add fdtd and test
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examples/test_fdtd.py
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175
examples/test_fdtd.py
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"""
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Example code for running an OpenCL FDTD simulation
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See main() for simulation setup.
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"""
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import sys
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import time
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import numpy
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import h5py
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from fdfd_tools import fdtd
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from masque import Pattern, shapes
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import gridlock
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import pcgen
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def perturbed_l3(a: float, radius: float, **kwargs) -> Pattern:
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"""
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Generate a masque.Pattern object containing a perturbed L3 cavity.
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:param a: Lattice constant.
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:param radius: Hole radius, in units of a (lattice constant).
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:param kwargs: Keyword arguments:
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hole_dose, trench_dose, hole_layer, trench_layer: Shape properties for Pattern.
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Defaults *_dose=1, hole_layer=0, trench_layer=1.
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shifts_a, shifts_r: passed to pcgen.l3_shift; specifies lattice constant (1 -
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multiplicative factor) and radius (multiplicative factor) for shifting
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holes adjacent to the defect (same row). Defaults are 0.15 shift for
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first hole, 0.075 shift for third hole, and no radius change.
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xy_size: [x, y] number of mirror periods in each direction; total size is
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2 * n + 1 holes in each direction. Default [10, 10].
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perturbed_radius: radius of holes perturbed to form an upwards-driected beam
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(multiplicative factor). Default 1.1.
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trench width: Width of the undercut trenches. Default 1.2e3.
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:return: masque.Pattern object containing the L3 design
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"""
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default_args = {'hole_dose': 1,
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'trench_dose': 1,
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'hole_layer': 0,
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'trench_layer': 1,
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'shifts_a': (0.15, 0, 0.075),
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'shifts_r': (1.0, 1.0, 1.0),
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'xy_size': (10, 10),
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'perturbed_radius': 1.1,
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'trench_width': 1.2e3,
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}
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kwargs = {**default_args, **kwargs}
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xyr = pcgen.l3_shift_perturbed_defect(mirror_dims=kwargs['xy_size'],
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perturbed_radius=kwargs['perturbed_radius'],
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shifts_a=kwargs['shifts_a'],
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shifts_r=kwargs['shifts_r'])
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xyr *= a
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xyr[:, 2] *= radius
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pat = Pattern()
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pat.name = 'L3p-a{:g}r{:g}rp{:g}'.format(a, radius, kwargs['perturbed_radius'])
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pat.shapes += [shapes.Circle(radius=r, offset=(x, y),
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dose=kwargs['hole_dose'],
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layer=kwargs['hole_layer'])
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for x, y, r in xyr]
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maxes = numpy.max(numpy.fabs(xyr), axis=0)
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pat.shapes += [shapes.Polygon.rectangle(
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lx=(2 * maxes[0]), ly=kwargs['trench_width'],
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offset=(0, s * (maxes[1] + a + kwargs['trench_width'] / 2)),
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dose=kwargs['trench_dose'], layer=kwargs['trench_layer'])
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for s in (-1, 1)]
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return pat
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def main():
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dtype = numpy.float32
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max_t = 8000 # number of timesteps
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dx = 40 # discretization (nm/cell)
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pml_thickness = 8 # (number of cells)
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wl = 1550 # Excitation wavelength and fwhm
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dwl = 200
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# Device design parameters
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xy_size = numpy.array([10, 10])
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a = 430
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r = 0.285
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th = 170
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# refractive indices
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n_slab = 3.408 # InGaAsP(80, 50) @ 1550nm
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n_air = 1.0 # air
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# Half-dimensions of the simulation grid
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xy_max = (xy_size + 1) * a * [1, numpy.sqrt(3)/2]
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z_max = 1.6 * a
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xyz_max = numpy.hstack((xy_max, z_max)) + pml_thickness * dx
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# Coordinates of the edges of the cells. The fdtd package can only do square grids at the moment.
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half_edge_coords = [numpy.arange(dx/2, m + dx, step=dx) for m in xyz_max]
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edge_coords = [numpy.hstack((-h[::-1], h)) for h in half_edge_coords]
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# #### Create the grid, mask, and draw the device ####
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grid = gridlock.Grid(edge_coords, initial=n_air**2, num_grids=3)
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grid.draw_slab(surface_normal=gridlock.Direction.z,
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center=[0, 0, 0],
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thickness=th,
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eps=n_slab**2)
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mask = perturbed_l3(a, r)
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grid.draw_polygons(surface_normal=gridlock.Direction.z,
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center=[0, 0, 0],
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thickness=2 * th,
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eps=n_air**2,
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polygons=mask.as_polygons())
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print(grid.shape)
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# #### Create the simulation grid ####
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epsilon = [eps.astype(dtype) for eps in grid.grids]
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dt = .99/numpy.sqrt(3)
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e = [numpy.zeros_like(epsilon[0], dtype=dtype) for _ in range(3)]
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h = [numpy.zeros_like(epsilon[0], dtype=dtype) for _ in range(3)]
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update_e = fdtd.maxwell_e(dt)
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update_h = fdtd.maxwell_h(dt)
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# PMLs in every direction
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pml_e_funcs = []
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pml_h_funcs = []
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pml_fields = {}
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for d in (0, 1, 2):
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for p in (-1, 1):
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ef, hf, psis = fdtd.cpml(direction=d, polarity=p, dt=dt, epsilon=epsilon, epsilon_eff=n_slab**2, dtype=dtype)
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pml_e_funcs.append(ef)
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pml_h_funcs.append(hf)
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pml_fields.update(psis)
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# Source parameters and function
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w = 2 * numpy.pi * dx / wl
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fwhm = dwl * w * w / (2 * numpy.pi * dx)
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alpha = (fwhm ** 2) / 8 * numpy.log(2)
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delay = 7/numpy.sqrt(2 * alpha)
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def field_source(i):
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t0 = i * dt - delay
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return numpy.sin(w * t0) * numpy.exp(-alpha * t0**2)
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# #### Run a bunch of iterations ####
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output_file = h5py.File('simulation_output.h5', 'w')
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start = time.perf_counter()
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for t in range(max_t):
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[f(e, h, epsilon) for f in pml_e_funcs]
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update_e(e, h, epsilon)
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e[1][tuple(grid.shape//2)] += field_source(t)
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[f(e, h) for f in pml_h_funcs]
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update_h(e, h)
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print('iteration {}: average {} iterations per sec'.format(t, (t+1)/(time.perf_counter()-start)))
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sys.stdout.flush()
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if t % 20 == 0:
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r = sum([(f * f * e).sum() for f, e in zip(e, epsilon)])
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print('E sum', r)
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# Save field slices
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if (t % 20 == 0 and (max_t - t <= 1000 or t <= 2000)) or t == max_t-1:
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print('saving E-field')
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for j, f in enumerate(e):
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output_file['/E{}_t{}'.format('xyz'[j], t)] = f[:, :, round(f.shape[2]/2)]
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if __name__ == '__main__':
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main()
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239
fdfd_tools/fdtd.py
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239
fdfd_tools/fdtd.py
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from typing import List, Callable, Tuple, Dict
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import numpy
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from . import dx_lists_t, field_t
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__author__ = 'Jan Petykiewicz'
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functional_matrix = Callable[[field_t], field_t]
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def curl_h(dxes: dx_lists_t = None) -> functional_matrix:
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"""
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Curl operator for use with the H field.
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:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header
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:return: Function for taking the discretized curl of the H-field, F(H) -> curlH
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"""
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if dxes:
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dxyz_b = numpy.meshgrid(*dxes[1], indexing='ij')
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def dh(f, ax):
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return (f - numpy.roll(f, 1, axis=ax)) / dxyz_b[ax]
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else:
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def dh(f, ax):
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return f - numpy.roll(f, 1, axis=ax)
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def ch_fun(h: field_t) -> field_t:
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e = [dh(h[2], 1) - dh(h[1], 2),
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dh(h[0], 2) - dh(h[2], 0),
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dh(h[1], 0) - dh(h[0], 1)]
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return e
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return ch_fun
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def curl_e(dxes: dx_lists_t = None) -> functional_matrix:
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"""
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Curl operator for use with the E field.
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:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header
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:return: Function for taking the discretized curl of the E-field, F(E) -> curlE
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"""
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if dxes is not None:
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dxyz_a = numpy.meshgrid(*dxes[0], indexing='ij')
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def de(f, ax):
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return (numpy.roll(f, -1, axis=ax) - f) / dxyz_a[ax]
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else:
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def de(f, ax):
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return numpy.roll(f, -1, axis=ax) - f
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def ce_fun(e: field_t) -> field_t:
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h = [de(e[2], 1) - de(e[1], 2),
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de(e[0], 2) - de(e[2], 0),
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de(e[1], 0) - de(e[0], 1)]
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return h
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return ce_fun
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def maxwell_e(dt: float, dxes: dx_lists_t = None) -> functional_matrix:
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curl_h_fun = curl_h(dxes)
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def me_fun(e: field_t, h: field_t, epsilon: field_t):
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ch = curl_h_fun(h)
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for ei, ci, epsi in zip(e, ch, epsilon):
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ei += dt * ci / epsi
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return e
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return me_fun
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def maxwell_h(dt: float, dxes: dx_lists_t = None) -> functional_matrix:
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curl_e_fun = curl_e(dxes)
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def mh_fun(e: field_t, h: field_t):
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ce = curl_e_fun(e)
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for hi, ci in zip(h, ce):
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hi -= dt * ci
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return h
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return mh_fun
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def conducting_boundary(direction: int,
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polarity: int
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) -> Tuple[functional_matrix, functional_matrix]:
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dirs = [0, 1, 2]
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if direction not in dirs:
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raise Exception('Invalid direction: {}'.format(direction))
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dirs.remove(direction)
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u, v = dirs
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if polarity < 0:
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boundary_slice = [slice(None)] * 3
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shifted1_slice = [slice(None)] * 3
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boundary_slice[direction] = 0
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shifted1_slice[direction] = 1
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def en(e: field_t):
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e[direction][boundary_slice] = 0
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e[u][boundary_slice] = e[u][shifted1_slice]
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e[v][boundary_slice] = e[v][shifted1_slice]
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return e
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def hn(h: field_t):
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h[direction][boundary_slice] = h[direction][shifted1_slice]
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h[u][boundary_slice] = 0
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h[v][boundary_slice] = 0
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return h
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return en, hn
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elif polarity > 0:
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boundary_slice = [slice(None)] * 3
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shifted1_slice = [slice(None)] * 3
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shifted2_slice = [slice(None)] * 3
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boundary_slice[direction] = -1
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shifted1_slice[direction] = -2
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shifted2_slice[direction] = -3
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def ep(e: field_t):
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e[direction][boundary_slice] = -e[direction][shifted2_slice]
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e[direction][shifted1_slice] = 0
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e[u][boundary_slice] = e[u][shifted1_slice]
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e[v][boundary_slice] = e[v][shifted1_slice]
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return e
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def hp(h: field_t):
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h[direction][boundary_slice] = h[direction][shifted1_slice]
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h[u][boundary_slice] = -h[u][shifted2_slice]
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h[u][shifted1_slice] = 0
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h[v][boundary_slice] = -h[v][shifted2_slice]
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h[v][shifted1_slice] = 0
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return h
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return ep, hp
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else:
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raise Exception('Bad polarity: {}'.format(polarity))
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def cpml(direction:int,
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polarity: int,
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dt: float,
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epsilon: field_t,
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thickness: int = 8,
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epsilon_eff: float = 1,
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dtype: numpy.dtype = numpy.float32,
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) -> Tuple[Callable, Callable, Dict[str, field_t]]:
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if direction not in range(3):
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raise Exception('Invalid direction: {}'.format(direction))
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if polarity not in (-1, 1):
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raise Exception('Invalid polarity: {}'.format(polarity))
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if thickness <= 2:
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raise Exception('It would be wise to have a pml with 4+ cells of thickness')
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if epsilon_eff <= 0:
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raise Exception('epsilon_eff must be positive')
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m = (3.5, 1)
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sigma_max = 0.8 * (m[0] + 1) / numpy.sqrt(epsilon_eff)
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alpha_max = 0 # TODO: Decide what to do about non-zero alpha
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transverse = numpy.delete(range(3), direction)
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u, v = transverse
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xe = numpy.arange(1, thickness+1, dtype=float)
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xh = numpy.arange(1, thickness+1, dtype=float)
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if polarity > 0:
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xe -= 0.5
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elif polarity < 0:
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xh -= 0.5
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xe = xe[::-1]
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xh = xh[::-1]
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else:
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raise Exception('Bad polarity!')
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expand_slice = [None] * 3
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expand_slice[direction] = slice(None)
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def par(x):
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sigma = ((x / thickness) ** m[0]) * sigma_max
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alpha = ((1 - x / thickness) ** m[1]) * alpha_max
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p0 = numpy.exp(-(sigma + alpha) * dt)
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p1 = sigma / (sigma + alpha) * (p0 - 1)
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return p0[expand_slice], p1[expand_slice]
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p0e, p1e = par(xe)
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p0h, p1h = par(xh)
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region = [slice(None)] * 3
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if polarity < 0:
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region[direction] = slice(None, thickness)
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elif polarity > 0:
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region[direction] = slice(-thickness, None)
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else:
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raise Exception('Bad polarity!')
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if direction == 1:
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se = 1
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else:
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se = -1
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# TODO check if epsilon is uniform?
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shape = list(epsilon[0].shape)
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shape[direction] = thickness
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psi_e = [numpy.zeros(shape, dtype=dtype), numpy.zeros(shape, dtype=dtype)]
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psi_h = [numpy.zeros(shape, dtype=dtype), numpy.zeros(shape, dtype=dtype)]
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fields = {
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'psi_e_u': psi_e[0],
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'psi_e_v': psi_e[1],
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'psi_h_u': psi_h[0],
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'psi_h_v': psi_h[1],
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}
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def pml_e(e: field_t, h: field_t, epsilon: field_t) -> Tuple[field_t, field_t]:
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psi_e[0] *= p0e
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psi_e[0] += p1e * (h[v][region] - numpy.roll(h[v], 1, axis=direction)[region])
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psi_e[1] *= p0e
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psi_e[1] += p1e * (h[u][region] - numpy.roll(h[u], 1, axis=direction)[region])
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e[u][region] += se * dt * psi_e[0] / epsilon[u][region]
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e[v][region] -= se * dt * psi_e[1] / epsilon[v][region]
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return e, h
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def pml_h(e: field_t, h: field_t) -> Tuple[field_t, field_t]:
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psi_h[0] *= p0h
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psi_h[0] += p1h * (numpy.roll(e[v], -1, axis=direction)[region] - e[v][region])
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psi_h[1] *= p0h
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psi_h[1] += p1h * (numpy.roll(e[u], -1, axis=direction)[region] - e[u][region])
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h[u][region] -= se * dt * psi_h[0]
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h[v][region] += se * dt * psi_h[1]
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return e, h
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return pml_e, pml_h, fields
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