Software metamaterials: Transformation media based multi-scale techniques for computational electromagnetics

Ozgun, Ozlem
Kuzuoğlu, Mustafa
This paper presents computational models employing special transformation-based media-which we call software metamaterials-for the purpose of enhancing the ability of numerical modeling methods for solving multi-scale electromagnetic boundary value problems involving features with multiple length or frequency scales or both. The multi-scale problems, in general, suffer from difficulties in mesh generation and the number of unknowns due to certain meshing requirements dictated by the fine features of the problem. The underlying idea in this study is to introduce transformation media into the computational domain of the finite element method (or finite difference methods) in order to allow uniform and easy-to-generate meshes by avoiding mesh refinement, and therefore, to develop efficient and simple computer-aided simulation tools. In other words, a virtual equivalent problem is created, which acts like the original problem. The techniques proposed in this paper are validated via several finite element simulations in the context of TMz electromagnetic scattering problems. Crown Copyright (C) 2012 Published by Elsevier Inc. All rights reserved.


Combining perturbation theory and transformation electromagnetics for finite element solution of Helmholtz-type scattering problems
Kuzuoğlu, Mustafa (2014-10-01)
A numerical method is proposed for efficient solution of scattering from objects with weakly perturbed surfaces by combining the perturbation theory, transformation electro-magnetics and the finite element method. A transformation medium layer is designed over the smooth surface, and the material parameters of the medium are determined by means of a coordinate transformation that maps the smooth surface to the perturbed surface. The perturbed fields within the domain are computed by employing the material p...
Numerical Solution of Multi-scale Electromagnetic Boundary Value Problems by Utilizing Transformation-Based Metamaterials
Ozgun, Ozlem; Kuzuoğlu, Mustafa (2011-06-23)
We present numerical solution techniques for efficiently handling multi-scale electromagnetic boundary value problems having fine geometrical details or features, by utilizing spatial coordinate transformations. The principle idea is to modify the computational domain of the finite methods (such as the finite element or finite difference methods) by suitably placing anisotropic metamaterial structures whose material parameters are obtained by coordinate transformations, and hence, to devise easier and effic...
A Transformation Media Based Approach for Efficient Monte Carlo Analysis of Scattering From Rough Surfaces With Objects
Ozgun, Ozlem; Kuzuoğlu, Mustafa (2013-03-01)
This paper presents a computational model that utilizes transformation-based metamaterials to enhance the performance of numerical modeling methods for achieving the statistical characterization of two-dimensional electromagnetic scattering from objects on or above one-dimensional rough sea surfaces. Monte Carlo simulation of the rough surface scattering problem by means of differential equation-based finite methods (such as finite element or finite difference methods) usually places a heavy burden on compu...
Remesh-Free Shape Optimization by Transformation Optics
ÖZGÜN, ÖZLEM; Kuzuoğlu, Mustafa (2016-12-01)
A remesh-free numerical method is developed for shape optimization problem by combining the transformation optics approach, the finite element method, and the genetic optimization algorithm. To overcome cumbersome remeshing processes, transformation media are designed within the elements where the contour of the object passes. A simple rectangular mesh is used and only the material parameters of the media are redefined according to the scatterer contour that is represented by B-spline curves. The proposed a...
Modeling Electromagnetic Scattering from Random Array of Objects by Form Invariance of Maxwell's Equations
ÖZGÜN, ÖZLEM; Kuzuoğlu, Mustafa (2015-07-24)
Electromagnetic scattering from a random array of objects is modeled by using special coordinate transformations that are based on the form invariance property of Maxwell's equations. The main motivation is to perform multiple realizations of Monte Carlo simulations corresponding to different positions of objects in an efficient way by using a single mesh. This is achieved by locating transformation media within the computational domain. The proposed approach is applied to finite element method and tested b...
Citation Formats
O. Ozgun and M. Kuzuoğlu, “Software metamaterials: Transformation media based multi-scale techniques for computational electromagnetics,” JOURNAL OF COMPUTATIONAL PHYSICS, pp. 203–219, 2013, Accessed: 00, 2020. [Online]. Available: