def test_Schur_Sp_solve(load_nse_step_matrix, initialize_petsc_options):
"""Tests a KSP solve using the Sp Schur complement approximation.
For this test, the global matrix does not have a null space."""
mat_A = load_nse_step_matrix
b, x = create_petsc_vecs(mat_A)
solver_info = LS.ModelInfo(3, 'interlaced')
schur_approx = LS.Schur_Sp(mat_A, '', solver_info=solver_info)
ksp_obj = initialize_schur_ksp_obj(mat_A, schur_approx)
ksp_obj.solve(b, x)
assert ksp_obj.converged == True
assert ksp_obj.its == 45
assert np.allclose(ksp_obj.norm, 394.7036050627)
assert ksp_obj.reason == 2
def test_Schur_Sp_solve_global_null_space(load_nse_cavity_matrix,
initialize_petsc_options):
"""Tests a KSP solve using the Sp Schur complement approximation.
For this test, the global matrix has a null space because the
boundary conditions are pure Dirichlet. """
mat_A = load_nse_cavity_matrix
b, x = create_petsc_vecs(mat_A)
solver_info = LS.ModelInfo('interlaced', 3, bdy_null_space=True)
schur_approx = LS.Schur_Sp(L=mat_A, prefix='', solver_info=solver_info)
petsc_options = initialize_petsc_options
ksp_obj = initialize_schur_ksp_obj(mat_A, schur_approx)
ksp_obj.solve(b, x)
assert ksp_obj.converged == True
assert ksp_obj.its == 89
assert ksp_obj.norm < np.linalg.norm(b) * 1.0e-9 + 1.0e-16
assert ksp_obj.reason == 2
def test_Schur_Sp_solve_global_null_space(load_nse_cavity_matrix,
initialize_petsc_options):
"""Tests a KSP solve using the Sp Schur complement approximation.
For this test, the global matrix has a null space because the
boundary conditions are pure Dirichlet. """
mat_A = load_nse_cavity_matrix
b, x = create_petsc_vecs(mat_A)
petsc_options = initialize_petsc_options
solver_info = LS.ModelInfo(3, 'interlaced')
schur_approx = LS.Schur_Sp(mat_A, '', True, solver_info=solver_info)
ksp_obj = initialize_schur_ksp_obj(mat_A, schur_approx)
ksp_obj.solve(b, x)
assert ksp_obj.converged == True
assert ksp_obj.its == 35
assert np.allclose(ksp_obj.norm, 0.0007464632)
assert ksp_obj.reason == 2
def test_Schur_Sp_solve():
"""Tests a KSP solve using the Sp Schur complement approximation.
For this test, the global matrix does not have a null space."""
mat_A = load_matrix_step_noslip()
petsc_options = initialize_petsc_options()
b, x = create_petsc_vecs(mat_A)
solver_info = LS.ModelInfo('interlaced', 3)
schur_approx = LS.Schur_Sp(mat_A,
'',
solver_info=solver_info)
ksp_obj = initialize_schur_ksp_obj(mat_A, schur_approx)
ksp_obj.solve(b,x)
assert ksp_obj.converged == True
assert ksp_obj.reason == 2
assert float(ksp_obj.norm) < 1.0e-5
assert ksp_obj.its == 63