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fdfd_tools/fdfd_tools/test_fdtd.py

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import unittest
import numpy
from fdfd_tools import fdtd
class BasicTests():
def test_initial_fields(self):
# Make sure initial fields didn't change
e0 = self.es[0]
h0 = self.hs[0]
mask = self.src_mask
self.assertEqual(e0[mask], self.j_mag / self.epsilon[mask])
self.assertFalse(e0[~mask].any())
self.assertFalse(h0.any())
def test_initial_energy(self):
e0 = self.es[0]
h0 = self.hs[0]
h1 = self.hs[1]
mask = self.src_mask[1]
dxes = self.dxes if self.dxes is not None else tuple(tuple(numpy.ones(s) for s in e0.shape[1:]) for _ in range(2))
dV = numpy.prod(numpy.meshgrid(*dxes[0], indexing='ij'), axis=0)
u0 = self.j_mag * self.j_mag / self.epsilon[self.src_mask] * dV[mask]
args = {'dxes': self.dxes,
'epsilon': self.epsilon}
# Make sure initial energy and E dot J are correct
energy0 = fdtd.energy_estep(h0=h0, e1=e0, h2=self.hs[1], **args)
e_dot_j_0 = fdtd.delta_energy_j(j0=(e0 - 0) * self.epsilon, e1=e0, dxes=self.dxes)
self.assertEqual(energy0[mask], u0)
self.assertFalse(energy0[~mask].any(), msg='energy0: {}'.format(energy0))
self.assertEqual(e_dot_j_0[mask], u0)
self.assertFalse(e_dot_j_0[~mask].any(), msg='e_dot_j_0: {}'.format(e_dot_j_0))
def test_energy_conservation(self):
e0 = self.es[0]
u0 = fdtd.delta_energy_j(j0=(e0 - 0) * self.epsilon, e1=e0, dxes=self.dxes).sum()
args = {'dxes': self.dxes,
'epsilon': self.epsilon}
for ii in range(1, 8):
with self.subTest(i=ii):
u_hstep = fdtd.energy_hstep(e0=self.es[ii-1], h1=self.hs[ii], e2=self.es[ii], **args)
u_estep = fdtd.energy_estep(h0=self.hs[ii], e1=self.es[ii], h2=self.hs[ii + 1], **args)
self.assertTrue(numpy.allclose(u_hstep.sum(), u0), msg='u_hstep: {}\n{}'.format(u_hstep.sum(), numpy.rollaxis(u_hstep, -1)))
self.assertTrue(numpy.allclose(u_estep.sum(), u0), msg='u_estep: {}\n{}'.format(u_estep.sum(), numpy.rollaxis(u_estep, -1)))
def test_poynting_divergence(self):
args = {'dxes': self.dxes,
'epsilon': self.epsilon}
dxes = self.dxes if self.dxes is not None else tuple(tuple(numpy.ones(s) for s in self.epsilon.shape[1:]) for _ in range(2))
dV = numpy.prod(numpy.meshgrid(*dxes[0], indexing='ij'), axis=0)
u_eprev = None
for ii in range(1, 8):
with self.subTest(i=ii):
u_hstep = fdtd.energy_hstep(e0=self.es[ii-1], h1=self.hs[ii], e2=self.es[ii], **args)
u_estep = fdtd.energy_estep(h0=self.hs[ii], e1=self.es[ii], h2=self.hs[ii + 1], **args)
du_half_h2e = u_estep - u_hstep
div_s_h2e = self.dt * fdtd.poynting_divergence(e=self.es[ii], h=self.hs[ii], dxes=self.dxes) * dV
self.assertTrue(numpy.allclose(du_half_h2e, -div_s_h2e, rtol=1e-4),
msg='du_half_h2e\n{}\ndiv_s_h2e\n{}'.format(numpy.rollaxis(du_half_h2e, -1),
-numpy.rollaxis(div_s_h2e, -1)))
if u_eprev is None:
u_eprev = u_estep
continue
# previous half-step
du_half_e2h = u_hstep - u_eprev
div_s_e2h = self.dt * fdtd.poynting_divergence(e=self.es[ii-1], h=self.hs[ii], dxes=self.dxes) * dV
self.assertTrue(numpy.allclose(du_half_e2h, -div_s_e2h, rtol=1e-4),
msg='du_half_e2h\n{}\ndiv_s_e2h\n{}'.format(numpy.rollaxis(du_half_e2h, -1),
-numpy.rollaxis(div_s_e2h, -1)))
u_eprev = u_estep
def test_poynting_planes(self):
args = {'dxes': self.dxes,
'epsilon': self.epsilon}
dxes = self.dxes if self.dxes is not None else tuple(tuple(numpy.ones(s) for s in self.epsilon.shape[1:]) for _ in range(2))
dV = numpy.prod(numpy.meshgrid(*dxes[0], indexing='ij'), axis=0)
