Browsing by Author "Gürel, Levent"

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Open Access
Accelerating the multilevel fast multipole algorithm with the sparse-approximate-inverse (SAI) preconditioning
(Society for Industrial and Applied Mathematics, 2009) Malas, T.; Gürel, Levent
With the help of the multilevel fast multipole algorithm, integral-equation methods can be used to solve real-life electromagnetics problems both accurately and efficiently. Increasing problem dimensions, on the other hand, necessitate effective parallel preconditioners with low setup costs. In this paper, we consider sparse approximate inverses generated from the sparse near-field part of the dense coefficient matrix. In particular, we analyze pattern selection strategies that can make efficient use of the block structure of the near-field matrix, and we propose a load-balancing method to obtain high scalability during the setup. We also present some implementation details, which reduce the computational cost of the setup phase. In conclusion, for the open-surface problems that are modeled by the electric-field integral equation, we have been able to solve ill-conditioned linear systems involving millions of unknowns with moderate computational requirements. For closed surface problems that can be modeled by the combined-field integral equation, we reduce the solution times significantly compared to the commonly used block-diagonal preconditioner.
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 considerations for the integral-equation solutions of some canonical problems
(2012) Gürel, Levent
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
Accurate modeling of metamaterials with MLFMA
(ESA Publications, 2006) Ergül, Özgür; Ünal, Alper; Gürel, Levent
Electromagnetic modelling of large metamaterial (MM) structures employing multilevel fast multipole algorithm (MLFMA) is reported. MMs are usually constructed by periodically embedding unit cells, such as split-ring resonators (SRRs), into a host medium. Without utilizing any homogenization techniques, we accurately model large numbers of unit cells that translate into very large computational problems. By considering all of the electromagnetic interactions, the resulting dense matrix equations are solved iteratively with the accelerated matrix-vector products by MLFMA. To increase the efficiency, we also employ parallel computing in the solutions of large SRR problems.
Open Access
Accurate plane-wave excitation in the FDTD method
(IEEE, 1997) Gürel, Levent; Oğuz, Uğur; Arıkan, Orhan
Different techniques are developed to implement plane-wave excitation on the finite-difference time-domain (FDTD) method, such as the initial-condition, the hard-source, and the connecting-condition techniques, for the total-field/scattered field (TF/SF) formulation. In the TF/SF formulation, the incident field is computed and fed to the 3D FDTD grid on the boundary separating the total-field and the scattered-field regions. Since the incedent field is a known quantity, a closed-form expression can be evaluated on every point of this boundary. A more efficient way of computing the incedent field is by using an incedent-field array (IFA), which is a 1D FDTD grid set-up to numerically propagate the incedent field into the 3D FDTD.
Open Access
Accurate solutions of extremely large integral-equation problems in computational electromagnetics
(IEEE, 2013-02) Ergül, Ö; Gürel, Levent
Accurate simulations of real-life electromagnetics problems with integral equations require the solution of dense matrix equations involving millions of unknowns. Solutions of these extremely large problems cannot be achieved easily, even when using the most powerful computers with state-of-the-art technology. However, with the multilevel fast multipole algorithm (MLFMA) and parallel MLFMA, we have been able to obtain full-wave solutions of scattering problems discretized with hundreds of millions of unknowns. Some of the complicated real-life problems (such as scattering from a realistic aircraft) involve geometries that are larger than 1000 wavelengths. Accurate solutions of such problems can be used as benchmarking data for many purposes and even as reference data for high-frequency techniques. Solutions of extremely large canonical benchmark problems involving sphere and National Aeronautics and Space Administration (NASA) Almond geometries are presented, in addition to the solution of complicated objects, such as the Flamme. The parallel implementation is also extended to solve very large dielectric problems, such as dielectric lenses and photonic crystals.
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
Advanced numerical techniques for the scattering of waves by dielectric scatterers
(2012) Gürel, Levent
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
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.
Open Access
Analysis of composite objects involving multiple dielectric and metallic partswith the parallel multilevel fast multipole algorithm
(Applied Computational Electromagnetics Society, 2012-04) Ergül, Özgür; Gürel, Levent
Open Access
Analysis of dielectric photonic-crystal problems with MLFMA and Schur-complement preconditioners
(IEEE, 2011-01-13) Ergül, Özgür; Malas, T.; Gürel, Levent
We present rigorous solutions of electromagnetics problems involving 3-D dielectric photonic crystals (PhCs). Problems are formulated with recently developed surface integral equations and solved iteratively using the multilevel fast multipole algorithm (MLFMA). For efficient solutions, iterations are accelerated via robust Schur-complement preconditioners. We show that complicated PhC structures can be analyzed with unprecedented efficiency and accuracy by an effective solver based on the combined tangential formulation, MLFMA, and Schur-complement preconditioners.
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 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
Application of signal-processing techniques to dipole excitations in the finite-difference time-domain method
(Taylor & Francis, 2002) Oğuz, U.; Gürel, Levent
The applications of discrete-time signal-processing techniques, such as windowing and filtering for the purpose of implementing accurate excitation schemes in the finite-difference time-domain (FDTD) method are demonstrated. The effects of smoothing windows of various lengths and digital lowpass filters of various bandwidths and characteristics are investigated on finite-source excitations of the FDTD computational domain. Both single-frequency sinusoidal signals and multifrequency arbitrary signals are considered.
Open Access
Application of signal-processing techniques to reduce the errors related to the FDTD excitations
(IEEE, 2001) Gürel, Levent; Oğuz, Uğur
A study on the reduction of the errors related to the finite-difference time-domain (FDTD) excitations was performed by employing signal-processing techniques. Plane-wave scattering problems were simulated. The improvements in both plane-wave and finite-source excitation schemes were demonstrated. The result showed that a visible DC offset value was exhibited even after five periods of the incident wave.
Open Access
Approximate MLFMA as an efficient preconditioner
(IEEE, 2007) Malas, Tahir; Ergül, Özgür; Gürel, Levent
In this work, we propose a preconditioner that approximates the dense system operator. For this purpose, we develop an approximate multilevel fast multipole algorithm (AMLFMA), which performs a much faster matrix-vector multiplication with some relative error compared to the original MLFMA. We use AMLFMA to solve a closely related system, which makes up the preconditioner. Then, this solution is embedded in the main solution that uses MLFMA. By taking into account the far-field elements wisely, this preconditioner proves to be much more effective compared to the near-field preconditioners.
Open Access
Approximate Schur preconditioners for efficient solutions of dielectric problems formulated with surface integral equations
(IEEE, 2009-07) Malas, Tahir; Gürel, Levent
We propose direct and iterative versions of approximate Schur preconditioners to increase robustness and efficiency of iterative solutions of dielectric problems formulated with surface integral equations. The performance of these preconditioners depends on the availability of fast and approximate solutions to reduced matrix systems. We show that sparse-approximate-inverse techniques provide a suitable mechanism for this purpose. The proposed preconditioners are demonstrated to significantly improve convergence rates of dielectric problems formulated with two different surface integral equations. ©2009 IEEE.
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.