An Efficient Finite Element-Boundary Integral Formulation for Numerical Modeling of Scattering by Discrete Body-of-Revolution

Abstract

In this paper, we consider a special class of geometry, which exhibits angular periodicity. By rotating a certain fixed angle about its axis, this special geometry recovers itself. Such an object can be referred to as an angular periodic object (APO), which has also been known as a discrete body-of-revolution (DBOR). Because of the angular periodicity, the discretization of the entire object can be reduced to that of a slice corresponding to one period of the object. This reduced discretization can be exploited to increase the efficiency of its numerical simulation as well as to reduce the memory requirements for the simulation. The method developed here is based on the hybrid finite element-boundary integral (FE-BI) formulation for solving Maxwell's equations in open space. Our approach is to decouple the original FE-BI system into K smaller problems, with K denoting the total number of slices in a DBOR. Each decoupled problem is K times smaller than the original system and is solved independently for each discrete Fourier mode. Once the field for each mode is computed, the summation of all the modes yields the final solution to the problem. The formulation for this proposed FE-BI DBOR method is given in the following section. Then the speedup curve for solving coated sphere scattering problems and a numerical simulation for the scattering of a coated cylinder with 30 coated fins are presented as a validation example for the proposed algorithm