An efficient full wave solver for eddy currents

TL;DR

This paper introduces a new integral equation-based solver for eddy current problems that achieves high accuracy and well-conditioned systems across different surface topologies, improving computational efficiency.

Contribution

It presents a novel reformulation of the Maxwell transmission problem with techniques for better conditioning and accuracy, applicable to surfaces of genus 0 and 1 in the eddy current regime.

Findings

Achieves 13-digit accuracy in numerical examples

Works well for surfaces of genus 0 and 1

Provides well-conditioned systems despite ill-conditioning issues

Abstract

An integral equation reformulation of the Maxwell transmission problem is presented. The reformulation uses techniques such as tuning of free parameters and augmentation of close-to-rank-deficient operators. It is designed for the eddy current regime and works both for surfaces of genus $0$ and $1$. Well-conditioned systems and field representations are obtained despite the Maxwell transmission problem being ill-conditioned for genus $1$ surfaces due to the presence of Neumann eigenfields. Furthermore, it is shown that these eigenfields, for ordinary conductors in the eddy current regime, are different from the classical Neumann eigenfields for superconductors. Numerical examples, based on the reformulation, give an unprecedented $13$-digit accuracy both for transmitted and scattered fields.