Dear students and friends, welcome to my webpage.

I am a Professor of Electrical & Electronics Engineering Department @ Hacettepe University, Ankara, Turkey. My main research and teaching area is Electromagnetics. I invite you to surf through my webpage to learn the details about my activites. Enjoy !

• Resume
• Publications
• Projects
• Courses
• Students
• Research -1
• Research -2
• Research-3
• Research-4
• Research-5
• Contact

Resume

Publications

	Author(s)	Title	Publisher	Year
	O.Ozgun, M.Kuzuoglu	MATLAB-based Finite Element Programming in Electromagnetic Modeling   Book Review	CRC Press (ISBN: 9781498784078)	2018

Projects

Courses

Students

Research - 1

Transformation Electromagnetics (TEM)

1) Reshaping

Metamaterials –artificial materials with engineered electromagnetic properties—is a young but rapidly growing topic that breaks down traditional rules, and fascinates scientists in the field of physics, optics and electromagnetics. One of the major breakthroughs in the development of metamaterials is the cloaking device for obtaining electromagnetic invisibility, which can bend light around an object as if it weren't there. The design of the cloaking device is realized by the coordinate transformation technique, which is based on the fact that Maxwell’s equations are form-invariant under coordinate transformations. In other words, Maxwell’s equations preserve their form inside the transformed space, but the medium transforms into an anisotropic medium so that the electromagnetic fields are tuned by the coordinate transformation. Although the coordinate transformation technique has long been used in electromagnetic/physics, the novel interpretation of this technique realizing a cloaking device has emerged as one of the most exciting subjects in science and the general public alike. Being inspired by the cloaking device, we have focused on the design of anisotropic metamaterials using coordinate transformation techniques to control the propagation of electromagnetic fields in several useful applications. Our initial works on this topic were among the first attempts in designing such metamaterial structures. The purposes of these works were as follows: (i) reshaping objects in electromagnetic scattering via metamaterial coatings (this technique is a generalization of the cloaking approach for invisibility, and can be used to reduce the radar cross-section (RCS) of the objects); and (ii) reshaping and miniaturizing waveguides via metamaterial fillings.

Please refer to [7], [8], [14], [21], [35] in "international journal papers"; to [2] in "papers in other indexed international journals"; to [3], [6] in "international refereed conference papers"; to [3] in "national refereed conference papers", and to the book chapter in "Publications" section.

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2) Transformation Electromagnetics-aided Computational Electromagnetics

The reshaping approach inspired us to use the principles of transformation electromagnetics (TEM) to alleviate certain difficulties that arise in CEM methods. Therefore, we named such materials as "software metamaterials". The central idea is to modify the computational domain of the finite methods (such as the finite element method (FEM), or finite difference time domain method (FDTD)) and to place coordinate transformation-based metamaterial structures within the modified domain, and thus, to devise simple and efficient computer-aided simulation tools. Within this context, we worked on two approaches: (i) A method to fit curved geometries to a simple Cartesian grid or mesh in the finite methods. This technique can be helpful especially in the FDTD method in alleviating the effects of errors introduced by the staircasing approximation of curved geometries that do not conform to a Cartesian grid. (ii) Domain compression method to compress the excessive white space. (iii) Methods for solving electromagnetic boundary value problems involving large-scale or multi-scale features with multiple length or frequency scales or both. Multi-scale problems, in general, suffer from difficulties in mesh generation and the number of unknowns due to certain meshing requirements dictated by the fine features of the problem. Our metamaterial-based techniques allow uniform and easy-to-generate meshes by creating a virtual equivalent problem acting like the original problem.

Please refer to [11], [20], [26], [28], [36] in "international journal papers"; to [2], [3] in "papers in other indexed international journals"; to [12], [19], [20], [21], [22], [24] in "international refereed conference papers"; and to the book chapter in "Publications" section.

