1 /*T
2 Concepts: KSP^solving a system of linear equations
3 Concepts: KSP^Laplacian, 2d
4 Processors: n
5 T*/
6
7 /*
8 Added at the request of Marc Garbey.
9
10 Inhomogeneous Laplacian in 2D. Modeled by the partial differential equation
11
12 -div \rho grad u = f, 0 < x,y < 1,
13
14 with forcing function
15
16 f = e^{-x^2/\nu} e^{-y^2/\nu}
17
18 with Dirichlet boundary conditions
19
20 u = f(x,y) for x = 0, x = 1, y = 0, y = 1
21
22 or pure Neumman boundary conditions
23
24 This uses multigrid to solve the linear system
25 */
26
27 static char help[] = "Solves 2D inhomogeneous Laplacian using multigrid.\n\n";
28
29 #include <petscdm.h>
30 #include <petscdmda.h>
31 #include <petscksp.h>
32
33 extern PetscErrorCode ComputeMatrix(KSP,Mat,Mat,void*);
34 extern PetscErrorCode ComputeRHS(KSP,Vec,void*);
35
36 typedef enum {DIRICHLET, NEUMANN} BCType;
37
38 typedef struct {
39 PetscReal rho;
40 PetscReal nu;
41 BCType bcType;
42 } UserContext;
43
main(int argc,char ** argv)44 int main(int argc,char **argv)
45 {
46 KSP ksp;
47 DM da;
48 UserContext user;
49 const char *bcTypes[2] = {"dirichlet","neumann"};
50 PetscErrorCode ierr;
51 PetscInt bc;
52 Vec b,x;
53 PetscBool testsolver = PETSC_FALSE;
54
55 ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
56 ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
57 ierr = DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,3,3,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,&da);CHKERRQ(ierr);
58 ierr = DMSetFromOptions(da);CHKERRQ(ierr);
59 ierr = DMSetUp(da);CHKERRQ(ierr);
60 ierr = DMDASetUniformCoordinates(da,0,1,0,1,0,0);CHKERRQ(ierr);
61 ierr = DMDASetFieldName(da,0,"Pressure");CHKERRQ(ierr);
62
63 ierr = PetscOptionsBegin(PETSC_COMM_WORLD, "", "Options for the inhomogeneous Poisson equation", "DMqq");CHKERRQ(ierr);
64 user.rho = 1.0;
65 ierr = PetscOptionsReal("-rho", "The conductivity", "ex29.c", user.rho, &user.rho, NULL);CHKERRQ(ierr);
66 user.nu = 0.1;
67 ierr = PetscOptionsReal("-nu", "The width of the Gaussian source", "ex29.c", user.nu, &user.nu, NULL);CHKERRQ(ierr);
68 bc = (PetscInt)DIRICHLET;
69 ierr = PetscOptionsEList("-bc_type","Type of boundary condition","ex29.c",bcTypes,2,bcTypes[0],&bc,NULL);CHKERRQ(ierr);
70 user.bcType = (BCType)bc;
71 ierr = PetscOptionsBool("-testsolver", "Run solver multiple times, useful for performance studies of solver", "ex29.c", testsolver, &testsolver, NULL);CHKERRQ(ierr);
72 ierr = PetscOptionsEnd();CHKERRQ(ierr);
73
74 ierr = KSPSetComputeRHS(ksp,ComputeRHS,&user);CHKERRQ(ierr);
75 ierr = KSPSetComputeOperators(ksp,ComputeMatrix,&user);CHKERRQ(ierr);
76 ierr = KSPSetDM(ksp,da);CHKERRQ(ierr);
77 ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
78 ierr = KSPSetUp(ksp);CHKERRQ(ierr);
79 ierr = KSPSolve(ksp,NULL,NULL);CHKERRQ(ierr);
80
81 if (testsolver) {
82 ierr = KSPGetSolution(ksp,&x);CHKERRQ(ierr);
83 ierr = KSPGetRhs(ksp,&b);CHKERRQ(ierr);
84 KSPSetDMActive(ksp,PETSC_FALSE);
85 ierr = KSPSolve(ksp,b,x);CHKERRQ(ierr);
86 {
87 #if defined(PETSC_USE_LOG)
88 PetscLogStage stage;
89 #endif
90 PetscInt i,n = 20;
91
92 ierr = PetscLogStageRegister("Solve only",&stage);CHKERRQ(ierr);
93 ierr = PetscLogStagePush(stage);CHKERRQ(ierr);
94 for (i=0; i<n; i++) {
95 ierr = KSPSolve(ksp,b,x);CHKERRQ(ierr);
96 }
97 ierr = PetscLogStagePop();CHKERRQ(ierr);
98 }
99 }
100
101 ierr = DMDestroy(&da);CHKERRQ(ierr);
102 ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
103 ierr = PetscFinalize();
104 return ierr;
105 }
106
