Actual source code: ex3.c
2: static char help[] = "Bilinear elements on the unit square for Laplacian. To test the parallel\n\
3: matrix assembly, the matrix is intentionally laid out across processors\n\
4: differently from the way it is assembled. Input arguments are:\n\
5: -m <size> : problem size\n\n";
7: /* Addendum: piggy-backing on this example to test KSPChebyshev methods */
9: #include <petscksp.h>
11: int FormElementStiffness(PetscReal H,PetscScalar *Ke)
12: {
14: Ke[0] = H/6.0; Ke[1] = -.125*H; Ke[2] = H/12.0; Ke[3] = -.125*H;
15: Ke[4] = -.125*H; Ke[5] = H/6.0; Ke[6] = -.125*H; Ke[7] = H/12.0;
16: Ke[8] = H/12.0; Ke[9] = -.125*H; Ke[10] = H/6.0; Ke[11] = -.125*H;
17: Ke[12] = -.125*H; Ke[13] = H/12.0; Ke[14] = -.125*H; Ke[15] = H/6.0;
18: return 0;
19: }
20: int FormElementRhs(PetscReal x,PetscReal y,PetscReal H,PetscScalar *r)
21: {
23: r[0] = 0.; r[1] = 0.; r[2] = 0.; r[3] = 0.0;
24: return 0;
25: }
27: int main(int argc,char **args)
28: {
29: Mat C;
30: PetscMPIInt rank,size;
31: PetscInt i,m = 5,N,start,end,M,its;
32: PetscScalar val,Ke[16],r[4];
33: PetscReal x,y,h,norm;
34: PetscInt idx[4],count,*rows;
35: Vec u,ustar,b;
36: KSP ksp;
37: PetscBool viewkspest = PETSC_FALSE;
39: PetscInitialize(&argc,&args,(char*)0,help);
40: PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
41: PetscOptionsGetBool(NULL,NULL,"-ksp_est_view",&viewkspest,NULL);
42: N = (m+1)*(m+1); /* dimension of matrix */
43: M = m*m; /* number of elements */
44: h = 1.0/m; /* mesh width */
45: MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
46: MPI_Comm_size(PETSC_COMM_WORLD,&size);
48: /* Create stiffness matrix */
49: MatCreate(PETSC_COMM_WORLD,&C);
50: MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,N,N);
51: MatSetFromOptions(C);
52: MatSetUp(C);
53: start = rank*(M/size) + ((M%size) < rank ? (M%size) : rank);
54: end = start + M/size + ((M%size) > rank);
56: /* Assemble matrix */
57: FormElementStiffness(h*h,Ke); /* element stiffness for Laplacian */
58: for (i=start; i<end; i++) {
59: /* node numbers for the four corners of element */
60: idx[0] = (m+1)*(i/m) + (i % m);
61: idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
62: MatSetValues(C,4,idx,4,idx,Ke,ADD_VALUES);
63: }
64: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
65: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
67: /* Create right-hand-side and solution vectors */
68: VecCreate(PETSC_COMM_WORLD,&u);
69: VecSetSizes(u,PETSC_DECIDE,N);
70: VecSetFromOptions(u);
71: PetscObjectSetName((PetscObject)u,"Approx. Solution");
72: VecDuplicate(u,&b);
73: PetscObjectSetName((PetscObject)b,"Right hand side");
74: VecDuplicate(b,&ustar);
75: VecSet(u,0.0);
76: VecSet(b,0.0);
78: /* Assemble right-hand-side vector */
79: for (i=start; i<end; i++) {
80: /* location of lower left corner of element */
81: x = h*(i % m); y = h*(i/m);
82: /* node numbers for the four corners of element */
83: idx[0] = (m+1)*(i/m) + (i % m);
84: idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
85: FormElementRhs(x,y,h*h,r);
86: VecSetValues(b,4,idx,r,ADD_VALUES);
87: }
88: VecAssemblyBegin(b);
89: VecAssemblyEnd(b);
91: /* Modify matrix and right-hand-side for Dirichlet boundary conditions */
92: PetscMalloc1(4*m,&rows);
93: for (i=0; i<m+1; i++) {
94: rows[i] = i; /* bottom */
95: rows[3*m - 1 +i] = m*(m+1) + i; /* top */
96: }
97: count = m+1; /* left side */
98: for (i=m+1; i<m*(m+1); i+= m+1) rows[count++] = i;
100: count = 2*m; /* left side */
101: for (i=2*m+1; i<m*(m+1); i+= m+1) rows[count++] = i;
102: for (i=0; i<4*m; i++) {
103: val = h*(rows[i]/(m+1));
104: VecSetValues(u,1,&rows[i],&val,INSERT_VALUES);
105: VecSetValues(b,1,&rows[i],&val,INSERT_VALUES);
106: }
107: MatZeroRows(C,4*m,rows,1.0,0,0);
109: PetscFree(rows);
110: VecAssemblyBegin(u);
111: VecAssemblyEnd(u);
112: VecAssemblyBegin(b);
113: VecAssemblyEnd(b);
115: { Mat A;
116: MatConvert(C,MATSAME,MAT_INITIAL_MATRIX,&A);
117: MatDestroy(&C);
118: MatConvert(A,MATSAME,MAT_INITIAL_MATRIX,&C);
119: MatDestroy(&A);
120: }
122: /* Solve linear system */
123: KSPCreate(PETSC_COMM_WORLD,&ksp);
124: KSPSetOperators(ksp,C,C);
125: KSPSetFromOptions(ksp);
126: KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);
127: KSPSolve(ksp,b,u);
129: if (viewkspest) {
130: KSP kspest;
132: KSPChebyshevEstEigGetKSP(ksp,&kspest);
133: if (kspest) KSPView(kspest,PETSC_VIEWER_STDOUT_WORLD);
134: }
136: /* Check error */
137: VecGetOwnershipRange(ustar,&start,&end);
138: for (i=start; i<end; i++) {
139: val = h*(i/(m+1));
140: VecSetValues(ustar,1,&i,&val,INSERT_VALUES);
141: }
142: VecAssemblyBegin(ustar);
143: VecAssemblyEnd(ustar);
144: VecAXPY(u,-1.0,ustar);
145: VecNorm(u,NORM_2,&norm);
146: KSPGetIterationNumber(ksp,&its);
147: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g Iterations %D\n",(double)(norm*h),its);
149: /* Free work space */
150: KSPDestroy(&ksp);
151: VecDestroy(&ustar);
152: VecDestroy(&u);
153: VecDestroy(&b);
154: MatDestroy(&C);
155: PetscFinalize();
156: return 0;
157: }
159: /*TEST
161: test:
162: args: -pc_type jacobi -ksp_monitor_short -m 5 -ksp_gmres_cgs_refinement_type refine_always
164: test:
165: suffix: 2
166: nsize: 2
167: args: -pc_type jacobi -ksp_monitor_short -m 5 -ksp_gmres_cgs_refinement_type refine_always
169: test:
170: suffix: 2_kokkos
171: nsize: 2
172: args: -pc_type jacobi -ksp_monitor_short -m 5 -ksp_gmres_cgs_refinement_type refine_always -mat_type aijkokkos -vec_type kokkos
173: output_file: output/ex3_2.out
174: requires: kokkos_kernels
176: test:
177: suffix: nocheby
178: args: -ksp_est_view
180: test:
181: suffix: chebynoest
182: args: -ksp_est_view -ksp_type chebyshev -ksp_chebyshev_eigenvalues 0.1,1.0
184: test:
185: suffix: chebyest
186: args: -ksp_est_view -ksp_type chebyshev -ksp_chebyshev_esteig
187: filter: sed -e "s/Iterations 19/Iterations 20/g"
189: TEST*/