def test_interal_2d_1():
frequency = 400.0 # frequency [Hz]
(
k,
interior_points,
interior_incident_phi,
solver,
boundary_incidence,
) = initialize(frequency)
# Test Problem 1
# Dirichlet boundary condition with phi = sin(k/sqrt(2)*x) * sin(k/sqrt(2)*y)
#
boundary_condition = solver.dirichlet_boundary_condition()
boundary_condition.f[:] = np.sin(
k / np.sqrt(2.0) * solver.centers[:, 0]) * np.sin(
k / np.sqrt(2.0) * solver.centers[:, 1])
boundary_solution = solver.solve_boundary(k, boundary_condition,
boundary_incidence)
sample_solution = boundary_solution.solve_samples(interior_incident_phi,
interior_points)
phi_golden = [
0.0000e00 + 0.0000e00j,
0.0000e00 + 0.0000e00j,
0.0000e00 + 0.0000e00j,
0.0000e00 + 0.0000e00j,
0.0000e00 + 0.0000e00j,
0.0000e00 + 0.0000e00j,
0.0000e00 + 0.0000e00j,
0.0000e00 + 0.0000e00j,
0.1595e-01 + 0.0000e00j,
0.4777e-01 + 0.0000e00j,
0.7940e-01 + 0.0000e00j,
0.1107e00 + 0.0000e00j,
0.1415e00 + 0.0000e00j,
0.1718e00 + 0.0000e00j,
0.2013e00 + 0.0000e00j,
0.2300e00 + 0.0000e00j,
0.2300e00 + 0.0000e00j,
0.2013e00 + 0.0000e00j,
0.1718e00 + 0.0000e00j,
0.1415e00 + 0.0000e00j,
0.1107e00 + 0.0000e00j,
0.7940e-01 + 0.0000e00j,
0.4777e-01 + 0.0000e00j,
0.1595e-01 + 0.0000e00j,
0.0000e00 + 0.0000e00j,
0.0000e00 + 0.0000e00j,
0.0000e00 + 0.0000e00j,
0.0000e00 + 0.0000e00j,
0.0000e00 + 0.0000e00j,
0.0000e00 + 0.0000e00j,
0.0000e00 + 0.0000e00j,
0.0000e00 + 0.0000e00j,
]
assert_almost_equal(phi_golden, boundary_solution.phis, 0.0001)
def test_internal_rad_2():
frequency = 40.0 # frequency [Hz]
k, interior_points, interior_incident_phi, solver, boundary_incidence = initialize(
frequency)
# Test Problem 2
# von Neumann boundary condition such that phi = sin(k/sqrt(2) * x) * sin(k/sqrt(2) * y)
# Differentiate with respect to x and y to obtain outward normal
boundary_condition = solver.neumann_boundary_condition()
centers = solver.geometry.centers()
normals = solver.geometry.normals()
for i in range(centers.shape[0]):
z = centers[i, 1]
n = -normals[i]
boundary_condition.f[i] = k * np.cos(k * z) * n[1]
boundary_solution = solver.solve_boundary(k, boundary_condition,
boundary_incidence)
sample_solution = boundary_solution.solve_samples(interior_incident_phi,
interior_points)
phi_golden = [
0.6564e00 + 0.2434e-02j,
0.6397e00 + 0.2398e-02j,
0.6063e00 + 0.2226e-02j,
0.5555e00 + 0.1963e-02j,
0.4870e00 + 0.1653e-02j,
0.4012e00 + 0.1298e-02j,
0.2996e00 + 0.9183e-03j,
0.1854e00 + 0.5598e-03j,
0.6281e-01 + 0.1946e-03j,
-0.6281e-01 - 0.1946e-03j,
-0.1854e00 - 0.5598e-03j,
-0.2996e00 - 0.9183e-03j,
-0.4012e00 - 0.1298e-02j,
-0.4870e00 - 0.1653e-02j,
-0.5555e00 - 0.1963e-02j,
-0.6063e00 - 0.2226e-02j,
-0.6397e00 - 0.2398e-02j,
-0.6564e00 - 0.2434e-02j,
]
assert_almost_equal(phi_golden, boundary_solution.phis, 0.001)
phi_golden = [
0.2234e-07 - 0.1671e-07j,
0.3536e00 + 0.9056e-03j,
-0.3536e00 - 0.9056e-03j,
0.2128e-07 - 0.1615e-07j,
]
assert_almost_equal(phi_golden, sample_solution.phis, 0.0001)
def test_internal_rad_1():
frequency = 40.0 # frequency [Hz]
k, interior_points, interior_incident_phi, solver, boundary_incidence = initialize(
frequency)
# Test Problem 1
# Dirichlet boundary condition with phi = sin(k*z)
#
boundary_condition = solver.dirichlet_boundary_condition()
boundary_condition.f[:] = np.sin(k * solver.centers[:, 1])
boundary_solution = solver.solve_boundary(k, boundary_condition,
boundary_incidence)
sample_solution = boundary_solution.solve_samples(interior_incident_phi,
interior_points)
phi_golden = [
0.6632e00 + 0.0000e0j,
0.6467e00 + 0.0000e0j,
0.6129e00 + 0.0000e0j,
0.5615e00 + 0.0000e0j,
0.4923e00 + 0.0000e0j,
0.4055e00 + 0.0000e0j,
0.3028e00 + 0.0000e0j,
0.1874e00 + 0.0000e0j,
0.6352e-01 + 0.0000e0j,
-0.6352e-01 + 0.0000e0j,
-0.1874e00 + 0.0000e0j,
-0.3028e00 + 0.0000e0j,
-0.4055e00 + 0.0000e0j,
-0.4923e00 + 0.0000e0j,
-0.5615e00 + 0.0000e0j,
-0.6129e00 + 0.0000e0j,
-0.6467e00 + 0.0000e0j,
-0.6632e00 + 0.0000e0j,
]
assert_almost_equal(phi_golden, boundary_solution.phis, 0.0001)
phi_golden = [
0.2826e-08 + -0.5606e-09j,
0.3574e00 + -0.3513e-03j,
-0.3574e00 + 0.3513e-03j,
0.2897e-08 + -0.7412e-09j,
]
assert_almost_equal(phi_golden, sample_solution.phis, 0.0001)
def test_internal_2d_3():
# Test Problem 3
# The test problem computes the field produced by a unit source at
# the point (0.5,0.25) within the square with a rigid boundary.
# The rigid boundary implies the boundary condition v=0.
# The test problem computes the field produced by a unit source at
# the point (0.5,0.25) within the square with a rigid boundary.
# The incident velocity potential is given by {\phi}_inc=i*h0(kr)/4
# where r is the distance from the point (0.5,0.25)
frequency = 400.0 # frequency [Hz]
k, interior_points, interior_incident_phi, solver, boundary_incidence = initialize(
frequency)
boundary_condition = solver.neumann_boundary_condition()
boundary_condition.f.fill(0.0)
p = np.array([0.05, 0.025], dtype=np.float32)
for i in range(solver.centers.shape[0]):
r = solver.centers[i] - p
R = norm(r)
boundary_incidence.phi[i] = 0.25j * hankel1(0, k * R)
if solver.centers[i, 0] < 1e-7:
boundary_incidence.v[i] = -0.25j * k * hankel1(1,
k * R) * (-r[0] / R)
elif solver.centers[i, 0] > 0.1 - 1e-7:
boundary_incidence.v[i] = -0.25j * k * hankel1(1,
k * R) * (r[0] / R)
elif solver.centers[i, 1] < 1e-7:
boundary_incidence.v[i] = -0.25j * k * hankel1(1,
k * R) * (-r[1] / R)
elif solver.centers[i, 1] > 0.1 - 1e-7:
boundary_incidence.v[i] = -0.25j * k * hankel1(1,
k * R) * (r[1] / R)
else:
assert False, "All cases must be handled above."
