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Analysis of finite and curved frequency-selective surfaces using the hybrid volume-surface integral equation approach

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MICROWAVE AND OPTICAL TECHNOLOGY LETTERS 2005年第2期45卷 107-112页

作者： Yu, C Lu, CC Univ Kentucky Dept Elect & Comp Engn Lexington KY 40506 USA

In practical applications, frequency-selective surfaces (FSSs) are finite, and sometimes even curved. In this paper, we present a hybrid volume-surface integral-equation approach to analyze the transmission and reflection characteristics of finite and curved FFS structures. The hybrid integral equations are established using the surface- and volume-equivalent principles. This approach has two advantages. One is the capability of modeling arbitrarily shaped FSS structures in detail, the other one allows its to easily apply the multilevel fast multiple algorithm to speed up the solution process. The scattering characteristics and frequency responses of several FSSs are analyzed. The simulation results show that for a finite-sized FSS, reducing the radius of curvature causes amplitude variation, frequency shift, and bandwidth change in the reflection and transmission responses. (c) 2005 Wiley Periodicals, Inc.

关键词： frequency-selective surface finite array effect of curvature volume-surface integral equation integral equation multilevel fast multipole algorithm

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Interpolation of translation matrix in MLFMA

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MICROWAVE AND OPTICAL TECHNOLOGY LETTERS 2001年第2期30卷 109-114页

作者： Song, JM Chew, WC Motorola Inc Digital DNA Res Lab Phoenix AZ 85008 USA Univ Illinois Dept Elect & Comp Engn Ctr Computat Electromagnet Urbana IL 61801 USA

The translation matrix for the multilevel fast multipole algorithm (MLFMA) in an FISC (fast Illinois solver code) is calculated directly, and the complexity is O(N-3/2), where N is the number of unknowns. For a problem with a small electrical size, the CPU time for calculating the translation matrix can be negligible. But for large problems, the calculation time increases significantly. In this paper, we use interpolation to calculate the translation matrix, and the complexity is reduced to O(N). Different interpolation techniques are tested, and it is found that the Lagrange polynomial interpolation with high sampling rates is the best. The saving factor is 10 for the VFY218 at 4 GHz. (C) 2001 John Wiley & Sons, Inc.

关键词： multilevel fast multipole algorithm numerical methods iterative solver

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Design and optimization of nanooptical couplers based on photonic crystals involving dielectric rods of varying lengths

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TURKISH JOURNAL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCES 2022年第6期30卷 2339-2354页

作者： Yazar, Sirin Ergul, Ozgur Salih Middle East Tech Univ Fac Engn Dept Elect & Elect Engn Ankara Turkey

This study presents design and optimization of compact and efficient nanooptical couplers involving photonic crystals. Nanooptical couplers that have single and double input ports are designed to obtain efficient transmission of electromagnetic waves in desired directions. In addition, these nanooptical couplers are cascaded by adding one after another to realize electromagnetic transmission systems. In the design and optimization of all these nanooptical couplers, the multilevel fast multipole algorithm, which is an efficient full-wave solution method, is used to perform electromagnetic analyses and simulations. A heuristic optimization method based on genetic algorithms is employed to obtain effective designs that provide the highest efficiency values. Two types of optimization strategies are applied using nanorods with a fixed length and using nanorods with varying lengths. This way, photonic crystals consisting of irregular arrays of both identical and nonidentical dielectric elements are designed for the realization of nanooptical couplers. The designs and their numerical results show that it is possible to design and further improve efficient nanooptical couplers with simple and compact geometries based on the principles of photonic crystals. Using relatively simple geometries and a single material, the designed nanooptical couplers are more preferable than the available designs in the literature.