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3) Transformation Electromagnetics-aided Stochastic Electromagnetics (rough surface scattering problems)

When an object is placed near or within a "random" medium, the interaction or multiple scattering of both incident and scattered waves with the medium cause variations in the radar cross-section (RCS) of the object. A proper statistical characterization of the rough scattering problem is essential to understand the multiple scattering phenomenon in random media and rough surfaces. This topic is vital in a wide range of real-life applications, such as target detection and tracking, imaging and remote sensing, radar surveillance, and so on. To analyze this composite problem statistically, Monte Carlo technique can be realized by generating a set of random rough surfaces from a given probability distribution, and by solving the problem involving each surface using a numerical method. In this manner, a family of fields is generated arising from the repeated solutions, which are considered as the samples of a random process. Afterwards, various statistical parameters (such as mean, variance, probability density function, correlation functions, etc.) can be extracted from this random process. In this technique, one challenging issue is the repeated solution of the problem, which may put a heavy burden on computational resources. For example, if N number of surfaces are generated and if the problem is to be solved by using a finite method (such as finite element method), the mesh must be generated N times with respect to each surface and the problem must be solved N times. Given the large number of realizations and large size of the problem, computation time increases dramatically. We have proposed some computational models that make efficient repeated solutions in the Monte Carlo simulation of rough surface scattering problems by utilizing the concept of transformation electromagnetics. The main advantage is the ability to employ the same mesh in all realizations of the Monte Carlo simulation. Therefore, instead of generating the mesh N times, a single mesh is created over the smooth object and only the material parameters are altered for each of N surfaces. This achieves considerable saving in time and memory, and simplifies the mesh generation process.

Please refer to [29], [30], [31], [33], [34] in "international journal papers"; to [2] in "papers in other indexed international journals"; to [1] in "national journal papers"; to [23], [25], [27] in "international refereed conference papers"; to [8] in "national refereed conference papers" in "Publications" section.

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Research - 2

PETOOL v2.0: Parabolic Equation Toolbox with evaporation duct models and real environment data

Parabolic Equation Tool (PETOOL)

(Click to enlarge)

Radio-wave propagation over the Earth’s surface and in an inhomogeneous atmosphere is affected by several scattering phenomena, such as reflection, refraction, and diffraction. The rigorous analytical and numerical modeling of radio-wave propagation in such environments is a challenging task and has attracted the attention of researchers for many decades. The difficulty stems from the vast variability of the properties of the medium and also the surfaces and obstacles that re-direct the propagating energy, making the radio wave propagation somewhat unpredictable. Parabolic Equation (PE) model has been widely used in propagation modeling to predict the wave behavior between a transmitter and a receiver over the two-dimensional Earth’s surface, because of its high capability in modeling both horizontally- and vertically-varying atmospheric refraction (especially ducting) effects. However, standard PE handles only the forward-propagating waves (hence called one-way PE), and neglects the backscattered waves. The forward waves provide almost accurate results for typical long-range propagation problems, only if there does not exist obstacles that redirect the incoming wave in the form of reflections and diffractions. However, the accurate estimation of the multipath effects, occurring during propagation over terrain, requires the correct treatment of backward waves as well.

In 2009, I developed a two-way PE algorithm incorporating the backward-propagating waves into the standard one-way PE by utilizing an iterative forward-backward scheme for modeling multipath effects over a staircase-approximated terrain. This paper, which was published in Sept. 2009, has immediately initiated a collaboration with Dr. Sevgi, Dr. Apaydin and Dr. Kuzuoglu. We have developed a MATLAB-based software tool (called PETOOL) with a graphical user interface for educational/research purposes, and our computer codes are available for public use.

Please refer to [12], [22], [23], [25], [32] in "international journal papers"; to [10], [11], [17] in "international refereed conference papers"; to [5], [6], [9] in "national refereed conference papers" in "Publications" section.

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Click the video below to see the short demo of PETOOL:

Research - 3

Electromagnetic Tools

1) GO+UTD (Geometrical Optics and Uniform Theory of Diffraction Toolbox)

A MATLAB-based tool (GO+UTD) with a user-friendly graphical user interface (GUI) for the simulation of electromagnetic wave propagation and diffraction effects over variable terrain by using the geometrical optics (GO) and the uniform theory of diffraction (UTD) techniques.

Program download

Please refer to [41] for details.

2) VectGUI Tool

A simple MATLAB tool that visualizes functions and operators (e.g., gradient of scalar fields and divergence of vector fields) in the cylindrical and spherical coordinate systems.

Program download

Please refer to [37] for details.

