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Item Open AccessOn the accuracy of MFIE and CFIE in the solution of large electromagnetic scattering problems(ESA Publications, 2006) Ergül, Özgür; Gürel, Levent; Gürel, Levent; Ergül, ÖzgürWe 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 AccessCircular arrays of log-periodic antennas for broadband applications(IEEE, 2006) Ergül, Özgür; Gürel, Levent; Gürel, Levent; Ergül, ÖzgürCircular 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. Item Open AccessIncomplete LU preconditioning for the electric-field integral equation(2006) Malas, Tahir; Gürel, Levent; Gürel, LeventLinear systems resulting from the electric-field integral equation (EFIE) become ill-conditioned, particularly for large-scale problems. Hence, effective preconditioners should be used to obtain the iterative solution with the multilevel fast multipole algorithm in a reasonable time. In this paper, we show that a threshold-based incomplete LU (ILU) preconditioner, i.e., ILUT, can be used safely for such systems, provided that column pivoting is applied for the stability of the incomplete factors. It is observed that the resulting preconditioner ILUTP reduces the solution times by an order of magnitude, compared to simple Jacobi preconditioner. Moreover, we also use the iterative solution of the near-field system as a preconditioner, and use ILUTP as the preconditioner for the near-field system. This way, the effectiveness of the ILUTP is further improved. Item Open AccessAccurate modeling of metamaterials with MLFMA(ESA Publications, 2006) Ergül, Özgür; Ünal, Alper; Gürel, Levent; Gürel, Levent; Ergül, ÖzgürElectromagnetic 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. Item Open AccessThe solution of large EFIE problems via preconditioned multilevel fast multipole algorithm(Institution of Engineering and Technology, 2007) Malas, Tahir; Gürel, Levent; Gürel, LeventWe propose an effective preconditioning scheme for the iterative solution of the systems formulated by the electric- field integral equation (EFIE). EFIE is notorious for producing difficult-to-solve systems. Especially, if the target is complex and the utilized frequency is high, it becomes a challenge to solve these dense systems with even robust solvers such as full GMRES. For this purpose, we use an inner-outer solver scheme and use an approximate multilevel fast multipole algorithm for the inner solver to provide a very efficient approximation to the dense linear system matrix. We explore approximation level and inner-solver accuracy to optimize the efficiency of the inner-outer solution scheme. We report the solution of large EFIE systems of several targets to show the effectiveness of the proposed approach. Item Open AccessIterative solution of composite problems with the combined-field integral equation(IEEE, 2007) Ergül, Özgür; Gürel, Levent; Gürel, Levent; Ergül, ÖzgürWe 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. Item Open AccessApproximate MLFMA as an efficient preconditioner(IEEE, 2007) Malas, Tahir; Ergül, Özgür; Gürel, Levent; Gürel, Levent; Ergül, ÖzgürIn 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. Item Open AccessInvestigation of various metamaterial structures using multilevel fast multipole algorithm(IEEE, 2007) Ergül, Özgür; Yavuz, Çağlar; Ünal, Alper; Gürel, Levent; Gürel, Levent; Ergül, ÖzgürWe consider accurate simulations of metamaterial (MM) structures consisting of split- ring-resonators (SRRs) and thin wires (TWs). We employ electric-field integral equation (EFIE) to formulate the scattering problems involving these complicated structures. Accurate modelling of MMs translates into very large computational problems, which can be solved with the aid of advanced acceleration techniques, such as the multilevel fast multipole algorithm (MLFMA). We investigate various multilayer structures of SRRs as well as composite metamaterials (CMMs) constructed by the arrangements of SRR and TW arrays. In addition, we consider various disordering scenarios, where the unit cells are not placed perfectly and they are misaligned. This way, we investigate the electromagnetic properties of MMs when the arrays are defected. In this paper, we briefly report the accurate solutions of various real-life MM problems and present power transmission properties of these important structures. Item Open AccessMultilevel physical optics algorithm for fast solution of scattering problems involving nonuniform triangulations(IEEE, 2007) Gürel, Levent; Manyas, Alp; Gürel, LeventThis paper shows the computational efficiency of the multilevel physical optics (MLPO) algorithm can be further increased by employing nonuniform triangulations of the target surface so that the triangle size is not nearly uniform, but instead, is determined by the surface curvature. Item Open