A coordinate transformation approach for efficient repeated solution of Helmholtz equation pertaining to obstacle scattering by shape deformations

Ozgun, Ozlem
Kuzuoğlu, Mustafa
A computational model is developed for efficient solutions of electromagnetic scattering from obstacles having random surface deformations or irregularities (such as roughness or randomly-positioned bump on the surface), by combining the Monte Carlo method with the principles of transformation electromagnetics in the context of finite element method. In conventional implementation of the Monte Carlo technique in such problems, a set of random rough surfaces is defined from a given probability distribution; a mesh is generated anew for each surface realization; and the problem is solved for each surface. Hence, this repeated mesh generation process places a heavy burden on CPU time. In the proposed approach, a single mesh is created assuming smooth surface, and a transformation medium is designed on the smooth surface of the object. Constitutive parameters of the medium are obtained by the coordinate transformation technique combined with the form-invariance property of Maxwell's equations. At each surface realization, only the material parameters are modified according to the geometry of the deformed surface, thereby avoiding repeated mesh generation process. In this way, a simple, single and uniform mesh is employed; and CPU time is reduced to a great extent. The technique is demonstrated via various finite element simulations for the solution of two-dimensional, Helmholtz-type and transverse magnetic scattering problems.


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...
A Numerical Model for Investigating the Effect of Rough Surface Parameters on Radar Cross Section Statistics
Kuzuoğlu, Mustafa (2017-07-14)
Electromagnetic scattering from rough surfaces is modeled by combining the periodic finite element method and the transformation electromagnetics approach. The behavior of the radar cross section (RCS) at both specular and backscattering directions is analyzed as a function of rms height and correlation length with the help of Monte Carlo simulations. The concept of backscattering enhancement is illustrated, and some conclusions are drawn about the RCS statistics.
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 ...
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...
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...
Citation Formats
O. Ozgun and M. Kuzuoğlu, “A coordinate transformation approach for efficient repeated solution of Helmholtz equation pertaining to obstacle scattering by shape deformations,” COMPUTER PHYSICS COMMUNICATIONS, pp. 1616–1627, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/36603.