A Comparison of Two Lattice Boltzmann Models for Electrodynamics

TL;DR

This paper systematically compares two Lattice Boltzmann models for electrodynamics, evaluating their efficiency and accuracy across standard tests, and finds the modified Hauser-Verhey model to be a promising alternative.

Contribution

It provides a direct comparison of two Lattice Boltzmann models for electrodynamics, highlighting their performance differences and potential for optimization.

Findings

Both models accurately simulate electrodynamics tests.

The Mendoza-Mu ilde{n}oz model is faster but less memory-efficient.

The modified Hauser-Verhey model shows promising performance.

Abstract

In recent years, various Lattice Boltzmann models for electrodynamics have been developed as alternatives to classical methods such as Finite Difference Time Domain (FDTD) and Finite Element Methods (FEM). However, there has been a lack of systematic comparisons between these models. This paper addresses this gap by comparing two specific Lattice Boltzmann models, published by Mendoza and Mu\~noz (MM), and Hauser and Verhey (HV), respectively. To compare the models, we utilize time and memory as indicators, considering the same achieved error, in four standard tests: a dielectric pulse traveling through two interfaces, the skin effect, the Hertz dipole, and a dielectric pulse traveling through several interfaces. The results indicate that both methods accurately simulate the tests and exhibit convergence as the mesh is refined. However, the MM method outperforms the HV method regarding time, while its memory efficiency was lower. The modified Hauser-Verhey model demonstrates itself to be a promising alternative to the Mendoza-Mu\~noz model. These findings contribute to the ongoing development and optimization of numerical methods for electromagnetics simulations.