u_eprev = None
for ii in range(1, 8):
with self.subTest(i=ii):
u_hstep = fdtd.energy_hstep(e0=self.es[ii-1], h1=self.hs[ii], e2=self.es[ii], **args)
u_estep = fdtd.energy_estep(h0=self.hs[ii], e1=self.es[ii], h2=self.hs[ii + 1], **args)
mx = numpy.roll(self.src_mask, (-1, -1), axis=(0, 1))
my = numpy.roll(self.src_mask, -1, axis=2)
mz = numpy.roll(self.src_mask, (+1, -1), axis=(0, 3))
px = numpy.roll(self.src_mask, -1, axis=0)
py = self.src_mask.copy()
pz = numpy.roll(self.src_mask, +1, axis=0)
s_h2e = -fdtd.poynting(e=self.es[ii], h=self.hs[ii]) * self.dt
s_h2e[0] *= dxes[0][1][None, :, None] * dxes[0][2][None, None, :]
s_h2e[1] *= dxes[0][0][:, None, None] * dxes[0][2][None, None, :]
s_h2e[2] *= dxes[0][0][:, None, None] * 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()]
self.assertTrue(numpy.allclose(sum(planes), (u_estep - u_hstep)[self.src_mask[1]]),
msg='planes: {} (sum: {})\n du:\n {}'.format(planes, sum(planes), (u_estep - u_hstep)[self.src_mask[1]]))
class Basic2DNoDXOnlyVacuum(unittest.TestCase, BasicTests):
def setUp(self):
shape = [3, 5, 5, 1]
self.dt = 0.5
self.epsilon = numpy.ones(shape, dtype=float)
self.j_mag = 32
self.dxes = None
self.src_mask = numpy.zeros_like(self.epsilon, dtype=bool)
self.src_mask[1, 2, 2, 0] = True
e = numpy.zeros_like(self.epsilon)
h = numpy.zeros_like(self.epsilon)
e[self.src_mask] = self.j_mag / self.epsilon[self.src_mask]
self.es = [e]
self.hs = [h]
eh2h = fdtd.maxwell_h(dt=self.dt, dxes=self.dxes)
eh2e = fdtd.maxwell_e(dt=self.dt, dxes=self.dxes)
for _ in range(9):
e = e.copy()
h = h.copy()
eh2h(e, h)
eh2e(e, h, self.epsilon)
self.es.append(e)
self.hs.append(h)
class Basic2DUniformDX3(unittest.TestCase, BasicTests):
def setUp(self):
shape = [3, 5, 5, 1]
self.dt = 0.5
self.j_mag = 32
self.dxes = tuple(tuple(numpy.full(s, 2.0) for s in shape[1:]) for _ in range(2))
self.src_mask = numpy.zeros(shape, dtype=bool)
self.src_mask[1, 2, 2, 0] = True
self.epsilon = numpy.full(shape, 1, dtype=float)
self.epsilon[self.src_mask] = 2
e = numpy.zeros_like(self.epsilon)
h = numpy.zeros_like(self.epsilon)
e[self.src_mask] = self.j_mag / self.epsilon[self.src_mask]
self.es = [e]
self.hs = [h]
eh2h = fdtd.maxwell_h(dt=self.dt, dxes=self.dxes)
eh2e = fdtd.maxwell_e(dt=self.dt, dxes=self.dxes)
for _ in range(9):
e = e.copy()
h = h.copy()
eh2h(e, h)
eh2e(e, h, self.epsilon)
self.es.append(e)
self.hs.append(h)
class Basic3DUniformDXOnlyVacuum(unittest.TestCase, BasicTests):
def setUp(self):
shape = [3, 5, 5, 5]
self.dt = 0.5
self.epsilon = numpy.ones(shape, dtype=float)
self.j_mag = 32
self.dxes = tuple(tuple(numpy.ones(s) for s in shape[1:]) for _ in range(2))
self.src_mask = numpy.zeros_like(self.epsilon, dtype=bool)
self.src_mask[1, 2, 2, 2] = True
e = numpy.zeros_like(self.epsilon)
h = numpy.zeros_like(self.epsilon)
e[self.src_mask] = self.j_mag / self.epsilon[self.src_mask]
self.es = [e]
self.hs = [h]
eh2h = fdtd.maxwell_h(dt=self.dt, dxes=self.dxes)
eh2e = fdtd.maxwell_e(dt=self.dt, dxes=self.dxes)
for _ in range(9):
e = e.copy()
h = h.copy()
eh2h(e, h)
eh2e(e, h, self.epsilon)
self.es.append(e)
self.hs.append(h)
class Basic3DUniformDXUniformN(unittest.TestCase, BasicTests):
def setUp(self):
shape = [3, 5, 5, 5]
self.dt = 0.5
self.epsilon = numpy.full(shape, 2, dtype=float)
self.j_mag = 32
self.dxes = tuple(tuple(numpy.ones(s) for s in shape[1:]) for _ in range(2))
self.src_mask = numpy.zeros_like(self.epsilon, dtype=bool)
