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README.md
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# fdfd_tools # meanas
**fdfd_tools** is a python package containing utilities for **meanas** is a python package for electromagnetic simulations
creating and analyzing 2D and 3D finite-difference frequency-domain (FDFD)
electromagnetic simulations. This package is intended for building simulation inputs, analyzing
simulation outputs, and running short simulations on unspecialized hardware.
It is designed to provide tooling and a baseline for other, high-performance
purpose- and hardware-specific solvers.
**Contents** **Contents**
* Library of sparse matrices for representing the electromagnetic wave - Finite difference frequency domain (FDFD)
equation in 3D, as well as auxiliary matrices for conversion between fields * Library of sparse matrices for representing the electromagnetic wave
* Waveguide mode solver and waveguide mode operators equation in 3D, as well as auxiliary matrices for conversion between fields
* Stretched-coordinate PML boundaries (SCPML) * Waveguide mode operators
* Functional versions of most operators * Waveguide mode eigensolver
* Anisotropic media (eps_xx, eps_yy, eps_zz, mu_xx, ...) * Stretched-coordinate PML boundaries (SCPML)
* Arbitrary distributions of perfect electric and magnetic conductors (PEC / PMC) * Functional versions of most operators
* Anisotropic media (limited to diagonal elements eps_xx, eps_yy, eps_zz, mu_xx, ...)
* Arbitrary distributions of perfect electric and magnetic conductors (PEC / PMC)
- Finite difference time domain (FDTD)
* Basic Maxwell time-steps
* Poynting vector and energy calculation
* Convolutional PMLs
This package does *not* provide a fast matrix solver, though by default This package does *not* provide a fast matrix solver, though by default
```fdfd_tools.solvers.generic(...)``` will call `meanas.fdfd.solvers.generic(...)` will call
```scipy.sparse.linalg.qmr(...)``` to perform a solve. `scipy.sparse.linalg.qmr(...)` to perform a solve.
For 2D problems this should be fine; likewise, the waveguide mode For 2D FDFD problems this should be fine; likewise, the waveguide mode
solver uses scipy's eigenvalue solver, with reasonable results. solver uses scipy's eigenvalue solver, with reasonable results.
For solving large (or 3D) problems, I recommend a GPU-based iterative For solving large (or 3D) FDFD problems, I recommend a GPU-based iterative
solver, such as [opencl_fdfd](https://mpxd.net/gogs/jan/opencl_fdfd) or solver, such as [opencl_fdfd](https://mpxd.net/code/jan/opencl_fdfd) or
those included in [MAGMA](http://icl.cs.utk.edu/magma/index.html)). Your those included in [MAGMA](http://icl.cs.utk.edu/magma/index.html)). Your
solver will need the ability to solve complex symmetric (non-Hermitian) solver will need the ability to solve complex symmetric (non-Hermitian)
linear systems, ideally with double precision. linear systems, ideally with double precision.
## Installation ## Installation
**Requirements:** **Requirements:**
* python 3 (written and tested with 3.5) * python 3 (tests require 3.7)
* numpy * numpy
* scipy * scipy
Install with pip, via git: Install with pip, via git:
```bash ```bash
pip install git+https://mpxd.net/gogs/jan/fdfd_tools.git@release pip install git+https://mpxd.net/code/jan/meanas.git@release
``` ```
## Use ## Use
See examples/test.py for some simple examples; you may need additional See `examples/` for some simple examples; you may need additional
packages such as [gridlock](https://mpxd.net/gogs/jan/gridlock) packages such as [gridlock](https://mpxd.net/code/jan/gridlock)
to run the examples. to run the examples.

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fdfd_tools/__init__.py
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"""
Electromagnetic FDFD simulation tools
Tools for 3D and 2D Electromagnetic Finite Difference Frequency Domain (FDFD)
simulations. These tools handle conversion of fields to/from vector form,
creation of the wave operator matrix, stretched-coordinate PMLs, PECs and PMCs,
field conversion operators, waveguide mode operator, and waveguide mode
solver.
This package only contains a solver for the waveguide mode eigenproblem;
if you want to solve 3D problems you can use your favorite iterative sparse
matrix solver (so long as it can handle complex symmetric [non-Hermitian]
matrices, ideally with double precision).
Dependencies:
- numpy
- scipy
"""
from .vectorization import vec, unvec, field_t, vfield_t
from .grid import dx_lists_t
__author__ = 'Jan Petykiewicz'
version = '0.5'

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fdfd_tools/fdtd.py
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from typing import List, Callable, Tuple, Dict
import numpy
from . import dx_lists_t, field_t
#TODO fix pmls
__author__ = 'Jan Petykiewicz'
functional_matrix = Callable[[field_t], field_t]
def curl_h(dxes: dx_lists_t = None) -> functional_matrix:
"""
Curl operator for use with the H field.
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header
:return: Function for taking the discretized curl of the H-field, F(H) -> curlH
"""
if dxes:
dxyz_b = numpy.meshgrid(*dxes[1], indexing='ij')
def dh(f, ax):
return (f - numpy.roll(f, 1, axis=ax)) / dxyz_b[ax]
else:
def dh(f, ax):
return f - numpy.roll(f, 1, axis=ax)
def ch_fun(h: field_t) -> field_t:
output = numpy.empty_like(h)
output[0] = dh(h[2], 1)
output[1] = dh(h[0], 2)
output[2] = dh(h[1], 0)
output[0] -= dh(h[1], 2)
output[1] -= dh(h[2], 0)
output[2] -= dh(h[0], 1)
return output
return ch_fun
def curl_e(dxes: dx_lists_t = None) -> functional_matrix:
"""
Curl operator for use with the E field.
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header
:return: Function for taking the discretized curl of the E-field, F(E) -> curlE
"""
if dxes is not None:
dxyz_a = numpy.meshgrid(*dxes[0], indexing='ij')
def de(f, ax):
return (numpy.roll(f, -1, axis=ax) - f) / dxyz_a[ax]
else:
def de(f, ax):
return numpy.roll(f, -1, axis=ax) - f
def ce_fun(e: field_t) -> field_t:
output = numpy.empty_like(e)
output[0] = de(e[2], 1)
output[1] = de(e[0], 2)
output[2] = de(e[1], 0)
output[0] -= de(e[1], 2)
output[1] -= de(e[2], 0)
output[2] -= de(e[0], 1)
return output
return ce_fun
def maxwell_e(dt: float, dxes: dx_lists_t = None) -> functional_matrix:
curl_h_fun = curl_h(dxes)
def me_fun(e: field_t, h: field_t, epsilon: field_t):
e += dt * curl_h_fun(h) / epsilon
return e
return me_fun
def maxwell_h(dt: float, dxes: dx_lists_t = None) -> functional_matrix:
curl_e_fun = curl_e(dxes)
def mh_fun(e: field_t, h: field_t):
h -= dt * curl_e_fun(e)
return h
return mh_fun
def conducting_boundary(direction: int,
polarity: int
) -> Tuple[functional_matrix, functional_matrix]:
dirs = [0, 1, 2]
if direction not in dirs:
raise Exception('Invalid direction: {}'.format(direction))
dirs.remove(direction)
u, v = dirs
if polarity < 0:
boundary_slice = [slice(None)] * 3
shifted1_slice = [slice(None)] * 3
boundary_slice[direction] = 0
shifted1_slice[direction] = 1
def en(e: field_t):
e[direction][boundary_slice] = 0
e[u][boundary_slice] = e[u][shifted1_slice]
e[v][boundary_slice] = e[v][shifted1_slice]
return e
def hn(h: field_t):
h[direction][boundary_slice] = h[direction][shifted1_slice]
h[u][boundary_slice] = 0
h[v][boundary_slice] = 0
return h
return en, hn
elif polarity > 0:
boundary_slice = [slice(None)] * 3
shifted1_slice = [slice(None)] * 3
shifted2_slice = [slice(None)] * 3
boundary_slice[direction] = -1
shifted1_slice[direction] = -2
shifted2_slice[direction] = -3
def ep(e: field_t):
e[direction][boundary_slice] = -e[direction][shifted2_slice]
e[direction][shifted1_slice] = 0
e[u][boundary_slice] = e[u][shifted1_slice]
e[v][boundary_slice] = e[v][shifted1_slice]
return e
def hp(h: field_t):
h[direction][boundary_slice] = h[direction][shifted1_slice]
h[u][boundary_slice] = -h[u][shifted2_slice]
h[u][shifted1_slice] = 0
h[v][boundary_slice] = -h[v][shifted2_slice]
h[v][shifted1_slice] = 0
return h
return ep, hp
else:
raise Exception('Bad polarity: {}'.format(polarity))
def cpml(direction:int,
polarity: int,
dt: float,
epsilon: field_t,
thickness: int = 8,
ln_R_per_layer: float = -1.6,
epsilon_eff: float = 1,
mu_eff: float = 1,
m: float = 3.5,
ma: float = 1,
cfs_alpha: float = 0,
dtype: numpy.dtype = numpy.float32,
) -> Tuple[Callable, Callable, Dict[str, field_t]]:
if direction not in range(3):
raise Exception('Invalid direction: {}'.format(direction))
if polarity not in (-1, 1):
raise Exception('Invalid polarity: {}'.format(polarity))
if thickness <= 2:
raise Exception('It would be wise to have a pml with 4+ cells of thickness')
if epsilon_eff <= 0:
raise Exception('epsilon_eff must be positive')
sigma_max = -ln_R_per_layer / 2 * (m + 1)
kappa_max = numpy.sqrt(epsilon_eff * mu_eff)
alpha_max = cfs_alpha
transverse = numpy.delete(range(3), direction)
u, v = transverse
xe = numpy.arange(1, thickness+1, dtype=float)
xh = numpy.arange(1, thickness+1, dtype=float)
if polarity > 0:
xe -= 0.5
elif polarity < 0:
xh -= 0.5
xe = xe[::-1]
xh = xh[::-1]
else:
raise Exception('Bad polarity!')
expand_slice = [None] * 3
expand_slice[direction] = slice(None)
def par(x):
scaling = (x / thickness) ** m
sigma = scaling * sigma_max
kappa = 1 + scaling * (kappa_max - 1)
alpha = ((1 - x / thickness) ** ma) * alpha_max
p0 = numpy.exp(-(sigma / kappa + alpha) * dt)
p1 = sigma / (sigma + kappa * alpha) * (p0 - 1)
p2 = 1 / kappa
return p0[expand_slice], p1[expand_slice], p2[expand_slice]
p0e, p1e, p2e = par(xe)
p0h, p1h, p2h = par(xh)
region = [slice(None)] * 3
if polarity < 0:
region[direction] = slice(None, thickness)
elif polarity > 0:
region[direction] = slice(-thickness, None)
else:
raise Exception('Bad polarity!')
se = 1 if direction == 1 else -1
# TODO check if epsilon is uniform in pml region?
shape = list(epsilon[0].shape)
shape[direction] = thickness
psi_e = [numpy.zeros(shape, dtype=dtype), numpy.zeros(shape, dtype=dtype)]
psi_h = [numpy.zeros(shape, dtype=dtype), numpy.zeros(shape, dtype=dtype)]
fields = {
'psi_e_u': psi_e[0],
'psi_e_v': psi_e[1],
'psi_h_u': psi_h[0],
'psi_h_v': psi_h[1],
}
# Note that this is kinda slow -- would be faster to reuse dHv*p2h for the original
# H update, but then you have multiple arrays and a monolithic (field + pml) update operation
def pml_e(e: field_t, h: field_t, epsilon: field_t) -> Tuple[field_t, field_t]:
dHv = h[v][region] - numpy.roll(h[v], 1, axis=direction)[region]
dHu = h[u][region] - numpy.roll(h[u], 1, axis=direction)[region]
psi_e[0] *= p0e
psi_e[0] += p1e * dHv * p2e
psi_e[1] *= p0e
psi_e[1] += p1e * dHu * p2e
e[u][region] += se * dt / epsilon[u][region] * (psi_e[0] + (p2e - 1) * dHv)
e[v][region] -= se * dt / epsilon[v][region] * (psi_e[1] + (p2e - 1) * dHu)
return e, h
def pml_h(e: field_t, h: field_t) -> Tuple[field_t, field_t]:
dEv = (numpy.roll(e[v], -1, axis=direction)[region] - e[v][region])
dEu = (numpy.roll(e[u], -1, axis=direction)[region] - e[u][region])
psi_h[0] *= p0h
psi_h[0] += p1h * dEv * p2h
psi_h[1] *= p0h
psi_h[1] += p1h * dEu * p2h
h[u][region] -= se * dt * (psi_h[0] + (p2h - 1) * dEv)
h[v][region] += se * dt * (psi_h[1] + (p2h - 1) * dEu)
return e, h
return pml_e, pml_h, fields
def poynting(e, h):
s = (numpy.roll(e[1], -1, axis=0) * h[2] - numpy.roll(e[2], -1, axis=0) * h[1],
numpy.roll(e[2], -1, axis=1) * h[0] - numpy.roll(e[0], -1, axis=1) * h[2],
numpy.roll(e[0], -1, axis=2) * h[1] - numpy.roll(e[1], -1, axis=2) * h[0])
return numpy.array(s)
def poynting_divergence(s=None, *, e=None, h=None, dxes=None): # TODO dxes
if dxes is None:
dxes = tuple(tuple(numpy.ones(1) for _ in range(3)) for _ in range(2))
if s is None:
s = poynting(e, h)
ds = ((s[0] - numpy.roll(s[0], 1, axis=0)) / numpy.sqrt(dxes[0][0] * dxes[1][0])[:, None, None] +
(s[1] - numpy.roll(s[1], 1, axis=1)) / numpy.sqrt(dxes[0][1] * dxes[1][1])[None, :, None] +
(s[2] - numpy.roll(s[2], 1, axis=2)) / numpy.sqrt(dxes[0][2] * dxes[1][2])[None, None, :] )
return ds
def energy_hstep(e0, h1, e2, epsilon=None, mu=None, dxes=None):
u = dxmul(e0 * e2, h1 * h1, epsilon, mu, dxes)
return u
def energy_estep(h0, e1, h2, epsilon=None, mu=None, dxes=None):
u = dxmul(e1 * e1, h0 * h2, epsilon, mu, dxes)
return u
def delta_energy_h2e(dt, e0, h1, e2, h3, epsilon=None, mu=None, dxes=None):
"""
This is just from (e2 * e2 + h3 * h1) - (h1 * h1 + e0 * e2)
"""
de = e2 * (e2 - e0) / dt
dh = h1 * (h3 - h1) / dt
du = dxmul(de, dh, epsilon, mu, dxes)
return du
def delta_energy_e2h(dt, h0, e1, h2, e3, epsilon=None, mu=None, dxes=None):
"""
This is just from (h2 * h2 + e3 * e1) - (e1 * e1 + h0 * h2)
"""
de = e1 * (e3 - e1) / dt
dh = h2 * (h2 - h0) / dt
du = dxmul(de, dh, epsilon, mu, dxes)
return du
def delta_energy_j(j0, e1, dxes=None):
if dxes is None:
dxes = tuple(tuple(numpy.ones(1) for _ in range(3)) for _ in range(2))
du = ((j0 * e1).sum(axis=0) *
dxes[0][0][:, None, None] *
dxes[0][1][None, :, None] *
dxes[0][2][None, None, :])
return du
def dxmul(ee, hh, epsilon=None, mu=None, dxes=None):
if epsilon is None:
epsilon = 1
if mu is None:
mu = 1
if dxes is None:
dxes = tuple(tuple(numpy.ones(1) for _ in range(3)) for _ in range(2))
result = ((ee * epsilon).sum(axis=0) *
dxes[0][0][:, None, None] *
dxes[0][1][None, :, None] *
dxes[0][2][None, None, :] +
(hh * mu).sum(axis=0) *
dxes[1][0][:, None, None] *
dxes[1][1][None, :, None] *
dxes[1][2][None, None, :])
return result