关键词： Photonic crystals nanooptical couplers genetic algorithms multilevel fast multipole algorithm

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Computational Design of Optical Couplers for Bended Nanowire Transmission Lines

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APPLIED COMPUTATIONAL ELECTROMAGNETICS SOCIETY JOURNAL 2017年第7期32卷 562-568页

作者： Tuncyurek, Yunus Emre Karaosmanoglu, Bariscan Ergul, Ozgur Middle East Tech Univ Dept Elect & Elect Engn Ankara Turkey

We present computational analysis, optimization, and design of optical couplers that can be useful to improve the transmission along bended nanowires. After demonstrating the deteriorated energy transmission due to sharp bends, which lead to out-of-phase nanowires and diffraction, we use a rigorous simulation environment to design efficient couplers made of spherical particles. For this purpose, an optimization module based on genetic algorithms is combined with the multilevel fast multipole algorithm, leading to a full-wave environment for precise designs of couplers. Numerical examples involving silver nanowires are presented to demonstrate the effectiveness of the optimization mechanism.

关键词： Genetic algorithms multilevel fast multipole algorithm nanowires optical couplers surface integral equations

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A Modified Hybrid Integral Equation to Electromagnetic Scattering from Composite PEC-Dielectric Objects Containing Closed-Open PEC Junctions

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APPLIED COMPUTATIONAL ELECTROMAGNETICS SOCIETY JOURNAL 2021年第6期36卷 642-649页

作者： Liu, Jinbo Chen, Hongyang Zhang, Hui Yuan, Jin Li, Zengrui Commun Univ China State Key Lab Media Convergence Beijing 100024 Peoples R China Commun Univ China Sch Informat & Commun Engn Beijing 100024 Peoples R China

To efficiently analyze the electromagnetic scattering from composite perfect electric conductor (PEC)-dielectric objects with coexisting closed-open PEC junctions, a modified hybrid integral equation (HIE) is established as the surface integral equation (SIE) part of the volume surface integral equation (VSIE), which employs the combined field integral equation (CFIE) and the electric field integral equation (EFIE) on the closed and open PEC surfaces, respectively. Different from the traditional HIE modeled for the objects whose closed and open PEC surfaces are strictly separate, the modified HIE can be applied to the objects containing closed-open junctions. A matrix equation is obtained by using the Galerkin's method of moments (MoM), which is augmented with the spherical harmonics expansion-based multilevel fast multipole algorithm (SE-MLFMA), improved by the mixed-potential representation and the triangle/tetrahedron-based grouping scheme. Because in the improved SE-MLFMA, the memory usage for storing the radiation patterns of basis functions is independent of the SIE type in the VSIE, it is highly appropriate for the fast solution of the VSIE that contains the HIE. Various numerical experiments demonstrate that during the calculation of composite objects containing closed-open PEC junctions, the application of the modified HIE in the VSIE can give reliable results with fast convergence speed.

关键词： fast solver integral equation method of moments multilevel fast multipole algorithm

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Enhanced GMRES method combined with MLFMA for solving electromagnetic wave scattering problems

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MICROWAVE AND OPTICAL TECHNOLOGY LETTERS 2008年第5期50卷 1433-1439页

作者： Rui, P. L. Chen, R. S. Nanjing Univ Sci & Technol Dept Commun Engn Nanjing 210094 Peoples R China

For efficiently solving large dense complex linear systems that arise in the electric field integral equation (EFIE) formulation of electromagnetic wave scattering problems, the multilevel fast multipole algorithm (MLFMA) is used to speed up the matrix vector product operations, and the sparse approximate inverse (SAI) preconditioning technique is employed to accelerate the convergence rate of the generalized minimal residual (GMRES) iterative method. We show that the convergence rate can be greatly improved by augmenting to the GMRES method a few eigenvectors associated with the smallest eigenvalues of the preconditioned system. Numerical experiments indicate that this new variant GMRES method is very effective with the MLFMA and can reduce both the iteration number and the computational time significantly. (C) 2008 Wiley Periodicals, Inc.

