Actual source code: ex32.c

  1: /*T
2:    Concepts: KSP^solving a system of linear equations
3:    Concepts: KSP^Laplacian, 2d
4:    Processors: n
5: T*/

7: /*
8: Laplacian in 2D. Modeled by the partial differential equation

10:    div  grad u = f,  0 < x,y < 1,

12: with forcing function

14:    f = e^{-(1 - x)^2/\nu} e^{-(1 - y)^2/\nu}

16: with pure Neumann boundary conditions

18: The functions are cell-centered

20: This uses multigrid to solve the linear system

22:        Contributed by Andrei Draganescu <aidraga@sandia.gov>

24: Note the nice multigrid convergence despite the fact it is only using
25: peicewise constant interpolation/restriction. This is because cell-centered multigrid
26: does not need the same rule:

28:     polynomial degree(interpolation) + polynomial degree(restriction) + 2 > degree of PDE

30: that vertex based multigrid needs.
31: */

33: static char help[] = "Solves 2D inhomogeneous Laplacian using multigrid.\n\n";

35: #include <petscdm.h>
36: #include <petscdmda.h>
37: #include <petscksp.h>

39: extern PetscErrorCode ComputeMatrix(KSP,Mat,Mat,void*);
40: extern PetscErrorCode ComputeRHS(KSP,Vec,void*);

42: typedef enum {DIRICHLET, NEUMANN} BCType;

44: typedef struct {
45:   PetscScalar nu;
46:   BCType      bcType;
47: } UserContext;

49: int main(int argc,char **argv)
50: {
51:   KSP            ksp;
52:   DM             da;
53:   UserContext    user;
54:   const char     *bcTypes[2] = {"dirichlet","neumann"};
56:   PetscInt       bc;

58:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
59:   KSPCreate(PETSC_COMM_WORLD,&ksp);
60:   DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,12,12,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,&da);
61:   DMSetFromOptions(da);
62:   DMSetUp(da);
63:   DMDASetInterpolationType(da, DMDA_Q0);

65:   KSPSetDM(ksp,da);

67:   PetscOptionsBegin(PETSC_COMM_WORLD, "", "Options for the inhomogeneous Poisson equation", "DM");
68:   user.nu     = 0.1;
69:   PetscOptionsScalar("-nu", "The width of the Gaussian source", "ex29.c", 0.1, &user.nu, NULL);
70:   bc          = (PetscInt)NEUMANN;
71:   PetscOptionsEList("-bc_type","Type of boundary condition","ex29.c",bcTypes,2,bcTypes[0],&bc,NULL);
72:   user.bcType = (BCType)bc;
73:   PetscOptionsEnd();

75:   KSPSetComputeRHS(ksp,ComputeRHS,&user);
76:   KSPSetComputeOperators(ksp,ComputeMatrix,&user);
77:   KSPSetFromOptions(ksp);
78:   KSPSolve(ksp,NULL,NULL);
79:   KSPDestroy(&ksp);
80:   DMDestroy(&da);
81:   PetscFinalize();
82:   return ierr;
83: }

85: PetscErrorCode ComputeRHS(KSP ksp,Vec b,void *ctx)
86: {
87:   UserContext    *user = (UserContext*)ctx;
89:   PetscInt       i,j,mx,my,xm,ym,xs,ys;
90:   PetscScalar    Hx,Hy;
91:   PetscScalar    **array;
92:   DM             da;

95:   KSPGetDM(ksp,&da);
96:   DMDAGetInfo(da, 0, &mx, &my, 0,0,0,0,0,0,0,0,0,0);
97:   Hx   = 1.0 / (PetscReal)(mx);
98:   Hy   = 1.0 / (PetscReal)(my);
99:   DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);
100:   DMDAVecGetArray(da, b, &array);
101:   for (j=ys; j<ys+ym; j++) {
102:     for (i=xs; i<xs+xm; i++) {
103:       array[j][i] = PetscExpScalar(-(((PetscReal)i+0.5)*Hx)*(((PetscReal)i+0.5)*Hx)/user->nu)*PetscExpScalar(-(((PetscReal)j+0.5)*Hy)*(((PetscReal)j+0.5)*Hy)/user->nu)*Hx*Hy;
104:     }
105:   }
106:   DMDAVecRestoreArray(da, b, &array);
107:   VecAssemblyBegin(b);
108:   VecAssemblyEnd(b);

