Combining perturbation theory and transformation electromagnetics for finite element solution of Helmholtz-type scattering problems

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 parameters and the fields of the smooth surface as source terms in the Helmholtz equation. The main advantage of the proposed approach is that if repeated solutions are needed (such as in Monte Carlo technique or in optimization problems requiring multiple solutions for a set of perturbed surfaces), computational resources considerably decrease because a single mesh is used and the global matrix is formed only once. Only the right hand side vector is changed with respect to the perturbed material parameters corresponding to each of the perturbed surfaces. The technique is validated via finite element simulations.


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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...
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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 ...
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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...
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...
A Transformation Media Based Approach for Efficient Monte Carlo Analysis of Scattering From Rough Surfaces With Objects
Ozgun, Ozlem; Kuzuoğlu, Mustafa (2013-03-01)
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Citation Formats
M. Kuzuoğlu, “Combining perturbation theory and transformation electromagnetics for finite element solution of Helmholtz-type scattering problems,” JOURNAL OF COMPUTATIONAL PHYSICS, pp. 883–897, 2014, Accessed: 00, 2020. [Online]. Available: