Computational Electromagnetics Research Center (BİLCEM)

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Open Access
Accuracy and efficiency considerations in the solution of extremely large electromagnetics problems
(IEEE, 2011) Gürel, Levent; Ergül, Özgür
This study considers fast and accurate solutions of extremely large electromagnetics problems. Surface formulations of large-scale objects lead to dense matrix equations involving millions of unknowns. Thanks to recent developments in parallel algorithms and high-performance computers, these problems can easily be solved with unprecedented levels of accuracy and detail. For example, using a parallel implementation of the multilevel fast multipole algorithm (MLFMA), we are able to solve electromagnetics problems discretized with hundreds of millions of unknowns. Unfortunately, as the problem size grows, it becomes difficult to assess the accuracy and efficiency of the solutions, especially when comparing different implementations. This paper presents our efforts to solve extremely large electromagnetics problems with an emphasis on accuracy and efficiency. We present a list of benchmark problems, which can be used to compare different implementations for large-scale problems. © 2011 IEEE.
Open Access
Accurate modeling of metamaterials with MLFMA
(ESA Publications, 2006) Ergül, Özgür; Ünal, Alper; Gürel, Levent
Electromagnetic modelling of large metamaterial (MM) structures employing multilevel fast multipole algorithm (MLFMA) is reported. MMs are usually constructed by periodically embedding unit cells, such as split-ring resonators (SRRs), into a host medium. Without utilizing any homogenization techniques, we accurately model large numbers of unit cells that translate into very large computational problems. By considering all of the electromagnetic interactions, the resulting dense matrix equations are solved iteratively with the accelerated matrix-vector products by MLFMA. To increase the efficiency, we also employ parallel computing in the solutions of large SRR problems.
Open Access
Accurate solutions of scattering problems involving low-contrast dielectric objects with surface integral equations
(Institution of Engineering and Technology, 2007) Ergül, Özgür; Gürel, Levent
We present the stabilization of the surface integral equations for accurate solutions of scattering problems involving low-contrast dielectric objects. Unlike volume formulations, conventional surface formulations fail to provide accurate results for the scattered fields when the contrast of the object is small. Therefore, surface formulations are required to be stabilized by extracting the nonradiating parts of the equivalent currents. In addition to previous strategies for the stabilization, we introduce a novel procedure called field-based stabilization (FBS) based on using fictitious incident fields and rearranging the right-hand-side of the equations. The results show that the formulations using FBS provide accurate results even for scattering problems involving extremely low-contrast objects, while the extra cost due to the stabilization procedure is negligible.
Open Access
Analysis of dielectric photonic-crystal problems with MLFMA and Schur-complement preconditioners
(IEEE, 2011-01-13) Ergül, Özgür; Malas, T.; Gürel, Levent
We present rigorous solutions of electromagnetics problems involving 3-D dielectric photonic crystals (PhCs). Problems are formulated with recently developed surface integral equations and solved iteratively using the multilevel fast multipole algorithm (MLFMA). For efficient solutions, iterations are accelerated via robust Schur-complement preconditioners. We show that complicated PhC structures can be analyzed with unprecedented efficiency and accuracy by an effective solver based on the combined tangential formulation, MLFMA, and Schur-complement preconditioners.
Open Access
Analysis of photonic-crystal problems with MLFMA and approximate Schur preconditioners
(IEEE, 2009-07) Ergül, Özgür; Malas, Tahir; Kılınç, Seçil; Sarıtaş, Serkan; Gürel, Levent
We consider fast and accurate solutions of electromagnetics problems involving three-dimensional photonic crystals (PhCs). Problems are formulated with the combined tangential formulation (CTF) and the electric and magnetic current combined-field integral equation (JMCFIE) discretized with the Rao-Wilton-Glisson functions. Matrix equations are solved iteratively by the multilevel fast multipole algorithm. Since PhC problems are difficult to solve iteratively, robust preconditioning techniques are required to accelerate iterative solutions. We show that novel approximate Schur preconditioners enable efficient solutions of PhC problems by reducing the number of iterations significantly for both CTF and JMCFIE. ©2009 IEEE.
Open Access
Approximate MLFMA as an efficient preconditioner
(IEEE, 2007) Malas, Tahir; Ergül, Özgür; Gürel, Levent
In this work, we propose a preconditioner that approximates the dense system operator. For this purpose, we develop an approximate multilevel fast multipole algorithm (AMLFMA), which performs a much faster matrix-vector multiplication with some relative error compared to the original MLFMA. We use AMLFMA to solve a closely related system, which makes up the preconditioner. Then, this solution is embedded in the main solution that uses MLFMA. By taking into account the far-field elements wisely, this preconditioner proves to be much more effective compared to the near-field preconditioners.
Open Access
Circular arrays of log-periodic antennas for broadband applications
(IEEE, 2006) Ergül, Özgür; Gürel, Levent
Circular arrays of log-periodic (LP) antennas are designed for broadband applications. A sophisticated electromagnetic simulation environment involving integral equations and fast solvers is developed to analyze the LP arrays both accurately and efficienuy. The resulting matrix equation obtained by the discretization of the electric field integral equation is solved iteratively via the multilevel fast multipole algorithm (MLFMA). Genetic algorithms interacting with MLFMA is employed to optimize the excitations of the array elements to increase the frequency independence and also to add the beam-steering ability to the arrays.
Open Access
Comparison of integral-equation formulations for the fast and accurate solution of scattering problems involving dielectric objects with the multilevel fast multipole algorithm
(Institute of Electrical and Electronics Engineers, 2009) Ergül, Özgür; Gürel, Levent
We consider fast and accurate solutions of scattering problems involving increasingly large dielectric objects formulated by surface integral equations. We compare various formulations when the objects are discretized with Rao-Wilton-Glisson functions, and the resulting matrix equations are solved iteratively by employing the multilevel fast multipole algorithm (MLFMA). For large problems, we show that a combined-field formulation, namely, the electric and magnetic current combined-field integral equation (JMCFIE), requires fewer iterations than other formulations within the context of MLFMA. In addition to its efficiency, JMCFIE is also more accurate than the normal formulations and becomes preferable, especially when the problems cannot be solved easily with the tangential formulations.
Open Access
Computational analysis of complicated metamaterial structures using MLFMA and nested preconditioners
(IEEE, 2007-11) Ergül, Özgür; Malas, Tahir; Yavuz, Ç; Ünal, Alper; Gürel, Levent
We consider accurate solution of scattering problems involving complicated metamaterial (MM) structures consisting of thin wires and split-ring resonators. The scattering problems are formulated by the electric-field integral equation (EFIE) discretized with the Rao-Wilton- Glisson basis functions defined on planar triangles. The resulting dense matrix equations are solved iteratively, where the matrix-vector multiplications that are required by the iterative solvers are accelerated with the multilevel fast multipole algorithm (MLFMA). Since EFIE usually produces matrix equations that are ill-conditioned and difficult to solve iteratively, we employ nested preconditioners to achieve rapid convergence of the iterative solutions. To further accelerate the simulations, we parallelize our algorithm and perform the solutions on a cluster of personal computers. This way, we are able to solve problems of MMs involving thousands of unit cells.
Open Access
Computational study of scattering from healthy and diseased red blood cells
(Society of Photo Optical Instrumentation Engineers, 2010-08-05) Ergül, Özgür; Arslan-Ergül, A.; Gürel, Levent
We present a comparative study of scattering from healthy red blood cells (RBCs) and diseased RBCs with deformed shapes. Scattering problems involving three-dimensional RBCs are formulated accurately with the electric and magnetic current combined-field integral equation and solved efficiently by the multilevel fast multipole algorithm. We compare scattering cross section values obtained for different RBC shapes and different orientations. In this way, we determine strict guidelines to distinguish deformed RBCs from healthy RBCs and to diagnose various diseases using scattering cross section values. The results may be useful for designing new and improved flow cytometry procedures.
Open Access
Contamination of the accuracy of the combined-field integral equation with the discretization error of the magnetic-field integral equation
(Institute of Electrical and Electronics Engineers, 2009) Gürel, Levent; Ergül, Özgür
We investigate the accuracy of the combined-field integral equation (CFIE) discretized with the Rao-Wilton-Glisson (RWG) basis functions for the solution of scattering and radiation problems involving three-dimensional conducting objects. Such a low-order discretization with the RWG functions renders the two components of CFIE, i.e., the electric-field integral equation (EFIE) and the magnetic-field integral equation (MFIE), incompatible, mainly because of the excessive discretization error of MFIE. Solutions obtained with CFIE are contaminated with the MFIE inaccuracy, and CFIE is also incompatible with EFIE and MFIE. We show that, in an iterative solution, the minimization of the residual error for CFIE involves a breakpoint, where a further reduction of the residual error does not improve the solution in terms of compatibility with EFIE, which provides a more accurate reference solution. This breakpoint corresponds to the last useful iteration, where the accuracy of CFIE is saturated and a further reduction of the residual error is practically unnecessary.
Open Access
Design and simulation of circular arrays of trapezoidal-tooth log-periodic antennas via genetic optimization
(Electromagnetics Academy, 2008) Gürel, Levent; Ergül, Özgür
Circular arrays of log-periodic (LP) antennas are designed and their operational properties are investigated in a sophisticated simulation environment that is based on the recent advances in computational electromagnetics. Due to the complicated structures of the trapezoidal-tooth array elements and the overall array configuration, their analytical treatments are prohibitively difficult. Therefore, the simulation results presented in this paper are essential for their analysis and design. We present the design of a three-element LP array showing broadband characteristics. The directive gain is stabilized in the operation band using optimization by genetic algorithms. We demonstrate that the optimization procedure can also be used to provide beam-steering ability to LP arrays.
Open Access
Discretization error due to the identity operator in surface integral equations
(ELSEVIER, 2009-05-03) Ergül, Özgür; Gürel, Levent
We consider the accuracy of surface integral equations for the solution of scattering and radiation problems in electromagnetics. In numerical solutions, second-kind integral equations involving well-tested identity operators are preferable for efficiency, because they produce diagonally-dominant matrix equations that can be solved easily with iterative methods. However, the existence of the well-tested identity operators leads to inaccurate results, especially when the equations are discretized with low-order basis functions, such as the Rao-Wilton-Glisson functions. By performing a computational experiment based on the nonradiating property of the tangential incident fields on arbitrary surfaces, we show that the discretization error of the identity operator is a major error source that contaminates the accuracy of the second-kind integral equations significantly.
Open Access
Effective preconditioners for large integral-equation problems
(IET, 2007-11) Malas, Tahir; Ergül, Özgür; Gürel, Levent
We consider effective preconditioning schemes for the iterative solution of integral-equation methods. For parallel implementations, the sparse approximate inverse or the iterative solution of the near-field system enables fast convergence up to certain problem sizes. However, for very large problems, the near-field matrix itself becomes too crude approximation to the dense system matrix and preconditioners generated from the near-field interactions cannot be effective. Therefore, we propose an approximation strategy to the multilevel fast multipole algorithm (MLFMA) to be used as a preconditioner. Our numerical experiments reveal that this scheme significantly outperforms other preconditioners. With the combined effort of effective preconditioners and an efficiently parallelized MLFMA, we are able to solve targets with tens of millions of unknowns in a few hours.
Open Access
Efficient parallelization of the multilevel fast multipole algorithm for the solution of large-scale scattering problems
(Institute of Electrical and Electronics Engineers, 2008-08) Ergül, Özgür; Gürel, Levent
We present fast and accurate solutions of large-scale scattering problems involving three-dimensional closed conductors with arbitrary shapes using the multilevel fast multipole algorithm (MLFMA). With an efficient parallelization of MLFMA, scattering problems that are discretized with tens of millions of unknowns are easily solved on a cluster of computers. We extensively investigate the parallelization of MLFMA, identify the bottlenecks, and provide remedial procedures to improve the efficiency of the implementations. The accuracy of the solutions is demonstrated on a scattering problem involving a sphere of radius 110 discretized with 41 883 638 unknowns, the largest integral-equation problem solved to date. In addition to canonical problems, we also present the solution of real-life problems involving complicated targets with large dimensions
Open Access
Efficient solution of the combined-field integral equation with the parallel multilevel fast multipole algorithm
(IEEE, 2007-08) Gürel, Levent; Ergül, Özgür
We present fast and accurate solutions of large-scale scattering problems formulated with the combined-field integral equation. Using the multilevel fast multipole algorithm (MLFMA) parallelized on a cluster of computers, we easily solve scattering problems that are discretized with tens of millions of unknowns. For the efficient parallelization of MLFMA, we propose a hierarchical partitioning scheme based on distributing the multilevel tree among the processors with an improved load-balancing. The accuracy of the solutions is demonstrated on scattering problems involving spheres of various radii from 80λ to 110λ. In addition to canonical problems, we also present the solution of real-life problems involving complicated targets with large dimensions. © 2007 IEEE.
