def test_gauss_1d_coax():
cc = CoaxCapacitor(0.5e-3, 5.2, 3.5e-3)
X, er = cc.get_arrays(101)
v1 = 10.0
V = cc.potential(X, Va=v1)
# 1D gauss returns a charge density over circumference
# Result is negative due to direction of X
Q = np.array([
-2 * np.pi * X[i] * fdm.gauss_1d(X, V, er, i)
for i in range(1,
len(X) - 1)
])
Qa = cc.charge(v1)
assert Q == approx(Qa, rel=0.01)
def test_gauss_2d_coax_xysym():
ri = 1.0e-3
ro = 4.0e-3
rm = 0.5 * (ri + ro)
assert rm * 1.414 < ro
w = 1.1 * ro
dx = ri / 40
Va = 10.0
x = np.arange(0, w, dx)
y = np.arange(0, w, dx)
X, Y = np.meshgrid(x, y, indexing='ij')
cc = CoaxCapacitor(ri, 1.0, ro - ri)
V = cc.potential(X, Y, Va=Va)
expected = cc.charge(Va)
er = np.ones_like(V)[:-1, :-1]
xi1 = 0
xi2 = np.searchsorted(x, rm)
yi1 = 0
yi2 = np.searchsorted(y, rm)
gauss = fdm.gauss_2d(X, Y, V, er, xi1, xi2, yi1, yi2)
assert gauss == approx(expected, rel=0.01, abs=1e-14)
def test_charge():
cc = CoaxCapacitor(0.5e-3, 5.2, 3.5e-3)
Va = 10.0
expected = cc.capacitance() * Va
assert cc.charge(Va) == approx(expected)
