TY - JOUR
T1 - An efficient full-wave solver for eddy currents
AU - Helsing, Johan
AU - Karlsson, Anders
AU - Rosén, Andreas
PY - 2022/12
Y1 - 2022/12
N2 - 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.
AB - 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.
KW - Boundary integral equation
KW - Eddy current
KW - Low-frequency breakdown
KW - Maxwell transmission problem
KW - Neumann eigenfield
U2 - 10.1016/j.camwa.2022.10.018
DO - 10.1016/j.camwa.2022.10.018
M3 - Article
AN - SCOPUS:85140650499
SN - 0898-1221
VL - 128
SP - 145
EP - 162
JO - Computers and Mathematics with Applications
JF - Computers and Mathematics with Applications
ER -