关键词： electromagnetic wave scattering multilevel fast multipole algorithm preconditioning techniques generalized minimal residual iterative method

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PERFORMANCE COMPARISON BETWEEN TWO COMMERCIAL EM SOFTWARES USING HIGHER ORDER AND PIECEWISE RWG BASIS FUNCTIONS

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MICROWAVE AND OPTICAL TECHNOLOGY LETTERS 2009年第5期51卷 1219-1225页

作者： Zhao, X. W. Liang, C. H. Xidian Univ Natl Key Lab Antennas & Microwave Technol Xian 710071 Shaanxi Peoples R China

In this article, numerical result obtained using two different commercially available electromagnetic (EM) codes based on an integral equation method are presented. One of the methods solves the integral equation by the method of moments (MoM) using higher order basis functions (the commercially available parallel software named TIDES), and the other one solves the integral equation by MoM with a multilevel fast multipole algorithm (MLFMA) incorporating the RWG basis functions (the commercially available software FEKO). Numerical results indicate that the integral equation solver with higher order basis functions occupies less than 40% of the RAM and the execution little is significantly less when compared with that of using the RWG basis functions along with MLFMA. (C) 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 1219-1225, 2009;Published online in Wiley Inter-Science (***). DOI 10.1002/mop.24271

关键词： higher order basis functions RWG basis functions method of moments multilevel fast multipole algorithm preconditioner

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Error control of the translation operator in 3D MLFMA

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MICROWAVE AND OPTICAL TECHNOLOGY LETTERS 2003年第3期37卷 184-188页

作者： Hastriter, ML Ohnuki, S Chew, WC Univ Illinois Dept Elect & Comp Engn Ctr Computat Electromagnet Urbana IL 61801 USA

This paper Presents an extension of a new, approach to select the truncation number for translation operators in a 3D multilevel fast multipole algorithm (MLFMA). Although en-or is harder to control in 3D than in 2D problems, this recently developed new approach provides better error control in 3D problems over the excess bandwidth formula. (C) 2003 Wiley Periodicals. Inc.

关键词： multilevel fast multipole algorithm fast multipole method addition theorem error analysis

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Analysis of Electromagnetic Scattering Problems by Means of a VSIE-ODDM-MLFMA Method

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APPLIED COMPUTATIONAL ELECTROMAGNETICS SOCIETY JOURNAL 2012年第8期27卷 660-667页

作者： Chen, Jialin Li, Shangsheng Song, Yaping Naval Aeronaut Engn Inst Dept Elect & Commun Engn Yantai 2640017 Japan 91919th Unit PLA Huanggang 438021 Peoples R China

The hybrid volume-surface integral equation (VSIE) method has the advantage of solving electromagnetic scattering problems involving complex structure mixed metal with dielectric. In this paper, a method combining VSIE with overlapped domain decomposition method (ODDM) is used to analyze electromagnetic scattering problems successfully. To further improve efficiency, the multilevel fast multipole algorithm (MLFMA) is adopted, then a novel VSIE-ODDM-MLFMA is proposed. Numerical results show that the proposed method has low memory requirement, fast convergence, and accurate simulation result. It indicates that the proposed method has the ability to analyze complicated electromagnetic problems.

关键词： volume-surface integral equation electromagnetic scattering overlapped domain decomposition method multilevel fast multipole algorithm

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A short survey on preconditioning techniques for large-scale dense complex linear systems in electromagnetics

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2007年第8期84卷 1211-1223页

作者： Wang, Yin Lee, Jeonghwa Zhang, Jun Univ Kentucky Dept Comp Sci Lab High Performance Sci Comp & Comp Simulat Lexington KY 40506 USA Shippensburg Univ Dept Comp Sci Shippensburg PA 17257 USA

In solving systems of linear equations arising from practical scientific and engineering modelling and simulations such as electromagnetics applications, it is important to choose a fast and robust solver. Due to the large scale of those problems, preconditioned Krylov subspace methods are most suitable. In electromagnetics simulations, the use of preconditioned Krylov subspace methods in the context of multilevel fast multipole algorithms (MLFMA) is particularly attractive. In this paper, we present a short survey of a few preconditioning techniques in this application. We also compare several preconditioning techniques combined with the Krylov subspace methods to solve large dense linear systems arising from electromagnetic scattering problems and present some numerical results.

关键词： dense matrices electromagnetics integral formulation multilevel fast multipole algorithm preconditioning techniques

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