Remesh-Free Shape Optimization by Transformation Optics

Kuzuoğlu, Mustafa
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 approach is validated through benchmark inverse electromagnetic scattering problems.


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...
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...
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...
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...
Citation Formats
Ö. ÖZGÜN and M. Kuzuoğlu, “Remesh-Free Shape Optimization by Transformation Optics,” IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, pp. 5479–5482, 2016, Accessed: 00, 2020. [Online]. Available: