Computational Electromagnetics Research Center (BiLCEM)

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https://hdl.handle.net/11693/48239

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Open Access
Modeling and synthesis of circular‐sectoral arrays of log‐periodic antennas using multilevel fast multipole algorithm and genetic algorithms
(Wiley-Blackwell Publishing, Inc., 2007-06-17) Ergül, Özgür; Gürel, Levent
Circular‐sectoral arrays of log‐periodic (LP) antennas are presented for frequency‐independent operation and beam‐steering capability. Specifically, nonplanar trapezoidal tooth LP antennas are considered in a circular array configuration, where closely spaced antennas occupy a sector of the circle. Electromagnetic interactions of the array elements, each of which is a complicated LP antenna structure, are rigorously computed with the multilevel fast multipole algorithm (MLFMA). Genetic algorithms (GAs) are also employed in combination with MLFMA for synthesis and design purposes. By optimizing the excitations of the array elements via GAs, beam‐steering ability is achieved in addition to the broadband (nearly frequency‐independent) characteristics of the designed arrays. Computational results are presented to demonstrate the important properties of LP arrays.
Open Access
Reply to "Comments on 'The Use of curl-conforming basis functions for the magnetic-field integral equation'"
(Institute of Electrical and Electronics Engineers, 2008) Ergül, Özgür; Gürel, Levent
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 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
Accelerating the multilevel fast multipole algorithm with the sparse-approximate-inverse (SAI) preconditioning
(Society for Industrial and Applied Mathematics, 2009) Malas, T.; Gürel, Levent
With the help of the multilevel fast multipole algorithm, integral-equation methods can be used to solve real-life electromagnetics problems both accurately and efficiently. Increasing problem dimensions, on the other hand, necessitate effective parallel preconditioners with low setup costs. In this paper, we consider sparse approximate inverses generated from the sparse near-field part of the dense coefficient matrix. In particular, we analyze pattern selection strategies that can make efficient use of the block structure of the near-field matrix, and we propose a load-balancing method to obtain high scalability during the setup. We also present some implementation details, which reduce the computational cost of the setup phase. In conclusion, for the open-surface problems that are modeled by the electric-field integral equation, we have been able to solve ill-conditioned linear systems involving millions of unknowns with moderate computational requirements. For closed surface problems that can be modeled by the combined-field integral equation, we reduce the solution times significantly compared to the commonly used block-diagonal preconditioner.
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.
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
Hybridizing physical optics with MLFMA for efficient scattering computations of three-dimensional complex targets
(IEEE, 2009-07) Manyas, Alp; Ergül, Özgür; Gürel, Levent
The multilevel fast multipole algorithm (MLFMA) provides accurate and efficient solutions of electromagnetic scattering problems involving large and complicated structures. On the other hand, whenever applicable, accelerations provided by approximation techniques can be useful to further improve the efficiency of solutions. In this paper, we present a hybrid technique, which combines the physical-optics (PO) method and MLFMA for efficient scattering computations of three-dimensional objects. We show that, with a careful choice of MLFMA and PO regions on the structure, the number of unknowns can be reduced and solutions can be accelerated significantly, without sacrificing the accuracy. The proposed hybrid technique is easy to implement by modifying existing MLFMA codes. ©2009 IEEE.
Open Access
Fast and accurate solutions of extremely large scattering problems involving three-dimensional canonical and complicated objects
(IEEE, 2009-07) Ergül, Özgür; Gürel, Levent
We present fast and accurate solutions of extremely large scattering problems involving three-dimensional metallic objects discretized with hundreds of millions of unknowns. Solutions are performed by the multilevel fast multipole algorithm, which is parallelized efficiently via a hierarchical partition strategy. Various examples involving canonical and complicated objects are presented in order to demonstrate the feasibility of accurately solving large-scale problems on relatively inexpensive computing platforms without resorting to approximation techniques. ©2009 IEEE.
Open Access
An effective preconditioner based on schur complement reduction for integral-equation formulations of dielectric problems
(IEEE, 2009) Malas, Tahir; Gürel, Levent
The author consider effective preconditioning of recently proposed two integral-equation formulations for dielectrics; the combined tangential formulation (CTF) and the electric and magnetic current combined-field integral equation (JMCFIE). These two formulations are of utmost interest since CTF yields more accurate results and JMCFIE yields better-conditioned systems than other formulations.