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meanas/__init__.py Normal file
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"""
Electromagnetic simulation tools
This package is intended for building simulation inputs, analyzing
simulation outputs, and running short simulations on unspecialized hardware.
It is designed to provide tooling and a baseline for other, high-performance
purpose- and hardware-specific solvers.
**Contents**
- Finite difference frequency domain (FDFD)
* Library of sparse matrices for representing the electromagnetic wave
equation in 3D, as well as auxiliary matrices for conversion between fields
* Waveguide mode operators
* Waveguide mode eigensolver
* Stretched-coordinate PML boundaries (SCPML)
* Functional versions of most operators
* Anisotropic media (limited to diagonal elements eps_xx, eps_yy, eps_zz, mu_xx, ...)
* Arbitrary distributions of perfect electric and magnetic conductors (PEC / PMC)
- Finite difference time domain (FDTD)
* Basic Maxwell time-steps
* Poynting vector and energy calculation
* Convolutional PMLs
This package does *not* provide a fast matrix solver, though by default
```meanas.fdfd.solvers.generic(...)``` will call
```scipy.sparse.linalg.qmr(...)``` to perform a solve.
For 2D FDFD problems this should be fine; likewise, the waveguide mode
solver uses scipy's eigenvalue solver, with reasonable results.
For solving large (or 3D) FDFD problems, I recommend a GPU-based iterative
solver, such as [opencl_fdfd](https://mpxd.net/code/jan/opencl_fdfd) or
those included in [MAGMA](http://icl.cs.utk.edu/magma/index.html)). Your
solver will need the ability to solve complex symmetric (non-Hermitian)
linear systems, ideally with double precision.
Dependencies:
- numpy
- scipy
"""
from .types import dx_lists_t, field_t, vfield_t, field_updater
from .vectorization import vec, unvec
__author__ = 'Jan Petykiewicz'
version = '0.5'

0
fdfd_tools/eigensolvers.py → meanas/eigensolvers.py
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0
fdfd_tools/bloch.py → meanas/fdfd/bloch.py
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0
fdfd_tools/farfield.py → meanas/fdfd/farfield.py
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16
fdfd_tools/functional.py → meanas/fdfd/functional.py
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@ -2,8 +2,8 @@
Functional versions of many FDFD operators. These can be useful for performing Functional versions of many FDFD operators. These can be useful for performing
FDFD calculations without needing to construct large matrices in memory. FDFD calculations without needing to construct large matrices in memory.
The functions generated here expect inputs in the form E = [E_x, E_y, E_z], where each The functions generated here expect field inputs with shape (3, X, Y, Z),
component E_* is an ndarray of equal shape. e.g. E = [E_x, E_y, E_z] where each component has shape (X, Y, Z)
""" """
from typing import List, Callable from typing import List, Callable
import numpy import numpy
@ -20,7 +20,7 @@ def curl_h(dxes: dx_lists_t) -> functional_matrix:
""" """
Curl operator for use with the H field. Curl operator for use with the H field.
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header :param dxes: Grid parameters [dx_e, dx_h] as described in meanas.types
:return: Function for taking the discretized curl of the H-field, F(H) -> curlH :return: Function for taking the discretized curl of the H-field, F(H) -> curlH
""" """
dxyz_b = numpy.meshgrid(*dxes[1], indexing='ij') dxyz_b = numpy.meshgrid(*dxes[1], indexing='ij')
@ -41,7 +41,7 @@ def curl_e(dxes: dx_lists_t) -> functional_matrix:
""" """
Curl operator for use with the E field. Curl operator for use with the E field.
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header :param dxes: Grid parameters [dx_e, dx_h] as described in meanas.types
:return: Function for taking the discretized curl of the E-field, F(E) -> curlE :return: Function for taking the discretized curl of the E-field, F(E) -> curlE
""" """
dxyz_a = numpy.meshgrid(*dxes[0], indexing='ij') dxyz_a = numpy.meshgrid(*dxes[0], indexing='ij')
@ -69,7 +69,7 @@ def e_full(omega: complex,
(del x (1/mu * del x) - omega**2 * epsilon) E = -i * omega * J (del x (1/mu * del x) - omega**2 * epsilon) E = -i * omega * J
:param omega: Angular frequency of the simulation :param omega: Angular frequency of the simulation
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header :param dxes: Grid parameters [dx_e, dx_h] as described in meanas.types
:param epsilon: Dielectric constant :param epsilon: Dielectric constant
:param mu: Magnetic permeability (default 1 everywhere) :param mu: Magnetic permeability (default 1 everywhere)
:return: Function implementing the wave operator A(E) -> E :return: Function implementing the wave operator A(E) -> E
@ -100,7 +100,7 @@ def eh_full(omega: complex,
Wave operator for full (both E and H) field representation. Wave operator for full (both E and H) field representation.
:param omega: Angular frequency of the simulation :param omega: Angular frequency of the simulation
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header :param dxes: Grid parameters [dx_e, dx_h] as described in meanas.types
:param epsilon: Dielectric constant :param epsilon: Dielectric constant
:param mu: Magnetic permeability (default 1 everywhere) :param mu: Magnetic permeability (default 1 everywhere)
:return: Function implementing the wave operator A(E, H) -> (E, H) :return: Function implementing the wave operator A(E, H) -> (E, H)
@ -131,7 +131,7 @@ def e2h(omega: complex,
For use with e_full -- assumes that there is no magnetic current M. For use with e_full -- assumes that there is no magnetic current M.
:param omega: Angular frequency of the simulation :param omega: Angular frequency of the simulation
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header :param dxes: Grid parameters [dx_e, dx_h] as described in meanas.types
:param mu: Magnetic permeability (default 1 everywhere) :param mu: Magnetic permeability (default 1 everywhere)
:return: Function for converting E to H :return: Function for converting E to H
""" """
@ -159,7 +159,7 @@ def m2j(omega: complex,
For use with e.g. e_full(). For use with e.g. e_full().
:param omega: Angular frequency of the simulation :param omega: Angular frequency of the simulation
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header :param dxes: Grid parameters [dx_e, dx_h] as described in meanas.types
:param mu: Magnetic permeability (default 1 everywhere) :param mu: Magnetic permeability (default 1 everywhere)
:return: Function for converting M to J :return: Function for converting M to J
""" """

