A skin effect approximation for eddy current problems
type: Item
instance of: scholarly article
title: A skin effect approximation for eddy current problems
zbMATH Open document ID: 0595.35096
DOI: 10.1007/BF00281588
published in: Archive for Rational Mechanics and Analysis
publication date: 1985-01-01T00:00:00Z
review text: Given a simple closed curve \(\Gamma\) in \({\mathbb{R}}^ 2\) with interior domain \(\Omega_-\) and exterior domain \(\Omega_+\), the authors study the following two problems: P(\(\alpha)\): Given \(\alpha >0\), \(a\in {\mathbb{R}}\), \(f\in C(\Gamma)\), \(g\in C(\Gamma)\), find u such that \(\Delta u=\{\alpha^ 2u\) in \(\Omega_-\); \(\Delta u=0\) in \(\Omega_+\); \(u^- =u^++f\) and \(u^-_ n=u^+_ n+g\) on \(\Gamma\) ; u(x)-a log \(| x| =O(1)\) as \(| x| \to \infty.\) P(\(\infty):\) Given \(a\in {\mathbb{R}}\), \(f\in C(\Gamma)\), find u such that \(\Delta u=0\) in \(\Omega_+\); \(u^++f=0\) on \(\Gamma\) ; u(x)-a log \(| x| =O(1)\) as \(| x| \to \infty.\) This paper essentially continuous that of \textit{S. I. Hariharan} and the first author [J. Comp. Phys. 45, 80-89 (1982; Zbl 0478.65080)].
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 78A25
zbMATH DE Number: 3957810
zbMATH Keywords: eddy currents
zbMATH Keywords: asymptotic expansion
author: Richard C. MacCamy
author: Ernst P. Stephan
reviewed by: Jürgen Appell
MaRDI profile type: Publication
cites work: An approximation theorem for functionals, with applications in continuum mechanics
cites work: Integral equation procedures for Eddy current problems
cites work: A finite element method for some integral equations of the first kind
cites work: Solution procedures for three-dimensional eddy current problems
cites work: Q3051526
description: scientific article; zbMATH DE number 3957810