for i in range(interior_incident_phi.size):
r = interior_points[i] - p
R = norm(r)
interior_incident_phi[i] = 0.25j * hankel1(0, k * R)
boundary_solution = solver.solve_boundary(k, boundary_condition,
boundary_incidence)
sample_solution = boundary_solution.solve_samples(interior_incident_phi,
interior_points)
print("Test3 boundary solution")
print(boundary_solution)
print("Test3 sample solution")
print(sample_solution)
phi_golden = [
-0.1813e01 + 0.3210e-03j,
-0.1827e01 + 0.2720e-03j,
-0.1855e01 + 0.2822e-03j,
-0.1895e01 + 0.3356e-03j,
-0.1938e01 + 0.4039e-03j,
-0.1976e01 + 0.4646e-03j,
-0.2004e01 + 0.5079e-03j,
-0.2019e01 + 0.5301e-03j,
-0.2020e01 + 0.4892e-03j,
-0.2018e01 + 0.4470e-03j,
-0.2016e01 + 0.4173e-03j,
-0.2014e01 + 0.4012e-03j,
-0.2014e01 + 0.4012e-03j,
-0.2016e01 + 0.4173e-03j,
-0.2018e01 + 0.4470e-03j,
-0.2020e01 + 0.4892e-03j,
-0.2019e01 + 0.5301e-03j,
-0.2004e01 + 0.5079e-03j,
-0.1976e01 + 0.4646e-03j,
-0.1938e01 + 0.4039e-03j,
-0.1895e01 + 0.3356e-03j,
-0.1855e01 + 0.2822e-03j,
-0.1827e01 + 0.2720e-03j,
-0.1813e01 + 0.3210e-03j,
-0.1810e01 + 0.4337e-03j,
-0.1782e01 + 0.3972e-03j,
-0.1731e01 + 0.2555e-03j,
-0.1681e01 + 0.3855e-04j,
-0.1681e01 + 0.3855e-04j,
-0.1731e01 + 0.2555e-03j,
-0.1782e01 + 0.3972e-03j,
-0.1810e01 + 0.4337e-03j,
]
assert_almost_equal(phi_golden, boundary_solution.phis, 0.00001)
def test_internal_2d_2():
# Test Problem 2
# von Neumann boundary condition such that phi = sin(k/sqrt(2) * x) * sin(k/sqrt(2) * y)
# Differentiate with respect to x and y to obtain outward normal:
# dPhi/dX = k/sqrt(2) * cos(k/sqrt(2) * x) * sin(k/sqrt(2) * y)
# dPhi/dY = k/sqrt(2) * sin(k/sqrt(2) * x) * cos(k/sqrt(2) * y)
frequency = 400.0 # frequency [Hz]
(
k,
interior_points,
interior_incident_phi,
solver,
boundary_incidence,
) = initialize(frequency)
boundary_condition = solver.neumann_boundary_condition()
w = k / np.sqrt(2.0)
for i in range(solver.centers.shape[0]):
x = solver.centers[i, 0]
y = solver.centers[i, 1]
if x < 1e-7:
boundary_condition.f[i] = -w * np.cos(w * x) * np.sin(w * y)
elif x > 0.1 - 1e-7:
boundary_condition.f[i] = w * np.cos(w * x) * np.sin(w * y)
elif y < 1e-7:
boundary_condition.f[i] = -w * np.sin(w * x) * np.cos(w * y)
else:
boundary_condition.f[i] = w * np.sin(w * x) * np.cos(w * y)
boundary_solution = solver.solve_boundary(k, boundary_condition,
boundary_incidence)
sample_solution = boundary_solution.solve_samples(interior_incident_phi,
interior_points)
phi_golden = [
-0.3647e-03 + 0.8013e-03j,
-0.3205e-03 + 0.8641e-03j,
-0.2681e-03 + 0.9276e-03j,
-0.1668e-03 + 0.9850e-03j,
0.3219e-04 + 0.1031e-02j,
0.4063e-03 + 0.1060e-02j,
0.1118e-02 + 0.1066e-02j,
0.2859e-02 + 0.1050e-02j,
0.1937e-01 + 0.9291e-03j,
0.4881e-01 + 0.1150e-02j,
0.7902e-01 + 0.1426e-02j,
0.1092e00 + 0.1723e-02j,
0.1388e00 + 0.2028e-02j,
0.1677e00 + 0.2333e-02j,
