Lattice Boltzmann Method for Electromagnetic Wave Scattering

Abstract

In this work, the lattice Boltzmann method (LBM) is assessed as a time-domain numerical approach for electromagnetic wave scattering. Owing to its explicit formulation and suitability for parallel computation on structured grids, LBM provides an alternative framework for solving Maxwell's equations. The formulation is first validated using canonical benchmarks, including reflection and refraction at a planar dielectric interface and two-dimensional scattering from infinitely long circular cylinders, where the computed angular scattering intensities are compared with analytical Lorenz-Mie solutions. Additional comparisons are performed for circular cylinders with varying dielectric constants to examine performance across different material contrasts. The framework is then extended to three-dimensional scattering from dielectric spheres, representing the most computationally demanding case considered in this work, and the resulting angular scattering intensities are compared with exact Lorenz-Mie solutions. To further examine performance for non-circular geometries, scattering from an infinitely long hexagonal dielectric cylinder is investigated and benchmarked against results obtained using the Discretized-Mie Formalism. Across all cases, the LBM predictions show close agreement with analytical and semi-analytical reference solutions over a range of size-to-wavelength ratios.