Browsing by Subject "Scattering problems"
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Item 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, LeventWe 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.Item Open Access Advanced partitioning and communication strategies for the efficient parallelization of the multilevel fast multipole algorithm(IEEE, 2010) Ergül O.; Gürel, LeventLarge-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.Item 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, LeventWe 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.Item 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, LeventWe 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.Item 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, LeventIn 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.Item Open Access Fast algorithms for large 3-D electromagnetic scattering and radiation problems(1997) Şendur, İbrahim KürşatSome interesting real-life radiation and scattering problems are electrically very large and cannot be solved using traditional solution algorithms. Despite the difficulties involved, the solution of these problems usually offer valuable results that are immediately useful in real-life applications. The fast multipole method (FMM) enables the solution of larger problems with existing computational resources by reducing the computational complexity and the memory requirement of the solution without sacrificing the accuracy. This is achieved by replacing the matrix-vector multiplications of O(N^) complexity by a faster equivalent of complexity in each iteration of an iterative scheme. Fast Far-Field Algorithm(FAFFA) further reduces 0{N^) complexity to 0{N^·^). A direct solution would require 0{N^) operations.Item 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.Item Open Access Fast and accurate solutions of extremely large scattering problems involving three-dimensional canonical and complicated objects(IEEE, 2009-07) Ergül, Özgür; Gürel, LeventWe 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.Item Open Access Fast solution of electromagnetic scattering problems with multiple excitations using the recompressed adaptive cross approximation(IEEE, 2014) Kazempour, Mahdi; Gürel, LeventWe 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.Item Open Access Hierarchical parallelization of the multilevel fast multipole algorithm (MLFMA)(IEEE, 2013) Gürel, Levent; Ergül, ÖzgürDue 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.Item Open Access A hierarchical partitioning strategy for an efficient parallelization of the multilevel fast multipole algorithm(IEEE, 2009) Ergül, Özgür; Gürel, LeventWe present a novel hierarchical partitioning strategy for the efficient parallelization of the multilevel fast multipole algorithm (MLFMA) on distributed-memory architectures to solve large-scale problems in electromagnetics. Unlike previous parallelization techniques, the tree structure of MLFMA is distributed among processors by partitioning both clusters and samples of fields at each level. Due to the improved load-balancing, the hierarchical strategy offers a higher parallelization efficiency than previous approaches, especially when the number of processors is large. We demonstrate the improved efficiency on scattering problems discretized with millions of unknowns. In addition, we present the effectiveness of our algorithm by solving very large scattering problems involving a conducting sphere of radius 210 wavelengths and a complicated real-life target with a maximum dimension of 880 wavelengths. Both of the objects are discretized with more than 200 million unknowns.Item Open Access Lasing modes of infinite periodic chain of quantum wires(IEEE, 2009-06-07) Byelobrov, V. O.; Benson, T. M.; Sewell, P.; Altıntaş, Ayhan; Nosich, A. I.In this paper, we study the scattering and eigenvalue problems for a periodic open optical resonator that is an infinite chain of active circular cylindrical quantum wires standing in free space. The scattering problem is solved by the method of partial separation of variables. The eigenvalue problem differs from the first one by the absence of the incident field and presence of "active properties" of cylinders and yields the frequencies and thresholds of lasing. ©2009 IEEE.Item Open Access Multilevel PO algorithm for non-uniform triangulations(ESA Publications, 2006) Manyas, Alp; Gürel, LeventFast physical optics (FPO) algorithm provides a speedup for computing the physical optics (PO) integral over complex bodies for a range of aspect angles and frequencies. In this paper, this algorithm is further developed in order to compute the scattered field from nonuniform triangulations of complex bodies. In the original "uniform" FPO algorithm, only the radiation patterns of the smallest subdomains in the bottom level are directly computed and the radiation patterns of the larger subdomains in the upper levels are computed via interpolation and aggregation. In this modified "nonuniform" algorithm, the radiation patterns of the larger triangles, which are too large to fit in the bottom-level subdomains, are directly computed and incorporated in the appropriate aggregation levels. It is also shown that, by applying different interpolation methods, accuracy of the FPO algorithm can be improved without any computational cost.Item Open Access On the accuracy of MFIE and CFIE in the solution of large electromagnetic scattering problems(ESA Publications, 2006) Ergül, Özgür; Gürel, LeventWe present the linear-linear (LL) basis functions to improve the accuracy of the magnetic-field integral equation (MFIE) and the combined-field integral equation (CFIE) for three-dimensional electromagnetic scattering problems involving large scatterers. MFIE and CFIE with the conventional Rao-Wilton-Glisson (RWG) basis functions are significantly inaccurate even for large and smooth geometries, such as a sphere, compared to the solutions by the electric-field integral equation (EFIE). By using the LL functions, the accuracy of MFIE and CFIE can be improved to the levels of EFIE without increasing the computational requirements and with only minor modifications in the existing codes based on the RWG functions.Item Open Access Rigorous solutions of large-scale dielectric problems with the parallel multilevel fast multipole algorithm(IEEE, 2011) Ergül, Özgür; Gürel, LeventWe 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.Item Open Access Rigorous solutions of large-scale scattering problems discretized with hundreds of millions of unknowns(2009-09) Gürel, Levent; Ergül, ÖzgürWe 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.Item Open Access Rigorous solutions of scattering problems involving red blood cells(IEEE, 2010) Ergül, Özgür; Arslan-Ergül, Ayça; Gürel, LeventWe 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.