Investigation of nonplanar perfectly matched absorbers for finite-element mesh truncation

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, it is possible to solve the boundary value problems in these geometries. The analytical solutions demonstrate that under certain conditions, outgoing waves are absorbed with negligible reflection, and the transmitted wave is attenuated within the PML, To reduce the white space in radiation or scattering problems, conformal PML's are constructed via parametric mappings, It is also verified that the PML concept, which was originally introduced for problems governed by Maxwell's equations, can be extended to cases governed by the scalar Helmholtz equation, Finally, numerical results are presented to demonstrate the use of the PML in FEM mesh truncation.


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...
Questioning Degree of Accuracy Offered by the Spectral Element Method in Computational Electromagnetics
Mahariq, I.; KURT, HAMZA; Kuzuoğlu, Mustafa (2015-07-01)
In this paper, a comparison amongst the spectral element method (SEM), the finite difference method (FDM), and the first-order finite element method (FEM) is presented. For the sake of consistency, the comparison is carried out on one-dimensional and two-dimensional boundary value problems based on the same measure of error in order to emphasize on the high accuracy gained by the SEM. Then, the deterioration in the accuracy of the SEM due to the elemental deformation is demonstrated. Following this, we try ...
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...
Conformal black hole solutions of axidilaton gravity in D dimensions
Cebeci, H; Dereli, T (2002-02-15)
Static, spherically symmetric solutions of axidilaton gravity in D dimensions are given in the Brans-Dicke frame for arbitrary values of the Brans-Dicke constant omega and an axion-dilaton coupling parameter k. The mass and the dilaton and axion charges are determined and a BPS bound is derived. There exists a one-parameter family of black hole solutions in the scale-invariant limit.
A Non-iterative Domain Decomposition Method for Finite Element Analysis of 3D Electromagnetic Scattering Problems
Ozgun, Ozlem; Kuzuoğlu, Mustafa (2008-07-11)
In this paper, we generalize this algorithm to 3D scattering problems, and we demonstrate that the algorithm is actually non-iterative in problems involving smooth convex geometries (such as sphere, cube, missile, cone, plate, etc.) and some special geometries (such as inlet). The most distinguished feature of the algorithm is the utilization of the locally-conformal perfectly matched layer (PML) method along the boundaries of the subdomains. In this algorithm, the original computational domain is partition...
Citation Formats
M. Kuzuoğlu, “Investigation of nonplanar perfectly matched absorbers for finite-element mesh truncation,” IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, pp. 474–486, 1997, Accessed: 00, 2020. [Online]. Available: