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

Actual source code: ex28.c

      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*/