A 3D Nonlinear Maxwell's Equations Solver Based On A Hybrid Numerical Method

TL;DR

This paper introduces a hybrid numerical method combining boundary integral and domain-based techniques to efficiently solve 3D nonlinear Maxwell's equations in complex materials, reducing computational cost.

Contribution

It presents a novel hybrid approach for 3D nonlinear Maxwell's equations that integrates boundary integral and domain methods, improving efficiency over traditional techniques.

Findings

Successfully applied to 3D nonlinear electromagnetic problems

Reduces computational complexity by avoiding external grids

Demonstrates effectiveness in inhomogeneous media

Abstract

In this paper we explore the possibility for solving the 3D Maxwell's equations in the presence of nonlinear and/or inhomogeneous material response. We propose using a hybrid approach which combines a bound- ary integral representation with a domain-based method. This hybrid approach has previously been successfully applied to 1D linear and non- linear transient wave scattering problems. The basic idea of the approach is to propagate the Maxwell's equations inside the scattering objects for- ward in time by using a domain-based method, while a boundary integral representation of the electromagnetic field is used to supply the domain- based method with the required surface values. Thus no grids outside the scattering objects are needed and this greatly reduces the computational cost and complexity.