Accurate and Efficient Algorithms for Boundary Element Methods in Electromagnetic Scattering - A Tribute to the Work of Professor F. Olyslager

Boundary element methods (BEMs) are an increasingly popular approach to model electromagnetic scattering both by perfect conductors and dielectric objects. Several mathematical, numerical, and computaI. Bogaert, Department of Information Technology, Ghent University, SintPietersnieuwstraat 41, 9000 Gent, Belgium. ([email protected]) K. Cools, Department of Information Technology, Ghent University, SintPietersnieuwstraat 41, 9000 Gent, Belgium. ([email protected]) D. De Zutter, Department of Information Technology, Ghent University, SintPietersnieuwstraat 41, 9000 Gent, Belgium. ([email protected]) J. Fostier, Department of Information Technology, Ghent University, SintPietersnieuwstraat 41, 9000 Gent, Belgium. ([email protected]) J. Peeters, Department of Information Technology, Ghent University, SintPietersnieuwstraat 41, 9000 Gent, Belgium. ([email protected]) H. Rogier, Department of Information Technology, Ghent University, SintPietersnieuwstraat 41, 9000 Gent, Belgium. ([email protected]) D. Vande Ginste, Department of Information Technology, Ghent University, SintPietersnieuwstraat 41, 9000 Gent, Belgium. ([email protected]) Department of Information Technology, Ghent University, 9000 Gent, Belgium. D R A F T January 4, 2012, 10:50am D R A F T COOLS ET AL.: RECENT ADVANCES IN BEMS 3 tional techniques pullulated from the research into BEMs, enhancing its efficiency and applicability. In designing a viable implementation of the BEM, both theoretical and practical aspects need to be taken into account. Theoretical aspects include the choice of an integral equation for the sought after current densities on the geometry’s boundaries and the choice of a discretization strategy (i.e. a finite element space) for this equation. Practical aspects include efficient algorithms to execute the multiplication of the system matrix by a test vector (such as a fast multipole method) and the parallelization of this multiplication algorithm that allows the distribution of the computation and communication requirements between multiple computational nodes. In honor of our former colleague and mentor, Prof. F. Olyslager, an overview of the BEMs for large and complex EM problems developed within the Electromagnetics Group at Ghent University is presented. Recent results that ramified from Prof. Olyslager’s scientific endeavors are included in the survey. D R A F T January 4, 2012, 10:50am D R A F T 4 COOLS ET AL.: RECENT ADVANCES IN BEMS