Browsing by Subject "Multilevel fast multipole algorithms"

Now showing 1 - 17 of 17

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
Accuracy: The Frequently Overlooked Parameter in the Solution of Extremely Large Problems
(IEEE, 2011) Ergul, O.; Gürel, Levent
We investigate error sources and their effects on the accuracy of solutions of extremely large electromagnetics problems with parallel implementations of the multilevel fast multipole algorithm (MLFMA). Accuracy parameters and their effects on the accuracy of MLFMA solutions are studied for large-scale problems discretized with hundreds of millions of unknowns. We show that some error sources are more dominant and should be suppressed for more accurate solutions; identifying less-effective error sources may allow us to derive more efficient implementations. Based on our analysis, we determine a set of benchmark problems that can be used to compare the accuracy of solvers for large-scale computations. A benchmarking tool is provided at www.cem.bilkent.edu.tr/ benchmark.
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
Benchmark Solutions of Large Problems for Evaluating Accuracy and Efficiency of Electromagnetics Solvers
(IEEE, 2011) Ergul, O.; Gürel, Levent
We present a set of benchmark problems involving conducting spheres and their solutions using a parallel implementation of the multilevel fast multipole algorithm (MLFMA). Accuracy of the implementation is tested by comparing the computational results with analytical Mie-series solutions. Reference solutions are made available on an interactive website to evaluate and compare the accuracy and efficiency of fast solvers. We also demonstrate the capabilities of our solver on real-life problems involving complicated targets, such as the Flamme.
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
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
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
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.
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
Parallel-MLFMA solutions of large-scale problems involving composite objects
(IEEE, 2012-07) Ergül, Özgür; Gürel, Levent
We present a parallel implementation of the multilevel fast multipole algorithm (MLFMA) for fast and accurate solutions of large-scale electromagnetics problems involving composite objects with dielectric and metallic parts. Problems are formulated with the electric and magnetic current combined-field integral equation (JMCFIE) and solved iteratively with MLFMA on distributed-memory architectures. Numerical examples involving canonical and complicated objects, such as optical metamaterials, are presented to demonstrate the accuracy and efficiency of the implementation. © 2012 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
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 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
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.