Mesh refinement

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from collections import OrderedDict

import matplotlib.pyplot as plt
import numpy as np
import shapely
import shapely.affinity
from skfem import Basis, ElementTriP0, adaptive_theta
from skfem.io.meshio import from_meshio

from femwell.maxwell.waveguide import compute_modes, eval_error_estimator
from femwell.mesh import mesh_from_OrderedDict

polygons_paper = OrderedDict(
    left=shapely.LineString(((0, 0), (0, 1))),
    right=shapely.LineString(((1, 0), (1, 1))),
    top=shapely.LineString(((0, 1), (1, 1))),
    core=shapely.box(0, 0, 0.5, 0.5),
    clad=shapely.box(0, 0, 1, 1),
)

boundaries = [
    [lambda x: x[0] == np.min(x[0]), lambda x: x[0] == np.max(x[0])],
    [lambda x: x[0] == np.min(x[0]), lambda x: x[0] == np.max(x[0])],
    [lambda x: x[0] == np.min(x[0]), lambda x: x[1] == np.max(x[1])],
    [lambda x: x[0] == np.min(x[0]), lambda x: x[1] == np.max(x[1])],
]

epsilons_paper = [
    {"core": 2.25, "clad": 1},
    {"core": 8, "clad": 1},
    {"core": 1, "clad": 2.25},
    {"core": 1, "clad": 8},
]

neff_values_paper = [1.27627404, 2.65679692, 1.387926425, 2.761465320]
num = 3

mesh = from_meshio(
    mesh_from_OrderedDict(polygons_paper, {}, default_resolution_max=0.1, filename="mesh.msh")
)
mesh.draw().show()

for i in range(16):
    basis0 = Basis(mesh, ElementTriP0())
    epsilon = basis0.zeros()
    for subdomain, e in epsilons_paper[num].items():
        epsilon[basis0.get_dofs(elements=subdomain)] = e

    modes = compute_modes(
        basis0, epsilon, wavelength=1.5, num_modes=1, order=1, metallic_boundaries=boundaries[num]
    )
    modes[0].show(modes[0].E.real, direction="x")
    print(f"Error: {modes[0].n_eff - neff_values_paper[num]:.5g}")

    mesh = mesh.refined(adaptive_theta(eval_error_estimator(modes[0].basis, modes[0].E), theta=0.5))
    mesh.draw().show()

/tmp/ipykernel_7902/275219315.py:10: DeprecationWarning: The behavior of passing an array directly to `show` is deprecated and will be removed in the future. Use `plot` instead.
  modes[0].show(modes[0].E.real, direction="x")

Error: 4.2371e-05+0j

Error: -0.00011698+0j

Error: -0.00014164+0j

Error: -0.00014494+0j

Error: -0.00014891+0j

Error: -0.00013566+0j

Error: -0.00013255+0j

Named boundaries invalidated by a call to Mesh.refined()

Error: -9.8289e-05+0j

Error: -5.0584e-05+0j

Error: -4.1234e-05+0j

Error: -3.4453e-05+0j

Error: -2.3801e-05+0j

Error: -1.5849e-05+0j

Error: -1.139e-05+0j

Error: -9.823e-06+0j

Error: -7.9428e-06+0j