self.src_mask[1, 2, 2, 2] = True
e = numpy.zeros_like(self.epsilon)
h = numpy.zeros_like(self.epsilon)
e[self.src_mask] = self.j_mag / self.epsilon[self.src_mask]
self.es = [e]
self.hs = [h]
eh2h = fdtd.maxwell_h(dt=self.dt, dxes=self.dxes)
eh2e = fdtd.maxwell_e(dt=self.dt, dxes=self.dxes)
for _ in range(9):
e = e.copy()
h = h.copy()
eh2h(e, h)
eh2e(e, h, self.epsilon)
self.es.append(e)
self.hs.append(h)
class Basic3DUniformDX(unittest.TestCase, BasicTests):
def setUp(self):
shape = [3, 5, 5, 5]
self.dt = 0.33
self.j_mag = 32
self.dxes = tuple(tuple(numpy.ones(s) for s in shape[1:]) for _ in range(2))
self.src_mask = numpy.zeros(shape, dtype=bool)
self.src_mask[1, 2, 2, 2] = True
self.epsilon = numpy.full(shape, 1, dtype=float)
self.epsilon[self.src_mask] = 2
e = numpy.zeros_like(self.epsilon)
h = numpy.zeros_like(self.epsilon)
e[self.src_mask] = self.j_mag / self.epsilon[self.src_mask]
self.es = [e]
self.hs = [h]
eh2h = fdtd.maxwell_h(dt=self.dt, dxes=self.dxes)
eh2e = fdtd.maxwell_e(dt=self.dt, dxes=self.dxes)
for _ in range(9):
e = e.copy()
h = h.copy()
eh2h(e, h)
eh2e(e, h, self.epsilon)
self.es.append(e)
self.hs.append(h)
class Basic3DUniformDX3(unittest.TestCase, BasicTests):
def setUp(self):
shape = [3, 5, 5, 5]
self.dt = 0.5
self.j_mag = 32
self.dxes = tuple(tuple(numpy.full(s, 3.0) for s in shape[1:]) for _ in range(2))
self.src_mask = numpy.zeros(shape, dtype=bool)
self.src_mask[1, 2, 2, 2] = True
self.epsilon = numpy.full(shape, 1, dtype=float)
self.epsilon[self.src_mask] = 2
e = numpy.zeros_like(self.epsilon)
h = numpy.zeros_like(self.epsilon)
e[self.src_mask] = self.j_mag / self.epsilon[self.src_mask]
self.es = [e]
self.hs = [h]
eh2h = fdtd.maxwell_h(dt=self.dt, dxes=self.dxes)
eh2e = fdtd.maxwell_e(dt=self.dt, dxes=self.dxes)
for _ in range(9):
e = e.copy()
h = h.copy()
eh2h(e, h)
eh2e(e, h, self.epsilon)
self.es.append(e)
self.hs.append(h)
logging.basicConfig(level=logging.DEBUG)
def tearDown(self):
logging.basicConfig(level=logging.INFO)
class JdotE_3DUniformDX(unittest.TestCase):
def setUp(self):
shape = [3, 5, 5, 5]
self.dt = 0.5
self.j_mag = 32
self.dxes = tuple(tuple(numpy.full(s, 2.0) for s in shape[1:]) for _ in range(2))
self.src_mask = numpy.zeros(shape, dtype=bool)
self.src_mask[1, 2, 2, 2] = True
self.epsilon = numpy.full(shape, 4, dtype=float)
self.epsilon[self.src_mask] = 2
e = numpy.random.randint(-128, 128 + 1, size=shape).astype(numpy.float32)
h = numpy.random.randint(-128, 128 + 1, size=shape).astype(numpy.float32)
self.es = [e]
self.hs = [h]
eh2h = fdtd.maxwell_h(dt=self.dt, dxes=self.dxes)
eh2e = fdtd.maxwell_e(dt=self.dt, dxes=self.dxes)
for ii in range(9):
e = e.copy()
h = h.copy()
eh2h(e, h)
eh2e(e, h, self.epsilon)
self.es.append(e)
self.hs.append(h)
if ii == 1:
e[self.src_mask] += self.j_mag / self.epsilon[self.src_mask]
self.j_dot_e = self.j_mag * e[self.src_mask]
def test_j_dot_e(self):
e0 = self.es[2]
j0 = numpy.zeros_like(e0)
j0[self.src_mask] = self.j_mag
u0 = fdtd.delta_energy_j(j0=j0, e1=e0, dxes=self.dxes)
args = {'dxes': self.dxes,
'epsilon': self.epsilon}
ii=2
u_hstep = fdtd.energy_hstep(e0=self.es[ii-1], h1=self.hs[ii], e2=self.es[ii], **args)
u_estep = fdtd.energy_estep(h0=self.hs[ii], e1=self.es[ii], h2=self.hs[ii + 1], **args)
#print(u0.sum(), (u_estep - u_hstep).sum())
self.assertTrue(numpy.allclose(u0.sum(), (u_estep - u_hstep).sum(), rtol=1e-4))
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