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Analysis of the parameters of an approach that combines the characteristic basis function method and the multilevel fast multipole

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IET MICROWAVES ANTENNAS & PROPAGATION 2011年第4期5卷 419-425页

作者： Garcia, E. Delgado, C. Lozano, L. Catedra, F. Univ Alcala Dept Automat Madrid 28871 Spain Univ Alcala Dept Ciencias Computac Madrid 28871 Spain

A study on the parameters of an approach that combines the characteristic basis function method and the multilevel fast multipole algorithm is presented. This approach is a very efficient scheme for the rigorous computation of electrically large problems. An analysis of the configuration parameters of the method to obtain accurate results reducing CPU time is shown. Non-uniform rational B-splines surfaces are employed for the representation of the geometry and the characteristic basis functions are described in terms of curved rooftops generated in the parametric space. The associated macro-testing functions are defined as aggregations of curved razor-blade functions.

关键词： non-uniform rational B-splines surfaces splines (mathematics) geometry curved razor-blade functions Electromagnetic wave propagation electromagnetic wave propagation Interpolation and function approximation (numerical analysis) multilevel fast multipole algorithm curved rooftops electrically large problems computational electromagnetics Combinatorial mathematics macro-testing functions characteristic basis function method

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multilevel fast multipole Acceleration in the Nystrom Discretization of Surface Electromagnetic Integral Equations for Composite Objects

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 2010年第10期58卷 3411-3416页

作者： Tong, Mei Song Chew, Weng Cho Univ Illinois Dept Elect & Comp Engn Urbana IL 61801 USA

The multilevel fast multipole algorithm (MLFMA) based on the Nystrom discretization of surface integral equations (SIEs) is developed for solving electromagnetic (EM) scattering by large composite objects. Traditionally, the MLFMA is based on the method of moments (MoM) discretization for the SIEs and it usually works well when the robust Rao-Wilton- Glisson (RWG) basis function is enough to represent unknown currents. However, the RWG basis function may not represent both the electric and magnetic current in solving the electric field integral equation (EFIE) and magnetic field integral equation (MFIE) for penetrable objects, and how one represents another current could be a problem in the MoM. In this work, we use the Nystrm method as a tool to discretize the SIEs and incorporate the MLFMA to accelerate the solutions for electrically large problems. The advantages of the Nystrm discretization include the simple mechanism of implementation, lower requirements on mesh quality, and no use of basis and testing functions. These benefits are particularly desired in the MLFMA because the solved problems are very large and complex in general. Numerical examples are presented to demonstrate the effectiveness of the proposed scheme.

关键词： Electromagnetic scattering multilevel fast multipole algorithm Nystrom discretization surface integral equations

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fast 3D EM scattering and radiation solvers based on MLFMA

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Journal of Systems Engineering and Electronics 2008年第2期19卷 252-258页

作者： Hu Jun Nie Zaiping Lei Lin Hu Jie Gong Xiaodong Zhao Huapeng Coll. of Electronic Engineering Univ. of Electronic Science and Technology of China Chengdu 610054 P. R. China

As the fastest integral equation solver to date, the multilevel fast multipole algorithm （MLFMA） has been applied successfully to solve electromagnetic scattering and radiation from 3D electrically large objects. But for very large-scale problems, the storage and CPU time required in MLFMA are still expensive. fast 3D electromagnetic scattering and radiation solvers are introduced based on MLFMA. A brief review of MLFMA is first given. Then, four fast methods including higher-order MLFMA （HO-MLFMA）, fast far field approximation combined with adaptive ray propagation MLFMA （FAFFA-ARP-MLFMA）, local MLFMA and parallel MLFMA are introduced. Some typical numerical results demonstrate the efficiency of these fast methods.

关键词： scattering and radiation multilevel fast multipole algorithm higher order far field approximation,ray propagation local interaction parallel.

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Hybrid IE-DDM-MLFMA with Gauss-Seidel Iterative Technique for Scattering from Conducting Body of Translation

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APPLIED COMPUTATIONAL ELECTROMAGNETICS SOCIETY JOURNAL 2015年第2期30卷 148-156页

作者： Jiang, Ming Hu, Jun Zhao, Ran Wei, Xiang Nie, Zai-ping Univ Elect Sci & Technol China Sch Elect Engn Chengdu 611731 Peoples R China

In this paper, a hybrid Integral Equation-Domain Decomposition Method-multilevel fast multipole algorithm (IE-DDMMLFMA) with Gauss-Seidel iterative technique is proposed to calculate the scattering from perfectly electric conducting Body of Translation (BoT). The BoT can be partitioned into translational nonoverlapping sub-domains. A hybrid local/global MLFMA framework is adopted to realize efficient matrix-vector multiplication in sub-domains and between sub-domains by utilizing the feature of translational invariance of BoT. To reduce the number of interactions between sub-domains, Gaussian-Seidel iterative technique is applied. Numerical examples are presented to demonstrate the efficiency of the present method.

