various fixes and improvements

examples/fdfd.py

@@ -4,7 +4,7 @@ from numpy.linalg import norm
 
 import meanas
 from meanas import vec, unvec
-from meanas.fdfd import waveguide_mode, functional, scpml
+from meanas.fdfd import waveguide_mode, functional, scpml, operators
 from meanas.fdfd.solvers import generic as generic_solver
 
 import gridlock
@@ -56,18 +56,23 @@ def test0(solver=generic_solver):
     dxes = [grid.dxyz, grid.autoshifted_dxyz()]
     for a in (0, 1, 2):
         for p in (-1, 1):
-            dxes = meanas.scpml.stretch_with_scpml(dxes, axis=a, polarity=p, omega=omega,
-                                                   thickness=pml_thickness)
+            dxes = meanas.fdfd.scpml.stretch_with_scpml(dxes, axis=a, polarity=p, omega=omega,
+                                                        thickness=pml_thickness)
 
     J = [numpy.zeros_like(grid.grids[0], dtype=complex) for _ in range(3)]
-    J[1][15, grid.shape[1]//2, grid.shape[2]//2] = 1e5
+    J[1][15, grid.shape[1]//2, grid.shape[2]//2] = 1
 
     '''
     Solve!
     '''
+    sim_args = {
+        'omega': omega,
+        'dxes': dxes,
+        'epsilon': vec(grid.grids),
+    }
     x = solver(J=vec(J), **sim_args)
 
-    A = functional.e_full(omega, dxes, vec(grid.grids)).tocsr()
+    A = operators.e_full(omega, dxes, vec(grid.grids)).tocsr()
     b = -1j * omega * vec(J)
     print('Norm of the residual is ', norm(A @ x - b))
 
@@ -208,7 +213,7 @@ def module_available(name):
 
 
 if __name__ == '__main__':
-    # test0()
+    test0()
 
     if module_available('opencl_fdfd'):
         from opencl_fdfd import cg_solver as opencl_solver

meanas/fdfd/farfield.py

@@ -6,9 +6,11 @@ import numpy
 from numpy.fft import fft2, fftshift, fftfreq, ifft2, ifftshift
 from numpy import pi
 
+from .. import field_t
 
-def near_to_farfield(E_near: List[numpy.ndarray],
-                     H_near: List[numpy.ndarray],
+
+def near_to_farfield(E_near: field_t,
+                     H_near: field_t,
                      dx: float,
                      dy: float,
                      padded_size: List[int] = None
@@ -115,8 +117,8 @@ def near_to_farfield(E_near: List[numpy.ndarray],
 
 
 
-def far_to_nearfield(E_far: List[numpy.ndarray],
-                     H_far: List[numpy.ndarray],
+def far_to_nearfield(E_far: field_t,
+                     H_far: field_t,
                      dkx: float,
                      dky: float,
                      padded_size: List[int] = None

meanas/fdfd/functional.py

@@ -8,7 +8,7 @@ e.g. E = [E_x, E_y, E_z] where each component has shape (X, Y, Z)
 from typing import List, Callable
 import numpy
 
-from . import dx_lists_t, field_t
+from .. import dx_lists_t, field_t
 
 __author__ = 'Jan Petykiewicz'
 

meanas/fdfd/operators.py

@@ -32,7 +32,7 @@ from typing import List, Tuple
 import numpy
 import scipy.sparse as sparse
 
-from . import vec, dx_lists_t, vfield_t
+from .. import vec, dx_lists_t, vfield_t
 
 
 __author__ = 'Jan Petykiewicz'

meanas/fdfd/scpml.py

@@ -5,6 +5,8 @@ Functions for creating stretched coordinate PMLs.
 from typing import List, Callable
 import numpy
 
+from .. import dx_lists_t
+
 __author__ = 'Jan Petykiewicz'
 
 

meanas/fdfd/waveguide.py

@@ -23,7 +23,7 @@ import numpy
 from numpy.linalg import norm
 import scipy.sparse as sparse
 
-from . import vec, unvec, dx_lists_t, field_t, vfield_t
+from .. import vec, unvec, dx_lists_t, field_t, vfield_t
 from . import operators
 
