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
def test_interlaced_vel_bdy_dof_order(ownership_range, num_components,
bdy_nodes):
interlaced = LS.InterlacedDofOrderType()
num_equations = ownership_range[1] - ownership_range[0] + 1
bdy_nodes = [bdy_nodes, bdy_nodes]
strong_vel_is = interlaced.create_no_dirichlet_bdy_nodes_is(
ownership_range, num_equations, num_components, bdy_nodes)
test_array = strong_vel_is.array - np.array([13, 14, 22, 23, 31, 32])
assert np.linalg.norm(test_array) < 1.0E-12
def test_blocked_dof_order(ownership_range, num_components, n_DOF_pressure):
array_start = ownership_range[0]
array_end = ownership_range[1]
blocked = LS.BlockedDofOrderType(n_DOF_pressure)
num_equations = array_end - array_start + 1
velocity, pressure = blocked.create_DOF_lists(ownership_range,
num_equations,
num_components)
pressure_idx = np.arange(array_start, array_start + n_DOF_pressure)
velocity_idx = np.arange(pressure_idx[-1] + 1, array_end + 1)
assert np.array_equal(pressure_idx, pressure)
assert np.array_equal(velocity_idx, velocity)
def test_interlaced_dof_order(ownership_range, num_components):
interlaced = LS.InterlacedDofOrderType()
num_equations = ownership_range[1] - ownership_range[0] + 1
velocity, pressure = interlaced.create_DOF_lists(ownership_range,
num_equations,
num_components)
idx_range = np.arange(ownership_range[0], ownership_range[1] + 1)
pressure_idx = np.arange(ownership_range[0], ownership_range[1],
num_components)
velocity_mask = np.ones(len(idx_range), dtype='bool')
velocity_mask[pressure_idx - ownership_range[0]] = 0
assert np.array_equal(pressure_idx, pressure)
assert np.array_equal(idx_range[velocity_mask], velocity)
def test_chebyshev_iteration_1(self):
''' Tests the pcd_shell operators produce correct output. '''
A = self.quad_mass_matrix
n = self.quad_mass_matrix.shape[0]
alpha = 1. / 4
beta = 9. / 4
x0 = np.zeros(n)
b1 = np.ones(n)
for i in range(0, n, 2):
b1[i] = 0.
A_petsc = LAT.dense_numpy_2_petsc4py(A)
x0_petsc = p4pyPETSc.Vec().createWithArray(x0)
b1_petsc = p4pyPETSc.Vec().createWithArray(b1)
solver = LS.ChebyshevSemiIteration(A_petsc, alpha, beta, True)
solver.apply(b1_petsc, x0_petsc, 20)
expected = np.load(
os.path.join(self._scriptdir, 'import_modules/sol_10.npy'))
actual = x0_petsc
assert np.allclose(expected, actual.getArray())
def test_interlaced_vel_dof_order(ownership_range,
num_components):
interlaced = LS.InterlacedDofOrderType()
num_equations = ownership_range[1] - ownership_range[0] + 1
global_IS, vel_IS = interlaced.create_vel_DOF_IS(ownership_range,
num_equations,
num_components)
for i in range(1,num_components):
global_vals = np.arange(ownership_range[0]+i,
ownership_range[1]+1,
num_components)
assert np.array_equal(global_IS[i-1].array , global_vals)
for i in range(1,num_components):
scaled_ownership_range = ownership_range[0] * (num_components-1) // num_components
local_vals = np.arange(start=scaled_ownership_range + i - 1,
stop=scaled_ownership_range + int( num_equations * (num_components-1) // num_components ),
step=num_components-1)
assert np.array_equal(vel_IS[i-1].array, local_vals)
def test_chebyshev_iteration_2(self):
''' Tests the pcd_shell operators produce correct output. '''
A = np.diag(1. / np.diag(self.quad_mass_matrix)).dot(
self.quad_mass_matrix)
n = self.quad_mass_matrix.shape[0]
alpha = 1. / 4
beta = 9. / 4
x0 = np.zeros(n)
b1 = np.zeros(n)
for i in range(0, n):
b1[i] = i
A_petsc = LAT.dense_numpy_2_petsc4py(A)
x0_petsc = p4pyPETSc.Vec().createWithArray(x0)
b1_petsc = p4pyPETSc.Vec().createWithArray(b1)
solver = LS.ChebyshevSemiIteration(A_petsc,
alpha,
beta,
save_iterations=True)
solver.apply(b1_petsc, x0_petsc, 20)
expected = np.load(
os.path.join(self._scriptdir, 'import_modules/sol_20_lst.npy'))
for i, item in enumerate(expected):
assert np.allclose(item, solver.iteration_results[i], 1e-12)
