Actual source code: ex50.c

petsc-master 2020-11-30
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```  1: /*   DMDA/KSP solving a system of linear equations.
2:      Poisson equation in 2D:

4:      div(grad p) = f,  0 < x,y < 1
5:      with
6:        forcing function f = -cos(m*pi*x)*cos(n*pi*y),
7:        Neuman boundary conditions
8:         dp/dx = 0 for x = 0, x = 1.
9:         dp/dy = 0 for y = 0, y = 1.

11:      Contributed by Michael Boghosian <boghmic@iit.edu>, 2008,
12:          based on petsc/src/ksp/ksp/tutorials/ex29.c and ex32.c

14:      Compare to ex66.c

16:      Example of Usage:
17:           ./ex50 -da_grid_x 3 -da_grid_y 3 -pc_type mg -da_refine 3 -ksp_monitor -ksp_view -dm_view draw -draw_pause -1
18:           ./ex50 -da_grid_x 100 -da_grid_y 100 -pc_type mg  -pc_mg_levels 1 -mg_levels_0_pc_type ilu -mg_levels_0_pc_factor_levels 1 -ksp_monitor -ksp_view
19:           ./ex50 -da_grid_x 100 -da_grid_y 100 -pc_type mg -pc_mg_levels 1 -mg_levels_0_pc_type lu -mg_levels_0_pc_factor_shift_type NONZERO -ksp_monitor
20:           mpiexec -n 4 ./ex50 -da_grid_x 3 -da_grid_y 3 -pc_type mg -da_refine 10 -ksp_monitor -ksp_view -log_view
21: */

23: static char help[] = "Solves 2D Poisson equation using multigrid.\n\n";

25: #include <petscdm.h>
26: #include <petscdmda.h>
27: #include <petscksp.h>
28: #include <petscsys.h>
29: #include <petscvec.h>

31: extern PetscErrorCode ComputeJacobian(KSP,Mat,Mat,void*);
32: extern PetscErrorCode ComputeRHS(KSP,Vec,void*);

34: typedef struct {
35:   PetscScalar uu, tt;
36: } UserContext;

38: int main(int argc,char **argv)
39: {
40:   KSP            ksp;
41:   DM             da;
42:   UserContext    user;

45:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
46:   KSPCreate(PETSC_COMM_WORLD,&ksp);
47:   DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,11,11,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);
48:   DMSetFromOptions(da);
49:   DMSetUp(da);
50:   KSPSetDM(ksp,(DM)da);
51:   DMSetApplicationContext(da,&user);

53:   user.uu     = 1.0;
54:   user.tt     = 1.0;

56:   KSPSetComputeRHS(ksp,ComputeRHS,&user);
57:   KSPSetComputeOperators(ksp,ComputeJacobian,&user);
58:   KSPSetFromOptions(ksp);
59:   KSPSolve(ksp,NULL,NULL);

61:   DMDestroy(&da);
62:   KSPDestroy(&ksp);
63:   PetscFinalize();
64:   return ierr;
65: }

67: PetscErrorCode ComputeRHS(KSP ksp,Vec b,void *ctx)
68: {
69:   UserContext    *user = (UserContext*)ctx;
71:   PetscInt       i,j,M,N,xm,ym,xs,ys;
72:   PetscScalar    Hx,Hy,pi,uu,tt;
73:   PetscScalar    **array;
74:   DM             da;
75:   MatNullSpace   nullspace;

78:   KSPGetDM(ksp,&da);
79:   DMDAGetInfo(da, 0, &M, &N, 0,0,0,0,0,0,0,0,0,0);
80:   uu   = user->uu; tt = user->tt;
81:   pi   = 4*atan(1.0);
82:   Hx   = 1.0/(PetscReal)(M);
83:   Hy   = 1.0/(PetscReal)(N);

85:   DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0); /* Fine grid */
86:   DMDAVecGetArray(da, b, &array);
87:   for (j=ys; j<ys+ym; j++) {
88:     for (i=xs; i<xs+xm; i++) {
89:       array[j][i] = -PetscCosScalar(uu*pi*((PetscReal)i+0.5)*Hx)*PetscCosScalar(tt*pi*((PetscReal)j+0.5)*Hy)*Hx*Hy;
90:     }
91:   }
92:   DMDAVecRestoreArray(da, b, &array);
93:   VecAssemblyBegin(b);
94:   VecAssemblyEnd(b);

96:   /* force right hand side to be consistent for singular matrix */
97:   /* note this is really a hack, normally the model would provide you with a consistent right handside */
98:   MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
99:   MatNullSpaceRemove(nullspace,b);
100:   MatNullSpaceDestroy(&nullspace);
101:   return(0);
102: }

