Past Event: Oden Institute Seminar

Large-scale BEM for Industrial Electromagnetic Applications

Sergej Rjasanow, Saarland University, Germany

Abstract

We discuss efficient numerical methods for three-dimensional integral equations based on the Boundary Element Methods (BEM). One of the most challenging equations of this kind is the boundary integral formulation of electromagnetic scattering, especially for large industrial problems. Such problems can be solved by the use of the FEKO Suite, a leading electromagnetic analysis software of the company EM Software & Systems GmbH, Boeblingen, Germany. The main mathematical subject is the so called EFIE, electric field integral equation, which will be solved by the Method of Moments (MoM). This is a variant of the Galerkin method leading to a dense system matrix. A naive strategy for the solution of the corresponding linear system would need at least $O(N^2)$ arithmetical operations and memory. In contrast, the Adaptive Cross Approximation method (ACA) [1,2,3]} generates the low-rank approximant of the matrix with almost linear complexity and without any explicit a priori known degenerate kernel approximation as it is necessary by the use of the Fast Multipole Method (FMM). In the talk, the efficiency of the numerical method (ACA approximation of MoM matrices, high order elements, iterative and direct solution techniques) will be illustrated for a number of different FEKO test problems and for different surfaces. [1] M. Bebendorf and S.Rjasanow, Adaptive low-rank approximation of collocation matrices. Computing, 70(1):1-24, 2003. [2] S.Rjasanow and O.Steinbach. The Fast Solution of Boundary Integral Equations. Number 12 in Springer Series in Mathematical and Analytical Technology with Applications to Engineering. Springer-Verlag, Berlin-Heidelberg-NewYork, 2007. [3] S.Rjasanow and L.Weggler. ACA accelerated high order BEM for Maxwell problems. Computational Mechanics, 51:431-441, 2013.