Browsing by Subject "Multilevel fast multipole algorithm"

Now showing 1 - 20 of 27

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, Levent
We 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.
Open Access
A broadband multilevel fast multipole algorithm with incomplete-leaf tree structures for multiscale electromagnetic problems
(IEEE, 2016) Takrimi, Manouchehr; Ergül, Ö.; Ertürk, Vakur B.
An efficient, broadband, and accurate multilevel fast multipole algorithm (MLFMA) is proposed to solve a wide range of multiscale electromagnetic problems with orders of magnitude differences in the mesh sizes. Given a maximum RWG population threshold, only overcrowded boxes are recursively bisected into smaller ones, which leads to novel incomplete-leaf tree structures. Simulations reveal that, for surface discretizations possessing highly overmeshed local regions, the proposed method presents a more efficient and/or accurate results than the conventional MLFMA. The key feature of such a population-based clustering scenario is that the error is controllable, and hence, regardless of the number of levels, the efficiency can be optimized based on the population threshold. Numerical examples are provided to demonstrate the superior efficiency and accuracy of the proposed algorithm in comparison to the conventional MLFMA.
Open Access
Circular arrays of log-periodic antennas for broadband applications
(IEEE, 2006) Ergül, Özgür; Gürel, Levent
Circular arrays of log-periodic (LP) antennas are designed for broadband applications. A sophisticated electromagnetic simulation environment involving integral equations and fast solvers is developed to analyze the LP arrays both accurately and efficienuy. The resulting matrix equation obtained by the discretization of the electric field integral equation is solved iteratively via the multilevel fast multipole algorithm (MLFMA). Genetic algorithms interacting with MLFMA is employed to optimize the excitations of the array elements to increase the frequency independence and also to add the beam-steering ability to the arrays.
Open Access
Comparisons of FMM implementations employing different formulations and iterative solvers
(IEEE, 2003-06) Gürel, Levent; Ergül, Özgür
The implementation of multi-level fast multipole algorithm (MLFMA) requires the consideration of several parameters. The preferred combination of the parameters given is not trivially obvious and requires a careful investigation. This paper extensively investigates such parameters by using a series of scattering problems of various sizes containing different numbers of unknowns as a testbed.
Open Access
Computational study of scattering from healthy and diseased red blood cells
(Society of Photo Optical Instrumentation Engineers, 2010-08-05) Ergül, Özgür; Arslan-Ergül, A.; Gürel, Levent
We present a comparative study of scattering from healthy red blood cells (RBCs) and diseased RBCs with deformed shapes. Scattering problems involving three-dimensional RBCs are formulated accurately with the electric and magnetic current combined-field integral equation and solved efficiently by the multilevel fast multipole algorithm. We compare scattering cross section values obtained for different RBC shapes and different orientations. In this way, we determine strict guidelines to distinguish deformed RBCs from healthy RBCs and to diagnose various diseases using scattering cross section values. The results may be useful for designing new and improved flow cytometry procedures.
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, Levent
In 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.
Open Access
Electromagnetic modeling of split-ring resonators
(IEEE, 2007) Gürel, Levent; Ünal, Alper; Ergül, Özgür
In this paper, we report our efforts to model splitring resonators (SRRs) and their large arrays accurately and efficiently in a sophisticated simulation environment based on recent advances in the computational electromagnetics. The resulting linear system obtained from the simultaneous discretization of the geometry and Maxwell's equations is solved iteratively with the multilevel fast multipole algorithm. As an example, we present an array of 125 SRRs showing a negative effective permeability about 92 GHz.
Open Access
Enhancing the accuracy of the interpolations and anterpolations in MLFMA
(Institute of Electrical and Electronics Engineers, 2006) Ergül, Özgür; Gürel, Levent
We present an efficient technique to reduce the interpolation and anterpolation (transpose interpolation) errors in the aggregation and disaggregation processes of the multilevel fast multipole algorithm (MLFMA), which is based on the sampling of the radiated and incoming fields over all possible solid angles, i.e., all directions on the sphere. The fields sampled on the sphere are subject to various operations, such as interpolation, aggregation, translation, disaggregation, anterpolation, and integration. We identify the areas on the sphere, where the highest levels of interpolation errors are encountered. The error is reduced by employing additional samples on such parts of the sphere. Since the interpolation error is propagated and amplified by every level of aggregation, this technique is particulary useful for large problems. The additional costs in the memory and processing time are negligible, and the technique can easily be adapted into the existing implementations of MLFMA.
Open Access
Error control in MLFMA with multiple-precision arithmetic
(Institution of Engineering and Technology, 2018-04) Kalfa, Mert; Ergül, Ö.; Ertürk, Vakur B.
We present a new error control method that provides the truncation numbers as well as the required digits of machine precision for the translation operator of the multilevel fast multipole algorithm (MLFMA). The proposed method is valid for all frequencies, whereas the previous studies on error control are valid only for high-frequency problems (i.e., electrically large translation distances). When combined with a multiple-precision implementation of MLFMA, the proposed method can be used to solve low-frequency problems that are problematic with a fixed-precision implementation. Numerical results in the form of optimal truncation numbers and machine precisions for a variety of box sizes and desired relative error thresholds are presented and compared with the methods or numerical surveys available in the literature.
Open Access
Extending the applicability of the combined-field integral equation to geometries containing open surfaces
(Institute of Electrical and Electronics Engineers, 2006) Gürel, Levent; Ergül, Özgür
In this letter, we consider the solution of large electromagnetics problems of composite structures with coexisting open and closed conductors. By modifying the construction of the combined-field integral equation (CFIE), we demonstrate a significant improvement in the iterative solution of these problems compared to the conventional electric-field formulation.
Open Access
Fast and efficient solutions of multiscale electromagnetic problems
(2020-09) Khalichi, Bahram
Frequency-domain surface integral equations (SIEs) used together with the method of moments (MoM), and/or its accelerated versions, such as the multilevel fast multipole algorithm (MLFMA), are usually the most promising choices in solving electromagnetic problems including perfect electric conductors (PEC). However, the electric-ﬁeld integral equation (EFIE) (as one of the most popular SIEs) is susceptible to the well-known low-frequency (LF) breakdown problem, which prohibits its use at low frequencies and/or dense discretizations. Although the magnetic-ﬁeld integral equation (MFIE) is less aﬀected from the LF-breakdown, it is usually criticized for being less accurate, and being applicable only to closed surfaces. In addition, the conventional MLFMA which enables the solution of electrically large problems with an extremely large number of unknowns by reducing the computational complexity for memory requirements and CPU time suﬀers from the LF breakdown when applied to the geometries with electrically small features. We proposed a mixed-form MLFMA and incorporated it with the recently introduced potential integral equations (PIEs), which are immune to the LF-breakdown problem, to obtain an eﬃcient and accurate broadband solver to analyze electromagnetic scattering/radiation problems from PEC surfaces over a wide frequency range. The mixed-form MLFMA uses the conventional MLFMA at middle/high frequencies and the nondirective stable plane wave MLFMA (NSPWMLFMA) at low frequencies (i.e., electrically small boxes). We demonstrated that the proposed algorithm is accurate enough to be applied for both open and closed surfaces. In addition, we modiﬁed and utilized incomplete tree structures in conjunction with the mixed-form MLFMA to have a novel broadband incomplete-leaf (IL) MLFMA (IL-MLFMA) for the fast and accurate solution of multiscale scattering/radiation problems using PIEs. The proposed method is capable of handling multiscale electromagnetic problems containing ﬁne geometrical details in their structures. The algorithm is population based and deploys a nonuniform clustering that enables to use deep levels safely and, when necessary, without compromising the accuracy, and hence the error is controllable. As a result, by using the proposed IL-MLFMA for PIEs (i) the eﬃciency is improved and (ii) the memory requirements are signiﬁcantly reduced (order of magnitude) while the accuracy is maintained.
Open Access
Hierarchical parallelization of the multilevel fast multipole algorithm for the efficient solution of large-scale scattering problems
(IEEE, 2008-07) Ergül, Özgür; Gürel, Levent
We present the details of a hierarchical parallelization strategy, which provides higher efficiency than the previous parallelization approaches for MLFMA. We demonstrate the effectiveness of our algorithm on sphere problems involving large numbers of unknowns, such as a sphere of radius 120 lambda discretized with 53 million unknowns.
Open Access
A hierarchical partitioning strategy for an efficient parallelization of the multilevel fast multipole algorithm
(IEEE, 2009) Ergül, Özgür; Gürel, Levent
We 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.
Open Access
Incomplete LU preconditioning with the multilevel fast multipole algorithm for electromagnetic scattering
(Society for Industrial and Applied Mathematics, 2007) Malas, T.; Gürel, Levent
Iterative solution of large-scale scattering problems in computational electromagnetics with the multilevel fast multipole algorithm (MLFMA) requires strong preconditioners, especially for the electric-field integral equation (EFIE) formulation. Incomplete LU (ILU) preconditioners are widely used and available in several solver packages. However, they lack robustness due to potential instability problems. In this study, we consider various ILU-class preconditioners and investigate the parameters that render them safely applicable to common surface integral formulations without increasing the script O sign(n log n) complexity of MLFMA. We conclude that the no-fill ILU(O) preconditioner is an optimal choice for the combined-field integral equation (CFIE). For EFIE, we establish the need to resort to methods depending on drop tolerance and apply pivoting for problems with high condition estimate. We propose a strategy for the selection of the parameters so that the preconditioner can be used as a black-box method. Robustness and efficiency of the employed preconditioners are demonstrated over several test problems.
Open Access
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.
Open Access
Iterative solutions of hybrid integral equations for coexisting open and closed surfaces
(IEEE, 2009) Ergül, Özgür; Gürel, Levent
We consider electromagnetics problems involving composite geometries with coexisting open and closed conductors. Hybrid integral equations are presented to improve the efficiency of the solutions, compared to the conventional electric-field integral equation. We investigate the convergence characteristics of iterative solutions of large composite problems with the multilevel fast multipole algorithm. Following a thorough study of how the convergence characteristics depends on the problem geometry, formulation, and iterative solvers, we provide concrete guidelines for efficient solutions.