104: PetscErrorCode ComputeJacobian(KSP ksp,Mat J, Mat jac,void *ctx)
105: {
107:   PetscInt       i, j, M, N, xm, ym, xs, ys, num, numi, numj;
108:   PetscScalar    v[5], Hx, Hy, HydHx, HxdHy;
109:   MatStencil     row, col[5];
110:   DM             da;
111:   MatNullSpace   nullspace;

114:   KSPGetDM(ksp,&da);
115:   DMDAGetInfo(da,0,&M,&N,0,0,0,0,0,0,0,0,0,0);
116:   Hx    = 1.0 / (PetscReal)(M);
117:   Hy    = 1.0 / (PetscReal)(N);
118:   HxdHy = Hx/Hy;
119:   HydHx = Hy/Hx;
120:   DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);
121:   for (j=ys; j<ys+ym; j++) {
122:     for (i=xs; i<xs+xm; i++) {
123:       row.i = i; row.j = j;

125:       if (i==0 || j==0 || i==M-1 || j==N-1) {
126:         num=0; numi=0; numj=0;
127:         if (j!=0) {
128:           v[num] = -HxdHy;              col[num].i = i;   col[num].j = j-1;
129:           num++; numj++;
130:         }
131:         if (i!=0) {
132:           v[num] = -HydHx;              col[num].i = i-1; col[num].j = j;
133:           num++; numi++;
134:         }
135:         if (i!=M-1) {
136:           v[num] = -HydHx;              col[num].i = i+1; col[num].j = j;
137:           num++; numi++;
138:         }
139:         if (j!=N-1) {
140:           v[num] = -HxdHy;              col[num].i = i;   col[num].j = j+1;
141:           num++; numj++;
142:         }
143:         v[num] = ((PetscReal)(numj)*HxdHy + (PetscReal)(numi)*HydHx); col[num].i = i;   col[num].j = j;
144:         num++;
145:         MatSetValuesStencil(jac,1,&row,num,col,v,INSERT_VALUES);
146:       } else {
147:         v[0] = -HxdHy;              col[0].i = i;   col[0].j = j-1;
148:         v[1] = -HydHx;              col[1].i = i-1; col[1].j = j;
149:         v[2] = 2.0*(HxdHy + HydHx); col[2].i = i;   col[2].j = j;
150:         v[3] = -HydHx;              col[3].i = i+1; col[3].j = j;
151:         v[4] = -HxdHy;              col[4].i = i;   col[4].j = j+1;
152:         MatSetValuesStencil(jac,1,&row,5,col,v,INSERT_VALUES);
153:       }
154:     }
155:   }
156:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
157:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);

159:   MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
160:   MatSetNullSpace(J,nullspace);
161:   MatNullSpaceDestroy(&nullspace);
162:   return(0);
163: }

167: /*TEST

169:    build:
170:       requires: !complex !single

172:    test:
173:       args: -pc_type mg -pc_mg_type full -ksp_type cg -ksp_monitor_short -da_refine 3 -mg_coarse_pc_type svd -ksp_view

175:    test:
176:       suffix: 2
177:       nsize: 4
178:       args: -pc_type mg -pc_mg_type full -ksp_type cg -ksp_monitor_short -da_refine 3 -mg_coarse_pc_type redundant -mg_coarse_redundant_pc_type svd -ksp_view

180:    test:
181:       suffix: 3
182:       nsize: 2
183:       args: -pc_type mg -pc_mg_type full -ksp_monitor_short -da_refine 5 -mg_coarse_ksp_type cg -mg_coarse_ksp_converged_reason -mg_coarse_ksp_rtol 1e-2 -mg_coarse_ksp_max_it 5 -mg_coarse_pc_type none -pc_mg_levels 2 -ksp_type pipefgmres -ksp_pipefgmres_shift 1.5

185:    test:
186:       suffix: tut_1
187:       nsize: 1
188:       args: -da_grid_x 4 -da_grid_y 4 -mat_view

190:    test:
191:       suffix: tut_2
192:       requires: superlu_dist parmetis
193:       nsize: 4
194:       args: -da_grid_x 120 -da_grid_y 120 -pc_type lu -pc_factor_mat_solver_type superlu_dist -ksp_monitor -ksp_view

196:    test:
197:       suffix: tut_3
198:       nsize: 4
199:       args: -da_grid_x 1025 -da_grid_y 1025 -pc_type mg -pc_mg_levels 9 -ksp_monitor

201: TEST*/
```