30
fdfd_tools/operators.py → meanas/fdfd/operators.py
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@ -3,17 +3,13 @@ Sparse matrix operators for use with electromagnetic wave equations.
These functions return sparse-matrix (scipy.sparse.spmatrix) representations of These functions return sparse-matrix (scipy.sparse.spmatrix) representations of
a variety of operators, intended for use with E and H fields vectorized using the a variety of operators, intended for use with E and H fields vectorized using the
fdfd_tools.vec() and .unvec() functions (column-major/Fortran ordering). meanas.vec() and .unvec() functions (column-major/Fortran ordering).
E- and H-field values are defined on a Yee cell; epsilon values should be calculated for E- and H-field values are defined on a Yee cell; epsilon values should be calculated for
cells centered at each E component (mu at each H component). cells centered at each E component (mu at each H component).
Many of these functions require a 'dxes' parameter, of type fdfd_tools.dx_lists_type, Many of these functions require a 'dxes' parameter, of type meanas.dx_lists_type; see
which contains grid cell width information in the following format: the meanas.types submodule for details.
[[[dx_e_0, dx_e_1, ...], [dy_e_0, ...], [dz_e_0, ...]],
[[dx_h_0, dx_h_1, ...], [dy_h_0, ...], [dz_h_0, ...]]]
where dx_e_0 is the x-width of the x=0 cells, as used when calculating dE/dx,
and dy_h_0 is the y-width of the y=0 cells, as used when calculating dH/dy, etc.
The following operators are included: The following operators are included:
@ -57,7 +53,7 @@ def e_full(omega: complex,
To make this matrix symmetric, use the preconditions from e_full_preconditioners(). To make this matrix symmetric, use the preconditions from e_full_preconditioners().
:param omega: Angular frequency of the simulation :param omega: Angular frequency of the simulation
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header :param dxes: Grid parameters [dx_e, dx_h] as described in meanas.types
:param epsilon: Vectorized dielectric constant :param epsilon: Vectorized dielectric constant
:param mu: Vectorized magnetic permeability (default 1 everywhere). :param mu: Vectorized magnetic permeability (default 1 everywhere).
:param pec: Vectorized mask specifying PEC cells. Any cells where pec != 0 are interpreted :param pec: Vectorized mask specifying PEC cells. Any cells where pec != 0 are interpreted
@ -101,7 +97,7 @@ def e_full_preconditioners(dxes: dx_lists_t
The preconditioner matrices are diagonal and complex, with Pr = 1 / Pl The preconditioner matrices are diagonal and complex, with Pr = 1 / Pl
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header :param dxes: Grid parameters [dx_e, dx_h] as described in meanas.types
:return: Preconditioner matrices (Pl, Pr) :return: Preconditioner matrices (Pl, Pr)
""" """
p_squared = [dxes[0][0][:, None, None] * dxes[1][1][None, :, None] * dxes[1][2][None, None, :], p_squared = [dxes[0][0][:, None, None] * dxes[1][1][None, :, None] * dxes[1][2][None, None, :],
@ -127,7 +123,7 @@ def h_full(omega: complex,
(del x (1/epsilon * del x) - omega**2 * mu) H = i * omega * M (del x (1/epsilon * del x) - omega**2 * mu) H = i * omega * M
:param omega: Angular frequency of the simulation :param omega: Angular frequency of the simulation
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header :param dxes: Grid parameters [dx_e, dx_h] as described in meanas.types
:param epsilon: Vectorized dielectric constant :param epsilon: Vectorized dielectric constant
:param mu: Vectorized magnetic permeability (default 1 everywhere) :param mu: Vectorized magnetic permeability (default 1 everywhere)
:param pec: Vectorized mask specifying PEC cells. Any cells where pec != 0 are interpreted :param pec: Vectorized mask specifying PEC cells. Any cells where pec != 0 are interpreted
@ -177,7 +173,7 @@ def eh_full(omega: complex,
for use with a field vector of the form hstack(vec(E), vec(H)). for use with a field vector of the form hstack(vec(E), vec(H)).
:param omega: Angular frequency of the simulation :param omega: Angular frequency of the simulation
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header :param dxes: Grid parameters [dx_e, dx_h] as described in meanas.types
:param epsilon: Vectorized dielectric constant :param epsilon: Vectorized dielectric constant
:param mu: Vectorized magnetic permeability (default 1 everywhere) :param mu: Vectorized magnetic permeability (default 1 everywhere)
:param pec: Vectorized mask specifying PEC cells. Any cells where pec != 0 are interpreted :param pec: Vectorized mask specifying PEC cells. Any cells where pec != 0 are interpreted
@ -216,7 +212,7 @@ def curl_h(dxes: dx_lists_t) -> sparse.spmatrix:
""" """
Curl operator for use with the H field. Curl operator for use with the H field.
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header :param dxes: Grid parameters [dx_e, dx_h] as described in meanas.types
:return: Sparse matrix for taking the discretized curl of the H-field :return: Sparse matrix for taking the discretized curl of the H-field
""" """
return cross(deriv_back(dxes[1])) return cross(deriv_back(dxes[1]))
@ -226,7 +222,7 @@ def curl_e(dxes: dx_lists_t) -> sparse.spmatrix:
""" """
Curl operator for use with the E field. Curl operator for use with the E field.
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header :param dxes: Grid parameters [dx_e, dx_h] as described in meanas.types
:return: Sparse matrix for taking the discretized curl of the E-field :return: Sparse matrix for taking the discretized curl of the E-field
""" """
return cross(deriv_forward(dxes[0])) return cross(deriv_forward(dxes[0]))
@ -242,7 +238,7 @@ def e2h(omega: complex,
For use with e_full -- assumes that there is no magnetic current M. For use with e_full -- assumes that there is no magnetic current M.
:param omega: Angular frequency of the simulation :param omega: Angular frequency of the simulation
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header :param dxes: Grid parameters [dx_e, dx_h] as described in meanas.types
:param mu: Vectorized magnetic permeability (default 1 everywhere) :param mu: Vectorized magnetic permeability (default 1 everywhere)
:param pmc: Vectorized mask specifying PMC cells. Any cells where pmc != 0 are interpreted :param pmc: Vectorized mask specifying PMC cells. Any cells where pmc != 0 are interpreted
as containing a perfect magnetic conductor (PMC). as containing a perfect magnetic conductor (PMC).
@ -270,7 +266,7 @@ def m2j(omega: complex,
For use with eg. e_full. For use with eg. e_full.
:param omega: Angular frequency of the simulation :param omega: Angular frequency of the simulation
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header :param dxes: Grid parameters [dx_e, dx_h] as described in meanas.types
:param mu: Vectorized magnetic permeability (default 1 everywhere) :param mu: Vectorized magnetic permeability (default 1 everywhere)
:return: Sparse matrix for converting E to H :return: Sparse matrix for converting E to H
""" """
@ -454,7 +450,7 @@ def poynting_e_cross(e: vfield_t, dxes: dx_lists_t) -> sparse.spmatrix:
Operator for computing the Poynting vector, containing the (E x) portion of the Poynting vector. Operator for computing the Poynting vector, containing the (E x) portion of the Poynting vector.
:param e: Vectorized E-field for the ExH cross product :param e: Vectorized E-field for the ExH cross product
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header :param dxes: Grid parameters [dx_e, dx_h] as described in meanas.types
:return: Sparse matrix containing (E x) portion of Poynting cross product :return: Sparse matrix containing (E x) portion of Poynting cross product
""" """
shape = [len(dx) for dx in dxes[0]] shape = [len(dx) for dx in dxes[0]]
@ -483,7 +479,7 @@ def poynting_h_cross(h: vfield_t, dxes: dx_lists_t) -> sparse.spmatrix:
Operator for computing the Poynting vector, containing the (H x) portion of the Poynting vector. Operator for computing the Poynting vector, containing the (H x) portion of the Poynting vector.
:param h: Vectorized H-field for the HxE cross product :param h: Vectorized H-field for the HxE cross product
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header :param dxes: Grid parameters [dx_e, dx_h] as described in meanas.types
:return: Sparse matrix containing (H x) portion of Poynting cross product :return: Sparse matrix containing (H x) portion of Poynting cross product
""" """
shape = [len(dx) for dx in dxes[0]] shape = [len(dx) for dx in dxes[0]]

