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Numerical Solutions of the Integral Equation for Excitation-Transmission-Radiation of the Beam Waveguide

JOURNAL OF INFRARED MILLIMETER AND TERAHERTZ WAVES 2012年第9期33卷 963-971页

作者： Qing, Tao Nie, Zaiping He, Shiquan Zong, Xianzheng Univ Elect Sci & Technol China Sch Elect Engn Chengdu 610054 Peoples R China

The numerical method of the Integral Equation has been used to model the electromagnetic excitation, transmission, and radiation problems of the beam waveguide. The Mode Matching Method has been used to describe the impedance matching situation at the exciting aperture of the waveguide. The excitation conditions were established based on the expansion of the waveguide modes and the continuity of the tangential components of the fields. The volume-surface integral equations combined with the equavalence principle have been used to model the wave transmission in the beam waveguide. The numerical solutions of the electromagnetic transmission and aperture radiation of the waveguide have been given by using the multilevel fast multipole algorithm (MLFMA). It has been demonstrated that the method proposed by this paper is able to provide the efficient and accurate numerical solution for the excitation, propagation and radiation problems of the beam waveguide with arbitrary shape and electrically large size.

关键词： Beam waveguide Equivalence principle Volume-surface integral equations Numerical solutions multilevel fast multipole algorithm

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Convergence Property of IDR(s) Method Implemented along with Method of Moments for Solving Large-Scale Electromagnetic Scattering Problems Involving Conducting Objects

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IEICE TRANSACTIONS ON ELECTRONICS 2011年第2期E94C卷 198-205页

作者： Chiba, Hidetoshi Fukasawa, Toru Miyashita, Hiroaki Konishi, Yoshihiko Mitsubishi Electr Corp Informat Technol R&D Ctr Kamakura Kanagawa 2478501 Japan

In this paper, the performance of the induced dimension reduction (IDR) method implemented along with the method of moments (MoM) is described. The MoM is based on a combined field integral equation for solving large-scale electromagnetic scattering problems involving conducting objects. The IDR method is one of Krylov subspace methods. This method was initially developed by Peter Sonneveld in 1979;it was subsequently generalized to the IDR(s) method. The method has recently attracted considerable attention in the field of computational physics. However, the performance of the IDR(s) has hardly been studied or practiced for electromagnetic wave problems. In this study, the performance of the IDR(s) is investigated and clarified by comparing the convergence property and memory requirement of the IDR(s) with those of other representative Krylov solvers such as biconjugate gradient (BiCG) methods and generalized minimal residual algorithm (GMRES). Numerical experiments reveal that the characteristics of the IDR(s) against the parameter s strongly depend on the geometry of the problem;in a problem with a complex geometry, s should be set to an adequately small value in order to avoid the "spurious convergence" which is a problem that the IDR(s) inherently holds. As for the convergence behavior, we observe that the 1DR(s) has a better convergence ability than GPBiCG and GMRES(m) in a variety of problems with different complexities. Furthermore, we also confirm the IDR(s)'s inherent advantage in terms of the memory requirements over GMRES(m).

关键词： IDR(s) method Krylov subspace methods integral equation methods method of moments multilevel fast multipole algorithm

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A Sophisticated parallel MLFMA for scattering by extremely large targets

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IEEE ANTENNAS AND PROPAGATION MAGAZINE 2008年第3期50卷 129-138页

作者： Pan, Xiao-Min Sheng, Xin-Qing Beijing Inst Technol Ctr Electromagnet Simulat Sch Informat Sci & Technol Beijing Peoples R China

The development of the MLFMA for realistic targets is currently at the stage where clever implementation, using a series of tricks based on the characteristics of the MLFMA and current computer technology, is required. A sophisticated parallel MLFMA for use on distributed-memory computers is presented as a whole picture of developing the program using a style of multilevel development in this paper. A series of implementation tricks for the parallel MLFMA are analyzed and compared. Particularly, a novel trick for reducing the truncation numbers is presented for extremely large targets, in the paper. These tricks are integrated into a sophisticated parallel MLFMA. The memory requirement and the CPU time for each part in each level are analyzed numerically by typical numerical experiments. The capability of this sophisticated parallel MLFMA is demonstrated by computing scattering by a sphere with a diameter of 480 wavelengths, containing around 130 million unknowns, and for a plane model with a fuselage of more than 1000 wavelengths, containing more than 72 million unknowns. These are the largest scattering problems ever solved by full-wave numerical methods, to our knowledge.

关键词： multilevel fast multipole algorithm parallel programming electromagnetic scaftering radar cross section

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Curve linear-linear basis functions of magnetic-field and combined-field integral equations for EM scattering problems

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ELECTRONICS LETTERS 2014年第25期50卷 1977-1978页

作者： He, Zi Zha, Liping Chen, Ru Shan Nanjing Univ Sci & Technol Nanjing Jiangsu Peoples R China

The curve linear-linear (CLL) basis functions are proposed to improve the accuracy of both the magnetic-field integral equation (MFIE) and the combined-field integral equation (CFIE) for electromagnetic scattering from PEC objects. The CLL basis functions are derived first and then the multilevel fast multipole algorithm is applied to accelerate the matrix-vector multiplication. The accuracy of the CLL basis functions for both the MFIE and the CFIE are compared with both the curve RWG basis functions and the linear-linear basis functions. Numerical results demonstrate the efficiency of the proposed method.

关键词： electric field integral equations electromagnetic wave scattering magnetic field integral equations matrix multiplication CFIE CLL basis function EM scattering problems MFIE PEC objects combined-field integral equation combined-field integral equations curve RWG basis functions curve linear-linear basis functions electromagnetic scattering magnetic-field integral equation matrix-vector multiplication multilevel fast multipole algorithm

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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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On the computing algorithms of the hybrid FEM/MLFMA

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MICROWAVE AND OPTICAL TECHNOLOGY LETTERS 2002年第4期33卷 265-268页

作者： Sheng, XQ Yung, EKN Chinese Acad Sci Inst Elect Beijing 100864 Peoples R China City Univ Hong Kong Dept Elect Engn Hong Kong Hong Kong Peoples R China

Several computing algorithms of the hybrid FEM/MLFMA, the conventional algorithm (CA), the direct-iterative decomposition algorithm (DIDA), and a new one, the iterative-iterative decomposition algorithm (IIDA), are described in this Letter. The required computing resources of these three algorithms are compared analytically and numerically. Several important numerical features of these algorithms are pointed out and confirmed. Criteria are given for the choice of computing algorithms. (C) 2002 Wiley Periodicals, Inc.

关键词： numerical methods finite-element methods multilevel fast multipole algorithm

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Enhancing the accuracy of the interpolations and anterpolations in MLFMA

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IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS 2006年第1期5卷 467-470页

作者： Erguel, Oezguer Guerel, Levent Bilkent Univ Dept Elect & Elect Engn TR-06800 Ankara Turkey

We present an efficient technique to reduce the interpolation and anterpolation (transpose interpolation) errors in the aggregation and disaggregation processes of the multilevel fast multipole algorithm (MLFMA), which is based on the sampling of the radiated and incoming fields over all possible solid angles, i.e., all directions on the sphere. The fields sampled on the sphere are subject to various operations, such as interpolation, aggregation, translation, disaggregation, anterpolation, and integration. We identify the areas on the sphere, where the highest levels of interpolation errors are encountered. The error is reduced by employing additional samples on such parts of the sphere. Since the interpolation error is propagated and amplified by every level of aggregation, this technique is particulary useful for large problems. The additional costs in the memory and processing time are negligible, and the technique can easily be adapted into the existing implementations of MLFMA.