关键词： Body of translation Gauss-Seidel iteration multilevel fast multipole algorithm non-overlapping domain decomposition method

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Analysis of Electrically Large Problems Using the Augmented EFIE With a Calderon Preconditioner

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 2011年第6期59卷 2303-2314页

作者： Yan, Su Jin, Jian-Ming Nie, Zaiping Univ Elect Sci & Technol China Dept Microwave Engn Chengdu 610054 Sichuan Peoples R China Univ Illinois Dept Elect & Comp Engn Ctr Computat Electromagnet Urbana IL 61801 USA

Calderon preconditioned electric-field integral equation (CP-EFIE) is very efficient in analyzing electromagnetic problems with a moderate electrical size. For the analysis of electrically large problems with closed surfaces, the CP-EFIE, however, suffers from the well-known spurious internal resonance problem because both the EFIE and the Calderon preconditioner are singular at resonant frequencies. In this paper, the resonance problem of the Calderon preconditioner is removed by using a complex wavenumber, and that of the EFIE is eliminated by enforcing the boundary condition (n) over cap . D = rho(s) to the EFIE, resulting in the so-called augmented EFIE (AEFIE). It is shown that the proposed Calderon preconditioned AEFIE is a resonant-free formulation, and has a fast convergence rate for an iterative solution. Numerical examples are given to demonstrate the good accuracy and fast convergence of the proposed approach for the analysis of electrically large problems. The multilevel fast multipole algorithm (MLFMA) is employed to reduce the computational and storage complexities of the iterative solution.

关键词： Augmented EFIE Calderon preconditioner electrically large problems multilevel fast multipole algorithm perfect electric conductor spurious internal resonance

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Hybrid MLFMA/MILACA for Analysis of Electromagnetic Scattering from Inhomogeneous High-Contrast Objects

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APPLIED COMPUTATIONAL ELECTROMAGNETICS SOCIETY JOURNAL 2015年第7期30卷 765-772页

作者： Hu, Y. L. Fan, Z. H. Ding, D. Z. Chen, R. S. Nanjing Univ Sci & Technol Dept Commun Engn Nanjing 210094 Jiangsu Peoples R China

An efficient hybrid method is proposed to analyze the electromagnetic scattering from the composite structures comprising PEC and inhomogeneous high-contrast dielectric materials with the volume-surface integral equation (VSIE) approach, which uses the main framework of the multilevel fast multipole algorithm (MLFMA) but adopts the multilevel adaptive cross approximation algorithm (MLACA) and the equivalent dipole-moment (EDM) to deal with part of the "strong" interaction of MLFMA. Numerical results are presented to demonstrate the accuracy and efficiency of the proposed scheme.

关键词： Equivalent dipole-moment multilevel adaptive cross approximation algorithm multilevel fast multipole algorithm volume-surface integral equation

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Design, simulation, and measurement of near-zero-index shells for electromagnetic beam generation

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JOURNAL OF ELECTROMAGNETIC WAVES AND APPLICATIONS 2024年第2期38卷 213-233页

作者： Eris, Ozgur Ergul, Ozgur Middle East Tech Univ Dept Elect & Elect Engn Ankara Turkiye

We present design and simulation of three-dimensional (3D) shell structures, which generate directional radiation patterns from isotropic sources thanks to their near-zero-index (NZI) characteristics, as well as realizations of these shells via low-cost 3D printing. Throughout the design process of NZI beam generators, both homogenized structures, for which near-zero relative permittivity and/or permeability values are enforced, and actual models involving periodic arrangements of dielectric rods are considered. Solutions of the electromagnetic problems are obtained by using rigorous implementations of the state-of-the-art surface-integral-equation (SIE) formulations in frequency domain. Iterative solutions of matrix equations derived from SIEs are accelerated by different forms of the multilevel fast multipole algorithm (MLFMA) and suitable preconditioners, when necessary. In the design process of NZI shells, alternative strategies are employed to obtain customized radiation patterns. In this context, various cavities with strong resonance behaviors are designed as source regions. At the same time, outer surfaces are modified to either enhance or suppress outgoing electromagnetic fields. In addition to comprehensive simulations and analyses of NZI beam generators, their capabilities are verified by measurements, specifically at 10.3 GHz, on different prototypes fabricated via 3D printing. Measurements of diverse NZI shell structures are presented to demonstrate that NZI properties can successfully be achieved by well-designed arrangements of dielectric rods with proper materials. The results demonstrate the feasibility of efficient, effective, low-cost, and reconfigurable NZI shells to generate alternative beam configurations that can be useful in a plethora of microwave applications.

