Spherical harmonics B-field computation validation

Out:

l = 1 computed
l = 2 computed
l = 3 computed
l = 4 computed
l = 5 computed
l = 6 computed
l = 7 computed
l = 8 computed
l = 9 computed
Computing magnetic field coupling matrix, 676 vertices by 676 target points... took 0.13 seconds.
Relative RMS error 0.5606404914507133

import numpy as np
import trimesh
from mayavi import mlab

from bfieldtools.mesh_magnetics import magnetic_field_coupling
from bfieldtools.mesh_conductor import MeshConductor

from bfieldtools.sphtools import compute_sphcoeffs_mesh
from bfieldtools import sphtools


import pkg_resources

# Load simple plane mesh that is centered on the origin
file_obj = pkg_resources.resource_filename(
    "bfieldtools", "example_meshes/10x10_plane.obj"
)
coilmesh = trimesh.load(file_obj, process=False)
coil = MeshConductor(mesh_obj=coilmesh)

coil.mesh.vertices += np.array([0, -1, 0])
weights = np.zeros(coilmesh.vertices.shape[0])
weights[coil.inner_vertices] = 1

test_points = coilmesh.vertices.copy()
test_points[:, 1] = 0

lmax = 9


sph_C = compute_sphcoeffs_mesh(coil.mesh, lmax)

alms = sph_C[0] @ weights
blms = sph_C[1] @ weights

alms = np.zeros_like(alms)

B0 = (magnetic_field_coupling(coilmesh, test_points) @ weights).T
B1 = sphtools.field(test_points, alms, blms, lmax).T

mlab.figure(bgcolor=(1, 1, 1))

s = mlab.triangular_mesh(
    *coilmesh.vertices.T, coilmesh.faces, scalars=weights, colormap="viridis"
)
s.enable_contours = True
s.actor.property.render_lines_as_tubes = True
s.actor.property.line_width = 3.0

mlab.quiver3d(
    *test_points.T, *B0, color=(1, 0, 0), scale_factor=0.5e7, vmin=0, vmax=2e-7
)
mlab.quiver3d(
    *test_points.T, *B1, color=(0, 0, 1), scale_factor=0.5e7, vmin=0, vmax=2e-7
)
s.scene.isometric_view()


print(
    "Relative RMS error", np.sqrt(np.mean((B1 - B0) ** 2)) / np.sqrt(np.mean((B0) ** 2))
)

Estimated memory usage: 71 MB