Research - 4

Domain Decomposition Finite Element Algorithms

Finite Element Method (FEM) is a variational method developed for the approximate solution of Boundary Value Problems (BVPs) governed by partial differential equations, and is one of the most important developments in the history of computational methods, due to its two main advantages: (i) Flexibility to handle any type of geometry and material inhomogeneity without a need to alter the formulation or the computer code (geometrical fidelity). (ii) Low memory and CPU time requirements due to its highly sparse and banded matrix structure. The most distinctive feature of the FEM is the division of a given domain into a set of simple subdomains, called finite elements. The original domain (i.e., the FEM mesh) is then considered as an assembly of these elements connected at a finite number of preselected points, called nodes. The basic principle of the method is to replace the entire continuous domain with some number of finite elements in which the function is represented as a linear combination of some simple basis functions (also called shape, approximation or interpolation functions) with unknown coefficients. Hence, the solution of the entire system is approximated by a number of finite unknown coefficients. Then, the local system of algebraic relations is derived in each element by applying the Rayleigh-Ritz Method or most commonly the Weighted Residual Method (with Galerkin procedure). Finally, the local system of equations is assembled to obtain the global system of equations to solve for the unknown function.

In high-frequency applications (such as the calculation of the RCS of large targets, analysis and design of radar and communication systems), the FEM requires an electrically-large computational domain, implying a large number of unknowns, such that the numerical solution of the problem is not feasible even on state-of-the-art computers. Although the resultant matrix is sparse and can be stored by using a compressed storage scheme, the use of iterative solvers for these matrices usually creates a heavy burden on CPU memory and time due to the slow and unstable behavior of the convergence, even when accelerated by means of preconditioners. Hence, alternative techniques, such as the domain decomposition (DD) methods, have been employed to alleviate this difficulty. A general DD approach, which is based on the divide-and-conquer philosophy, breaks down a large-scale problem into a number of small subproblems whose solution is manageable. The subdomains are solved iteratively (or non-iteratively in some cases) by appropriately communicating with the others. Then, the solution of the original (whole) problem is reached by assembling the solution of all subdomains. A DD method is intrinsically suitable for the parallel computation of the subdomains, providing a further decrease in the overall computation time.

In the context of FEM, we have developed alternative domain decompositon techniques as below:

1) Characteristic Basis Finite Element Method (CBFEM)

My postdoctoral research in Pennsylvania State University concentrated on a novel domain decomposition finite element algorithm (called Characteristic Basis Finite Element Method (CBFEM)) that is tailored to a wide class of electromagnetic boundary problems, covering both quasi-static and time-harmonic regimes, by using the concept of Characteristic Basis Functions (CBFs). This is a non-iterative matrix-reduction technique, and is well-suited to the implementation of parallel processing techniques using such as the Message Passing Interface (MPI) library. Basically, this method utilizes a set of specially-defined CBFs in conjunction with a domain decomposition scheme that partitions the computational domain into a number of non-overlapping subdomains. The CBFs—macro-domain basis functions that are constructed in each subdomain by considering the physics of the problem—were originally proposed by Dr. Raj Mittra to solve time-harmonic electromagnetic problems in the context of the Method of Moments. he basic steps of the CBFEM technique are as follows: (i) partition the computational domain into a number of subdomains, and generate the CBFs tailored to each individual subdomain; (ii) express the unknowns as a series of these CBFs that are weighted with unknown coefficients yet to be determined; (iii) transform the original matrix into a "smaller" one (i.e., reduced matrix) by using the Galerkin procedure, which uses the CBFs as both basis and testing functions; (iv) solve the reduced matrix for the unknown coefficients, and substitute the coefficients into the series expressions to obtain the unknown quantities inside the entire computational domain. Common attributes of the CBFEM are: (i) capability to reduce the matrix size; (ii) non-iterative nature; and (iii) convenient parallelization, which decreases the memory and overall computation time when run on multiple processors.

First, we concentrated on the implementation of CBFEM in the static regime by generating the CBFs via point charges, and developed 3D parallel FEM and mesh generation codes to compute the capacitance matrices of 3D interconnect structures, which include vias, crossovers and bends, in integrated circuit packaging. Second, we extended this method to the dynamic case, and dealt with the RCS computation of large objects in 3D electromagnetic scattering problems by employing different approaches (such as hybridizing CBFEM with physical optics (PO) approach, generating the CBFs via dipole-type sources, or multi-level approach that applies CBFEM in a nested manner, etc.).

Please refer to [13], [15], [16], [18], [19], [24], [27] in "international journal papers"; to [4], [5], [8], [9], [13], [15], [16] in "international refereed conference papers"; to [4] in "national refereed conference papers" in "Publications" section.

