meanas/fdfd_tools/test/test_fdtd.py

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import numpy
import pytest
import dataclasses
from typing import List, Tuple
from numpy.testing import assert_allclose, assert_array_equal
from fdfd_tools import fdtd
prng = numpy.random.RandomState(12345)
def assert_fields_close(a, b, *args, **kwargs):
numpy.testing.assert_allclose(a, b, verbose=False, err_msg='Fields did not match:\n{}\n{}'.format(numpy.rollaxis(a, -1),
numpy.rollaxis(b, -1)), *args, **kwargs)
def assert_close(a, b, *args, **kwargs):
numpy.testing.assert_allclose(a, b, *args, **kwargs)
def test_initial_fields(sim):
# Make sure initial fields didn't change
e0 = sim.es[0]
h0 = sim.hs[0]
j0 = sim.js[0]
mask = (j0 != 0)
assert_fields_close(e0[mask], j0[mask] / sim.epsilon[mask])
assert not e0[~mask].any()
assert not h0.any()
def test_initial_energy(sim):
"""
Assumes fields start at 0 before J0 is added
"""
j0 = sim.js[0]
e0 = sim.es[0]
h0 = sim.hs[0]
h1 = sim.hs[1]
mask = (j0 != 0)
dV = numpy.prod(numpy.meshgrid(*sim.dxes[0], indexing='ij'), axis=0)
u0 = (j0 * j0.conj() / sim.epsilon * dV).sum(axis=0)
args = {'dxes': sim.dxes,
'epsilon': sim.epsilon}
# Make sure initial energy and E dot J are correct
energy0 = fdtd.energy_estep(h0=h0, e1=e0, h2=h1, **args)
e0_dot_j0 = fdtd.delta_energy_j(j0=j0, e1=e0, dxes=sim.dxes)
assert_fields_close(energy0, u0)
assert_fields_close(e0_dot_j0, u0)
def test_energy_conservation(sim):
"""
Assumes fields start at 0 before J0 is added
"""
e0 = sim.es[0]
j0 = sim.js[0]
u = fdtd.delta_energy_j(j0=j0, e1=e0, dxes=sim.dxes).sum()
args = {'dxes': sim.dxes,
'epsilon': sim.epsilon}
for ii in range(1, 8):
u_hstep = fdtd.energy_hstep(e0=sim.es[ii-1], h1=sim.hs[ii], e2=sim.es[ii], **args)
u_estep = fdtd.energy_estep(h0=sim.hs[ii], e1=sim.es[ii], h2=sim.hs[ii + 1], **args)
delta_j_A = fdtd.delta_energy_j(j0=sim.js[ii], e1=sim.es[ii-1], dxes=sim.dxes)
delta_j_B = fdtd.delta_energy_j(j0=sim.js[ii], e1=sim.es[ii], dxes=sim.dxes)
u += delta_j_A.sum()
assert_close(u_hstep.sum(), u)
u += delta_j_B.sum()
assert_close(u_estep.sum(), u)
def test_poynting_divergence(sim):
args = {'dxes': sim.dxes,
'epsilon': sim.epsilon}
dV = numpy.prod(numpy.meshgrid(*sim.dxes[0], indexing='ij'), axis=0)
u_eprev = None
for ii in range(1, 8):
u_hstep = fdtd.energy_hstep(e0=sim.es[ii-1], h1=sim.hs[ii], e2=sim.es[ii], **args)
u_estep = fdtd.energy_estep(h0=sim.hs[ii], e1=sim.es[ii], h2=sim.hs[ii + 1], **args)
delta_j_B = fdtd.delta_energy_j(j0=sim.js[ii], e1=sim.es[ii], dxes=sim.dxes)
du_half_h2e = u_estep - u_hstep - delta_j_B
div_s_h2e = sim.dt * fdtd.poynting_divergence(e=sim.es[ii], h=sim.hs[ii], dxes=sim.dxes) * dV
assert_fields_close(du_half_h2e, -div_s_h2e)
if u_eprev is None:
u_eprev = u_estep
continue
# previous half-step
delta_j_A = fdtd.delta_energy_j(j0=sim.js[ii], e1=sim.es[ii-1], dxes=sim.dxes)
du_half_e2h = u_hstep - u_eprev - delta_j_A
div_s_e2h = sim.dt * fdtd.poynting_divergence(e=sim.es[ii-1], h=sim.hs[ii], dxes=sim.dxes) * dV
assert_fields_close(du_half_e2h, -div_s_e2h)
u_eprev = u_estep
def test_poynting_planes(sim):
mask = (sim.js[0] != 0)
if mask.sum() > 1:
pytest.skip('test_poynting_planes can only test single point sources')
args = {'dxes': sim.dxes,
'epsilon': sim.epsilon}
dV = numpy.prod(numpy.meshgrid(*sim.dxes[0], indexing='ij'), axis=0)
mx = numpy.roll(mask, (-1, -1), axis=(0, 1))
my = numpy.roll(mask, -1, axis=2)
mz = numpy.roll(mask, (+1, -1), axis=(0, 3))
px = numpy.roll(mask, -1, axis=0)
py = mask.copy()
pz = numpy.roll(mask, +1, axis=0)
u_eprev = None
for ii in range(1, 8):
u_hstep = fdtd.energy_hstep(e0=sim.es[ii-1], h1=sim.hs[ii], e2=sim.es[ii], **args)
u_estep = fdtd.energy_estep(h0=sim.hs[ii], e1=sim.es[ii], h2=sim.hs[ii + 1], **args)
s_h2e = -fdtd.poynting(e=sim.es[ii], h=sim.hs[ii]) * sim.dt
s_h2e[0] *= sim.dxes[0][1][None, :, None] * sim.dxes[0][2][None, None, :]
s_h2e[1] *= sim.dxes[0][0][:, None, None] * sim.dxes[0][2][None, None, :]
s_h2e[2] *= sim.dxes[0][0][:, None, None] * sim.dxes[0][1][None, :, None]