0.1954e00 + 0.2627e-02j,
0.2205e00 + 0.2877e-02j,
0.2205e00 + 0.2877e-02j,
0.1954e00 + 0.2627e-02j,
0.1677e00 + 0.2333e-02j,
0.1388e00 + 0.2028e-02j,
0.1092e00 + 0.1723e-02j,
0.7902e-01 + 0.1426e-02j,
0.4881e-01 + 0.1150e-02j,
0.1937e-01 + 0.9291e-03j,
0.2859e-02 + 0.1050e-02j,
0.1118e-02 + 0.1066e-02j,
0.4063e-03 + 0.1060e-02j,
0.3219e-04 + 0.1031e-02j,
-0.1668e-03 + 0.9850e-03j,
-0.2681e-03 + 0.9276e-03j,
-0.3205e-03 + 0.8641e-03j,
-0.3647e-03 + 0.8013e-03j,
]
assert_almost_equal(phi_golden, boundary_solution.phis, 0.0001)
def test_internal_3d_2():
# Test Problem 2
# Neumann boundary condition with v = cos(k*z)
#
frequency = 20.0 # frequency [Hz]
k, interior_points, boundary_incidence, solver, interior_incident_phi = initialize(
frequency)
boundary_condition = solver.neumann_boundary_condition()
for i in range(solver.len()):
a, b, c = solver.geometry.triangle_vertices(i)
normal = ab.normal_3d(a, b, c)
boundary_condition.f[i] = k * np.cos(
k * solver.centers[i, 2]) * normal[2]
boundary_solution = solver.solve_boundary(k, boundary_condition,
boundary_incidence)
sample_solution = boundary_solution.solve_samples(interior_incident_phi,
interior_points)
phi_golden = [
0.2543e00 + 0.5479e-02j,
0.2543e00 + 0.5477e-02j,
0.2543e00 + 0.5479e-02j,
0.2543e00 + 0.5479e-02j,
0.2543e00 + 0.5477e-02j,
0.2543e00 + 0.5479e-02j,
0.1439e00 + 0.4738e-02j,
0.6877e-01 + 0.3551e-02j,
0.1439e00 + 0.4748e-02j,
0.6877e-01 + 0.3551e-02j,
0.1439e00 + 0.4738e-02j,
0.6877e-01 + 0.3554e-02j,
0.1439e00 + 0.4738e-02j,
0.6877e-01 + 0.3551e-02j,
0.1439e00 + 0.4748e-02j,
0.6877e-01 + 0.3551e-02j,
0.1439e00 + 0.4738e-02j,
0.6877e-01 + 0.3554e-02j,
-0.1439e00 - 0.4738e-02j,
-0.6877e-01 - 0.3551e-02j,
-0.1439e00 - 0.4748e-02j,
-0.6877e-01 - 0.3551e-02j,
-0.1439e00 - 0.4738e-02j,
-0.6877e-01 - 0.3554e-02j,
-0.1439e00 - 0.4738e-02j,
-0.6877e-01 - 0.3551e-02j,
-0.1439e00 - 0.4748e-02j,
-0.6877e-01 - 0.3551e-02j,
-0.1439e00 - 0.4738e-02j,
-0.6877e-01 - 0.3554e-02j,
-0.2543e00 - 0.5479e-02j,
-0.2543e00 - 0.5477e-02j,
-0.2543e00 - 0.5479e-02j,
-0.2543e00 - 0.5479e-02j,
-0.2543e00 - 0.5477e-02j,
-0.2543e00 - 0.5479e-02j,
]
assert_almost_equal(phi_golden, boundary_solution.phis, 0.0001)
phi_golden = [
-0.7286e-16 - 0.6075e-15j,
0.3205e-02 + 0.5491e-04j,
0.8002e-01 + 0.1338e-02j,
0.1586e00 + 0.2495e-02j,
0.2377e00 + 0.3530e-02j,
]
assert_almost_equal(phi_golden, sample_solution.phis, 0.0001)
def test_internal_3d_1():
# Test Problem 1
# Dirichlet boundary condition with phi = sin(k*z)
#
frequency = 20.0 # frequency [Hz]
k, interior_points, boundary_incidence, solver, interior_incident_phi = initialize(
frequency)
boundary_condition = solver.dirichlet_boundary_condition()
boundary_condition.f[:] = np.sin(k * solver.centers[:, 2])
boundary_solution = solver.solve_boundary(k, boundary_condition,
boundary_incidence)
sample_solution = boundary_solution.solve_samples(interior_incident_phi,
interior_points)
phi_golden = [
0.2804e00 + 0.0000e00j,
0.2804e00 + 0.0000e00j,
0.2804e00 + 0.0000e00j,
0.2804e00 + 0.0000e00j,
0.2804e00 + 0.0000e00j,
0.2804e00 + 0.0000e00j,
0.1617e00 + 0.0000e00j,
0.8113e-01 + 0.0000e00j,
0.1617e00 + 0.0000e00j,
0.8113e-01 + 0.0000e00j,
0.1617e00 + 0.0000e00j,
0.8113e-01 + 0.0000e00j,
0.1617e00 + 0.0000e00j,
0.8113e-01 + 0.0000e00j,
0.1617e00 + 0.0000e00j,
0.8113e-01 + 0.0000e00j,
0.1617e00 + 0.0000e00j,
0.8113e-01 + 0.0000e00j,
-0.1617e00 + 0.0000e00j,
-0.8113e-01 + 0.0000e00j,
-0.1617e00 + 0.0000e00j,
-0.8113e-01 + 0.0000e00j,
-0.1617e00 + 0.0000e00j,
-0.8113e-01 + 0.0000e00j,
-0.1617e00 + 0.0000e00j,
-0.8113e-01 + 0.0000e00j,
-0.1617e00 + 0.0000e00j,
-0.8113e-01 + 0.0000e00j,
-0.1617e00 + 0.0000e00j,
-0.8113e-01 + 0.0000e00j,
-0.2804e00 + 0.0000e00j,
-0.2804e00 + 0.0000e00j,
-0.2804e00 + 0.0000e00j,
-0.2804e00 + 0.0000e00j,
-0.2804e00 + 0.0000e00j,
-0.2804e00 + 0.0000e00j,
]
assert_almost_equal(phi_golden, boundary_solution.phis, 0.0001)
phi_golden = [
-0.1032e-15 - 0.5254e-16j,
0.3568e-02 - 0.3302e-04j,
0.8894e-01 - 0.8015e-03j,
0.1757e00 - 0.1477e-02j,
0.2623e00 - 0.1966e-02j,
]
assert_almost_equal(phi_golden, sample_solution.phis, 0.00001)
def test_internal_3d_3():
# Test Problem 3
# Neumann boundary condition with v = cos(k*z)
#
frequency = 20.0 # frequency [Hz]
k, interior_points, boundary_incidence, solver, interior_incident_phi = initialize(
frequency)
boundary_condition = solver.neumann_boundary_condition()
p = np.array([0.0, 0.0, 0.0], dtype=np.float32)
for i in range(solver.len()):
q = solver.centers[i, :]
r = p - q
R = norm(r)
boundary_incidence.phi[i] = np.exp(1.0j * k * R) / (4.0 * np.pi * R)
a, b, c = solver.geometry.triangle_vertices(i)
normal = ab.normal_3d(a, b, c)
drbdn = -np.dot(r, normal) / R
boundary_incidence.v[i] = (drbdn * np.exp(1.0j * k * R) *
(1.0j * k * R - 1.0) /
(4.0 * np.pi * R * R))
for i in range(interior_points.shape[0]):
q = interior_points[i, :]
r = p - q
R = norm(r)
interior_incident_phi[i] = np.exp(1.0j * k * R) / (4.0 * np.pi * R)
boundary_solution = solver.solve_boundary(k, boundary_condition,
boundary_incidence)
sample_solution = boundary_solution.solve_samples(interior_incident_phi,
interior_points)
phi_golden = [
-0.1398e01 + -0.5759e00j,
-0.1398e01 + -0.5759e00j,
-0.1398e01 + -0.5759e00j,
-0.1398e01 + -0.5759e00j,
-0.1398e01 + -0.5759e00j,
-0.1398e01 + -0.5759e00j,
-0.1399e01 + -0.5779e00j,
-0.1389e01 + -0.5760e00j,
-0.1399e01 + -0.5779e00j,
-0.1389e01 + -0.5760e00j,
-0.1399e01 + -0.5779e00j,
-0.1389e01 + -0.5760e00j,
-0.1399e01 + -0.5779e00j,
-0.1389e01 + -0.5760e00j,
-0.1399e01 + -0.5779e00j,
-0.1389e01 + -0.5760e00j,
-0.1399e01 + -0.5779e00j,
-0.1389e01 + -0.5760e00j,
-0.1399e01 + -0.5779e00j,
-0.1389e01 + -0.5760e00j,