Open Access
Large-scale solutions of electromagnetics problems using the multilevel fast multipole algorithm and physical optics
(2015-04) Hidayetoğlu, Mert
Integral equations provide full-wave (accurate) solutions of Helmholtz-type electromagnetics problems. The multilevel fast multipole algorithm (MLFMA) discretizes the equations and solves them numerically with O(NLogN) complexity, where N is the number of unknowns. For solving large-scale problems, MLFMA is parallelized on distributed-memory architectures. Despite the low complexity and parallelization, the computational requirements of MLFMA solutions grow immensely in terms of CPU time and memory when extremely-large geometries (in wavelengths) are involved. The thesis provides computational and theoretical techniques for solving large-scale electromagnetics problems with lower computational requirements. One technique is the out-of-core implementation for reducing the required memory via employing disk space for storing large data. Additionally, a pre-processing parallelization strategy, which eliminates memory bottlenecks, is presented. Another technique, MPI+OpenMP parallelization, uses distributed-memory and shared-memory schemes together in order to maintain the parallelization efficiency with high number of processes/threads. The thesis also includes the out-of-core implementation in conjunction with the MPI+OpenMP parallelization. With the applied techniques, full-wave solutions involving up to 1.3 billion unknowns are achieved with 2 TB memory. Physical optics is a high-frequency approximation, which provides fast solutions of scattering problems with O(N) complexity. A parallel physical optics algorithm is presented in order to achieve fast and approximate solutions. Finally, a hybrid integral-equation and physical-optics solution methodology is introduced.
Open Access
Linear-linear basis functions for MLFMA solutions of magnetic-field and combined-field integral equations
(Institute of Electrical and Electronics Engineers, 2007) Ergul, O.; Gurel, L.
We 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 closed conductors. We consider the solutions of relatively large scattering problems by employing the multilevel fast multipole algorithm. Accuracy problems of MFIE and CFIE arising from their implementations with the conventional Rao-Wilton-Glisson (RWG) basis functions can be mitigated by using the LL functions for discretization. This is achieved without increasing the computational requirements and with only minor modifications in the existing codes based on the RWG functions.
Open Access
Multiple-precision MLFMA for efficient and accurate solutions of broadband electromagnetic problems
(2020-08) Kalfa, Mert
The multilevel fast multipole algorithm (MLFMA) is a popular full-wave electromagnetic solver that enables the solution of electrically large problems with an extremely large number of unknowns. As with all computational electromagnetics solvers, active research is ongoing to extend the limitations of MLFMA for larger problems with ﬁner geometrical details. For electrically small structures MLFMA suﬀers from the low-frequency breakdown, while more eﬃcient schemes are required for electrically larger problems. We propose and demonstrate an elegant solution to the aforementioned problems by introducing a multiple-precision arithmetic (MPA) framework to the inherent hierarchical tree structure of MLFMA, dubbed the multiple-precision multilevel fast multipole algorithm (MP-MLFMA). With the introduction of MPMLFMA we show that a distinct machine precision can be assigned to each level of the tree structure of MLFMA, which enables accurate and eﬃcient solutions of problems with deep tree-structures over arbitrarily large frequency bandwidths. To determine the required machine precisions for a given tree structure, as well as the number of harmonics required for an accurate error control of the translation operator of MP-MLFMA, we introduce and validate a novel error control scheme with accurate design curves that is valid at all frequencies, for the ﬁrst time in the literature. Combined with the proposed error control scheme, we present the capabilities of MP-MLFMA over a wide range of broadband and deep tree-structure scattering problems. We also illustrate the true potential eﬃciency of MP-MLFMA, with a simple MPA framework implementation on a single-precision processor. With the hardware-deﬁned implementation, we show the super-linear speed-up potential of MP-MLFMA for low-precisions.
Open Access
Novel electromagnetic surface integral equations for highly accurate computations of dielectric bodies with arbitrarily low contrasts
(Journal of Computational Physics, 2008) Ergül O.; Gürel, Levent
We present a novel stabilization procedure for accurate surface formulations of electromagnetic scattering problems involving three-dimensional dielectric objects with arbitrarily low contrasts. Conventional surface integral equations provide inaccurate results for the scattered fields when the contrast of the object is low, i.e., when the electromagnetic material parameters of the scatterer and the host medium are close to each other. We propose a stabilization procedure involving the extraction of nonradiating currents and rearrangement of the right-hand side of the equations using fictitious incident fields. Then, only the radiating currents are solved to calculate the scattered fields accurately. This technique can easily be applied to the existing implementations of conventional formulations, it requires negligible extra computational cost, and it is also appropriate for the solution of large problems with the multilevel fast multipole algorithm. We show that the stabilization leads to robust formulations that are valid even for the solutions of extremely low-contrast objects. © 2008 Elsevier Inc. All rights reserved.