def test_poisson_3d_sphere_sym(xsym, ysym, zsym):
ri = 2.0e-3
ro = 4.0e-3
w = 1.1 * ro
N = 61
dx = 2 * w / N
Va = 10.0
x = np.arange(-w * (not xsym), w, dx)
y = np.arange(-w * (not ysym), w, dx)
z = np.arange(-w * (not zsym), w, dx)
X, Y, Z = np.meshgrid(x, y, z, indexing='ij')
R = np.sqrt(X**2 + Y**2 + Z**2)
bc_bool = np.logical_or(R < ri, R > ro)
bc_val = np.select([R < ri, R > ro], [Va, 0])
bc = (bc_bool, bc_val)
sc = SphereCapacitor(ri, 1.0, ro - ri)
expected = sc.potential(X, Y, Z, Va=Va)
potential = fdm.poisson_3d(X,
Y,
Z,
bc=bc,
conv=1e-5,
xsym=xsym,
ysym=ysym,
zsym=zsym)
assert potential == approx(expected, abs=0.9)
def test_potential():
ri = 30e-3
ro = 50e-3
N = 5
sc = SphereCapacitor(ri, 2.6, ro - ri)
X = np.linspace(ri, ro, N)
Va = 10.0
Q = sc.capacitance() * Va
expected = Va - Q / (4 * np.pi * EPS0 * 2.6) * (1 / ri - 1 / X)
potential = sc.potential(X, Va=Va)
assert potential == approx(expected)
def test_efield():
ri = 30e-3
ro = 50e-3
N = 5
sc = SphereCapacitor(ri, 2.6, ro - ri)
X = np.linspace(ri, ro, N)
Va = 10.0
Q = sc.capacitance() * Va
expected = Q / (4 * np.pi * EPS0 * 2.6 * X**2)
efield = sc.efield(X, Va=Va)
assert efield == approx(expected)
def test_poisson_3d_sphere_2layer():
ri = 2.0e-3
re = 2.8e-3
ro = 4.0e-3
er1, er2 = 4.0, 1.0
w = 1.1 * ro
N = 61
dx = 2 * w / N
Va = 10.0
x = np.arange(-w, w, dx)
y = np.arange(-w, w, dx)
z = np.arange(-w, w, dx)
X, Y, Z = np.meshgrid(x, y, z, indexing='ij')
R = np.sqrt(X**2 + Y**2 + Z**2)
er = np.select([R <= re, R > re], [er1, er2])[:-1, :-1, :-1]
bc_bool = np.logical_or(R < ri, R > ro)
bc_val = np.select([R < ri, R > ro], [Va, 0])
bc = (bc_bool, bc_val)
sc = SphereCapacitor(ri, (er1, er2), (re - ri, ro - re))
expected = sc.potential(X, Y, Z, Va=Va)
potential = fdm.poisson_3d(X, Y, Z, dielectric=er, bc=bc, conv=1e-7)
assert potential == approx(expected, abs=0.8)
def test_capacitance():
sc = SphereCapacitor(30e-3, 2.6, 20e-3)
assert sc.capacitance() == approx(21.7e-12, abs=0.1e-12)
def test_energy():
sc = SphereCapacitor(0.5e-3, 5.2, 3.5e-3)
Va = 10.0
expected = 0.5 * sc.capacitance() * Va**2
assert sc.energy(Va) == approx(expected)
def test_charge():
sc = SphereCapacitor(0.5e-3, 5.2, 3.5e-3)
Va = 10.0
expected = sc.capacitance() * Va
assert sc.charge(Va) == approx(expected)
def test_get_arrays():
N = 11
sc = SphereCapacitor(30e-3, 2.6, 20e-3)
X, er = sc.get_arrays(N=N)
assert X == approx(np.linspace(30e-3, 50e-3, N))
assert er == approx(2.6 * np.ones(N - 1))