-0.1399e01 + -0.5779e00j,
-0.1389e01 + -0.5760e00j,
-0.1399e01 + -0.5779e00j,
-0.1389e01 + -0.5760e00j,
-0.1399e01 + -0.5779e00j,
-0.1389e01 + -0.5760e00j,
-0.1399e01 + -0.5779e00j,
-0.1389e01 + -0.5760e00j,
-0.1399e01 + -0.5779e00j,
-0.1389e01 + -0.5760e00j,
-0.1398e01 + -0.5759e00j,
-0.1398e01 + -0.5759e00j,
-0.1398e01 + -0.5759e00j,
-0.1398e01 + -0.5759e00j,
-0.1398e01 + -0.5759e00j,
-0.1398e01 + -0.5759e00j,
]
assert_almost_equal(phi_golden, boundary_solution.phis, 0.001)
phi_golden = [
-0.1291e01 - 0.5891e00j,
0.6496e01 - 0.5949e00j,
-0.1143e01 - 0.5941e00j,
-0.1296e01 - 0.5904e00j,
-0.1372e01 - 0.5989e00j,
]
assert_almost_equal(phi_golden, sample_solution.phis, 0.001)
def test_internal_rad_3():
frequency = 40.0 # frequency [Hz]
k, interior_points, interior_incident_phi, solver, boundary_incidence = initialize(
frequency)
# Test Problem 3
# Dirichlet boundary condition, such that phi = sin(k/ sqrt(2) * x) * sin(k/sqrt(2) * y)
# Differentiate with respect to x and y to obtain outward normal
boundary_condition = solver.neumann_boundary_condition()
boundary_condition.alpha.fill(1.0)
boundary_condition.beta.fill(0.0)
centers = solver.geometry.centers()
normals = solver.geometry.normals()
zp = 0.25
for i in range(centers.shape[0]):
r = centers[i, 0]
z = centers[i, 1]
# make input complex so proper sqrt is called
rpq = np.sqrt(0.0j + r**2 + (z - zp)**2)
boundary_condition.f[i] = np.exp(1j * k * rpq) / (4.0 * np.pi * rpq)
boundary_incidence.phi[i] = np.exp(1j * k * rpq) / (4.0 * np.pi * rpq)
n = -normals[i]
drbdn = (r * n[0] + (z - zp) * n[1]) / rpq
boundary_incidence.v[i] = (drbdn * np.exp(1j * k * rpq) *
(1j * k * rpq - 1.0) /
(4.0 * np.pi * rpq * rpq))
for i in range(interior_points.shape[0]):
r = interior_points[i, 0]
z = interior_points[i, 1]
# make input complex so proper sqrt is called
rpq = np.sqrt(0.0j + r**2 + (zp - z)**2)
interior_incident_phi[i] = np.exp(1j * k * rpq) / (4.0 * np.pi * rpq)
boundary_solution = solver.solve_boundary(k, boundary_condition,
boundary_incidence)
sample_solution = boundary_solution.solve_samples(interior_incident_phi,
interior_points)
phi_golden = [
0.9096e-01 + 0.5529e-01j,
0.8933e-01 + 0.5521e-01j,
0.8636e-01 + 0.5507e-01j,
0.8234e-01 + 0.5485e-01j,
0.7766e-01 + 0.5457e-01j,
0.7273e-01 + 0.5424e-01j,
0.6779e-01 + 0.5387e-01j,
0.6306e-01 + 0.5346e-01j,
0.5870e-01 + 0.5305e-01j,
0.5473e-01 + 0.5262e-01j,
0.5120e-01 + 0.5220e-01j,
0.4816e-01 + 0.5181e-01j,
0.4557e-01 + 0.5145e-01j,
0.4342e-01 + 0.5113e-01j,
0.4173e-01 + 0.5086e-01j,
0.4046e-01 + 0.5065e-01j,
0.3962e-01 + 0.5051e-01j,
0.3921e-01 + 0.5044e-01j,
]
assert_almost_equal(phi_golden, boundary_solution.phis, 0.00001)
phi_golden = [
0.3118e00 + 0.5882e-01j,
0.3116e00 + 0.5901e-01j,
0.8958e-01 + 0.5608e-01j,
0.1295e00 + 0.5751e-01j,
]
assert_almost_equal(phi_golden, sample_solution.phis, 0.0001)