Actual source code: ex68.c
1: static char help[] = "Test problems for Schur complement solvers.\n\n\n";
3: #include <petscsnes.h>
5: /*
6: Test 1:
7: I u = b
9: solution: u = b
11: Test 2:
12: / I 0 I \ / u_1 \ / b_1 \
13: | 0 I 0 | | u_2 | = | b_2 |
14: \ I 0 0 / \ u_3 / \ b_3 /
16: solution: u_1 = b_3, u_2 = b_2, u_3 = b_1 - b_3
17: */
19: PetscErrorCode ComputeFunctionLinear(SNES snes, Vec x, Vec f, void *ctx)
20: {
21: Mat A = (Mat)ctx;
23: PetscFunctionBeginUser;
24: PetscCall(MatMult(A, x, f));
25: PetscFunctionReturn(PETSC_SUCCESS);
26: }
28: PetscErrorCode ComputeJacobianLinear(SNES snes, Vec x, Mat A, Mat J, void *ctx)
29: {
30: PetscFunctionBeginUser;
31: PetscFunctionReturn(PETSC_SUCCESS);
32: }
34: PetscErrorCode ConstructProblem1(Mat A, Vec b)
35: {
36: PetscInt rStart, rEnd, row;
38: PetscFunctionBeginUser;
39: PetscCall(VecSet(b, -3.0));
40: PetscCall(MatGetOwnershipRange(A, &rStart, &rEnd));
41: for (row = rStart; row < rEnd; ++row) {
42: PetscScalar val = 1.0;
44: PetscCall(MatSetValues(A, 1, &row, 1, &row, &val, INSERT_VALUES));
45: }
46: PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
47: PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
48: PetscFunctionReturn(PETSC_SUCCESS);
49: }
51: PetscErrorCode CheckProblem1(Mat A, Vec b, Vec u)
52: {
53: Vec errorVec;
54: PetscReal norm, error;
56: PetscFunctionBeginUser;
57: PetscCall(VecDuplicate(b, &errorVec));
58: PetscCall(VecWAXPY(errorVec, -1.0, b, u));
59: PetscCall(VecNorm(errorVec, NORM_2, &error));
60: PetscCall(VecNorm(b, NORM_2, &norm));
61: PetscCheck(error / norm <= 1000. * PETSC_MACHINE_EPSILON, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "Relative error %g is too large", (double)(error / norm));
62: PetscCall(VecDestroy(&errorVec));
63: PetscFunctionReturn(PETSC_SUCCESS);
64: }
66: PetscErrorCode ConstructProblem2(Mat A, Vec b)
67: {
68: PetscInt N = 10, constraintSize = 4;
69: PetscInt row;
71: PetscFunctionBeginUser;
72: PetscCall(VecSet(b, -3.0));
73: for (row = 0; row < constraintSize; ++row) {
74: PetscScalar vals[2] = {1.0, 1.0};
75: PetscInt cols[2];
77: cols[0] = row;
78: cols[1] = row + N - constraintSize;
79: PetscCall(MatSetValues(A, 1, &row, 2, cols, vals, INSERT_VALUES));
80: }
81: for (row = constraintSize; row < N - constraintSize; ++row) {
82: PetscScalar val = 1.0;
84: PetscCall(MatSetValues(A, 1, &row, 1, &row, &val, INSERT_VALUES));
85: }
86: for (row = N - constraintSize; row < N; ++row) {
87: PetscInt col = row - (N - constraintSize);
88: PetscScalar val = 1.0;
90: PetscCall(MatSetValues(A, 1, &row, 1, &col, &val, INSERT_VALUES));
91: }
92: PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
93: PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
94: PetscFunctionReturn(PETSC_SUCCESS);
95: }
97: PetscErrorCode CheckProblem2(Mat A, Vec b, Vec u)
98: {
99: PetscInt N = 10, constraintSize = 4, r;
100: PetscReal norm, error;
101: const PetscScalar *uArray, *bArray;
103: PetscFunctionBeginUser;
104: PetscCall(VecNorm(b, NORM_2, &norm));
105: PetscCall(VecGetArrayRead(u, &uArray));
106: PetscCall(VecGetArrayRead(b, &bArray));
107: error = 0.0;
