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Efficient MLFMA, RPFMA, and FAFFA algorithms for EM scattering by very large structures

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 2004年第3期52卷 759-770页

作者： Cui, TJ Chew, WC Chen, G Song, JM Southeast Univ Ctr Computat Electromagnet Nanjing 210096 Peoples R China Southeast Univ Dept Radio Engn State Key Lab Millimeter Waves Nanjing 210096 Peoples R China Univ Illinois Dept Elect & Comp Engn Ctr Computat Electromagnet Urbana IL 61801 USA Iowa State Univ Dept Elect & Comp Engn Ames IA 50011 USA

Based on the addition theorem, the principle of a multilevel ray-propagation fast multipole algorithm (RPFMA) and fast far-field approximation (FAFFA) has been demonstrated for three-dimensional (3-D) electromagnetic scattering problems. From a rigorous mathematical derivation, the relation among RPFMA, FAFFA, and a conventional multilevel fast multipole algorithm (MLFMA) has been clearly stated. For very large-scale problems, the translation between groups in the conventional MLFMA is expensive because the translator is defined on an Ewald sphere with many sampling (k) over cap directions. When two groups are well separated, the translation can be simplified using RPFMA, where only a few sampling (k) over cap directions are required within a cone zone on the Ewald sphere. When two groups are in the far-field region, the translation can be further simplified by using FAFFA where only a single (k) over cap is involved in the translator along the ray-propagation direction. Combining RPFMA and FAFFA with MLFMA, three algorithms RPFMA-MLFMA, FAFFA-MLFMA, and RPFMA-FAFFA-MLFMA have been developed, which are more efficient than the conventional MLFMA in 3-D electromagnetic scattering and radiation for very large structures. Numerical results are given to verify the efficiency of the algorithms.

关键词： electromagnetic scattering fast far-field approximation (FAFFA) method of moments multilevel fast multipole algorithm multilevel ray-propagation fast multipole algorithm

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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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Error analysis for the numerical evaluation of the diagonal forms of the scalar spherical addition theorem

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SIAM JOURNAL ON NUMERICAL ANALYSIS 1999年第3期36卷 906-921页

作者： Koc, S Song, JM Chew, WC Middle E Tech Univ Dept Elect & Elect Engn TR-06531 Ankara Turkey Univ Illinois Dept Elect & Comp Engn Ctr Computat Electromagnet Urbana IL 61801 USA

The numerical solution of wave scattering from large objects or from a large cluster of scatterers requires excessive computational resources and it becomes necessary to use approximate-but fast-methods such as the fast multipole method;however, since these methods are only approximate, it is important to have an estimate for the error introduced in such calculations. An analysis of the error for the fast multipole method is presented and estimates for truncation and numerical integration errors are obtained. The error caused by polynomial interpolation in a multilevel fast multipole algorithm is also analyzed. The total error introduced in a multilevel implementation is also investigated numerically.

关键词： fast multipole method multilevel fast multipole algorithm error analysis truncation error integration error interpolation error

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Truncation error analysis of multipole expansion

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 2003年第4期25卷 1293-1306页

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

The multilevel fast multipole algorithm is based on the multipole expansion, which has numerical error sources such as truncation of the addition theorem, numerical integration, and interpolation/anterpolation. Of these, we focus on the truncation error and discuss its control precisely. The conventional selection rule fails when the buffer size is small compared to the desired numerical accuracy. We propose a new approach and show that the truncation error can be controlled and predicted regardless of the number of buffer sizes.

关键词： fast multipole method multilevel fast multipole algorithm error analysis truncation error

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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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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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Multiscale simulation of complex structures using equivalence principle algorithm with high-order field point sampling scheme

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 2008年第8期56卷 2389-2397页

作者： Li, Mao-Kun Chew, Weng Cho Univ Illinois Ctr Computat Electromagnet Urbana IL 61801 USA Univ Illinois Electromagnet Lab Dept Elect & Comp Engn Urbana IL 61801 USA Univ Hong Kong Hong Kong Hong Kong Peoples R China

In this paper, an updated equivalence principle algorithm (EPA) is presented. Compared with previous work by the authors, the high-order point sampling scheme is used to reduce the high-frequency noise in field projection. An updated tap basis scheme is introduced to simplify the formulation. With these schemes, the equivalence principle algorithm can be used to solve multiscale problems by substituting the oversampled region with a proper equivalence surface. Moreover, EPA can also be accelerated using attached unknown accelerations and multilevel fast multipole algorithm so that large multiscale problems can be solved efficiently.

关键词： domain decomposition methods equivalence principle high-order point sampling scheme integral equation solvers integral equations method of moments (MoM) multilevel fast multipole algorithm Nystrom methods tap basis

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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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Incomplete LU preconditioning for large scale dense complex linear systems from electromagnetic wave scattering problems

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JOURNAL OF COMPUTATIONAL PHYSICS 2003年第1期185卷 158-175页

作者： Lee, J Zhang, J Lu, CC Univ Kentucky Dept Comp Sci Lab High Performance Sci Comp & Comp Simulat Lexington KY 40506 USA Univ Kentucky Dept Elect & Comp Engn Lexington KY 40506 USA

We consider the preconditioned iterative solution of large dense linear systems, where the coefficient matrix is a complex valued matrix arising from discretizing the integral equation of electromagnetic scattering. For some scattering structures this matrix can be poorly conditioned. The main purpose of this study is to evaluate the efficiency of a class of incomplete LU (ILU) factorization preconditioners for solving this type of matrices. We solve the electromagnetic wave equations using the BiCG method with an ILU preconditioner in the context of a multilevel fast multipole algorithm (MLFMA). The novelty of this work is that the ILU preconditioner is constructed using the near part block diagonal submatrices generated from the MLFMA. Experimental results show that the ILU preconditioner reduces the number of BiCG iterations substantially, compared to the block diagonal preconditioner. The preconditioned iteration scheme also maintains the computational complexity of the MLFMA, and consequently reduces the total CPU time. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： Krylov subspace methods ILU preconditioning multilevel fast multipole algorithm electromagnetic scattering

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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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