Numerical Solution of Multi-scale Electromagnetic Boundary Value Problems by Utilizing Transformation-Based Metamaterials

Ozgun, Ozlem
Kuzuoğlu, Mustafa
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 efficient numerical simulation tools in computational electromagnetics by allowing uniform and easy-to-generate meshes or by decreasing the number of unknowns. Inside the modified computational domain, Maxwell's equations are still satisfied, but the medium where the coordinate transformation is applied turns into an anisotropic medium whose constitutive parameters are determined by the Jacobian of the coordinate transformation. In other words, by employing the form-invariance property of Maxwell's equations under coordinate transformations, an equivalent model that mimics the original problem is created to get rid of mesh refinement around the small-scale features. Various numerical applications of electromagnetic scattering problems are illustrated via finite element simulations.


Monte Carlo simulations of Helmholtz scattering from randomly positioned array of scatterers by utilizing coordinate transformations in finite element method
ÖZGÜN, ÖZLEM; Kuzuoğlu, Mustafa (2015-07-01)
Electromagnetic scattering from randomly distributed array of scatterers is numerically analyzed by Monte Carlo simulations by utilizing coordinate transformations in the context of finite element method solution of Helmholtz equation. The major goal in proposed approaches is to place transformation media into computational domain by employing the form invariance property of Maxwell's equations under coordinate transformations, and hence avoiding repeated mesh generation process in multiple realizations of ...
Implementation of coordinate transformations in periodic finite-element method for modeling rough surface scattering problems
ÖZGÜN, ÖZLEM; Kuzuoğlu, Mustafa (2016-05-01)
The coordinate transformation technique (with its current name of transformation electromagnetics) is applied to the finite-element method (FEM) with periodic boundary conditions for efficient Monte Carlo simulation of one-dimensional random rough surface scattering problems. In a unit cell of periodic structure, two coordinate transformations are used, one of which is a real transformation designed to model the rough surface with flat surface, and the other is a complex transformation used to design a perf...
Investigation of nonplanar perfectly matched absorbers for finite-element mesh truncation
Kuzuoğlu, Mustafa (1997-03-01)
In this paper, we present a detailed theoretical and numerical investigation of the perfectly matched layer (PML) concept as applied to the problem of mesh truncation in the finite-element method (FEM), We show that it is possible to extend the Cartesian PML concepts involving half-spaces to cylindrical and spherical geometries appropriate for closed boundaries in two and three dimensions by defining lossy anisotropic layers in the relevant coordinate systems, By using the method of separation of variables,...
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...
Software metamaterials: Transformation media based multi-scale techniques for computational electromagnetics
Ozgun, Ozlem; Kuzuoğlu, Mustafa (2013-03-01)
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 pro...
Citation Formats
O. Ozgun and M. Kuzuoğlu, “Numerical Solution of Multi-scale Electromagnetic Boundary Value Problems by Utilizing Transformation-Based Metamaterials,” 2011, vol. 6785, Accessed: 00, 2020. [Online]. Available: