def test_interface_bc(frequency):
# interface condition should act identical to impedance condition if no
# other domain exists
z = 1.205 * 343.4
k = 2 * np.pi * frequency / 343.4
lx, ly, n = 2, 1, 20
nodes = [(0, 0), (lx, 0), (lx, ly), (0, ly)]
elements = [(0, 1), (1, 2), (2, 3), (3, 0)]
kinds = ['v', 'p', 'v', 'i']
functions = [
lambda *args: 0, lambda *args: 1, lambda *args: 0, lambda *args: 2 * z
]
sd = Subdomain(nodes, elements, kinds, functions)
field_points = [(x, ly / 2) for x in np.linspace(0, lx, 10)]
solution = [sd.field_solution(x, y, z, k, n) for x, y in field_points]
# for impedance Z = 2*rho*c
g = 1 / 3
b = 1 / (g * np.exp(1j * k * lx) + np.exp(-1j * k * lx))
a = (1 - b * np.exp(-1j * k * lx)) / np.exp(1j * k * lx)
reference_solution = [
reference_pressure(a, b, k, x) for x, y in field_points
]
assert_allclose(np.array(reference_solution), np.array(solution))
def test_pressure_bc(frequency):
z = 1.205 * 343.4
k = 2 * np.pi * frequency / 343.4
lx, ly, n = 2, 1, 20
nodes = [(0, 0), (lx, 0), (lx, ly), (0, ly)]
elements = [(0, 1), (1, 2), (2, 3), (3, 0)]
kinds = ['v', 'v', 'v', 'p']
functions = 3 * [lambda *args: 0] + [lambda *args: 1]
sd = Subdomain(nodes, elements, kinds, functions)
field_points = [(x, ly / 2) for x in np.linspace(0, lx, 10)]
solution = [sd.field_solution(x, y, z, k, n) for x, y in field_points]
a = 1 / (np.exp(2 * 1j * k * lx) + 1)
b = 1 / (np.exp(-2 * 1j * k * lx) + 1)
reference_solution = [
reference_pressure(a, b, k, x) for x, y in field_points
]
assert_allclose(np.array(reference_solution), np.array(solution))
def test_lx_ly():
nodes = [(0, 0), (2, 0), (2, 2), (0, 2)]
elements = [(0, 1), (1, 2), (2, 3), (3, 0)]
sd = Subdomain(nodes, elements, 4 * ['i'], 4 * [lambda x, y, z, k: 0])
assert sd.lx == 2
assert sd.ly == 2
def test_subdomain_normals():
nodes = [(0, 0), (2, 0), (2, 2), (0, 2)]
elements = [(0, 1), (1, 2), (2, 3), (3, 0)]
sd = Subdomain(nodes, elements, 4 * ['i'], 4 * [lambda x, y, z, k: 0])
assert np.array_equal(np.array([(0, 1), (-1, 0), (0, -1), (1, 0)]),
sd.normals)
def test_point_inside(x, y, inside):
sd = Subdomain([(0, 0), (0, 1), (1, 1), (1, 0)], [(0, 1), (1, 2), (2, 3),
(3, 0)], None, None)
assert sd.point_inside(x, y) == inside
def test_invalid_element():
nodes = [(0, 0), (1, 0), (0, 1)]
elements = [(0, 1), (1, 2), (2, 3)]
with pytest.raises(ValueError):
Subdomain(nodes, elements, 4 * ['i'], 4 * [lambda x, y, z, k: 0])
r = np.sqrt((x - .5)**2 + (y - .5)**2)
return hankel2(0, k * r)
def gpp(n, x, y, k):
r = np.sqrt((x - .5)**2 + (y - .5)**2)
return k * (n[0] * (x - .5) / r *
(hankel2(-1, k * r) / 2 - hankel2(1, k * r) / 2) + n[1] *
(y - .5) / r *
(hankel2(-1, k * r) / 2 - hankel2(1, k * r) / 2))
if __name__ == '__main__':
z = 1.205 * 343.4
k = 2 * np.pi * 800 / 343.4
lx, ly, n = 2, 1, 20
nodes = [(0, 0), (lx, 0), (lx, ly), (0, ly)]
elements = [(0, 1), (1, 2), (2, 3), (3, 0)]
kinds = ['z', 'z', 'z', 'z']
functions = [zn, zn, zn, zn]
sd = Subdomain(nodes, elements, kinds, functions, [(pp, gpp)])
sd.solve(z, k, n, vn)
x, y = np.meshgrid(np.linspace(0, lx, 84), np.linspace(0, ly, 44))
z = np.real(sd.field_solution(x, y, z, k, n, vn))
plt.contourf(x, y, z)
plt.colorbar()
plt.show()