Actual source code: ex3.c
petsc-3.12.2 2019-11-22
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;
35: PetscInt idx[4],count,*rows;
36: Vec u,ustar,b;
37: KSP ksp;
38: PetscBool viewkspest = PETSC_FALSE;
40: PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
41: PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
42: PetscOptionsGetBool(NULL,NULL,"-ksp_est_view",&viewkspest,NULL);
43: N = (m+1)*(m+1); /* dimension of matrix */
44: M = m*m; /* number of elements */
45: h = 1.0/m; /* mesh width */
46: MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
47: MPI_Comm_size(PETSC_COMM_WORLD,&size);
49: /* Create stiffness matrix */
50: MatCreate(PETSC_COMM_WORLD,&C);
51: MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,N,N);
52: MatSetFromOptions(C);
53: MatSetUp(C);
54: start = rank*(M/size) + ((M%size) < rank ? (M%size) : rank);
55: end = start + M/size + ((M%size) > rank);
57: /* Assemble matrix */
58: FormElementStiffness(h*h,Ke); /* element stiffness for Laplacian */
59: for (i=start; i<end; i++) {
60: /* node numbers for the four corners of element */
61: idx[0] = (m+1)*(i/m) + (i % m);
62: idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
63: MatSetValues(C,4,idx,4,idx,Ke,ADD_VALUES);
64: }
65: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
66: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
68: /* Create right-hand-side and solution vectors */
69: VecCreate(PETSC_COMM_WORLD,&u);
70: VecSetSizes(u,PETSC_DECIDE,N);
71: VecSetFromOptions(u);
72: PetscObjectSetName((PetscObject)u,"Approx. Solution");
73: VecDuplicate(u,&b);
74: PetscObjectSetName((PetscObject)b,"Right hand side");
75: VecDuplicate(b,&ustar);
76: VecSet(u,0.0);
77: VecSet(b,0.0);
79: /* Assemble right-hand-side vector */
80: for (i=start; i<end; i++) {
81: /* location of lower left corner of element */
82: x = h*(i % m); y = h*(i/m);
83: /* node numbers for the four corners of element */
84: idx[0] = (m+1)*(i/m) + (i % m);
85: idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
86: FormElementRhs(x,y,h*h,r);
87: VecSetValues(b,4,idx,r,ADD_VALUES);
88: }
89: VecAssemblyBegin(b);
90: VecAssemblyEnd(b);
92: /* Modify matrix and right-hand-side for Dirichlet boundary conditions */
93: PetscMalloc1(4*m,&rows);
94: for (i=0; i<m+1; i++) {
95: rows[i] = i; /* bottom */
96: rows[3*m - 1 +i] = m*(m+1) + i; /* top */
97: }
98: count = m+1; /* left side */
99: for (i=m+1; i<m*(m+1); i+= m+1) rows[count++] = i;
101: count = 2*m; /* left side */
102: for (i=2*m+1; i<m*(m+1); i+= m+1) rows[count++] = i;
103: for (i=0; i<4*m; i++) {
104: val = h*(rows[i]/(m+1));
105: VecSetValues(u,1,&rows[i],&val,INSERT_VALUES);
106: VecSetValues(b,1,&rows[i],&val,INSERT_VALUES);
107: }
108: MatZeroRows(C,4*m,rows,1.0,0,0);
110: PetscFree(rows);
111: VecAssemblyBegin(u);
112: VecAssemblyEnd(u);
113: VecAssemblyBegin(b);
114: VecAssemblyEnd(b);
116: { Mat A;
117: MatConvert(C,MATSAME,MAT_INITIAL_MATRIX,&A);
118: MatDestroy(&C);
119: MatConvert(A,MATSAME,MAT_INITIAL_MATRIX,&C);
120: MatDestroy(&A);
121: }
123: /* Solve linear system */
124: KSPCreate(PETSC_COMM_WORLD,&ksp);
125: KSPSetOperators(ksp,C,C);
126: KSPSetFromOptions(ksp);
127: KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);
128: KSPSolve(ksp,b,u);
130: if (viewkspest) {
131: KSP kspest;
133: KSPChebyshevEstEigGetKSP(ksp,&kspest);
134: if (kspest) {KSPView(kspest,PETSC_VIEWER_STDOUT_WORLD);}
135: }
137: /* Check error */
138: VecGetOwnershipRange(ustar,&start,&end);
139: for (i=start; i<end; i++) {
140: val = h*(i/(m+1));
141: VecSetValues(ustar,1,&i,&val,INSERT_VALUES);
142: }
143: VecAssemblyBegin(ustar);
144: VecAssemblyEnd(ustar);
145: VecAXPY(u,-1.0,ustar);
146: VecNorm(u,NORM_2,&norm);
147: KSPGetIterationNumber(ksp,&its);
148: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g Iterations %D\n",(double)(norm*h),its);
150: /* Free work space */
151: KSPDestroy(&ksp);
152: VecDestroy(&ustar);
153: VecDestroy(&u);
154: VecDestroy(&b);
155: MatDestroy(&C);
156: PetscFinalize();
157: return ierr;
158: }
160: /*TEST
162: test:
163: args: -pc_type jacobi -ksp_monitor_short -m 5 -ksp_gmres_cgs_refinement_type refine_always
165: test:
166: suffix: 2
167: nsize: 2
168: args: -pc_type jacobi -ksp_monitor_short -m 5 -ksp_gmres_cgs_refinement_type refine_always
170: test:
171: suffix: nocheby
172: args: -ksp_est_view
174: test:
175: suffix: chebynoest
176: args: -ksp_est_view -ksp_type chebyshev -ksp_chebyshev_eigenvalues 0.1,1.0
178: test:
179: suffix: chebyest
180: args: -ksp_est_view -ksp_type chebyshev -ksp_chebyshev_esteig
182: TEST*/