Actual source code: ex25.c
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 petscda.h
19: #include petscksp.h
20: #include petscdmmg.h
25: typedef struct {
26: PetscInt k;
27: PetscScalar e;
28: } AppCtx;
32: int main(int argc,char **argv)
33: {
35: DMMG *dmmg;
36: PetscReal norm;
37: DA da;
38: AppCtx user;
40: PetscInitialize(&argc,&argv,(char *)0,help);
42: user.k = 1;
43: user.e = .99;
44: PetscOptionsGetInt(0,"-k",&user.k,0);
45: PetscOptionsGetScalar(0,"-e",&user.e,0);
47: DMMGCreate(PETSC_COMM_WORLD,3,&user,&dmmg);
48: DACreate1d(PETSC_COMM_WORLD,DA_NONPERIODIC,-3,1,1,0,&da);
49: DMMGSetDM(dmmg,(DM)da);
50: DADestroy(da);
52: DMMGSetKSP(dmmg,ComputeRHS,ComputeMatrix);
54: DMMGSolve(dmmg);
56: MatMult(DMMGGetJ(dmmg),DMMGGetx(dmmg),DMMGGetr(dmmg));
57: VecAXPY(DMMGGetr(dmmg),-1.0,DMMGGetRHS(dmmg));
58: VecNorm(DMMGGetr(dmmg),NORM_2,&norm);
59: /* PetscPrintf(PETSC_COMM_WORLD,"Residual norm %G\n",norm); */
61: DMMGDestroy(dmmg);
62: PetscFinalize();
64: return 0;
65: }
69: PetscErrorCode ComputeRHS(DMMG dmmg,Vec b)
70: {
72: PetscInt mx,idx[2];
73: PetscScalar h,v[2];
76: DAGetInfo((DA)dmmg->dm,0,&mx,0,0,0,0,0,0,0,0,0);
77: h = 1.0/((mx-1));
78: VecSet(b,h);
79: idx[0] = 0; idx[1] = mx -1;
80: v[0] = v[1] = 0.0;
81: VecSetValues(b,2,idx,v,INSERT_VALUES);
82: VecAssemblyBegin(b);
83: VecAssemblyEnd(b);
84: return(0);
85: }
86:
89: PetscErrorCode ComputeMatrix(DMMG dmmg,Mat J,Mat jac)
90: {
91: DA da = (DA)dmmg->dm;
93: PetscInt i,mx,xm,xs;
94: PetscScalar v[3],h,xlow,xhigh;
95: MatStencil row,col[3];
96: AppCtx *user = (AppCtx*)dmmg->user;
98: DAGetInfo(da,0,&mx,0,0,0,0,0,0,0,0,0);
99: DAGetCorners(da,&xs,0,0,&xm,0,0);
100: h = 1.0/(mx-1);
102: for(i=xs; i<xs+xm; i++){
103: row.i = i;
104: if (i==0 || i==mx-1){
105: v[0] = 2.0;
106: MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);
107: } else {
108: xlow = h*(PetscReal)i - .5*h;
109: xhigh = xlow + h;
110: v[0] = (-1.0 - user->e*PetscSinScalar(2.0*PETSC_PI*user->k*xlow))/h;col[0].i = i-1;
111: 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;
112: v[2] = (-1.0 - user->e*PetscSinScalar(2.0*PETSC_PI*user->k*xhigh))/h;col[2].i = i+1;
113: MatSetValuesStencil(jac,1,&row,3,col,v,INSERT_VALUES);
114: }
115: }
116: MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
117: MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
118: return 0;
119: }