AccessSolution of extremely large integral-equation problems(IEEE, 2007) Ergül, Özgür; Malas, Tahir; Gürel, Levent; Gürel, Levent; Ergül, ÖzgürWe report the solution of extremely large integral-equation problems involving electromagnetic scattering from conducting bodies. By orchestrating diverse activities, such as the multilevel fast multipole algorithm, iterative methods, preconditioning techniques, and parallelization, we are able to solve scattering problems that are discretized with tens of millions of unknowns. Specifically, we report the solution of a closed geometry containing 42 million unknowns and an open geometry containing 20 million unknowns, which are the largest problems of their classes, to the best of our knowledge. Item Open AccessMemory-efficient multilevel physical optics algorithm for fast computation of scattering from three-dimensional complex targets(IEEE, 2007) Manyas, Alp; Gürel, Levent; Gürel, LeventMultilevel physical optics (MLPO) algorithm provides a speed-up for computing the physical-optics integral over complex bodies for a range of aspect angles and frequencies. On the other hand, when computation of the RCS pattern as a function of θ, φ, and frequency is desired, the O N3 memory complexity of the algorithm may prevent the solution of electrically large problems. In this paper, we propose an improved version of the MLPO algorithm, for which the memory complexity is reduced to O N2 log N . The algorithm is based on the aggregation of only some portion of the scattering patterns at each aggregation step. This way, memory growth in each step is prevented, and a significant amount of saving is achieved. Item Open AccessImproving the accuracy of the surface integral equations for low-contrast dielectric scatterers(IEEE, 2007) Ergül, Özgür; Gürel, Levent; Gürel, Levent; Ergül, ÖzgürSolutions of scattering problems involving low-contrast dielectric objects are considered by employing surface integral equations. A stabilization procedure based on extracting the non-radiating part of the induced currents is applied so that the remaining radiating currents can be modelled appropriately and the scattered fields from the low-contrast objects can be calculated with improved accuracy. Stabilization is applied to both tangential (T) and normal (N) formulations in order to use the benefits of different formulations. Item Open AccessSequential and parallel preconditioners for large-scale integral-equation problems(IEEE, 2007) Malas, Tahir; Ergül, Özgür; Gürel, Levent; Gürel, Levent; Ergül, ÖzgürFor efficient solutions of integral-equation methods via the multilevel fast multipole algorithm (MLFMA), effective preconditioners are required. In this paper we review appropriate preconditioners that have been used for sparse systems and developed specially in the context of MLFMA. First we review the ILU-type preconditioners that are suitable for sequential implementations. We can make these preconditioners robust and efficient for integral-equation methods by making appropriate selections and by employing pivoting to suppress the instability problem. 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 insufficient to approximate the dense system matrix and preconditioners generated from the near-field interactions cannot be effective. Therefore, we propose an approximation strategy to MLFMA to be used as an effective 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 problems with tens of millions of unknowns in a few hours. We report the solution of integral-equation problems that are among the largest in their classes. © 2007 IEEE. Item Open AccessElectromagnetic modeling of split-ring resonators(IEEE, 2007) Gürel, Levent; Ünal, Alper; Ergül, Özgür; Gürel, Levent; Ergül, ÖzgürIn 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. Item Open AccessSolutions of large integral-equation problems with preconditioned MLFMA(IEEE, 2007) Ergül, Özgür; Malas, Tahir; Ünal, Alper; Gürel, Levent; Gürel, Levent; Ergül, ÖzgürWe report the solution of the largest integral-equation problems in computational electromagnetics. We consider matrix equations obtained from the discretization of the integral-equation formulations that are solved iteratively by employing parallel multilevel fast multipole algorithm (MLFMA). With the efficient parallelization of MLFMA, scattering and radiation problems with millions of unknowns are easily solved on relatively inexpensive computational platforms. For the iterative solutions of the matrix equations, we are able to obtain accelerated convergence even for ill-conditioned matrix equations using advanced preconditioning schemes, such as nested preconditioned based on an approximate MLFMA. By orchestrating these diverse activities, we have been able to solve a closed geometry formulated with the CFIE containing 33 millions of unknowns