coarse_pc_type redundant -mg_coarse_redundant_pc_type svd -ksp_view

152: TEST*/