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

• Published in: IEEE transactions on magnetics Vol. 50; no. 2; pp. 445 - 448
• Main Authors: Vinh Le-Van, Bannwarth, Bertrand, Carpentier, Anthony, Chadebec, Olivier, Guichon, Jean-Michel, Meunier, Gerard
• Format: Journal Article Conference Proceeding
• Language: English
• Published: New York, NY IEEE 01.02.2014; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive cross approximation; Approximation methods; Assembly; Cross-disciplinary physics: materials science; rheology; Electric power; Engineering Sciences; Exact sciences and technology; fixed-point method; Integral equations; Magnetic domains; Magnetism; Magnetostatic waves; Magnetostatics; Materials science; Matrix decomposition; nonlinear magnetostatic; Other topics in materials science; Physics; volume integral equations; fixed-point method; Integral equations; volume integral equations; Adaptive cross approximation; Magnetic properties; nonlinear magnetostatic
• ISSN: 0018-9464; 1941-0069
• DOI: 10.1109/TMAG.2013.2281568

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.