Open Access
Efficient solution of the electric and magnetic current combined‐field integral equation with the multilevel fast multipole algorithm and block‐diagonal preconditioning
(Wiley-Blackwell Publishing, Inc., 2009-12) Ergül, Özgür; Gürel, Levent
We consider the efficient solution of electromagnetics problems involving dielectric and composite dielectric-metallic structures, formulated with the electric and magnetic current combined-field integral equation (JMCFIE). Dense matrix equations obtained from the discretization of JMCFIE with Rao-Wilton-Glisson functions are solved iteratively, where the matrix-vector multiplications are performed efficiently with the multilevel fast multipole algorithm. JMCFIE usually provides well conditioned matrix equations that are easy to solve iteratively. However, iteration counts and the efficiency of solutions depend on the contrast, i.e., the relative variation of electromagnetic parameters across dielectric interfaces. Owing to the numerical imbalance of off-diagonal matrix partitions, solutions of JMCFIE become difficult with increasing contrast. We present a four-partition block-diagonal preconditioner (4PBDP), which provides efficient solutions of JMCFIE by reducing the number of iterations significantly. 4PBDP is useful, especially when the contrast increases, and the standard block-diagonal preconditioner fails to provide a rapid convergence.
Open Access
Efficient solution of the electric-field integral equation using the iterative LSQR algorithm
(Institute of Electrical and Electronics Engineers, 2008) Ergül, Özgür; Gürel, Levent
In this letter, we consider iterative solutions of the three-dimensional electromagnetic scattering problems formulated by surface integral equations. We show that solutions of the electric-field integral equation (EFIE) can be improved by employing an iterative least-squares QR (LSQR) algorithm. Compared to many other Krylov subspace methods, LSQR provides faster convergence and it becomes an alternative choice to the time-efficient no-restart generalized minimal residual (GMRES) algorithm that requires large amounts of memory. Improvements obtained with the LSQR algorithm become significant for the solution of large-scale problems involving open surfaces that must be formulated using EFIE, which leads to matrix equations that are usually difficult to solve iteratively, even when the matrix-vector multiplications are accelerated via the multilevel fast multipole algorithm.
Open Access
Efficient solutions of metamaterial problems using a low-frequency multilevel fast multipole algorithm
(2010) Ergül, Özgür; Gürel, Levent
We present fast and accurate solutions of electromagnetics problems involving realistic metamaterial structures using a lowfrequency multilevel fast multipole algorithm (LF-MLFMA). Accelerating iterative solutions using robust preconditioning techniques may not be sufficient to reduce the overall processing time when the ordinary high-frequency MLFMA is applied to metamaterial problems. The major bottleneck, i.e., the low-frequency breakdown, should be eliminated for efficient solutions. We show that the combination of an LF-MLFMA implementation based on the multipole expansion with the sparse-approximate-inverse preconditioner enables efficient and accurate analysis of realistic metamaterial structures. Using the robust LF-MLFMA implementation, we demonstrate how the transmission properties of metamaterial walls can be enhanced with randomlyoriented unit cells.
Open Access
Efficient surface integral equation methods for the analysis of complex metamaterial structures
(IEEE, 2009) Yla-Oijala, P.; Ergül, Özgür; Gürel, Levent; Taskinen, M.
Two approaches, the multilevel fast multipole algorithm with sparse approximate inverse preconditioner and the surface equivalence principle algorithm, are applied to analyze complex three-dimensional metamaterial structures. The efficiency and performance of these methods are studied and discussed.