Ozlem Ozgun

Non-Maxwellian Locally-Conformal PML Absorbers for Finite Element Mesh Truncation

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 those with curvature discontinuities. In order to implement this approach, we also introduce the concept of complex space FEM using elements with complex nodal coordinates. After developing the analytical background of this method, we present some numerical results to demonstrate the performance of this method in three-dimensional electromagnetic scattering problems

Utilization of Anisotropic Metamaterial Layers in Waveguide Miniaturization and Transitions

We introduce a new approach which enables a waveguide to support propagation of electromagnetic waves below the cutoff frequency, as well as which avoids undesirable reflections in a waveguide. These are achieved through the usage of an anisotropic metamaterial layer by employing the concept of coordinate transformation. The proposed method can be utilized for the fabrication of miniaturized waveguides, and for the elimination of discontinuities in abrupt waveguide transitions. We demonstrate some numerical experiments for finite element simulations of parallel-plate and dielectric slab waveguides.

Design of dual-frequency probe-fed microstrip antennas with genetic optimization algorithm

Dual-frequency operation of antennas has become a necessity for many applications in recent wireless communication systems, such as GPS, GSM services operating at two different frequency bands, and services of PCS and IMT-2000 applications. Although there are various techniques to achieve dual-band operation from various types of microstrip antennas, there is no efficient design tool that has been incorporated with a suitable optimization algorithm. In this paper, the cavity-model based simulation tool along with the genetic optimization algorithm is presented for the design of dual-band microstrip antennas, using multiple slots in the patch or multiple shorting strips between the patch and the ground plane. Since this approach is based on the cavity model, the multiport approach is efficiently employed to analyze the effects of the slots and shorting strips on the input impedance. Then, the optimization of the positions of slots and shorting strips is performed via a genetic optimization algorithm, to achieve an acceptable antenna operation over the desired frequency bands. The antennas designed by this efficient design procedure were realized experimentally, and the results are compared. In addition, these results are also compared to the results obtained by the commercial electromagnetic simulation tool, the FEM-based software HFSS by ANSOFT.

Recursive Two-Way Parabolic Equation Approach for Modeling Terrain Effects in Tropospheric Propagation

The Fourier split-step method is a one-way marching-type algorithm to efficiently solve the parabolic equation for modeling electromagnetic propagation in troposphere. The main drawback of this method is that it characterizes only forward-propagating waves, and neglects backward-propagating waves, which become important especially in the presence of irregular surfaces. Although ground reflecting boundaries are inherently incorporated into the split-step algorithm, irregular surfaces (such as sharp edges) introduce a formidable challenge. In this paper, a recursive two-way split-step algorithm is presented to model both forward and backward propagation in the presence of multiple knife-edges. The algorithm starts marching in the forward direction until the wave reaches a knife-edge. The wave arriving at the knife-edge is partially-reflected by imposing the boundary conditions at the edge, and is propagated in the backward direction by reversing the paraxial direction in the parabolic equation. In other words, the wave is split into two components, and the components travel in their corresponding directions. The reflected wave is added to the forward-wave in each range step to obtain the total wave. The wave-splitting is performed each time a wave is incident on one of the knife-edges. This procedure is repeated until convergence is achieved inside the entire domain.

Monte Carlo-Based Characteristic Basis Finite-Element Method (MC-CBFEM) for Numerical Analysis of Scattering From Objects On/Above Rough Sea Surfaces

The Monte Carlo-based Characteristic Basis Finite-Element Method (MC-CBFEM) is developed for predicting the statistical properties of the 2-D electromagnetic scattering from objects (such as ship- and decoy-like objects) on or above random rough sea surfaces. At each realization of the Monte Carlo technique, the 1-D rough sea surface is randomly generated by using the Pierson-Moskowitz spectrum, and the bistatic radar cross section (RCS) is computed by employing the CBFEM approach. The CBFEM is a noniterative domain decomposition finite-element algorithm, which is designed to alleviate the challenges of the conventional finite-element method in solving large-scale electromagnetic problems. The CBFEM partitions the problem into a number of nonoverlapping subdomains and generates physics-based characteristic basis functions for the representation of the fields in each subdomain. Since this approach reduces the matrix size and lends itself to convenient parallelization, it is attractive for efficiently solving large-scale problems many times in the Monte Carlo simulation with the use of direct solvers and small-sized matrices. For a number of surface realizations, each of which can be considered as a sample from the random process specifying the surface, a family of bistatic RCS values is obtained as a function of incidence angle and surface roughness (or wind speed). The coherent (mean) and incoherent (variance) components of the RCS are illustrated with particular emphasis on the effects of surface roughness and the angles near grazing. Statistical characterization is also achieved by other means, such as correlation coefficient and density functions represented by histograms.