关键词： anterpolation Lagrange interpolation multilevel fast multipole algorithm transpose interpolation

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A Concise and Efficient MLFMA Scheme for Electromagnetic Surface Integral Equations From Dielectric Objects

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IEEE ACCESS 2020年 8卷 92225-92234页

作者： Li, Wei-Dong Miao, Jun-Xia Hong, Wei Southeast Univ Sch Informat Sci & Engn State Key Lab Millimeter Waves Nanjing 210096 Peoples R China Nanjing Univ Finance & Econ Sch Appl Math Nanjing 210046 Peoples R China

In the surface field integral equations (SIEs) from three-dimensional homogeneous dielectric objects, the equivalence electric and magnetic currents on the discontinuous interfaces between different homogeneous media are two independent sources. When the SIEs are iteratively solved, as indicated by the published literatures, the multilevel fast multipole algorithm (MLFMA) needs to be implemented respectively for the electric field integral equation (EFIE) and the magnetic field integral equation (MFIE) with these two currents, and hence a few MLFMA implementations are necessary for each homogeneous medium. In this paper, a concise and efficient scheme is proposed for reducing the implementations of the SIEs-MLFMA. First, the summation of the EFIE and MFIE-MLFMA implementations with the two currents can be simplified into one EFIE or MFIE-MLFMA implementation with integrating electric and magnetic currents at the lowest-level aggregation stage. Secondly, the common matrix frameworks consisting of the EFIE and MFIE-MLFMA implementations used in the SIEs can be simplified into one MLFMA implementation with two lowest-level diaggregations. The enhanced MLFMA scheme has excellent applicability to eight kinds of SIEs in wide use. In this way, the resulted SIE-MLFMA scheme performs only once for each homogeneous medium when transforming outgoing wave expansions of the two currents into incoming wave expansions for bottom cubes. Compared with the widely-used implementation approach of the MLFMA one by one for the two currents, it reduces the computation complexity by one half without sacrificing accuracy and adding a little memory requirement. Some examples are presented to validate the enhanced MLFMA scheme.

关键词： Media Integral equations Dielectrics MLFMA Licenses Magnetic separation Electromagnetics Aggregation translation disaggregation multilevel fast multipole algorithm surface integral equations electromagnetic scattering

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fast analysis of finite and curved frequency-selective surfaces using the VSIE with MLFMA

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INTERNATIONAL JOURNAL OF NUMERICAL MODELLING-ELECTRONIC NETWORKS DEVICES AND FIELDS 2011年第5期24卷 425-436页

作者： Ding, Dazhi Tao, Shifei Chen, Rushan Nanjing Univ Sci & Technol Dept Commun Engn Nanjing 210094 Peoples R China Southeast Univ Key State Key Lab Millimeter Waves Nanjing Peoples R China

The hybrid volume-surface integral equation approach is proposed to analyze the transmission and reflection characteristics of finite and curved frequency-selective surfaces structures. The surface current and electric flux density are expanded by surface RWG and volume SWG basis functions, respectively. The multilevel fast multipole algorithm is applied to reduce the computational complexity. Simulated results are given to demonstrate the accuracy and efficiency of the proposed method. Copyright (C) 2010 John Wiley & Sons, Ltd.

关键词： volume-surface integral-equation finite and curved frequency selective surfaces multilevel fast multipole algorithm

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Error minimization of multipole expansion

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 2005年第6期26卷 2047-2065页

作者： Ohnuki, S Chew, WC Nihon Univ Coll Sci & Technol Dept Elect Engn Tokyo 1018308 Japan Univ Illinois Dept Elect & Comp Engn Ctr Computat Electromagnet & Electromagnet Lab Urbana IL 61801 USA

In this paper, we focus on the truncation error of the multipole expansion for the fast multipole method and the multilevel fast multipole algorithm. When the buffer size is large enough, the error can be controlled and minimized by using the conventional selection rules. On the other hand, if the buffer size is small, the conventional selection rules no longer hold, and the new approach which we have recently proposed is needed. However, this method is still not sufficient to minimize the error for small buffer cases. We clarify this fact and show that the information about the placement of true worst-case interaction is needed. A novel algorithm to minimize the truncation error is proposed.

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

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