ComputeRHS(KSP ksp,Vec b,void * ctx)107 PetscErrorCode ComputeRHS(KSP ksp,Vec b,void *ctx)
108 {
109 UserContext *user = (UserContext*)ctx;
110 PetscErrorCode ierr;
111 PetscInt i,j,mx,my,xm,ym,xs,ys;
112 PetscScalar Hx,Hy;
113 PetscScalar **array;
114 DM da;
115
116 PetscFunctionBeginUser;
117 ierr = KSPGetDM(ksp,&da);CHKERRQ(ierr);
118 ierr = DMDAGetInfo(da, 0, &mx, &my, 0,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
119 Hx = 1.0 / (PetscReal)(mx-1);
120 Hy = 1.0 / (PetscReal)(my-1);
121 ierr = DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);CHKERRQ(ierr);
122 ierr = DMDAVecGetArray(da, b, &array);CHKERRQ(ierr);
123 for (j=ys; j<ys+ym; j++) {
124 for (i=xs; i<xs+xm; i++) {
125 array[j][i] = PetscExpScalar(-((PetscReal)i*Hx)*((PetscReal)i*Hx)/user->nu)*PetscExpScalar(-((PetscReal)j*Hy)*((PetscReal)j*Hy)/user->nu)*Hx*Hy;
126 }
127 }
128 ierr = DMDAVecRestoreArray(da, b, &array);CHKERRQ(ierr);
129 ierr = VecAssemblyBegin(b);CHKERRQ(ierr);
130 ierr = VecAssemblyEnd(b);CHKERRQ(ierr);
131
132 /* force right hand side to be consistent for singular matrix */
133 /* note this is really a hack, normally the model would provide you with a consistent right handside */
134 if (user->bcType == NEUMANN) {
135 MatNullSpace nullspace;
136
137 ierr = MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);CHKERRQ(ierr);
138 ierr = MatNullSpaceRemove(nullspace,b);CHKERRQ(ierr);
139 ierr = MatNullSpaceDestroy(&nullspace);CHKERRQ(ierr);
140 }
141 PetscFunctionReturn(0);
142 }
143
144
ComputeRho(PetscInt i,PetscInt j,PetscInt mx,PetscInt my,PetscReal centerRho,PetscReal * rho)145 PetscErrorCode ComputeRho(PetscInt i, PetscInt j, PetscInt mx, PetscInt my, PetscReal centerRho, PetscReal *rho)
146 {
147 PetscFunctionBeginUser;
148 if ((i > mx/3.0) && (i < 2.0*mx/3.0) && (j > my/3.0) && (j < 2.0*my/3.0)) {
149 *rho = centerRho;
150 } else {
151 *rho = 1.0;
152 }
153 PetscFunctionReturn(0);
154 }
155
ComputeMatrix(KSP ksp,Mat J,Mat jac,void * ctx)156 PetscErrorCode ComputeMatrix(KSP ksp,Mat J,Mat jac,void *ctx)
157 {
158 UserContext *user = (UserContext*)ctx;
159 PetscReal centerRho;
160 PetscErrorCode ierr;
161 PetscInt i,j,mx,my,xm,ym,xs,ys;
162 PetscScalar v[5];
163 PetscReal Hx,Hy,HydHx,HxdHy,rho;
164 MatStencil row, col[5];
165 DM da;
166 PetscBool check_matis = PETSC_FALSE;
167
168 PetscFunctionBeginUser;
169 ierr = KSPGetDM(ksp,&da);CHKERRQ(ierr);
170 centerRho = user->rho;
171 ierr = DMDAGetInfo(da,0,&mx,&my,0,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
172 Hx = 1.0 / (PetscReal)(mx-1);
173 Hy = 1.0 / (PetscReal)(my-1);
174 HxdHy = Hx/Hy;
175 HydHx = Hy/Hx;
176 ierr = DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);CHKERRQ(ierr);
177 for (j=ys; j<ys+ym; j++) {
178 for (i=xs; i<xs+xm; i++) {
179 row.i = i; row.j = j;
180 ierr = ComputeRho(i, j, mx, my, centerRho, &rho);CHKERRQ(ierr);
181 if (i==0 || j==0 || i==mx-1 || j==my-1) {
182 if (user->bcType == DIRICHLET) {
183 v[0] = 2.0*rho*(HxdHy + HydHx);
184 ierr = MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);CHKERRQ(ierr);
185 } else if (user->bcType == NEUMANN) {
186 PetscInt numx = 0, numy = 0, num = 0;
187 if (j!=0) {
188 v[num] = -rho*HxdHy; col[num].i = i; col[num].j = j-1;
189 numy++; num++;
190 }
191 if (i!=0) {
192 v[num] = -rho*HydHx; col[num].i = i-1; col[num].j = j;
193 numx++; num++;
194 }
195 if (i!=mx-1) {
196 v[num] = -rho*HydHx; col[num].i = i+1; col[num].j = j;
197 numx++; num++;
198 }
199 if (j!=my-1) {
200 v[num] = -rho*HxdHy; col[num].i = i; col[num].j = j+1;
