Browsing by Subject "Multi-level fast multi-pole algorithm"

Now showing 1 - 19 of 19

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
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.
Open Access
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.
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
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.
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.
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
Fast and accurate analysis of large metamaterial structures using the multilevel fast multipole algorithm
(2009) Gürel, Levent; Ergül, Özgür; Ünal, A.; Malas, T.
We report fast and accurate simulations of metamaterial structures constructed with large numbers of unit cells containing split-ring resonators and thin wires. Scattering problems involving various metamaterial walls are formulated rigorously using the electric-field integral equation, discretized with the Rao-Wilton-Glisson basis functions. Resulting dense matrix equations are solved iteratively, where the matrix-vector multiplications are performed efficiently with the multilevel fast multipole algorithm. For rapid solutions at resonance frequencies, convergence of the iterations is accelerated by using robust preconditioning techniques, such as the sparse-approximate-inverse preconditioner. Without resorting to homogenization approximations and periodicity assumptions, we are able to obtain accurate solutions of realistic metamaterial problems discretized with millions of unknowns.
Open Access
Fast and accurate analysis of large-scale composite structures with the parallel multilevel fast multipole algorithm
(Optical Society of America, 2013) Ergül, Özgür; Gürel, Levent
Accurate electromagnetic modeling of complicated optical structures poses several challenges. Optical metamaterial and plasmonic structures are composed of multiple coexisting dielectric and/or conducting parts. Such composite structures may possess diverse values of conductivities and dielectric constants, including negative permittivity and permeability. Further challenges are the large sizes of the structures with respect to wavelength and the complexities of the geometries. In order to overcome these challenges and to achieve rigorous and efficient electromagnetic modeling of three-dimensional optical composite structures, we have developed a parallel implementation of the multilevel fast multipole algorithm (MLFMA). Precise formulation of composite structures is achieved with the so-called "electric and magnetic current combined-field integral equation." Surface integral equations are carefully discretized with piecewise linear basis functions, and the ensuing dense matrix equations are solved iteratively with parallel MLFMA. The hierarchical strategy is used for the efficient parallelization of MLFMA on distributed-memory architectures. In this paper, fast and accurate solutions of large-scale canonical and complicated real-life problems, such as optical metamaterials, discretized with tens of millions of unknowns are presented in order to demonstrate the capabilities of the proposed electromagnetic solver.
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
Fast solution of electromagnetic scattering problems with multiple excitations using the recompressed adaptive cross approximation
(IEEE, 2014) Kazempour, Mahdi; Gürel, Levent
We present an algebraic compression technique to accelerate the computation of multiple monostatic radar cross sections of arbitrary 3-D geometries. The method uses adaptive cross approximation, followed by a recompression technique to reduce the CPU time and the memory consumption. Each scattering problem due to a single excitation is solved with the multilevel fast multipole algorithm. The numerical results demonstrate the efficiency and accuracy of the proposed method. © 2014 IEEE.
Open Access
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.
Open Access
Iterative solution of dielectric waveguide problems via schur complement preconditioners
(IEEE, 2010-07) Malas, Tahir; Gürel, Levent
Surface integral-equation methods accelerated with the multilevel fast multipole algorithm provide suitable mechanisms for the solution of dielectric problems. In particular, recently developed formulations increase the stability of the resulting matrix equations, hence they are more suitable for iterative solutions [1]. Among those formulations, we consider the combined tangential formulation (CTF), which produces more accurate results, and the electric and magnetic current combined-field integral equation (JMCFIE), which produces better-conditioned matrix systems than other formulations [1, 2]. ©2010 IEEE.
Open Access
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.
Open Access
Rigorous analysis of double-negative materials with the multilevel fast multipole algorithm
(Applied Computational Electromagnetics Society, Inc., 2012) Ergül, Özgür; Gürel, Levent
We present rigorous analysis of double-negative materials (DNMs) with surface integral equations and the multilevel fast multipole algorithm (MLFMA). Accuracy and efficiency of numerical solutions are investigated when DNMs are formulated with two recently developed formulations, i.e., the combined tangential formulation (CTF) and the electric and magnetic current combined-field integral equation (JMCFIE). Simulation results on canonical objects are consistent with previous results in the literature on ordinary objects. MLFMA is also parallelized to solve extremely large electromagnetics problems involving DNMs.
Open Access
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.
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
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.