 
@@ -82,7 +82,8 @@ def normalized_fields(v: numpy.ndarray,
                       omega: complex,
                       dxes: dx_lists_t,
                       epsilon: vfield_t,
-                      mu: vfield_t = None
+                      mu: vfield_t = None,
+                      dx_prop: float = 0,
                       ) -> Tuple[vfield_t, vfield_t]:
     """
     Given a vector v containing the vectorized H_x and H_y fields,
@@ -94,6 +95,7 @@ def normalized_fields(v: numpy.ndarray,
     :param dxes: Grid parameters [dx_e, dx_h] as described in meanas.types (2D)
     :param epsilon: Vectorized dielectric constant grid
     :param mu: Vectorized magnetic permeability grid (default 1 everywhere)
+    :param dxes_prop: Grid cell width in the propagation direction. Default 0 (continuous).
     :return: Normalized, vectorized (e, h) containing all vector components.
     """
     e = v2e(v, wavenumber, omega, dxes, epsilon, mu=mu)
@@ -105,11 +107,10 @@ def normalized_fields(v: numpy.ndarray,
     E = unvec(e, shape)
     H = unvec(h, shape)
 
-    S1 = E[0] * numpy.roll(numpy.conj(H[1]), 1, axis=0) * dxes_real[0][1] * dxes_real[1][0]
-    S2 = E[1] * numpy.roll(numpy.conj(H[0]), 1, axis=1) * dxes_real[0][0] * dxes_real[1][1]
-    S = 0.25 * ((S1 + numpy.roll(S1, 1, axis=0)) -
-                (S2 + numpy.roll(S2, 1, axis=1)))
-    P = 0.5 * numpy.real(S.sum())
+    phase = numpy.exp(-1j * wavenumber * dx_prop / 2)
+    S1 = E[0] * numpy.conj(H[1] * phase) * dxes_real[0][1] * dxes_real[1][0]
+    S2 = E[1] * numpy.conj(H[0] * phase) * dxes_real[0][0] * dxes_real[1][1]
+    P = numpy.real(S1.sum() - S2.sum())
     assert P > 0, 'Found a mode propagating in the wrong direction! P={}'.format(P)
 
     energy = epsilon * e.conj() * e
@@ -120,8 +121,6 @@ def normalized_fields(v: numpy.ndarray,
     # Try to break symmetry to assign a consistent sign [experimental]
     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())
-    logger.debug('norm_angle = {}'.format(norm_angle))
-    logger.debug('norm_sign = {}'.format(sign)
 
     norm_factor = sign * norm_amplitude * numpy.exp(1j * norm_angle)
 

meanas/fdfd/waveguide_mode.py

@@ -2,9 +2,9 @@ from typing import Dict, List
 import numpy
 import scipy.sparse as sparse
 
-from . import vec, unvec, dx_lists_t, vfield_t, field_t
+from .. import vec, unvec, dx_lists_t, vfield_t, field_t
 from . import operators, waveguide, functional
-from .eigensolvers import signed_eigensolve, rayleigh_quotient_iteration
+from ..eigensolvers import signed_eigensolve, rayleigh_quotient_iteration
 
 
 def solve_waveguide_mode_2d(mode_number: int,
@@ -12,7 +12,7 @@ def solve_waveguide_mode_2d(mode_number: int,
                             dxes: dx_lists_t,
                             epsilon: vfield_t,
                             mu: vfield_t = None,
-                            wavenumber_correction: bool = True,
+                            dx_prop: float = 0,
                             ) -> Dict[str, complex or field_t]:
     """
     Given a 2d region, attempts to solve for the eigenmode with the specified mode number.
@@ -22,8 +22,8 @@ def solve_waveguide_mode_2d(mode_number: int,
     :param dxes: Grid parameters [dx_e, dx_h] as described in meanas.types
     :param epsilon: Dielectric constant
     :param mu: Magnetic permeability (default 1 everywhere)
-    :param wavenumber_correction: Whether to correct the wavenumber to
-        account for numerical dispersion (default True)
+    :param dx_prop: The cell width in the the propagation direction, used to apply a
+        correction to the wavenumber. Default 0 (i.e. continuous propagation direction)
     :return: {'E': List[numpy.ndarray], 'H': List[numpy.ndarray], 'wavenumber': complex}
     """
 