Open Access
Scalable parallelization of the sparse-approximate-inverse (SAl) preconditioner for the solution of large-scale integral-equation problems
(IEEE, 2009-06) Malas, Tahir; Gürel, Levent
In this paper, we consider efficient parallelization of the sparse approximate inverse (SAI) preconditioner in the context of the multilevel fast multipole algorithm (MLFMA). Then, we report the use of SAI in the solution of very large EFIE problems. The SAI preconditioner is important not only because it is a robust preconditioner that renders many difficult and large problems solvable, but also it can be utilized for the construction of more effective preconditioners.
Open Access
Solutions of electromagnetics problems involving hundreds of millions of unknowns with parallel multilevel fast multipole algorithmt
(IEEE, 2009-06) Ergül, Özgür; Gürel, Levent
We present the solution of extremely large electromagnetics problems formulated with surface integral equations (SIEs) and discretized with hundreds of millions of unknowns. Scattering and radiation problems involving three-dimensional closed metallic objects are formulated rigorously by using the combined-field integral equation (CFIE). Surfaces are discretized with small triangles, on which the Rao-Wilton-Glisson (RWG) functions are defined to expand the induced electric current and to test the boundary conditions for the tangential electric and magnetic fields. Discretizations of large objects with dimensions of hundreds of wavelengths lead to dense matrix equations with hundreds of millions of unknowns. Solutions are performed iteratively, where the matrix-vector multiplications are performed efficiently by using the multilevel fast multipole algorithm (MLFMA). Solutions are also parallelized on a cluster of computers using a hierarchical partitioning strategy, which is well suited for the multilevel structure of MLFMA. Accuracy and efficiency of the implementation are demonstrated on electromagnetic problems involving as many as 205 million unknowns, which are the largest integral-equation problems ever solved in the literature.
Open Access
Preconditioned MLFMA solution of multiple dielectric-metallic composite objects with the electric and magnetic current combined-field integral equation (JMCFIE)
(IEEE, 2009-06) Ergül, Özgür; Gürel, Levent
We consider fast and accurate solutions of scattering problems involving multiple dielectric and composite dielectric-metallic structures with three-dimensional arbitrary shapes. Problems are formulated rigorously with the electric and magnetic current combined-field integral equation (JMCFIE), which produces well-conditioned matrix equations. Equivalent electric and magnetic surface currents are discretized by using the Rao-Wilton-Glisson (RWG) functions defined on planar triangles. Matrix equations obtained with JMCFIE are solved iteratively by employing a Krylov subspace algorithm, where the required matrix- vector multiplications are performed efficiently with the multilevel fast multipole algorithm (MLFMA). We also present a four-partition block-diagonal preconditioner (4PBDP), which provides efficient solutions of JMCFIE by reducing the number of iterations significantly. The resulting implementation based on JMCFIE, MLFMA, and 4PBDP is tested on large electromagnetics problems.
Open Access
On the errors arising in surface integral equations due to the discretization of the identity operator
(IEEE, 2009) Ergül, Özgür; Gürel, Levent
Surface integral equations (SIEs) are commonly used to formulate scattering and radiation problems involving three-dimensional metallic and homogeneous dielectric objects with arbitrary shapes. For numerical solutions, equivalent electric and/or magnetic currents defined on surfaces are discretized and expanded in a series of basis functions. Then, the boundary conditions are tested on surfaces via a set of testing functions. Solutions of the resulting dense matrix equations provide the expansion coefficients of the equivalent currents, which can be used to compute the scattered or radiated electromagnetic fields. This study consists of two parts. In the first part, the authors show that the identity operator is truly a major error source in normal and mixed formulations that are discretized with low-order functions, e.g., Rao-Wilton-Glisson (RWG) functions. In the second part, the authors investigate the incompatibility of SIE formulations in the context of iterative solutions. The authors show that a compatibility test can be used to determine the breakpoint, where the accuracy of the solution is saturated and cannot be enhanced any more.
