Recent Developments in Transformation Optics-aided CEM

Authors:Ozlem Ozgun and Mustafa Kuzuoglu

Source: FERMAT, Volume 1, Article 3, Jan.-Feb., 2014

Abstract: This review paper presents a hybrid point of view that combines computational electromagnetics (CEM) and transformation electromagnetics/optics (TEM). The main purpose is to employ the salutary features of TEM to increase the effectiveness of finite methods (such as finite element method or finite difference methods) for solving electromagnetic boundary value problems. Synergies arising from the marriage of CEM and TEM enable us to overcome some of the difficulties, such as challenging meshing issues and high levels of computational burden, associated with the finite methods. Our previous studies basically concentrated on three types of problems: (i) modeling large-scale or multi-scale electromagnetic scattering problems; (ii) modeling curved geometries that do not conform to a Cartesian grid especially in finite difference methods; and (iii) modeling stochastic electromagnetic problems having significant uncertainty. The underlying idea is to insert transformation media into computational domain in order to alleviate certain difficulties associated with some of the meshing requirements dictated by the problem geometry. Our strategy is to create a virtual “equivalent” problem, which mimics the original problem, and which enables us to develop efficient and simple-to-use computer-aided simulation tools to solve it. This paper reviews some of our previously-published approaches based on the above strategy, and includes a discussion of some of the related issues.

Index Terms: Transformation electromagnetics/optics, computational electromagnetics, anisotropic metamaterials, transformation medium, coordinate transformation, finite element method (FEM), finite difference time domain method (FDTD), Monte Carlo, multi-scale, stochastic, rough surface scattering.

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Recent Developments in Transformation Optics-aided CEM