108: for (r = 0; r < constraintSize; ++r) error += PetscRealPart(PetscSqr(uArray[r] - bArray[r + N - constraintSize]));
110: PetscCheck(error / norm <= 10000 * PETSC_MACHINE_EPSILON, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "Relative error %g is too large", (double)(error / norm));
111: error = 0.0;
112: for (r = constraintSize; r < N - constraintSize; ++r) error += PetscRealPart(PetscSqr(uArray[r] - bArray[r]));
114: PetscCheck(error / norm <= 10000 * PETSC_MACHINE_EPSILON, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "Relative error %g is too large", (double)(error / norm));
115: error = 0.0;
116: for (r = N - constraintSize; r < N; ++r) error += PetscRealPart(PetscSqr(uArray[r] - (bArray[r - (N - constraintSize)] - bArray[r])));
118: PetscCheck(error / norm <= 10000 * PETSC_MACHINE_EPSILON, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "Relative error %g is too large", (double)(error / norm));
119: PetscCall(VecRestoreArrayRead(u, &uArray));
120: PetscCall(VecRestoreArrayRead(b, &bArray));
121: PetscFunctionReturn(PETSC_SUCCESS);
122: }
124: int main(int argc, char **argv)
125: {
126: MPI_Comm comm;
127: SNES snes; /* nonlinear solver */
128: Vec u, r, b; /* solution, residual, and rhs vectors */
129: Mat A, J; /* Jacobian matrix */
130: PetscInt problem = 1, N = 10;
132: PetscFunctionBeginUser;
133: PetscCall(PetscInitialize(&argc, &argv, NULL, help));
134: comm = PETSC_COMM_WORLD;
135: PetscCall(PetscOptionsGetInt(NULL, NULL, "-problem", &problem, NULL));
136: PetscCall(VecCreate(comm, &u));
137: PetscCall(VecSetSizes(u, PETSC_DETERMINE, N));
138: PetscCall(VecSetFromOptions(u));
139: PetscCall(VecDuplicate(u, &r));
140: PetscCall(VecDuplicate(u, &b));
142: PetscCall(MatCreate(comm, &A));
143: PetscCall(MatSetSizes(A, PETSC_DETERMINE, PETSC_DETERMINE, N, N));
144: PetscCall(MatSetFromOptions(A));
145: PetscCall(MatSeqAIJSetPreallocation(A, 5, NULL));
146: J = A;
148: switch (problem) {
149: case 1:
150: PetscCall(ConstructProblem1(A, b));
151: break;
152: case 2:
153: PetscCall(ConstructProblem2(A, b));
154: break;
155: default:
156: SETERRQ(comm, PETSC_ERR_ARG_OUTOFRANGE, "Invalid problem number %" PetscInt_FMT, problem);
157: }
159: PetscCall(SNESCreate(PETSC_COMM_WORLD, &snes));
160: PetscCall(SNESSetJacobian(snes, A, J, ComputeJacobianLinear, NULL));
161: PetscCall(SNESSetFunction(snes, r, ComputeFunctionLinear, A));
162: PetscCall(SNESSetFromOptions(snes));
164: PetscCall(SNESSolve(snes, b, u));
165: PetscCall(VecView(u, NULL));
167: switch (problem) {
168: case 1:
169: PetscCall(CheckProblem1(A, b, u));
170: break;
171: case 2:
172: PetscCall(CheckProblem2(A, b, u));
173: break;
174: default:
175: SETERRQ(comm, PETSC_ERR_ARG_OUTOFRANGE, "Invalid problem number %" PetscInt_FMT, problem);
176: }
178: if (A != J) PetscCall(MatDestroy(&A));
179: PetscCall(MatDestroy(&J));
180: PetscCall(VecDestroy(&u));
181: PetscCall(VecDestroy(&r));
182: PetscCall(VecDestroy(&b));
183: PetscCall(SNESDestroy(&snes));
184: PetscCall(PetscFinalize());
185: return 0;
186: }
188: /*TEST
190: test:
191: args: -snes_monitor
193: test:
194: suffix: 2
195: args: -problem 2 -pc_type jacobi -snes_monitor
197: TEST*/