2: /*
  3:  Partial differential equation

  5:    d  (1 + e*sine(2*pi*k*x)) d u = 1, 0 < x < 1,
  6:    --                        ---
  7:    dx                        dx
  8: with boundary conditions

 10:    u = 0 for x = 0, x = 1

 12:    This uses multigrid to solve the linear system

 14: */

 16: static char help[] = "Solves 1D variable coefficient Laplacian using multigrid.\n\n";

 18:  #include <petscdm.h>
 19:  #include <petscdmda.h>
 20:  #include <petscksp.h>

 22: static PetscErrorCode ComputeMatrix(KSP,Mat,Mat,void*);
 23: static PetscErrorCode ComputeRHS(KSP,Vec,void*);

 25: typedef struct {
 26:   PetscInt    k;
 27:   PetscScalar e;
 28: } AppCtx;

 30: int main(int argc,char **argv)
 31: {
 33:   KSP            ksp;
 34:   DM             da;
 35:   AppCtx         user;
 36:   Mat            A;
 37:   Vec            b,b2;
 38:   Vec            x;
 39:   PetscReal      nrm;

 41:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
 42:   user.k = 1;
 43:   user.e = .99;
 44:   PetscOptionsGetInt(NULL,0,"-k",&user.k,0);
 45:   PetscOptionsGetScalar(NULL,0,"-e",&user.e,0);

 47:   KSPCreate(PETSC_COMM_WORLD,&ksp);
 48:   DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,128,1,1,0,&da);
 49:   DMSetFromOptions(da);
 50:   DMSetUp(da);
 51:   KSPSetDM(ksp,da);
 52:   KSPSetComputeRHS(ksp,ComputeRHS,&user);
 53:   KSPSetComputeOperators(ksp,ComputeMatrix,&user);
 54:   KSPSetFromOptions(ksp);
 55:   KSPSolve(ksp,NULL,NULL);

 57:   KSPGetOperators(ksp,&A,NULL);
 58:   KSPGetSolution(ksp,&x);
 59:   KSPGetRhs(ksp,&b);
 60:   VecDuplicate(b,&b2);
 61:   MatMult(A,x,b2);
 62:   VecAXPY(b2,-1.0,b);
 63:   VecNorm(b2,NORM_MAX,&nrm);
 64:   PetscPrintf(PETSC_COMM_WORLD,"Residual norm %g\n",(double)nrm);

 66:   VecDestroy(&b2);
 67:   KSPDestroy(&ksp);
 68:   DMDestroy(&da);
 69:   PetscFinalize();
 70:   return ierr;
 71: }

 73: static PetscErrorCode ComputeRHS(KSP ksp,Vec b,void *ctx)
 74: {
 76:   PetscInt       mx,idx[2];
 77:   PetscScalar    h,v[2];
 78:   DM             da;

 81:   KSPGetDM(ksp,&da);
 82:   DMDAGetInfo(da,0,&mx,0,0,0,0,0,0,0,0,0,0,0);
 83:   h      = 1.0/((mx-1));
 84:   VecSet(b,h);
 85:   idx[0] = 0; idx[1] = mx -1;
 86:   v[0]   = v[1] = 0.0;
 87:   VecSetValues(b,2,idx,v,INSERT_VALUES);
 88:   VecAssemblyBegin(b);
 89:   VecAssemblyEnd(b);
 90:   return(0);
 91: }

 93: static PetscErrorCode ComputeMatrix(KSP ksp,Mat J,Mat jac,void *ctx)
 94: {
 95:   AppCtx         *user = (AppCtx*)ctx;
 97:   PetscInt       i,mx,xm,xs;
 98:   PetscScalar    v[3],h,xlow,xhigh;
 99:   MatStencil     row,col[3];
100:   DM             da;

103:   KSPGetDM(ksp,&da);
104:   DMDAGetInfo(da,0,&mx,0,0,0,0,0,0,0,0,0,0,0);
105:   DMDAGetCorners(da,&xs,0,0,&xm,0,0);
106:   h    = 1.0/(mx-1);

108:   for (i=xs; i<xs+xm; i++) {
109:     row.i = i;
110:     if (i==0 || i==mx-1) {
111:       v[0] = 2.0/h;
112:       MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);
113:     } else {
114:       xlow  = h*(PetscReal)i - .5*h;
115:       xhigh = xlow + h;
116:       v[0]  = (-1.0 - user->e*PetscSinScalar(2.0*PETSC_PI*user->k*xlow))/h;col[0].i = i-1;
117:       v[1]  = (2.0 + user->e*PetscSinScalar(2.0*PETSC_PI*user->k*xlow) + user->e*PetscSinScalar(2.0*PETSC_PI*user->k*xhigh))/h;col[1].i = row.i;
118:       v[2]  = (-1.0 - user->e*PetscSinScalar(2.0*PETSC_PI*user->k*xhigh))/h;col[2].i = i+1;
119:       MatSetValuesStencil(jac,1,&row,3,col,v,INSERT_VALUES);
120:     }
121:   }
122:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
123:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
124:   return(0);
125: }