Open Access
Fast and accurate analysis of complicated metamaterial structures using a low-frequency multilevel fast multipole algorithm
(2009-09) Ergül, Özgür; Gürel, Levent
We present efficient solutions of electromagnetics problems involving realistic metamaterial structures using a low-frequency multilevel fast multipole algorithm (LF-MLFMA). Ordinary implementations of MLFMA based on the diago-nalization of the Green's function suffer from the low-frequency breakdown, and they become inefficient for the solution of metamaterial problems dis-cretized with very small elements compared to the wavelength. We show that LF-MLFMA, which employs multipoles explicitly without diagonalization, significantly improves the solution of metamaterial problems in terms of both processing time and memory. © 2009 IEEE.
Open Access
Rigorous solutions of large-scale scattering problems discretized with hundreds of millions of unknowns
(2009-09) Gürel, Levent; Ergül, Özgür
We present fast and accurate solutions of large-scale scattering problems using a parallel implementation of the multilevel fast multipole algorithm (MLFMA). By employing a hierarchical partitioning strategy, MLFMA can be parallelized efficiently on distributed-memory architectures. This way, it becomes possible to solve very large problems discretized with hundreds of millions of unknowns. Effectiveness of the developed simulation environment is demonstrated on various scattering problems involving canonical and complicated objects. © 2009 IEEE.
Open Access
Rigorous solutions of scattering problems involving red blood cells
(IEEE, 2010) Ergül, Özgür; Arslan-Ergül, Ayça; Gürel, Levent
We present rigorous solutions of scattering problems involving healthy red blood cells (RBCs) and diseased RBCs with deformed shapes. Scattering cross-section (SCS) values for different RBC shapes and different orientations are obtained accurately and efficiently using a sophisticated simulation environment based on the electric and magnetic current combinedfield integral equation and the multilevel fast multipole algorithm. Using SCS values, we determine strict guidelines to distinguish deformed RBCs from healthy RBCs and to diagnose related diseases.
Open Access
Advanced partitioning and communication strategies for the efficient parallelization of the multilevel fast multipole algorithm
(IEEE, 2010) Ergül O.; Gürel, Levent
Large-scale electromagnetics problems can be solved efficiently with the multilevel fast multipole algorithm (MLFMA) [1], which reduces the complexity of matrix-vector multiplications required by iterative solvers from O(N 2) to O(N logN). Parallelization of MLFMA on distributed-memory architectures enables fast and accurate solutions of radiation and scattering problems discretized with millions of unknowns using limited computational resources. Recently, we developed a hierarchical partitioning strategy [2], which provides an efficient parallelization of MLFMA, allowing for the solution of very large problems involving hundreds of millions of unknowns. In this strategy, both clusters (sub-domains) of the multilevel tree structure and their samples are partitioned among processors, which leads to improved load-balancing. We also show that communications between processors are reduced and the communication time is shortened, compared to previous parallelization strategies in the literature. On the other hand, improved partitioning of the tree structure complicates the arrangement of communications between processors. In this paper, we discuss communications in detail when MLFMA is parallelized using the hierarchical partitioning strategy. We present well-organized arrangements of communications in order to maximize the efficiency offered by the improved partitioning. We demonstrate the effectiveness of the resulting parallel implementation on a very large scattering problem involving a conducting sphere discretized with 375 million unknowns. ©2010 IEEE.
Open Access
Preconditioning iterative MLFMA solutions of integral equations
(IEEE, 2010) Gürel, Levent; Malas, Tahir; Ergül, Özgür
The multilevel fast multipole algorithm (MLFMA) is a powerful method that enables iterative solutions of electromagnetics problems with low complexity. Iterative solvers, however, are not robust for three-dimensional complex reallife problems unless suitable preconditioners are used. In this paper, we present our efforts to devise effective preconditioners for MLFMA solutions of difficult electromagnetics problems involving both conductors and dielectrics. © 2010 IEEE.
Open Access
An efficient parallel implementation of the multilevel fast multipole algorithm for rigorous solutions of large-scale scattering problems
(IEEE, 2010) Ergül O.; Gürel, Levent
We present the solution of large-scale scattering problems discretized with hundreds of millions of unknowns. The multilevel fast multipole algorithm (MLFMA) is parallelized using the hierarchical partitioning strategy on distributed-memory architectures. Optimizations and load-balancing algorithms are extensively used to improve parallel MLFMA solutions. The resulting implementation is successfully employed on modest parallel computers to solve scattering problems involving metallic objects larger than 1000λ and discretized with more than 300 million unknowns. © 2010 IEEE.