ScatSol

ScatSol computes time-harmonic electromagnetic scattering from concentric cylindrical and spherical regions. It returns complex electric and magnetic fields at user-specified points.

The cylindrical solver supports TM and TE plane-wave incidence, layered materials, and a perfect electric conductor (PEC) core. The spherical solver uses both electric and magnetic multipole channels for an x-polarized plane wave. Materials can have real or complex relative permittivity and permeability.

Install

Clone the repository, then install its dependencies with uv:

uv sync

Quick start: cylinder

This example solves TM scattering from a dielectric cylinder in vacuum. Lengths are in meters and frequency is in hertz.

import numpy as np

from scatsol import (
    CylindricalGeometry,
    CylindricalRegion,
    CylindricalSolver,
    Material,
    Polarization,
)

vacuum = Material.vacuum()
dielectric = Material(epsilon_r=4.0)
geometry = CylindricalGeometry([
    CylindricalRegion(0.0, 0.5, dielectric),
    CylindricalRegion(0.5, float("inf"), vacuum),
])

solution = CylindricalSolver(geometry, frequency=300e6).solve(
    n=50, polarization=Polarization.TM
)
points = np.array([[0.75, 0.0, 0.0], [1.0, 0.5, 0.0]])
e_z = solution.e_z(points)
electric, magnetic = solution.total_field(points)

Points are Cartesian (x, y, z) coordinates in an (N, 3) array. Field components and full fields are complex; .real, .imag, and np.abs(...) provide access to the real part, imaginary part, or magnitude.

Quick start: sphere

The spherical solver returns both electric and magnetic multipole channels for each solution:

import numpy as np

from scatsol import Material, SphericalGeometry, SphericalRegion, SphericalSolver

vacuum = Material.vacuum()
geometry = SphericalGeometry([
    SphericalRegion(0.0, 1.0, Material(epsilon_r=2.56)),
    SphericalRegion(1.0, float("inf"), vacuum),
])
solution = SphericalSolver(geometry, frequency=300e6).solve(n=50)
points = np.array([[0.0, 0.0, 2.0], [1.5, 0.0, 0.0]])
magnetic_y = solution.h_y(points)

Examples and documentation

Run a demonstration from the repository root, for example:

uv run python demo/cylinder_diel.py
uv run python demo/sphere_diel.py

The documentation home includes the equations and conventions, API reference, and runnable examples. Build the documentation site with:

uv run mkdocs build

Reference

Jin, Jian-Ming. Theory and Computation of Electromagnetic Fields. 2nd ed. Hoboken, NJ: Wiley-IEEE Press, 2015.

License

ScatSol is licensed under the GNU General Public License v3.0 or later.