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2) Iterative Leap-field Domain Decomposition Method (ILF-DDM)

The main idea of the ILF-DDM approach is the iterative application of the Huygens' (or equivalence) Principle to the fields radiated by the equivalent currents calculated in each iteration. In other words, in each iteration, each subproblem is solved and equivalent currents are calculated using the fields radiated from the sources contained in other subdomains, and these currents are reradiated over all other subdomains, until a condition for convergence is satisfied. The most distinguished feature of the ILF-DDM approach is the utilization of the locally-conformal PML concept along the boundaries of the subdomains. With the aid of the locally-conformal PML approach, the ILF-DDM algorithm can be applied to not only cases involving multiple objects but also problems containing a single challenging object in FEM applications. In addition to this, due to the special character of the locally-conformal PML approach and the FEM, the ILF-DDM creates 'smaller' subdomains because the locally-conformal PML can be designed as conformal and very close to the surface of the object. The solution of each small subproblem is reduced to the solution of an ordinary scattering problem with appropriately defined boundary conditions, but with fewer unknowns. Thus, the most appealing advantage of the method is considerable reduction in memory requirements and computation time. It is observed that convergence is achieved after a few iterations and computation time may further be reduced via the parallel solution of the subproblems.

Please refer to [10], [17] in "international journal papers" in "Publications" section.

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3) Forward-Backward Domain Decomposition Method (FB-DDM)

The FB-DDM is established on the classical alternating Schwarz method with overlapping subdomains. However, the FB-DDM implements the Schwarz method by taking into account certain physical aspects of the original (whole) problem. That is, the Schwarz method is improved in terms of efficiency and rate of convergence by considering the geometry of the problem and the expected field behavior inside the original domain. This is achieved by the implementation of the locally-conformal PML (perfectly matched layer) method along the boundaries of the subdomains. In some problems involving smooth geometries, the FB-DDM converges in just a single forward iteration (i.e., the method is non-iterative), where the problem in each subdomain is solved only once by appropriately defined subdomains and additional PML regions attached to each subdomain. In other challenging geometries, the initial forward iteration of the FB-DDM provides an initial guess 'close' to the exact values of the boundary conditions (BCs) of each subdomain, unlike the 'arbitrary' initial guess in the Schwarz method. After the initial forward iteration, the problems defined on the subdomains are solved iteratively, similar to the Schwarz method, in a forward-backward fashion until convergence is achieved. It is obvious that the better initial guess for the BCs provides an increased convergence rate by decreasing the number of the forward-backward iterations during the field refinement process. In addition, the proposed method provides a considerable reduction in the memory requirements and computation time.

Please refer to [6] in "international journal papers";and to [7] in "international refereed conference papers" in "Publications" section.

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Research - 5

Perfectly Matched Layer (PML) Algorithms

In the numerical solution of open-region electromagnetic radiation and/or scattering problems via finite methods (such as the finite element method FEM, and the finite difference time domain method FDTD), the unbounded physical domain must be truncated by an artificial boundary or layer to achieve a bounded computational domain. One of the most widely-used approaches is to employ a Perfectly Matched Layer (PML), which is an artificial anisotropic layer absorbing outgoing plane waves irrespective of their frequency and angle of incidence, without any reflection. In other words, the PML medium achieves smooth field decay to couple the computational domain to the free-space region of infinite extent without any undesirable reflections. The main advantage of the PML is the minimization of the white space (i.e., free-space) due to its close proximity and conformity to the surface of the object. Almost all of the PML realizations introduced so far in the literature have been implemented in a rectangular prism that does not have arbitrary curvature discontinuities.

The novel PML methods (called "Locally-conformal PML" and "Multi-center PML" methods) that we have developed recently utilize specially- and locally-defined complex coordinate transformations, and thus, make possible the easy design of conformal PMLs having challenging geometries, especially having some intersection regions or abrupt changes in curvature. Such conformal PML domains are very crucial especially in radiation and scattering problems, because they decrease the computational demand (such as memory and processing power) on account of a minimization of the white space. The locally-conformal PML and multi-center PML methods are designed in complex space by just replacing the real coordinates with their complex counterparts calculated in terms of the complex coordinate transformation. In their formulations, Maxwell's equations are modified accordingly inside the complex space, and the elements in the real coordinate system are mapped to the complex elements (i.e., elements whose nodal coordinates are complex) in complex space. Then, the weak variational form of the wave equation is discretized using these complex elements which are determined by the complex coordinate transformation.

Please refer to [2], [3], [4], [5], [9] in "international journal papers"; to [2] in "international refereed conference papers"; to [2] in "national refereed conference papers" in "Publications" section.

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