A Novel Two-Way Finite-Element Parabolic Equation Groundwave Propagation Tool: Tests With Canonical Structures and Calibration

A novel two-way finite-element parabolic equation (PE) (2W-FEMPE) propagation model which handles both forward and backward scattering effects of the groundwave propagation above the Earths surface over irregular terrain paths through inhomogeneous atmosphere is introduced. A Matlab-based propagation tool for 2W-FEMPE is developed and tested against mathematical exact and asymptotic solutions as well as the recently introduced two-way split-step PE model through a canonical validation, verification, and calibration process for the first time in literature.

A Transformation Media Based Approach for Efficient Monte Carlo Analysis of Scattering From Rough Surfaces With Objects

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 computational resources because at each realization of the Monte Carlo technique, a mesh must be generated anew for each surface realization. The main purpose of the proposed approach in this paper is to create a single mesh, without repeating mesh generation at each step, by introducing a transformation medium above the rough surface in the computational domain of the finite methods. Material parameters of the medium are obtained by the coordinate transformation technique, which is based on the form-invariance property of Maxwells equations. At each realization, only the material parameters are modified with respect to the geometry of surface without changing the mesh. In this manner, a great reduction in CPU time is achieved. The proposed technique is analyzed and validated via various finite element simulations.

Form Invariance of Maxwell's Equations: The Pathway to Novel Metamaterial Specifications for Electromagnetic Reshaping

We present spatial-coordinate transformation techniques to control the propagation of electromagnetic fields in several surprising and useful applications. The implementation of this approach is based on the fact that Maxwells equations are form-invariant under coordinate transformations. Specifically, the effect of a general coordinate transformation can be realized by means of an equivalent anisotropic material, in which the original forms of Maxwells equations are still preserved in the transformed space. Constitutive parameters of the anisotropic material are determined to appropriately reflect the consequences of the coordinate transformation on the electromagnetic fields. In this paper, we introduce novel implementations and interpretations of the coordinate-transformation approach for the purpose of “reshaping” objects in electromagnetic scattering, and for reshaping and miniaturizing waveguides. We demonstrate the applications of the proposed techniques via several finite-element simulations.

Parallelized Characteristic Basis Finite Element Method (CBFEM-MPI)-A non-iterative domain decomposition algorithm for electromagnetic scattering problems

In this paper, we introduce a parallelized version of a novel, non-iterative domain decomposition algorithm, called Characteristic Basis Finite Element Method (CBFEM-MPI), for efficient solution of large-scale electromagnetic scattering problems, by utilizing a set of specially defined characteristic basis functions (CBFs). This approach is based on the decomposition of the computational domain into a number of non-overlapping subdomains wherein the CBFs are generated by employing a novel procedure, which differs from all those that have been used in the past. Clearly, the CBFs are obtained by calculating the fields radiated by a finite number of dipole-type sources, which are placed hypothetically along the boundary of the conducting object. The major advantages of the proposed technique are twofold: (i) it provides a substantial reduction in the matrix size, and thus, makes use of direct solvers efficiently and (ii) it enables the utilization of parallel processing techniques that considerably decrease the overall computation time. We illustrate the application of the proposed approach via several 3D electromagnetic scattering problems.

Domain compression via anisotropic metamaterials designed by coordinate transformations

We introduce a spatial coordinate transformation technique to compress the excessive white space (i.e. free-space) in the computational domain of finite methods. This approach is based on the form-invariance property of Maxwells equations under coordinate transformations. Clearly, Maxwells equations are still satisfied inside the transformed space, but the medium turns into an anisotropic medium whose constitutive parameters are determined by the coordinate transformation. The proposed technique can be employed to reduce the number of unknowns especially in high-frequency applications wherein a finite method requires an electrically-large computational domain. After developing the analytical background of this technique, we report some numerical results for finite element simulations of electromagnetic scattering problems.