1
fdfd_tools/grid.py → meanas/fdfd/scpml.py
View File

@ -8,7 +8,6 @@ import numpy
__author__ = 'Jan Petykiewicz' __author__ = 'Jan Petykiewicz'
dx_lists_t = List[List[numpy.ndarray]]
s_function_type = Callable[[float], float] s_function_type = Callable[[float], float]

2
fdfd_tools/solvers.py → meanas/fdfd/solvers.py
View File

@ -70,7 +70,7 @@ def generic(omega: complex,
""" """
Conjugate gradient FDFD solver using CSR sparse matrices. Conjugate gradient FDFD solver using CSR sparse matrices.
All ndarray arguments should be 1D array, as returned by fdfd_tools.vec(). All ndarray arguments should be 1D array, as returned by meanas.vec().
:param omega: Complex frequency to solve at. :param omega: Complex frequency to solve at.
:param dxes: [[dx_e, dy_e, dz_e], [dx_h, dy_h, dz_h]] (complex cell sizes) :param dxes: [[dx_e, dy_e, dz_e], [dx_h, dy_h, dz_h]] (complex cell sizes)

24
fdfd_tools/waveguide.py → meanas/fdfd/waveguide.py
View File

@ -51,7 +51,7 @@ def operator(omega: complex,
z-dependence is assumed for the fields). z-dependence is assumed for the fields).
:param omega: The angular frequency of the system :param omega: The angular frequency of the system
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header (2D) :param dxes: Grid parameters [dx_e, dx_h] as described in meanas.types (2D)
:param epsilon: Vectorized dielectric constant grid :param epsilon: Vectorized dielectric constant grid
:param mu: Vectorized magnetic permeability grid (default 1 everywhere) :param mu: Vectorized magnetic permeability grid (default 1 everywhere)
:return: Sparse matrix representation of the operator :return: Sparse matrix representation of the operator
@ -91,7 +91,7 @@ def normalized_fields(v: numpy.ndarray,
:param v: Vector containing H_x and H_y fields :param v: Vector containing H_x and H_y fields
:param wavenumber: Wavenumber satisfying A @ v == wavenumber**2 * v :param wavenumber: Wavenumber satisfying A @ v == wavenumber**2 * v
:param omega: The angular frequency of the system :param omega: The angular frequency of the system
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header (2D) :param dxes: Grid parameters [dx_e, dx_h] as described in meanas.types (2D)
:param epsilon: Vectorized dielectric constant grid :param epsilon: Vectorized dielectric constant grid
:param mu: Vectorized magnetic permeability grid (default 1 everywhere) :param mu: Vectorized magnetic permeability grid (default 1 everywhere)
:return: Normalized, vectorized (e, h) containing all vector components. :return: Normalized, vectorized (e, h) containing all vector components.
@ -120,6 +120,8 @@ def normalized_fields(v: numpy.ndarray,
# Try to break symmetry to assign a consistent sign [experimental] # Try to break symmetry to assign a consistent sign [experimental]
E_weighted = unvec(e * energy * numpy.exp(1j * norm_angle), shape) E_weighted = unvec(e * energy * numpy.exp(1j * norm_angle), shape)
sign = numpy.sign(E_weighted[:, :max(shape[0]//2, 1), :max(shape[1]//2, 1)].real.sum()) sign = numpy.sign(E_weighted[:, :max(shape[0]//2, 1), :max(shape[1]//2, 1)].real.sum())
logger.debug('norm_angle = {}'.format(norm_angle))
logger.debug('norm_sign = {}'.format(sign)
norm_factor = sign * norm_amplitude * numpy.exp(1j * norm_angle) norm_factor = sign * norm_amplitude * numpy.exp(1j * norm_angle)
@ -140,7 +142,7 @@ def v2h(v: numpy.ndarray,
:param v: Vector containing H_x and H_y fields :param v: Vector containing H_x and H_y fields
:param wavenumber: Wavenumber satisfying A @ v == wavenumber**2 * v :param wavenumber: Wavenumber satisfying A @ v == wavenumber**2 * v
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header (2D) :param dxes: Grid parameters [dx_e, dx_h] as described in meanas.types (2D)
:param mu: Vectorized magnetic permeability grid (default 1 everywhere) :param mu: Vectorized magnetic permeability grid (default 1 everywhere)
:return: Vectorized H field with all vector components :return: Vectorized H field with all vector components
""" """
@ -172,7 +174,7 @@ def v2e(v: numpy.ndarray,
:param v: Vector containing H_x and H_y fields :param v: Vector containing H_x and H_y fields
:param wavenumber: Wavenumber satisfying A @ v == wavenumber**2 * v :param wavenumber: Wavenumber satisfying A @ v == wavenumber**2 * v
:param omega: The angular frequency of the system :param omega: The angular frequency of the system
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header (2D) :param dxes: Grid parameters [dx_e, dx_h] as described in meanas.types (2D)
:param epsilon: Vectorized dielectric constant grid :param epsilon: Vectorized dielectric constant grid
:param mu: Vectorized magnetic permeability grid (default 1 everywhere) :param mu: Vectorized magnetic permeability grid (default 1 everywhere)
:return: Vectorized E field with all vector components. :return: Vectorized E field with all vector components.
@ -192,7 +194,7 @@ def e2h(wavenumber: complex,
:param wavenumber: Wavenumber satisfying A @ v == wavenumber**2 * v :param wavenumber: Wavenumber satisfying A @ v == wavenumber**2 * v
:param omega: The angular frequency of the system :param omega: The angular frequency of the system
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header (2D) :param dxes: Grid parameters [dx_e, dx_h] as described in meanas.types (2D)
:param mu: Vectorized magnetic permeability grid (default 1 everywhere) :param mu: Vectorized magnetic permeability grid (default 1 everywhere)
:return: Sparse matrix representation of the operator :return: Sparse matrix representation of the operator
""" """
@ -213,7 +215,7 @@ def h2e(wavenumber: complex,
:param wavenumber: Wavenumber satisfying A @ v == wavenumber**2 * v :param wavenumber: Wavenumber satisfying A @ v == wavenumber**2 * v
:param omega: The angular frequency of the system :param omega: The angular frequency of the system
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header (2D) :param dxes: Grid parameters [dx_e, dx_h] as described in meanas.types (2D)
:param epsilon: Vectorized dielectric constant grid :param epsilon: Vectorized dielectric constant grid
:return: Sparse matrix representation of the operator :return: Sparse matrix representation of the operator
""" """
@ -226,7 +228,7 @@ def curl_e(wavenumber: complex, dxes: dx_lists_t) -> sparse.spmatrix:
Discretized curl operator for use with the waveguide E field. Discretized curl operator for use with the waveguide E field.
:param wavenumber: Wavenumber satisfying A @ v == wavenumber**2 * v :param wavenumber: Wavenumber satisfying A @ v == wavenumber**2 * v
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header (2D) :param dxes: Grid parameters [dx_e, dx_h] as described in meanas.types (2D)
:return: Sparse matrix representation of the operator :return: Sparse matrix representation of the operator
""" """
n = 1 n = 1
@ -243,7 +245,7 @@ def curl_h(wavenumber: complex, dxes: dx_lists_t) -> sparse.spmatrix:
Discretized curl operator for use with the waveguide H field. Discretized curl operator for use with the waveguide H field.
:param wavenumber: Wavenumber satisfying A @ v == wavenumber**2 * v :param wavenumber: Wavenumber satisfying A @ v == wavenumber**2 * v
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header (2D) :param dxes: Grid parameters [dx_e, dx_h] as described in meanas.types (2D)
:return: Sparse matrix representation of the operator :return: Sparse matrix representation of the operator
""" """
n = 1 n = 1
@ -268,7 +270,7 @@ def h_err(h: vfield_t,
:param h: Vectorized H field :param h: Vectorized H field
:param wavenumber: Wavenumber satisfying A @ v == wavenumber**2 * v :param wavenumber: Wavenumber satisfying A @ v == wavenumber**2 * v
:param omega: The angular frequency of the system :param omega: The angular frequency of the system
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header (2D) :param dxes: Grid parameters [dx_e, dx_h] as described in meanas.types (2D)
:param epsilon: Vectorized dielectric constant grid :param epsilon: Vectorized dielectric constant grid
:param mu: Vectorized magnetic permeability grid (default 1 everywhere) :param mu: Vectorized magnetic permeability grid (default 1 everywhere)
:return: Relative error norm(OP @ h) / norm(h) :return: Relative error norm(OP @ h) / norm(h)
@ -299,7 +301,7 @@ def e_err(e: vfield_t,
:param e: Vectorized E field :param e: Vectorized E field
:param wavenumber: Wavenumber satisfying A @ v == wavenumber**2 * v :param wavenumber: Wavenumber satisfying A @ v == wavenumber**2 * v
:param omega: The angular frequency of the system :param omega: The angular frequency of the system
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header (2D) :param dxes: Grid parameters [dx_e, dx_h] as described in meanas.types (2D)
:param epsilon: Vectorized dielectric constant grid :param epsilon: Vectorized dielectric constant grid
:param mu: Vectorized magnetic permeability grid (default 1 everywhere) :param mu: Vectorized magnetic permeability grid (default 1 everywhere)
:return: Relative error norm(OP @ e) / norm(e) :return: Relative error norm(OP @ e) / norm(e)
@ -335,7 +337,7 @@ def cylindrical_operator(omega: complex,
theta-dependence is assumed for the fields). theta-dependence is assumed for the fields).
:param omega: The angular frequency of the system :param omega: The angular frequency of the system
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header (2D) :param dxes: Grid parameters [dx_e, dx_h] as described in meanas.types (2D)
:param epsilon: Vectorized dielectric constant grid :param epsilon: Vectorized dielectric constant grid
:param r0: Radius of curvature for the simulation. This should be the minimum value of :param r0: Radius of curvature for the simulation. This should be the minimum value of
r within the simulation domain. r within the simulation domain.

10
fdfd_tools/waveguide_mode.py → meanas/fdfd/waveguide_mode.py
View File

@ -19,7 +19,7 @@ def solve_waveguide_mode_2d(mode_number: int,
:param mode_number: Number of the mode, 0-indexed. :param mode_number: Number of the mode, 0-indexed.
:param omega: Angular frequency of the simulation :param omega: Angular frequency of the simulation
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header :param dxes: Grid parameters [dx_e, dx_h] as described in meanas.types
:param epsilon: Dielectric constant :param epsilon: Dielectric constant
:param mu: Magnetic permeability (default 1 everywhere) :param mu: Magnetic permeability (default 1 everywhere)
:param wavenumber_correction: Whether to correct the wavenumber to :param wavenumber_correction: Whether to correct the wavenumber to
@ -87,7 +87,7 @@ def solve_waveguide_mode(mode_number: int,
:param mode_number: Number of the mode, 0-indexed :param mode_number: Number of the mode, 0-indexed
:param omega: Angular frequency of the simulation :param omega: Angular frequency of the simulation
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header :param dxes: Grid parameters [dx_e, dx_h] as described in meanas.types
:param axis: Propagation axis (0=x, 1=y, 2=z) :param axis: Propagation axis (0=x, 1=y, 2=z)
:param polarity: Propagation direction (+1 for +ve, -1 for -ve) :param polarity: Propagation direction (+1 for +ve, -1 for -ve)
:param slices: epsilon[tuple(slices)] is used to select the portion of the grid to use :param slices: epsilon[tuple(slices)] is used to select the portion of the grid to use
@ -167,7 +167,7 @@ def compute_source(E: field_t,
:param H: H-field of the mode (advanced by half of a Yee cell from E) :param H: H-field of the mode (advanced by half of a Yee cell from E)
:param wavenumber: Wavenumber of the mode :param wavenumber: Wavenumber of the mode
:param omega: Angular frequency of the simulation :param omega: Angular frequency of the simulation
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header :param dxes: Grid parameters [dx_e, dx_h] as described in meanas.types
:param axis: Propagation axis (0=x, 1=y, 2=z) :param axis: Propagation axis (0=x, 1=y, 2=z)
:param polarity: Propagation direction (+1 for +ve, -1 for -ve) :param polarity: Propagation direction (+1 for +ve, -1 for -ve)
:param slices: epsilon[tuple(slices)] is used to select the portion of the grid to use :param slices: epsilon[tuple(slices)] is used to select the portion of the grid to use
@ -219,7 +219,7 @@ def compute_overlap_e(E: field_t,
:param H: H-field of the mode (advanced by half of a Yee cell from E) :param H: H-field of the mode (advanced by half of a Yee cell from E)
:param wavenumber: Wavenumber of the mode :param wavenumber: Wavenumber of the mode
:param omega: Angular frequency of the simulation :param omega: Angular frequency of the simulation
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header :param dxes: Grid parameters [dx_e, dx_h] as described in meanas.types
:param axis: Propagation axis (0=x, 1=y, 2=z) :param axis: Propagation axis (0=x, 1=y, 2=z)
:param polarity: Propagation direction (+1 for +ve, -1 for -ve) :param polarity: Propagation direction (+1 for +ve, -1 for -ve)
:param slices: epsilon[tuple(slices)] is used to select the portion of the grid to use :param slices: epsilon[tuple(slices)] is used to select the portion of the grid to use
@ -283,7 +283,7 @@ def solve_waveguide_mode_cylindrical(mode_number: int,
:param mode_number: Number of the mode, 0-indexed :param mode_number: Number of the mode, 0-indexed
:param omega: Angular frequency of the simulation :param omega: Angular frequency of the simulation
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header. :param dxes: Grid parameters [dx_e, dx_h] as described in meanas.types.
The first coordinate is assumed to be r, the second is y. The first coordinate is assumed to be r, the second is y.
:param epsilon: Dielectric constant :param epsilon: Dielectric constant
:param r0: Radius of curvature for the simulation. This should be the minimum value of :param r0: Radius of curvature for the simulation. This should be the minimum value of

9
meanas/fdtd/__init__.py Normal file
View File

@ -0,0 +1,9 @@
"""
Basic FDTD functionality
"""
from .base import maxwell_e, maxwell_h
from .pml import cpml
from .energy import (poynting, poynting_divergence, energy_hstep, energy_estep,
delta_energy_h2e, delta_energy_h2e, delta_energy_j)
from .boundaries import conducting_boundary

87
meanas/fdtd/base.py Normal file
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@ -0,0 +1,87 @@
"""
Basic FDTD field updates
"""
from typing import List, Callable, Tuple, Dict
import numpy
from .. import dx_lists_t, field_t, field_updater
__author__ = 'Jan Petykiewicz'
def curl_h(dxes: dx_lists_t = None) -> field_updater:
"""
Curl operator for use with the H field.
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header
:return: Function for taking the discretized curl of the H-field, F(H) -> curlH
"""
if dxes:
dxyz_b = numpy.meshgrid(*dxes[1], indexing='ij')
def dh(f, ax):
return (f - numpy.roll(f, 1, axis=ax)) / dxyz_b[ax]
else:
def dh(f, ax):
return f - numpy.roll(f, 1, axis=ax)
def ch_fun(h: field_t) -> field_t:
output = numpy.empty_like(h)
output[0] = dh(h[2], 1)
output[1] = dh(h[0], 2)
output[2] = dh(h[1], 0)
output[0] -= dh(h[1], 2)
output[1] -= dh(h[2], 0)
output[2] -= dh(h[0], 1)
return output
return ch_fun
def curl_e(dxes: dx_lists_t = None) -> field_updater:
"""
Curl operator for use with the E field.
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header
:return: Function for taking the discretized curl of the E-field, F(E) -> curlE
"""
if dxes is not None:
dxyz_a = numpy.meshgrid(*dxes[0], indexing='ij')
def de(f, ax):
return (numpy.roll(f, -1, axis=ax) - f) / dxyz_a[ax]
else:
def de(f, ax):
return numpy.roll(f, -1, axis=ax) - f
def ce_fun(e: field_t) -> field_t:
output = numpy.empty_like(e)
output[0] = de(e[2], 1)
output[1] = de(e[0], 2)
output[2] = de(e[1], 0)
output[0] -= de(e[1], 2)
output[1] -= de(e[2], 0)
output[2] -= de(e[0], 1)
return output
return ce_fun
def maxwell_e(dt: float, dxes: dx_lists_t = None) -> field_updater:
curl_h_fun = curl_h(dxes)
def me_fun(e: field_t, h: field_t, epsilon: field_t):
e += dt * curl_h_fun(h) / epsilon
return e
return me_fun
def maxwell_h(dt: float, dxes: dx_lists_t = None) -> field_updater:
curl_e_fun = curl_e(dxes)
def mh_fun(e: field_t, h: field_t):
h -= dt * curl_e_fun(e)
return h
return mh_fun

68
meanas/fdtd/boundaries.py Normal file
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@ -0,0 +1,68 @@
"""
Boundary conditions
"""
from typing import List, Callable, Tuple, Dict
import numpy
from .. import dx_lists_t, field_t, field_updater
def conducting_boundary(direction: int,
polarity: int
) -> Tuple[field_updater, field_updater]:
dirs = [0, 1, 2]
if direction not in dirs:
raise Exception('Invalid direction: {}'.format(direction))
dirs.remove(direction)
u, v = dirs
if polarity < 0:
boundary_slice = [slice(None)] * 3
shifted1_slice = [slice(None)] * 3
boundary_slice[direction] = 0
shifted1_slice[direction] = 1
def en(e: field_t):
e[direction][boundary_slice] = 0
e[u][boundary_slice] = e[u][shifted1_slice]
e[v][boundary_slice] = e[v][shifted1_slice]
return e
def hn(h: field_t):
h[direction][boundary_slice] = h[direction][shifted1_slice]
h[u][boundary_slice] = 0
h[v][boundary_slice] = 0
return h
return en, hn
elif polarity > 0:
boundary_slice = [slice(None)] * 3
shifted1_slice = [slice(None)] * 3
shifted2_slice = [slice(None)] * 3
boundary_slice[direction] = -1
shifted1_slice[direction] = -2
shifted2_slice[direction] = -3
def ep(e: field_t):
e[direction][boundary_slice] = -e[direction][shifted2_slice]
e[direction][shifted1_slice] = 0
e[u][boundary_slice] = e[u][shifted1_slice]
e[v][boundary_slice] = e[v][shifted1_slice]
return e
def hp(h: field_t):
h[direction][boundary_slice] = h[direction][shifted1_slice]
h[u][boundary_slice] = -h[u][shifted2_slice]
h[u][shifted1_slice] = 0
h[v][boundary_slice] = -h[v][shifted2_slice]
h[v][shifted1_slice] = 0
return h
return ep, hp
else:
raise Exception('Bad polarity: {}'.format(polarity))

84
meanas/fdtd/energy.py Normal file
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@ -0,0 +1,84 @@
from typing import List, Callable, Tuple, Dict
import numpy
from .. import dx_lists_t, field_t, field_updater
def poynting(e, h):
s = (numpy.roll(e[1], -1, axis=0) * h[2] - numpy.roll(e[2], -1, axis=0) * h[1],
numpy.roll(e[2], -1, axis=1) * h[0] - numpy.roll(e[0], -1, axis=1) * h[2],
numpy.roll(e[0], -1, axis=2) * h[1] - numpy.roll(e[1], -1, axis=2) * h[0])
return numpy.array(s)
def poynting_divergence(s=None, *, e=None, h=None, dxes=None): # TODO dxes
if dxes is None:
dxes = tuple(tuple(numpy.ones(1) for _ in range(3)) for _ in range(2))
if s is None:
s = poynting(e, h)
ds = ((s[0] - numpy.roll(s[0], 1, axis=0)) / numpy.sqrt(dxes[0][0] * dxes[1][0])[:, None, None] +
(s[1] - numpy.roll(s[1], 1, axis=1)) / numpy.sqrt(dxes[0][1] * dxes[1][1])[None, :, None] +
(s[2] - numpy.roll(s[2], 1, axis=2)) / numpy.sqrt(dxes[0][2] * dxes[1][2])[None, None, :] )
return ds
def energy_hstep(e0, h1, e2, epsilon=None, mu=None, dxes=None):
u = dxmul(e0 * e2, h1 * h1, epsilon, mu, dxes)
return u
def energy_estep(h0, e1, h2, epsilon=None, mu=None, dxes=None):
u = dxmul(e1 * e1, h0 * h2, epsilon, mu, dxes)
return u
def delta_energy_h2e(dt, e0, h1, e2, h3, epsilon=None, mu=None, dxes=None):
"""
This is just from (e2 * e2 + h3 * h1) - (h1 * h1 + e0 * e2)
"""
de = e2 * (e2 - e0) / dt
dh = h1 * (h3 - h1) / dt
du = dxmul(de, dh, epsilon, mu, dxes)
return du
def delta_energy_e2h(dt, h0, e1, h2, e3, epsilon=None, mu=None, dxes=None):
"""
This is just from (h2 * h2 + e3 * e1) - (e1 * e1 + h0 * h2)
"""
de = e1 * (e3 - e1) / dt
dh = h2 * (h2 - h0) / dt
du = dxmul(de, dh, epsilon, mu, dxes)
return du
def delta_energy_j(j0, e1, dxes=None):
if dxes is None:
dxes = tuple(tuple(numpy.ones(1) for _ in range(3)) for _ in range(2))
du = ((j0 * e1).sum(axis=0) *
dxes[0][0][:, None, None] *
dxes[0][1][None, :, None] *
dxes[0][2][None, None, :])
return du
def dxmul(ee, hh, epsilon=None, mu=None, dxes=None):
if epsilon is None:
epsilon = 1
if mu is None:
mu = 1
if dxes is None:
dxes = tuple(tuple(numpy.ones(1) for _ in range(3)) for _ in range(2))
result = ((ee * epsilon).sum(axis=0) *
dxes[0][0][:, None, None] *
dxes[0][1][None, :, None] *
dxes[0][2][None, None, :] +
(hh * mu).sum(axis=0) *
dxes[1][0][:, None, None] *
dxes[1][1][None, :, None] *
dxes[1][2][None, None, :])
return result

