Browsing by Subject "Combined field integral equations"

Now showing 1 - 11 of 11

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
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
EFIE and MFIE, why the difference?
(IEEE, 2008-07) Chew W.C.; Davis, C. P.; Warnick, K. F.; Nie, Z. P.; Hu, J.; Yan, S.; Gürel, Levent
EFIE (electric field integral equation) suffers from internal resonance, and the remedy is to use MFIE (magnetic field integral equation) to come up with a CFIE (combined field integral equation) to remove the internal resonance problem. However, MFIE is fundamentally a very different integral equation from EFIE. Many questions have been raised about the differences.
Open Access
Fast and accurate analysis of large-scale composite structures with the parallel multilevel fast multipole algorithm
(Optical Society of America, 2013) Ergül, Özgür; Gürel, Levent
Accurate electromagnetic modeling of complicated optical structures poses several challenges. Optical metamaterial and plasmonic structures are composed of multiple coexisting dielectric and/or conducting parts. Such composite structures may possess diverse values of conductivities and dielectric constants, including negative permittivity and permeability. Further challenges are the large sizes of the structures with respect to wavelength and the complexities of the geometries. In order to overcome these challenges and to achieve rigorous and efficient electromagnetic modeling of three-dimensional optical composite structures, we have developed a parallel implementation of the multilevel fast multipole algorithm (MLFMA). Precise formulation of composite structures is achieved with the so-called "electric and magnetic current combined-field integral equation." Surface integral equations are carefully discretized with piecewise linear basis functions, and the ensuing dense matrix equations are solved iteratively with parallel MLFMA. The hierarchical strategy is used for the efficient parallelization of MLFMA on distributed-memory architectures. In this paper, fast and accurate solutions of large-scale canonical and complicated real-life problems, such as optical metamaterials, discretized with tens of millions of unknowns are presented in order to demonstrate the capabilities of the proposed electromagnetic solver.
Open Access
Fast and accurate analysis of optical metamaterials using surface integral equations and the parallel multilevel fast multipole algorithm
(IEEE, 2013) Ergül, Özgür; Gürel, Levent
We present fast and accurate simulations of optical metamaterials using surface integral equations and the multilevel fast multipole algorithm (MLFMA). Problems are formulated with the electric and magnetic current combined-field integral equation and solved iteratively with MLFMA, which is parallelized using the hierarchical strategy on distributed-memory architectures. Realistic metamaterials involving dielectric, perfectly conducting, and plasmonic regions of finite extents are solved rigorously with the developed implementation without any periodicity assumptions.
Open Access
Iterative solution of dielectric waveguide problems via schur complement preconditioners
(IEEE, 2010-07) Malas, Tahir; Gürel, Levent
Surface integral-equation methods accelerated with the multilevel fast multipole algorithm provide suitable mechanisms for the solution of dielectric problems. In particular, recently developed formulations increase the stability of the resulting matrix equations, hence they are more suitable for iterative solutions [1]. Among those formulations, we consider the combined tangential formulation (CTF), which produces more accurate results, and the electric and magnetic current combined-field integral equation (JMCFIE), which produces better-conditioned matrix systems than other formulations [1, 2]. ©2010 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
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 scattering problems involving red blood cells
(IEEE, 2010) Ergül, Özgür; Arslan-Ergül, Ayça; Gürel, Levent
We 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.