An Iterative Domain Decomposition Method for Solving Wave Propagation Problems

• Published in: Electromagnetics Vol. 34; no. 3-4; pp. 210 - 221
• Main Authors: Koczka, Gergely, Bauernfeind, Thomas, Preis, Kurt, Bíró, Oszkár
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 03-04-2014; Taylor & Francis Ltd
• Subjects: Conduction; Convergence; Decomposition; Domain decomposition; Electromagnetic waves; Iterative methods; Mathematical analysis; Mathematical models; numerical methods; Propagation; Schur complement; Wave propagation
• ISSN: 0272-6343; 1532-527X
• DOI: 10.1080/02726343.2014.877751

Solving electromagnetic wave propagation problems with the finite-element method results in a large number of unknowns due to the necessity of modeling an extensive portion of the surroundings of the conducting structures. These equation systems are often ill-conditioned because of the great material differences as well as changes in size between neighboring elements. In addition, the resulting matrices are indefinite. Common iterative methods exhibit poor convergence due to these conditions. Direct solution techniques result in high memory requirements. The aim of this article is to present an approach with smaller memory demand than the direct methods and better convergence properties than common iterative techniques. An iterative method based on domain decomposition is presented and compared to various conventional iterative and direct solution techniques.