@@ -51,15 +51,9 @@ def solve_waveguide_mode_2d(mode_number: int,
 
     '''
     Perform correction on wavenumber to account for numerical dispersion.
-
-     See Numerical Dispersion in Taflove's FDTD book.
-     This correction term reduces the error in emitted power, but additional
-      error is introduced into the E_err and H_err terms. This effect becomes
-      more pronounced as the wavenumber increases.
     '''
-    if wavenumber_correction:
-        dx_mean = (numpy.hstack(dxes[0]) + numpy.hstack(dxes[1])).mean() / 2        #TODO figure out what dx to use here
-        wavenumber -= 2 * numpy.sin(numpy.real(wavenumber * dx_mean / 2)) / dx_mean - numpy.real(wavenumber)
+    if dx_prop != 0:
+        wavenumber = 2 / dx_prop * numpy.sin(wavenumber * dx_prop / 2)
 
     shape = [d.size for d in dxes[0]]
     fields = {
@@ -79,7 +73,6 @@ def solve_waveguide_mode(mode_number: int,
                          slices: List[slice],
                          epsilon: field_t,
                          mu: field_t = None,
-                         wavenumber_correction: bool = True
                          ) -> Dict[str, complex or numpy.ndarray]:
     """
     Given a 3D grid, selects a slice from the grid and attempts to
@@ -94,8 +87,6 @@ def solve_waveguide_mode(mode_number: int,
         as the waveguide cross-section. slices[axis] should select only one
     :param epsilon: Dielectric constant
     :param mu: Magnetic permeability (default 1 everywhere)
-    :param wavenumber_correction: Whether to correct the wavenumber to
-        account for numerical dispersion (default True)
     :return: {'E': List[numpy.ndarray], 'H': List[numpy.ndarray], 'wavenumber': complex}
     """
     if mu is None:
@@ -115,7 +106,7 @@ def solve_waveguide_mode(mode_number: int,
         'dxes': [[dx[i][slices[i]] for i in order[:2]] for dx in dxes],
         'epsilon': vec([epsilon[i][slices].transpose(order) for i in order]),
         'mu': vec([mu[i][slices].transpose(order) for i in order]),
-        'wavenumber_correction': wavenumber_correction,
+        'dx_prop': dxes[0][order[2]][slices[order[2]]],
     }
     fields_2d = solve_waveguide_mode_2d(mode_number, omega=omega, **args_2d)
 
@@ -175,9 +166,6 @@ def compute_source(E: field_t,
     :param mu: Magnetic permeability (default 1 everywhere)
     :return: J distribution for the unidirectional source
     """
-    if mu is None:
-        mu = numpy.ones(3)
-
     J = numpy.zeros_like(E, dtype=complex)
     M = numpy.zeros_like(E, dtype=complex)
 
@@ -275,9 +263,9 @@ def solve_waveguide_mode_cylindrical(mode_number: int,
                                      dxes: dx_lists_t,
                                      epsilon: vfield_t,
                                      r0: float,
-                                     wavenumber_correction: bool = True,
                                      ) -> Dict[str, complex or field_t]:
     """
+    TODO: fixup
     Given a 2d (r, y) slice of epsilon, attempts to solve for the eigenmode
      of the bent waveguide with the specified mode number.
 
@@ -288,8 +276,6 @@ def solve_waveguide_mode_cylindrical(mode_number: int,
     :param epsilon: Dielectric constant
     :param r0: Radius of curvature for the simulation. This should be the minimum value of
         r within the simulation domain.
-    :param wavenumber_correction: Whether to correct the wavenumber to
-        account for numerical dispersion (default True)
     :return: {'E': List[numpy.ndarray], 'H': List[numpy.ndarray], 'wavenumber': complex}
     """
 
@@ -313,16 +299,7 @@ def solve_waveguide_mode_cylindrical(mode_number: int,
     wavenumber = numpy.sqrt(eigval)
     wavenumber *= numpy.sign(numpy.real(wavenumber))
 
-    '''
-    Perform correction on wavenumber to account for numerical dispersion.
-
-     See Numerical Dispersion in Taflove's FDTD book.
-     This correction term reduces the error in emitted power, but additional
-      error is introduced into the E_err and H_err terms. This effect becomes
-      more pronounced as the wavenumber increases.
-    '''
-    if wavenumber_correction:
-        wavenumber -= 2 * numpy.sin(numpy.real(wavenumber / 2)) - numpy.real(wavenumber)
+    # TODO: Perform correction on wavenumber to account for numerical dispersion.
 
     shape = [d.size for d in dxes[0]]
     v = numpy.hstack((v, numpy.zeros(shape[0] * shape[1])))

meanas/test/test_fdtd.py

@@ -9,6 +9,7 @@ from meanas import fdtd
 
 prng = numpy.random.RandomState(12345)
 
+
 def assert_fields_close(a, b, *args, **kwargs):
     numpy.testing.assert_allclose(a, b, verbose=False, err_msg='Fields did not match:\n{}\n{}'.format(numpy.rollaxis(a, -1),
                                                                                                       numpy.rollaxis(b, -1)), *args, **kwargs)