FMM for Maxwell with segments

[pescap]

Hi, when I switch to fmm assembly for operators defined on segments, I get very different results.

I have attached a very simple script that reproduces the behavior.

import bempp.api
import numpy as np
import scipy
from matplotlib import pyplot as plt

# Define parameters: Even with a coarse resolution,
# where the FMM is expected to be dense, the results vary significantly across the multishape.

k0 = 1
precision = 1
#h = 2 * np.pi/(precision*k0)
h = 1
grid = bempp.api.shapes.multitrace_cube(h=h)

# Set the segments and swapped_normals corresponding to \Omega_1, the first half-cube in the multitrace_cube.
segments = [[1, 2, 3, 4, 5, 6]]
swapped_normals = [[]]

# The same half cube without more triangles.
grid1=bempp.api.shapes.cuboid(length = (1,1,0.5), origin=(0,0,0), h=h)

# Define the function spaces.
rwg = [bempp.api.function_space(grid, "RWG", 0, segments=seg, swapped_normals=normals, include_boundary_dofs=True)
              for seg, normals in zip(segments, swapped_normals)]

snc = [bempp.api.function_space(grid, "SNC", 0, segments=seg, swapped_normals=normals,include_boundary_dofs=True)
              for seg, normals in zip(segments, swapped_normals)]

rwg1 = bempp.api.function_space(grid1, "RWG", 0,include_boundary_dofs=True)
snc1 = bempp.api.function_space(grid1, "SNC", 0,include_boundary_dofs=True)

# Assembly A_1 in dense mode and fmm mode for both grids
efiem_dense = bempp.api.operators.boundary.maxwell.electric_field(rwg[0], rwg[0], snc[0], k0).weak_form()
efiem_fmm = bempp.api.operators.boundary.maxwell.electric_field(rwg[0], rwg[0], snc[0], k0, assembler='fmm').weak_form()
efie1m_dense = bempp.api.operators.boundary.maxwell.electric_field(rwg1, rwg1, snc1, k0).weak_form()
efie1m_fmm = bempp.api.operators.boundary.maxwell.electric_field(rwg1, rwg1, snc1, k0, assembler='fmm').weak_form()

N = efiem_dense.shape[0]
k = min(100,N-2)

# Plot the k first eigenvalues

eigvalsm_dense, eivects = scipy.sparse.linalg.eigs(efiem_dense, k = k)
eigvalsm_fmm, eivects = scipy.sparse.linalg.eigs(efiem_fmm, k = k)

eigvals1m_dense, eivects = scipy.sparse.linalg.eigs(efie1m_dense, k = k)
eigvals1m_fmm, eivects = scipy.sparse.linalg.eigs(efie1m_fmm, k = k)

fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(2, 2, sharex=True, sharey=True)

ax1.scatter(np.real(eigvalsm_dense), np.imag(eigvalsm_dense), label='efiem_dense')
ax2.scatter(np.real(eigvalsm_fmm), np.imag(eigvalsm_fmm), label='efiem_fmm')

ax3.scatter(np.real(eigvals1m_dense), np.imag(eigvals1m_dense), label='efiem_dense')
ax4.scatter(np.real(eigvals1m_fmm), np.imag(eigvals1m_fmm), label='efiem_fmm')

which results in:

For the multishape with FMM (top-right), there is a clear problem.