Recent advances in perfectly matched layers in finite element applications

Ozgun, Ozlem
Kuzuoğlu, Mustafa
We present a comparative evaluation of two novel and practical perfectly matched layer (PML) implementations to the problem of mesh truncation in the finite element method (FEM): locally-conformal PML, and multi-center PML techniques. The most distinguished feature of these methods is the simplicity and flexibility to design conformal PMLs over challenging geometries, especially those with curvature discontinuities, in a straightforward way without using artificial absorbers. These methods are based on specially- and locally-defined complex coordinate transformations inside the PML region. They can easily be implemented in a conventional FEM by just replacing the nodal coordinates inside the PML region by their complex counterparts obtained via complex coordinate transformation. After overviewing the theoretical bases of these methods, we present some numerical results in the context of two- and three-dimensional electromagnetic radiation/scattering problems.


Finite Element Modeling of Anisotropic Half-Space Problems by a Simple Mesh Truncation Scheme
ÖZGÜN, ÖZLEM; Kuzuoğlu, Mustafa (2017-07-14)
Anisotropic half-space problems are modeled with finite element method with a simple mesh truncation scheme based on the locally-conformal PML method. The PML is simply implemented by just using complex coordinates inside an anisotropic medium without introducing additional anisotropy and without modifying the finite element formulation. This approach is useful to model electromagnetic radiation and scattering from structures embedded within arbitrary anisotropic media. Simulation results are demonstrated t...
On the use of complex stretching coordinates in generalized finite difference method with applications in inhomogeneous visco-elasto dynamics
Korkut, Fuat; Mengi, Yalcin; Tokdemir, Turgut (2022-01-01)
In the study, in conjunction with perfectly matched layer (PML) analysis, an approach is proposed for the evaluation of complex derivatives directly in terms of complex stretching coordinates of points in PML. For doing this within the framework of generalized finite difference method (GFDM), a difference equation is formulated and presented, where both the function values and coordinates of data points might be complex. The use of the proposed approach is considered in the analysis of inhomogeneous visco-e...
Near-field performance analysis of locally-conformal perfectly matched absorbers via Monte Carlo simulations
Ozgun, Ozlem; Kuzuoğlu, Mustafa (2007-12-10)
In the numerical solution of some boundary value problems by the finite element method (FEM), the unbounded domain must be truncated by an artificial absorbing boundary or layer to have a bounded computational domain. The perfectly matched layer (PML) approach is based on the truncation of the computational domain by a reflectionless artificial layer which absorbs outgoing waves regardless of their frequency and angle of incidence. In this paper, we present the near-field numerical performance analysis of o...
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 ...
Non-Maxwellian locally-conformal PML absorbers for finite element mesh truncation
Ozgun, Ozlem; Kuzuoğlu, Mustafa (Institute of Electrical and Electronics Engineers (IEEE), 2007-03-01)
We introduce the locally-conformal perfectly matched layer (PML) approach, which is an easy and straightforward PML implementation, to the problem of mesh truncation in the finite element method (FEM). This method is based on a locally-defined complex coordinate transformation which has no explicit dependence on the differential geometric characteristics of the PML-free space interface. As a result, it is possible to handle challenging PML geometries with interfaces having arbitrary curvature, especially th...
Citation Formats
O. Ozgun and M. Kuzuoğlu, “Recent advances in perfectly matched layers in finite element applications,” TURKISH JOURNAL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCES, pp. 57–66, 2008, Accessed: 00, 2020. [Online]. Available: