Recent Advances in Boundary Element Methods Applied to Conducting and Dielectric Electromagnetic Scattering Problems

Abstract—Boundary element methods (BEMs) are an increas-ingly popular approach to the modeling of electromagnetic scat-tering both by perfect conductors and dielectric objects. Several mathematical, numerical, and computational techniques pullu-lated from the research into BEMs, enhancing its efficiency. The Fast Multipole Method (FMM) and its descendants accelerate the matrix-vector product that constitutes the BEM’s computational bottleneck. In particular, dedicated FMMs have been conceived for the computation of the electromagnetic scattering at complex metallic and/or dielectric objects in free space and in layered background media. Calderón preconditioning of the BEM’s system matrix lowers the number of matrix-vector products required to reach an accurate solution, and thus the time to reach it. Parallelization distributes the remaining workload over a battery of affordable computational nodes, diminishing the wall-clock computation time. In honor of our former colleague and mentor, Prof. F. Olyslager, an overview of some dedicated 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. I