Computational Electromagnetics Research Center (BİLCEM)

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Browsing Computational Electromagnetics Research Center (BİLCEM) by Subject "Algorithms"

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Now showing 1 - 13 of 13
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    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.
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    Algebraic acceleration and regularization of the source reconstruction method with the recompressed adaptive cross approximation
    (IEEE, 2014) Kazempour, Mahdi; Gürel, Levent
    We present a compression algorithm to accelerate the solution of source reconstruction problems that are formulated with integral equations and defined on arbitrary three-dimensional surfaces. This compression technique benefits from the adaptive cross approximation (ACA) algorithm in the first step. A further error-controllable recompression is applied after the ACA. The numerical results illustrate the efficiency and accuracy of the proposed method. © 2014 IEEE.
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    Analysis of double-negative materials with surface integral equations and the multilevel fast multipole algorithm
    (IEEE, 2011) Ergül O.; Gürel, Levent
    We present a fast and accurate analysis of double-negative materials (DNMs) with surface integral equations and the multilevel fast multipole algorithm (MLFMA). DNMs are commonly used as simplified models of metamaterials at resonance frequencies and are suitable to be formulated with surface integral equations. However, realistic metamaterials and their models are usually very large with respect to wavelength and their accurate solutions require fast algorithms, such as MLFMA. We consider iterative solutions of DNMs with MLFMA and we investigate the accuracy and efficiency of solutions when DNMs are formulated with two recently developed formulations, namely, the combined tangential formulation (CTF) and the electric and magnetic current combined-field integral equation (JMCFIE). Numerical results on canonical objects are consistent with previous results in the literature on ordinary objects. © 2011 IEEE.
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    Analysis of Lossy Dielectric Objects with the Multilevel Fast Multipole Algorithm
    (IEEE, 2011) Ergul, O.; Gurel, Levent
    Rigorous solutions of electromagnetics problems involving lossy dielectric objects are considered. Problems are formulated with two recently developed formulations, namely, the combined-tangential formulation (CTF) and the electric and magnetic current combined-field integral equation (JMCFIE), and solved iteratively using the multilevel fast multipole algorithm (MLFMA). Accuracy and efficiency of solutions are compared for different objects and conductivity values. We show that iterative solutions of CTF are significantly accelerated as the conductivity increases and CTF becomes a good alternative to JMCFIE in terms of efficiency. Considering also its high accuracy, CTF seems to be a suitable formulation for the analysis of lossy dielectric objects.
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    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.
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    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.
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    Hierarchical parallelization of the multilevel fast multipole algorithm (MLFMA)
    (IEEE, 2013) Gürel, Levent; Ergül, Özgür
    Due to its O(N log N) complexity, the multilevel fast multipole algorithm (MLFMA) is one of the most prized algorithms of computational electromagnetics and certain other disciplines. Various implementations of this algorithm have been used for rigorous solutions of large-scale scattering, radiation, and miscellaneous other electromagnetics problems involving 3-D objects with arbitrary geometries. Parallelization of MLFMA is crucial for solving real-life problems discretized with hundreds of millions of unknowns. This paper presents the hierarchical partitioning strategy, which provides a very efficient parallelization of MLFMA on distributed-memory architectures. We discuss the advantages of the hierarchical strategy over previous approaches and demonstrate the improved efficiency on scattering problems discretized with millions of unknowns. © 1963-2012 IEEE.
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    Improving iterative solutions of the electric-field integral equation via transformations into normal equations
    (Taylor and Francis, 2012-04-03) Ergül, Özgür; Gürel, Levent
    We consider the solution of electromagnetics problems involving perfectly conducting objects formulated with the electric-field integral equation (EFIE). Dense matrix equations obtained from the discretization of EFIE are solved iteratively by the generalized minimal residual (GMRES) algorithm accelerated with a parallel multilevel fast multipole algorithm. We show that the number of iterations is halved by transforming the original matrix equations into normal equations. This way, memory required for the GMRES algorithm is reduced by more than 50%, which is significant when the problem size is large.
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    Incomplete LU preconditioning for the electric-field integral equation
    (2006) Malas, Tahir; Gürel, Levent
    Linear systems resulting from the electric-field integral equation (EFIE) become ill-conditioned, particularly for large-scale problems. Hence, effective preconditioners should be used to obtain the iterative solution with the multilevel fast multipole algorithm in a reasonable time. In this paper, we show that a threshold-based incomplete LU (ILU) preconditioner, i.e., ILUT, can be used safely for such systems, provided that column pivoting is applied for the stability of the incomplete factors. It is observed that the resulting preconditioner ILUTP reduces the solution times by an order of magnitude, compared to simple Jacobi preconditioner. Moreover, we also use the iterative solution of the near-field system as a preconditioner, and use ILUTP as the preconditioner for the near-field system. This way, the effectiveness of the ILUTP is further improved.
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    Iterative solution of composite problems with the combined-field integral equation
    (IEEE, 2007) Ergül, Özgür; Gürel, Levent
    We consider the solution of electromagnetic problems related to microwave applications involving composite geometries with coexisting open and closed conductors. Combined-field integral equation is introduced on the closed parts of the geometry to improve the iterative solutions. It is demonstrated that the convergence rates are significantly increased compared to the conventional formulation with the electric-field integral equation.
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    MLFMA memory reduction techniques for solving large-scale problems
    (IEEE, 2014) Hidayetoğlu, Mert; Gürel, Levent
    We present two memory reduction methods for the parallel multilevel fast multipole algorithm. One of these methods uses data structures out of core, and the other parallelizes the data structures related to input geometry. With these methods, large-scale electromagnetic scattering problems can be solved on modest parallel computers. © 2014 IEEE.
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    Rigorous solutions of large-scale dielectric problems with the parallel multilevel fast multipole algorithm
    (IEEE, 2011) Ergül, Özgür; Gürel, Levent
    We present fast and accurate solutions of large-scale electromagnetics problems involving three-dimensional homogeneous dielectric objects. Problems are formulated rigorously with the electric and magnetic current combined-field integral equation (JMCFIE) and solved iteratively with the multilevel fast multipole algorithm (MLFMA). In order to solve large-scale problems, MLFMA is parallelized efficiently on distributed-memory architectures using the hierarchical partitioning strategy. Efficiency and accuracy of the developed implementation are demonstrated on very large scattering problems discretized with tens of millions of unknowns. © 2011 IEEE.
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    Solutions of large-scale electromagnetics problems using an iterative inner-outer scheme with ordinary and approximate multilevel fast multipole algorithms
    (2010) Ergül, A.; Malas, T.; Gürel, Levent
    We present an iterative inner-outer scheme for the efficient solution of large-scale electromagnetics problems involving perfectly-conducting objects formulated with surface integral equations. Problems are solved by employing the multilevel fast multipole algorithm (MLFMA) on parallel computer systems. In order to construct a robust preconditioner, we develop an approximate MLFMA (AMLFMA) by systematically increasing the efficiency of the ordinary MLFMA. Using a flexible outer solver, iterative MLFMA solutions are accelerated via an inner iterative solver, employing AMLFMA and serving as a preconditioner to the outer solver. The resulting implementation is tested on various electromagnetics problems involving both open and closed conductors. We show that the processing time decreases significantly using the proposed method, compared to the solutions obtained with conventional preconditioners in the literature.