planes = [s_h2e[px].sum(), -s_h2e[mx].sum(),
s_h2e[py].sum(), -s_h2e[my].sum(),
s_h2e[pz].sum(), -s_h2e[mz].sum()]
assert_close(sum(planes), (u_estep - u_hstep).sum())
if u_eprev is None:
u_eprev = u_estep
continue
s_e2h = -fdtd.poynting(e=sim.es[ii - 1], h=sim.hs[ii]) * sim.dt
s_e2h[0] *= sim.dxes[0][1][None, :, None] * sim.dxes[0][2][None, None, :]
s_e2h[1] *= sim.dxes[0][0][:, None, None] * sim.dxes[0][2][None, None, :]
s_e2h[2] *= sim.dxes[0][0][:, None, None] * sim.dxes[0][1][None, :, None]
planes = [s_e2h[px].sum(), -s_e2h[mx].sum(),
s_e2h[py].sum(), -s_e2h[my].sum(),
s_e2h[pz].sum(), -s_e2h[mz].sum()]
assert_close(sum(planes), (u_hstep - u_eprev).sum())
# previous half-step
u_eprev = u_estep
#####################################
# Test fixtures
#####################################
@pytest.fixture(scope='module',
params=[(5, 5, 1),
(5, 1, 5),
(5, 5, 5),
# (7, 7, 7),
])
def shape(request):
yield (3, *request.param)
@pytest.fixture(scope='module', params=[0.3])
def dt(request):
yield request.param
@pytest.fixture(scope='module', params=[1.0, 1.5])
def epsilon_bg(request):
yield request.param
@pytest.fixture(scope='module', params=[1.0, 2.5])
def epsilon_fg(request):
yield request.param
@pytest.fixture(scope='module', params=['center', '000', 'random'])
def epsilon(request, shape, epsilon_bg, epsilon_fg):
is3d = (numpy.array(shape) == 1).sum() == 0
if is3d:
if request.param == '000':
pytest.skip('Skipping 000 epsilon because test is 3D (for speed)')
if epsilon_bg != 1:
pytest.skip('Skipping epsilon_bg != 1 because test is 3D (for speed)')
if epsilon_fg not in (1.0, 2.0):
pytest.skip('Skipping epsilon_fg not in (1, 2) because test is 3D (for speed)')
epsilon = numpy.full(shape, epsilon_bg, dtype=float)
if request.param == 'center':
epsilon[:, shape[1]//2, shape[2]//2, shape[3]//2] = epsilon_fg
elif request.param == '000':
epsilon[:, 0, 0, 0] = epsilon_fg
elif request.param == 'random':
epsilon[:] = prng.uniform(low=min(epsilon_bg, epsilon_fg),
high=max(epsilon_bg, epsilon_fg),
size=shape)
yield epsilon
@pytest.fixture(scope='module', params=[1.0])#, 1.5])
def j_mag(request):
yield request.param
@pytest.fixture(scope='module', params=['center', 'random'])
def j_distribution(request, shape, j_mag):
j = numpy.zeros(shape)
if request.param == 'center':
j[:, shape[1]//2, shape[2]//2, shape[3]//2] = j_mag
elif request.param == '000':
j[:, 0, 0, 0] = j_mag
elif request.param == 'random':
j[:] = prng.uniform(low=-j_mag, high=j_mag, size=shape)
yield j
@pytest.fixture(scope='module', params=[1.0, 1.5])
def dx(request):
yield request.param
@pytest.fixture(scope='module', params=['uniform'])
def dxes(request, shape, dx):
if request.param == 'uniform':
dxes = [[numpy.full(s, dx) for s in shape[1:]] for _ in range(2)]
yield dxes
@pytest.fixture(scope='module',
params=[(0,),
(0, 4, 8),
]
)
def j_steps(request):
yield request.param
@dataclasses.dataclass()
class SimResult:
shape: Tuple[int]
dt: float
dxes: List[List[numpy.ndarray]]
epsilon: numpy.ndarray
j_distribution: numpy.ndarray
j_steps: Tuple[int]
es: List[numpy.ndarray] = dataclasses.field(default_factory=list)
hs: List[numpy.ndarray] = dataclasses.field(default_factory=list)
js: List[numpy.ndarray] = dataclasses.field(default_factory=list)
@pytest.fixture(scope='module')
def sim(request, shape, epsilon, dxes, dt, j_distribution, j_steps):
is3d = (numpy.array(shape) == 1).sum() == 0
if is3d:
if dt != 0.3:
pytest.skip('Skipping dt != 0.3 because test is 3D (for speed)')
sim = SimResult(
shape=shape,
dt=dt,
dxes=dxes,
epsilon=epsilon,
j_distribution=j_distribution,
j_steps=j_steps,
)
e = numpy.zeros_like(epsilon)
h = numpy.zeros_like(epsilon)
assert 0 in j_steps
j_zeros = numpy.zeros_like(j_distribution)
eh2h = fdtd.maxwell_h(dt=dt, dxes=dxes)
eh2e = fdtd.maxwell_e(dt=dt, dxes=dxes)
for tt in range(10):
e = e.copy()
h = h.copy()
eh2h(e, h)
eh2e(e, h, epsilon)
if tt in j_steps:
e += j_distribution / epsilon
sim.js.append(j_distribution)
else:
sim.js.append(j_zeros)
sim.es.append(e)
sim.hs.append(h)
return sim