Title :
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
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;
Journal_Title :
Magnetics, IEEE Transactions on
DOI :
10.1109/TMAG.2013.2281568