201 numy++; num++;
202 }
203 v[num] = numx*rho*HydHx + numy*rho*HxdHy; col[num].i = i; col[num].j = j;
204 num++;
205 ierr = MatSetValuesStencil(jac,1,&row,num,col,v,INSERT_VALUES);CHKERRQ(ierr);
206 }
207 } else {
208 v[0] = -rho*HxdHy; col[0].i = i; col[0].j = j-1;
209 v[1] = -rho*HydHx; col[1].i = i-1; col[1].j = j;
210 v[2] = 2.0*rho*(HxdHy + HydHx); col[2].i = i; col[2].j = j;
211 v[3] = -rho*HydHx; col[3].i = i+1; col[3].j = j;
212 v[4] = -rho*HxdHy; col[4].i = i; col[4].j = j+1;
213 ierr = MatSetValuesStencil(jac,1,&row,5,col,v,INSERT_VALUES);CHKERRQ(ierr);
214 }
215 }
216 }
217 ierr = MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
218 ierr = MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
219 ierr = MatViewFromOptions(jac,NULL,"-view_mat");CHKERRQ(ierr);
220 ierr = PetscOptionsGetBool(NULL,NULL,"-check_matis",&check_matis,NULL);CHKERRQ(ierr);
221 if (check_matis) {
222 void (*f)(void);
223 Mat J2;
224 MatType jtype;
225 PetscReal nrm;
226
227 ierr = MatGetType(jac,&jtype);CHKERRQ(ierr);
228 ierr = MatConvert(jac,MATIS,MAT_INITIAL_MATRIX,&J2);CHKERRQ(ierr);
229 ierr = MatViewFromOptions(J2,NULL,"-view_conv");CHKERRQ(ierr);
230 ierr = MatConvert(J2,jtype,MAT_INPLACE_MATRIX,&J2);CHKERRQ(ierr);
231 ierr = MatGetOperation(jac,MATOP_VIEW,&f);CHKERRQ(ierr);
232 ierr = MatSetOperation(J2,MATOP_VIEW,f);CHKERRQ(ierr);
233 ierr = MatSetDM(J2,da);CHKERRQ(ierr);
234 ierr = MatViewFromOptions(J2,NULL,"-view_conv_assembled");CHKERRQ(ierr);
235 ierr = MatAXPY(J2,-1.,jac,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
236 ierr = MatNorm(J2,NORM_FROBENIUS,&nrm);CHKERRQ(ierr);
237 ierr = PetscPrintf(PETSC_COMM_WORLD,"Error MATIS %g\n",(double)nrm);CHKERRQ(ierr);
238 ierr = MatViewFromOptions(J2,NULL,"-view_conv_err");CHKERRQ(ierr);
239 ierr = MatDestroy(&J2);CHKERRQ(ierr);
240 }
241 if (user->bcType == NEUMANN) {
242 MatNullSpace nullspace;
243
244 ierr = MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);CHKERRQ(ierr);
245 ierr = MatSetNullSpace(J,nullspace);CHKERRQ(ierr);
246 ierr = MatNullSpaceDestroy(&nullspace);CHKERRQ(ierr);
247 }
248 PetscFunctionReturn(0);
249 }
250
251
252 /*TEST
253
254 test:
255 args: -pc_type mg -pc_mg_type full -ksp_type fgmres -ksp_monitor_short -da_refine 8 -ksp_rtol 1.e-3
256
257 test:
258 suffix: 2
259 args: -bc_type neumann -pc_type mg -pc_mg_type full -ksp_type fgmres -ksp_monitor_short -da_refine 8 -mg_coarse_pc_factor_shift_type nonzero
260 requires: !single
261
262 test:
263 suffix: telescope
264 nsize: 4
265 args: -ksp_monitor_short -da_grid_x 257 -da_grid_y 257 -pc_type mg -pc_mg_galerkin pmat -pc_mg_levels 4 -ksp_type richardson -mg_levels_ksp_type chebyshev -mg_levels_pc_type jacobi -mg_coarse_pc_type telescope -mg_coarse_pc_telescope_ignore_kspcomputeoperators -mg_coarse_telescope_pc_type mg -mg_coarse_telescope_pc_mg_galerkin pmat -mg_coarse_telescope_pc_mg_levels 3 -mg_coarse_telescope_mg_levels_ksp_type chebyshev -mg_coarse_telescope_mg_levels_pc_type jacobi -mg_coarse_pc_telescope_reduction_factor 4
266
267 test:
268 suffix: 3
269 args: -ksp_view -da_refine 2 -pc_type mg -pc_mg_distinct_smoothup -mg_levels_up_pc_type jacobi
270
271 test:
272 suffix: 4
273 args: -ksp_view -da_refine 2 -pc_type mg -pc_mg_distinct_smoothup -mg_levels_up_ksp_max_it 3 -mg_levels_ksp_max_it 4
274
275 test:
276 suffix: 5
277 nsize: 2
278 requires: hypre !complex
279 args: -pc_type mg -da_refine 2 -ksp_monitor -matptap_via hypre -pc_mg_galerkin both
280
281 TEST*/
282