110:   /* force right hand side to be consistent for singular matrix */
111:   /* note this is really a hack, normally the model would provide you with a consistent right handside */
112:   if (user->bcType == NEUMANN) {
113:     MatNullSpace nullspace;

115:     MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
116:     MatNullSpaceRemove(nullspace,b);
117:     MatNullSpaceDestroy(&nullspace);
118:   }
119:   return(0);
120: }

122: PetscErrorCode ComputeMatrix(KSP ksp, Mat J,Mat jac, void *ctx)
123: {
124:   UserContext    *user = (UserContext*)ctx;
126:   PetscInt       i,j,mx,my,xm,ym,xs,ys,num, numi, numj;
127:   PetscScalar    v[5],Hx,Hy,HydHx,HxdHy;
128:   MatStencil     row, col[5];
129:   DM             da;

132:   KSPGetDM(ksp,&da);
133:   DMDAGetInfo(da,0,&mx,&my,0,0,0,0,0,0,0,0,0,0);
134:   Hx    = 1.0 / (PetscReal)(mx);
135:   Hy    = 1.0 / (PetscReal)(my);
136:   HxdHy = Hx/Hy;
137:   HydHx = Hy/Hx;
138:   DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);
139:   for (j=ys; j<ys+ym; j++) {
140:     for (i=xs; i<xs+xm; i++) {
141:       row.i = i; row.j = j;
142:       if (i==0 || j==0 || i==mx-1 || j==my-1) {
143:         if (user->bcType == DIRICHLET) {
144:           v[0] = 2.0*(HxdHy + HydHx);
145:           MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);
146:           SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Dirichlet boundary conditions not supported !\n");
147:         } else if (user->bcType == NEUMANN) {
148:           num = 0; numi=0; numj=0;
149:           if (j!=0) {
150:             v[num] = -HxdHy;
151:             col[num].i = i;
152:             col[num].j = j-1;
153:             num++; numj++;
154:           }
155:           if (i!=0) {
156:             v[num]     = -HydHx;
157:             col[num].i = i-1;
158:             col[num].j = j;
159:             num++; numi++;
160:           }
161:           if (i!=mx-1) {
162:             v[num]     = -HydHx;
163:             col[num].i = i+1;
164:             col[num].j = j;
165:             num++; numi++;
166:           }
167:           if (j!=my-1) {
168:             v[num]     = -HxdHy;
169:             col[num].i = i;
170:             col[num].j = j+1;
171:             num++; numj++;
172:           }
173:           v[num] = (PetscReal)(numj)*HxdHy + (PetscReal)(numi)*HydHx; col[num].i = i;   col[num].j = j;
174:           num++;
175:           MatSetValuesStencil(jac,1,&row,num,col,v,INSERT_VALUES);
176:         }
177:       } else {
178:         v[0] = -HxdHy;              col[0].i = i;   col[0].j = j-1;
179:         v[1] = -HydHx;              col[1].i = i-1; col[1].j = j;
180:         v[2] = 2.0*(HxdHy + HydHx); col[2].i = i;   col[2].j = j;
181:         v[3] = -HydHx;              col[3].i = i+1; col[3].j = j;
182:         v[4] = -HxdHy;              col[4].i = i;   col[4].j = j+1;
183:         MatSetValuesStencil(jac,1,&row,5,col,v,INSERT_VALUES);
184:       }
185:     }
186:   }
187:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
188:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
189:   if (user->bcType == NEUMANN) {
190:     MatNullSpace nullspace;

192:     MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
193:     MatSetNullSpace(J,nullspace);
194:     MatNullSpaceDestroy(&nullspace);
195:   }
196:   return(0);
197: }

199: /*TEST

201:    test:
202:       args: -pc_type mg -pc_mg_type full -ksp_type fgmres -ksp_monitor_short -pc_mg_levels 3 -mg_coarse_pc_factor_shift_type nonzero

204: TEST*/