2: static char help[] = "Solves 1D wave equation using multigrid.\n\n";

  4: #include <petscdm.h>
  5: #include <petscdmda.h>
  6: #include <petscksp.h>

  8: extern PetscErrorCode ComputeMatrix(KSP,Mat,Mat,void*);
  9: extern PetscErrorCode ComputeRHS(KSP,Vec,void*);
 10: extern PetscErrorCode ComputeInitialSolution(DM,Vec);

 12: int main(int argc,char **argv)
 13: {
 14:   PetscInt       i;
 15:   KSP            ksp;
 16:   DM             da;
 17:   Vec            x;

 19:   PetscInitialize(&argc,&argv,(char*)0,help);
 20:   KSPCreate(PETSC_COMM_WORLD,&ksp);
 21:   DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_PERIODIC,3,2,1,0,&da);
 22:   DMSetFromOptions(da);
 23:   DMSetUp(da);
 24:   KSPSetDM(ksp,da);
 25:   KSPSetComputeRHS(ksp,ComputeRHS,NULL);
 26:   KSPSetComputeOperators(ksp,ComputeMatrix,NULL);

 28:   KSPSetFromOptions(ksp);
 29:   DMCreateGlobalVector(da,&x);
 30:   ComputeInitialSolution(da,x);
 31:   DMSetApplicationContext(da,x);
 32:   KSPSetUp(ksp);
 33:   VecView(x,PETSC_VIEWER_DRAW_WORLD);
 34:   for (i=0; i<10; i++) {
 35:     KSPSolve(ksp,NULL,x);
 36:     VecView(x,PETSC_VIEWER_DRAW_WORLD);
 37:   }
 38:   VecDestroy(&x);
 39:   KSPDestroy(&ksp);
 40:   DMDestroy(&da);
 41:   PetscFinalize();
 42:   return 0;
 43: }

 45: PetscErrorCode ComputeInitialSolution(DM da,Vec x)
 46: {
 47:   PetscInt       mx,col[2],xs,xm,i;
 48:   PetscScalar    Hx,val[2];

 51:   DMDAGetInfo(da,0,&mx,0,0,0,0,0,0,0,0,0,0,0);
 52:   Hx   = 2.0*PETSC_PI / (PetscReal)(mx);
 53:   DMDAGetCorners(da,&xs,0,0,&xm,0,0);

 55:   for (i=xs; i<xs+xm; i++) {
 56:     col[0] = 2*i; col[1] = 2*i + 1;
 57:     val[0] = val[1] = PetscSinScalar(((PetscScalar)i)*Hx);
 58:     VecSetValues(x,2,col,val,INSERT_VALUES);
 59:   }
 60:   VecAssemblyBegin(x);
 61:   VecAssemblyEnd(x);
 62:   return 0;
 63: }

 65: PetscErrorCode ComputeRHS(KSP ksp,Vec b,void *ctx)
 66: {
 67:   PetscInt       mx;
 68:   PetscScalar    h;
 69:   Vec            x;
 70:   DM             da;

 73:   KSPGetDM(ksp,&da);
 74:   DMDAGetInfo(da,0,&mx,0,0,0,0,0,0,0,0,0,0,0);
 75:   DMGetApplicationContext(da,&x);
 76:   h    = 2.0*PETSC_PI/((mx));
 77:   VecCopy(x,b);
 78:   VecScale(b,h);
 79:   return 0;
 80: }

 82: PetscErrorCode ComputeMatrix(KSP ksp,Mat J,Mat jac,void *ctx)
 83: {
 84:   PetscInt       i,mx,xm,xs;
 85:   PetscScalar    v[7],Hx;
 86:   MatStencil     row,col[7];
 87:   PetscScalar    lambda;
 88:   DM             da;

 91:   KSPGetDM(ksp,&da);
 92:   PetscArrayzero(col,7);
 93:   DMDAGetInfo(da,0,&mx,0,0,0,0,0,0,0,0,0,0,0);
 94:   Hx     = 2.0*PETSC_PI / (PetscReal)(mx);
 95:   DMDAGetCorners(da,&xs,0,0,&xm,0,0);
 96:   lambda = 2.0*Hx;
 97:   for (i=xs; i<xs+xm; i++) {
 98:     row.i = i; row.j = 0; row.k = 0; row.c = 0;
 99:     v[0]  = Hx;     col[0].i = i;   col[0].c = 0;
100:     v[1]  = lambda; col[1].i = i-1;   col[1].c = 1;
101:     v[2]  = -lambda;col[2].i = i+1; col[2].c = 1;
102:     MatSetValuesStencil(jac,1,&row,3,col,v,INSERT_VALUES);

104:     row.i = i; row.j = 0; row.k = 0; row.c = 1;
105:     v[0]  = lambda; col[0].i = i-1;   col[0].c = 0;
106:     v[1]  = Hx;     col[1].i = i;   col[1].c = 1;
107:     v[2]  = -lambda;col[2].i = i+1; col[2].c = 0;
108:     MatSetValuesStencil(jac,1,&row,3,col,v,INSERT_VALUES);
109:   }
110:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
111:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
112:   MatView(jac,PETSC_VIEWER_BINARY_(PETSC_COMM_SELF));
113:   return 0;
114: }

116: /*TEST

118:    test:
119:       args: -ksp_monitor_short -pc_type mg -pc_mg_type full -ksp_type fgmres -da_refine 2 -mg_levels_ksp_type gmres -mg_levels_ksp_max_it 1 -mg_levels_pc_type ilu

121: TEST*/