关键词： Zero-index materials beam generators metamaterials multilevel fast multipole algorithm 3D printing microwave applications

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Improved hybrid FEM/MOM combining MLFMA for composite electromagnetic scattering

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ELECTROMAGNETICS 2017年第8期37卷 513-529页

作者： Sun, Hua Long Tong, Chuang Ming Peng, Peng Air Force Engn Univ Air & Missile Def Coll Xian 710051 Shaanxi Peoples R China

A generalized hybrid scheme combining finite element method (FEM) and the method of moments (MOM) is first presented to investigate scattering from a 3-D dielectric object above a 2-D dielectric rough surface. The hybrid FEM/MOM scheme is divided into the FEM region for the object based on Helmholtz's equation and the MOM region for the rough surface based on coupled integral function, which can greatly reduce the computed region. With the rough surface getting larger, the unknowns of the rough surface get more. So MLFMA is employed to reduce computation complexity of MOM region itself and coupling interaction matrices between MOM region and FEM region. Consequently, the iterative process can be greatly accelerated. This generalized hybrid FEM/MOM is very suitable for investigating scattering from composite model of a complex material object and electrically large dielectric rough surface. Some examples verify this generalized hybrid FEM/MOM in high efficiency, low storage requirement, high precision and generality.

关键词： Composite electromagnetic scattering multilevel fast multipole algorithm method of moments rough surface

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Novel electromagnetic surface integral equations for highly accurate computations of dielectric bodies with arbitrarily low contrasts

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JOURNAL OF COMPUTATIONAL PHYSICS 2008年第23期227卷 9898-9912页

作者： Erguel, Oezguer Guerel, Levent Bilkent Univ Dept Elect & Elect Engn TR-06800 Ankara Turkey Bilkent Univ Computat Electromagnet Res Ctr BiLCEM TR-06800 Ankara Turkey

We present a novel stabilization procedure for accurate surface formulations of electromagnetic scattering problems involving three-dimensional dielectric objects with arbitrarily low contrasts. Conventional surface integral equations provide inaccurate results for the scattered fields when the contrast of the object is low, i.e., when the electromagnetic material parameters of the scatterer and the host medium are close to each other. We propose a stabilization procedure involving the extraction of nonradiating currents and rearrangement of the right-hand side of the equations using fictitious incident fields. Then, only the radiating currents are solved to calculate the scattered fields accurately. This technique can easily be applied to the existing implementations of conventional formulations, it requires negligible extra computational cost, and it is also appropriate for the solution of large problems with the multilevel fast multipole algorithm. We show that the stabilization leads to robust formulations that are valid even for the solutions of extremely low-contrast objects. (C) 2008 Elsevier Inc. All rights reserved.

关键词： Dielectrics Low contrast Surface integral equations multilevel fast multipole algorithm

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Comparison of scattering diagrams of large non-spherical particles calculated by VCRM and MLFMA

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JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER 2015年 162卷 143-153页

作者： Yang, Minglin Wu, Yueqian Sheng, Xinqing Ren, Kuan Fang Beijing Inst Technol Sch Informat & Elect Ctr Electromagnet Simulat Beijing 100081 Peoples R China Univ Rouen CNRS Normandie Univ CORIA UMR6614 F-76801 Saint Etienne Du Rouvray France INSA Rouen F-76801 Saint Etienne Du Rouvray France

The vectorial complex ray model (VCRM) developed in recent years improves considerably the precision and the applicability of the ray model in the light scattering by large non-spherical particles. But its results for particles of complex shape remain to be validated. The surface integral equation (SIE) with parallel multilevel fast multipole algorithm (MLFMA) is a rigorous numerical method so it permits us to obtain accurate results of particles of any shape. With new improvement we have made, our parallelized code of MLFMA allows us to calculate the scattering of non-spherical dielectric particles of size much larger than the incident wavelength. This paper is devoted to the validation of the VCRM by comparison of the scattering diagrams with the MLFMA results. The scattering diagrams of large ellipsoidal particles with different size parameters and aspect ratios are computed by using the two methods. Good agreements between them prove the ability of both MLFMA and VCRM for large non-spherical particles. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Light scattering Vectorial complex ray model multilevel fast multipole algorithm Non-spherical particle

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