Boundary Element Procedure for 3D Electromagnetic Transmission Problems with Large Conductivity

TL;DR

This paper develops an asymptotic boundary element method for 3D electromagnetic scattering by highly conductive metals, simplifying computations by focusing on exterior problems and introducing a new FEM/BEM coupling approach.

Contribution

It introduces an asymptotic boundary element procedure tailored for large conductivity scenarios and a novel FEM/BEM coupling for electromagnetic transmission problems.

Findings

Significant reduction in computational complexity.

Effective numerical implementation demonstrated.

Accurate modeling of skin effect in metals.

Abstract

We consider the scattering of time periodic electro-magnetic fields by metallic obstacles, the eddy current problem. In this interface problem different sets of Maxwell equations must be solved in the obstacle and outside, while the tangential components of both electric and magnetic fields are continuous across the interface. We describe an asymptotic procedure, which applies for large conductivity and reflects the skin effect in metals. The key to our method is to introduce a special integral equation procedure for the exterior boundary value problem corresponding to perfect conductors. The asymptotic procedure leads to a great reduction in complexity for the numerical solution since it involves solving only the exterior boundary value problem. Furthermore we introduce a new fem/bem coupling procedure for the transmission problem and consider the implementation of the Galerkin elements for the perfect conductor problem and present numerical experiments.