Date: 2021-03-03T22:27:32+00:00

Actual source code: ex28.c
petsc-3.14.5 2021-03-03
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      3: static char help[] = "Solves 1D wave equation using multigrid.\n\n";

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

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

     14: int main(int argc,char **argv)
     15: {
     17:   PetscInt       i;
     18:   KSP            ksp;
     19:   DM             da;
     20:   Vec            x;

     22:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
     23:   KSPCreate(PETSC_COMM_WORLD,&ksp);
     24:   DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_PERIODIC,3,2,1,0,&da);
     25:   DMSetFromOptions(da);
     26:   DMSetUp(da);
     27:   KSPSetDM(ksp,da);
     28:   KSPSetComputeRHS(ksp,ComputeRHS,NULL);
     29:   KSPSetComputeOperators(ksp,ComputeMatrix,NULL);

     31:   KSPSetFromOptions(ksp);
     32:   DMCreateGlobalVector(da,&x);
     33:   ComputeInitialSolution(da,x);
     34:   DMSetApplicationContext(da,x);
     35:   KSPSetUp(ksp);
     36:   VecView(x,PETSC_VIEWER_DRAW_WORLD);
     37:   for (i=0; i<10; i++) {
     38:     KSPSolve(ksp,NULL,x);
     39:     VecView(x,PETSC_VIEWER_DRAW_WORLD);
     40:   }
     41:   VecDestroy(&x);
     42:   KSPDestroy(&ksp);
     43:   DMDestroy(&da);
     44:   PetscFinalize();
     45:   return ierr;
     46: }

     48: PetscErrorCode ComputeInitialSolution(DM da,Vec x)
     49: {
     51:   PetscInt       mx,col[2],xs,xm,i;
     52:   PetscScalar    Hx,val[2];

     55:   DMDAGetInfo(da,0,&mx,0,0,0,0,0,0,0,0,0,0,0);
     56:   Hx   = 2.0*PETSC_PI / (PetscReal)(mx);
     57:   DMDAGetCorners(da,&xs,0,0,&xm,0,0);

     59:   for (i=xs; i<xs+xm; i++) {
     60:     col[0] = 2*i; col[1] = 2*i + 1;
     61:     val[0] = val[1] = PetscSinScalar(((PetscScalar)i)*Hx);
     62:     VecSetValues(x,2,col,val,INSERT_VALUES);
     63:   }
     64:   VecAssemblyBegin(x);
     65:   VecAssemblyEnd(x);
     66:   return(0);
     67: }

     69: PetscErrorCode ComputeRHS(KSP ksp,Vec b,void *ctx)
     70: {
     72:   PetscInt       mx;
     73:   PetscScalar    h;
     74:   Vec            x;
     75:   DM             da;

     78:   KSPGetDM(ksp,&da);
     79:   DMDAGetInfo(da,0,&mx,0,0,0,0,0,0,0,0,0,0,0);
     80:   DMGetApplicationContext(da,&x);
     81:   h    = 2.0*PETSC_PI/((mx));
     82:   VecCopy(x,b);
     83:   VecScale(b,h);
     84:   return(0);
     85: }

     87: PetscErrorCode ComputeMatrix(KSP ksp,Mat J,Mat jac,void *ctx)
     88: {
     90:   PetscInt       i,mx,xm,xs;
     91:   PetscScalar    v[7],Hx;
     92:   MatStencil     row,col[7];
     93:   PetscScalar    lambda;
     94:   DM             da;

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

    110:     row.i = i; row.j = 0; row.k = 0; row.c = 1;
    111:     v[0]  = lambda; col[0].i = i-1;   col[0].c = 0;
    112:     v[1]  = Hx;     col[1].i = i;   col[1].c = 1;
    113:     v[2]  = -lambda;col[2].i = i+1; col[2].c = 0;
    114:     MatSetValuesStencil(jac,1,&row,3,col,v,INSERT_VALUES);
    115:   }
    116:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
    117:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
    118:   MatView(jac,PETSC_VIEWER_BINARY_(PETSC_COMM_SELF));
    119:   return(0);
    120: }

    123: /*TEST

    125:    test:
    126:       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

    128: TEST*/