122
meanas/fdtd/pml.py Normal file
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@ -0,0 +1,122 @@
"""
PML implementations
"""
# TODO retest pmls!
from typing import List, Callable, Tuple, Dict
import numpy
from .. import dx_lists_t, field_t, field_updater
__author__ = 'Jan Petykiewicz'
def cpml(direction:int,
polarity: int,
dt: float,
epsilon: field_t,
thickness: int = 8,
ln_R_per_layer: float = -1.6,
epsilon_eff: float = 1,
mu_eff: float = 1,
m: float = 3.5,
ma: float = 1,
cfs_alpha: float = 0,
dtype: numpy.dtype = numpy.float32,
) -> Tuple[Callable, Callable, Dict[str, field_t]]:
if direction not in range(3):
raise Exception('Invalid direction: {}'.format(direction))
if polarity not in (-1, 1):
raise Exception('Invalid polarity: {}'.format(polarity))
if thickness <= 2:
raise Exception('It would be wise to have a pml with 4+ cells of thickness')
if epsilon_eff <= 0:
raise Exception('epsilon_eff must be positive')
sigma_max = -ln_R_per_layer / 2 * (m + 1)
kappa_max = numpy.sqrt(epsilon_eff * mu_eff)
alpha_max = cfs_alpha
transverse = numpy.delete(range(3), direction)
u, v = transverse
xe = numpy.arange(1, thickness+1, dtype=float)
xh = numpy.arange(1, thickness+1, dtype=float)
if polarity > 0:
xe -= 0.5
elif polarity < 0:
xh -= 0.5
xe = xe[::-1]
xh = xh[::-1]
else:
raise Exception('Bad polarity!')
expand_slice = [None] * 3
expand_slice[direction] = slice(None)
def par(x):
scaling = (x / thickness) ** m
sigma = scaling * sigma_max
kappa = 1 + scaling * (kappa_max - 1)
alpha = ((1 - x / thickness) ** ma) * alpha_max
p0 = numpy.exp(-(sigma / kappa + alpha) * dt)
p1 = sigma / (sigma + kappa * alpha) * (p0 - 1)
p2 = 1 / kappa
return p0[expand_slice], p1[expand_slice], p2[expand_slice]
p0e, p1e, p2e = par(xe)
p0h, p1h, p2h = par(xh)
region = [slice(None)] * 3
if polarity < 0:
region[direction] = slice(None, thickness)
elif polarity > 0:
region[direction] = slice(-thickness, None)
else:
raise Exception('Bad polarity!')
se = 1 if direction == 1 else -1
# TODO check if epsilon is uniform in pml region?
shape = list(epsilon[0].shape)
shape[direction] = thickness
psi_e = [numpy.zeros(shape, dtype=dtype), numpy.zeros(shape, dtype=dtype)]
psi_h = [numpy.zeros(shape, dtype=dtype), numpy.zeros(shape, dtype=dtype)]
fields = {
'psi_e_u': psi_e[0],
'psi_e_v': psi_e[1],
'psi_h_u': psi_h[0],
'psi_h_v': psi_h[1],
}
# Note that this is kinda slow -- would be faster to reuse dHv*p2h for the original
# H update, but then you have multiple arrays and a monolithic (field + pml) update operation
def pml_e(e: field_t, h: field_t, epsilon: field_t) -> Tuple[field_t, field_t]:
dHv = h[v][region] - numpy.roll(h[v], 1, axis=direction)[region]
dHu = h[u][region] - numpy.roll(h[u], 1, axis=direction)[region]
psi_e[0] *= p0e
psi_e[0] += p1e * dHv * p2e
psi_e[1] *= p0e
psi_e[1] += p1e * dHu * p2e
e[u][region] += se * dt / epsilon[u][region] * (psi_e[0] + (p2e - 1) * dHv)
e[v][region] -= se * dt / epsilon[v][region] * (psi_e[1] + (p2e - 1) * dHu)
return e, h
def pml_h(e: field_t, h: field_t) -> Tuple[field_t, field_t]:
dEv = (numpy.roll(e[v], -1, axis=direction)[region] - e[v][region])
dEu = (numpy.roll(e[u], -1, axis=direction)[region] - e[u][region])
psi_h[0] *= p0h
psi_h[0] += p1h * dEv * p2h
psi_h[1] *= p0h
psi_h[1] += p1h * dEu * p2h
h[u][region] -= se * dt * (psi_h[0] + (p2h - 1) * dEv)
h[v][region] += se * dt * (psi_h[1] + (p2h - 1) * dEu)
return e, h
return pml_e, pml_h, fields

2
fdfd_tools/test/test_fdtd.py → meanas/test/test_fdtd.py
View File

@ -4,7 +4,7 @@ import dataclasses
from typing import List, Tuple from typing import List, Tuple
from numpy.testing import assert_allclose, assert_array_equal from numpy.testing import assert_allclose, assert_array_equal
from fdfd_tools import fdtd from meanas import fdtd
prng = numpy.random.RandomState(12345) prng = numpy.random.RandomState(12345)

22
meanas/types.py Normal file
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@ -0,0 +1,22 @@
"""
Types shared across multiple submodules
"""
import numpy
from typing import List, Callable
# Field types
field_t = numpy.ndarray # vector field with shape (3, X, Y, Z) (e.g. [E_x, E_y, E_z])
vfield_t = numpy.ndarray # linearized vector field (vector of length 3*X*Y*Z)
'''
'dxes' datastructure which contains grid cell width information in the following format:
[[[dx_e_0, dx_e_1, ...], [dy_e_0, ...], [dz_e_0, ...]],
[[dx_h_0, dx_h_1, ...], [dy_h_0, ...], [dz_h_0, ...]]]
where dx_e_0 is the x-width of the x=0 cells, as used when calculating dE/dx,
and dy_h_0 is the y-width of the y=0 cells, as used when calculating dH/dy, etc.
'''
dx_lists_t = List[List[numpy.ndarray]]
field_updater = Callable[[field_t], field_t]

10
fdfd_tools/vectorization.py → meanas/vectorization.py
View File

@ -4,15 +4,13 @@ and a 1D array representation of that field [f_x0, f_x1, f_x2,... f_y0,... f_z0,
Vectorized versions of the field use row-major (ie., C-style) ordering. Vectorized versions of the field use row-major (ie., C-style) ordering.
""" """
from typing import List from typing import List
import numpy import numpy
__author__ = 'Jan Petykiewicz' from .types import field_t, vfield_t
# Types
field_t = List[numpy.ndarray] # vector field (eg. [E_x, E_y, E_z] __author__ = 'Jan Petykiewicz'
vfield_t = numpy.ndarray # linearized vector field
def vec(f: field_t) -> vfield_t: def vec(f: field_t) -> vfield_t:
@ -27,7 +25,7 @@ def vec(f: field_t) -> vfield_t:
""" """
if numpy.any(numpy.equal(f, None)): if numpy.any(numpy.equal(f, None)):
return None return None
return numpy.hstack(tuple((fi.ravel(order='C') for fi in f))) return numpy.ravel(f, order='C')
def unvec(v: vfield_t, shape: numpy.ndarray) -> field_t: def unvec(v: vfield_t, shape: numpy.ndarray) -> field_t:

8
setup.py
View File

@ -1,14 +1,14 @@
#!/usr/bin/env python3 #!/usr/bin/env python3
from setuptools import setup, find_packages from setuptools import setup, find_packages
import fdfd_tools import meanas
with open('README.md', 'r') as f: with open('README.md', 'r') as f:
long_description = f.read() long_description = f.read()
setup(name='fdfd_tools', setup(name='meanas',
version=fdfd_tools.version, version=meanas.version,
description='FDFD Electromagnetic simulation tools', description='Electromagnetic simulation tools',
long_description=long_description, long_description=long_description,
long_description_content_type='text/markdown', long_description_content_type='text/markdown',
author='Jan Petykiewicz', author='Jan Petykiewicz',