Fast Multipole Accelerated Hybrid Finite Element-Boundary Integral-Ray-Optical Method Including Double Diffractions

Abstract

This recently developed, powerful hybrid technique, which combines the finite element–boundary integral (FEBI) method and the multilevel fast multipole method (MLFMM) with the uniform geometrical theory of diffraction (UTD), allows for an efficient and accurate computation of various radiation and scattering problems. Ray-optical fields are considered by modifying the Green functions and the incident field in the boundary integral (BI) part. Within the MLFMM part, ray-optical fields are also taken into account in the translation stage on the various levels using a far-field approximation of the translation operator. Ray-optical contributions are considered on flat conducting structures and, in this article, they are extended to double-diffracted fields on pairs of straight metallic skewed edges. The corresponding formulations, as well as numerical results, are presented.

Keywords:

• finite element methods
• boundary integral equations
• fast integral equation solvers
• geometrical theory of diffraction
• hybrid solution methods