The Adaptive Cross Approximation Technique for a Volume Integral Equation Method Applied to Nonlinear Magnetostatic Problems

Author

Vinh Le-Van ; Bannwarth, Bertrand ; Carpentier, Anthony ; Chadebec, Olivier ; Guichon, Jean-M ; Meunier, Gerard

Author_Institution

Grenoble Electr. Eng. Lab., Univ. of Grenoble, Grenoble, France

Volume

50

Issue

2

fYear

2014

fDate

Feb. 2014

Firstpage

445

Lastpage

448

Abstract

Volume integral equation methods are particularly well suited to solve electromagnetic problems, where the air domain is predominant. However, their use leads to the heavy resolution of a dense matrix system. The Adaptive Cross Approximation (ACA) combined with hierarchical matrices (H-matrices) decomposition is an algebraic method allowing the compression of fully populated matrices. This paper presents the ACA technique applied to a volume integral equation to solve nonlinear magnetostatic problems.

Keywords

approximation theory; electromagnetism; integral equations; magnetostatics; matrix decomposition; ACA technique; H-matrices; adaptive cross approximation technique; air domain; algebraic method; dense matrix system; electromagnetic problems; heavy resolution; hierarchical matrix decomposition; matrix compression; nonlinear magnetostatic problems; volume integral equation method; Approximation methods; Assembly; Integral equations; Magnetic domains; Magnetostatic waves; Magnetostatics; Matrix decomposition; Adaptive cross approximation; fixed-point method; nonlinear magnetostatic; volume integral equations;

fLanguage

English

Journal_Title

Magnetics, IEEE Transactions on

Publisher

ieee

ISSN

0018-9464

Type

jour

DOI

10.1109/TMAG.2013.2281568

Filename

6749030