and an open geometry formulated with the EFIE containing 12 millions of unknowns, which are the largest problems of their classes, to the best of our knowledge. Item Open AccessParallel-MLFMA solution of CFIE discretized with tens of millions of unknowns(Institution of Engineering and Technology, 2007) Ergül, Özgür; Gürel, Levent; Gürel, Levent; Ergül, ÖzgürWe consider the solution of large scattering problems in electromagnetics involving three-dimensional arbitrary geometries with closed surfaces. The problems are formulated accurately with the combined-field integral equation and the resulting dense matrix equations are solved iteratively by employing the multilevel fast multipole algorithm (MLFMA). With an efficient parallelization of MLFMA on relatively inexpensive computing platforms using distributed-memory architectures, we easily solve large-scale problems that are discretized with tens of millions of unknowns. Accuracy of the solutions is demonstrated on scattering problems involving spheres of various sizes, including a sphere of radius 110 λ discretized with 41,883,638 unknowns, which is the largest integral-equation problem ever solved, to the best of our knowledge. In addition to canonical problems, we also present the solution of real-life problems involving complicated targets with large dimensions. Item Open AccessPO-MLFMA hybrid technique for the solution of electromagnetic scattering problems involving complex targets(Institution of Engineering and Technology, 2007) Gürel, Levent; Manyas, Alp; Ergül, Özgür; Gürel, Levent; Ergül, ÖzgürThe multilevel fast multipole algorithm (MLFMA) is a powerful tool for efficient and accurate solutions of electromagnetic scattering problems involving large and complicated structures. On the other hand, it is still desirable to increase the efficiency of the solutions further by combining the MLFMA implementations with the high- frequency techniques such as the physical optics (PO). In this paper, we present our efforts in order to reduce the computational cost of the MLFMA solutions by introducing PO currents appropriately on the scatterer. Since PO is valid only on smooth and large surfaces that are illuminated strongly by the incident fields, accurate solutions require careful choices of the PO and MLFMA regions. Our hybrid technique is useful especially when multiple solutions are required for different frequencies, illuminations, and scenarios, so that the direct solutions with MLFMA become expensive. For these problems, we easily accelerate the MLFMA solutions by systematically introducing the PO currents and reducing the matrix dimensions without sacrificing the accuracy. Item Open AccessAccurate solutions of scattering problems involving low-contrast dielectric objects with surface integral equations(Institution of Engineering and Technology, 2007) Ergül, Özgür; Gürel, Levent; Gürel, Levent; Ergül, ÖzgürWe 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 AccessModeling and synthesis of circular‐sectoral arrays of log‐periodic antennas using multilevel fast multipole algorithm and genetic algorithms(Wiley-Blackwell Publishing, Inc., 2007-06-17) Ergül, Özgür; Gürel, Levent; Gürel, Levent; Ergül, ÖzgürCircular‐sectoral arrays of log‐periodic (LP) antennas are presented for frequency‐independent operation and beam‐steering capability. Specifically, nonplanar trapezoidal tooth LP antennas are considered in a circular array configuration, where closely spaced antennas occupy a sector of the circle. Electromagnetic interactions of the array elements, each of which is a complicated LP antenna structure, are rigorously computed with the multilevel fast multipole algorithm (MLFMA). Genetic algorithms (GAs) are also employed in combination with MLFMA for synthesis and design purposes. By optimizing the excitations of the array elements via GAs, beam‐steering ability is achieved in addition to the broadband (nearly frequency‐independent) characteristics of the designed arrays. Computational results are presented to demonstrate the important properties of LP arrays. Item Open AccessMLFMA solutions of transmission problems Involving realistic metamaterial walls(IEEE, 2007-08) Ergül, Özgür; Ünal, Alper; Gürel, Levent; Gürel, Levent; Ergül, ÖzgürWe present the solution of multilayer metamaterial (MM) structures containing large numbers of unit cells, such as split-ring resonators. Integral-equation formulations of scattering problems are solved iteratively by employing a parallel implementation of the multilevel fast multipole algorithm. Due to ill-conditioned nature of the problems, advanced preconditioning techniques are used to obtain rapid convergence in the iterative solutions. By constructing a sophisticated simulation environment, we accurately and efficiently investigate large and complicated MM structures. © 2007 IEEE.