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

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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Novel Buffa-Christiansen Functions for Improving CFIE With Impedance Boundary Condition

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 2012年第8期60卷 3763-3771页

作者： Li, Wei-Dong Hong, Wei Zhou, Hou-Xing Song, Zhe Southeast Univ State Key Lab Millimeter Waves Nanjing 210096 Jiangsu Peoples R China

A novel kind of Buffa-Christiansen (BC) functions is developed for improving the surface combined field integral equation with impedance boundary condition (CFIE-IBC) from three-dimensional imperfectly conducting objects. With difference from the original BC function in wide use, the novel BC function is dimensionless as the RWG function, which makes the L and K components of the resulting matrix element from the CFIE-IBC dimensionally homogeneous. As a result, the eigenvalue condition number of the matrix is very low, which leads to a fast-convergence solution whether the surface impedance is low or high. The CFIE-IBC with the novel BC function is combined with the overlapped domain decomposition method for reducing the memory requirement. In its application to the multilevel fast multipole algorithm, the far-field interactions can be simplified for reducing the computational cost.

关键词： Buffa-Christiansen function electromagnetic scattering impedance boundary condition multilevel fast multipole algorithm overlapped domain decomposition method

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Extending the applicability of the combined-field integral equation to geometries containing open surfaces

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IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS 2006年第1期5卷 515-516页

作者： Guerel, Levent Erguel, Oezguer Bilkent Univ TR-06800 Ankara Turkey

In this letter, we consider the solution of large electromagnetics problems of composite structures with coexisting open and closed conductors. By modifying the construction of the combined-field integral equation (CFIE), we demonstrate a significant improvement in the iterative solution of these problems compared to the conventional electric-field formulation.

关键词： integral equations iterative methods multilevel fast multipole algorithm

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On the Use of Continuity Condition in the fast Solution of Volume-Surface Integral Equation

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IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS 2017年 16卷 625-628页

作者： He, Mang Liu, Jinbo Wang, Binbin Zhang, Chuanfang Sun, Houjun Beijing Inst Technol Sch Informat & Elect Beijing 100081 Peoples R China

The validity of the use of continuity condition (CC) is studied when it is combined with the volume-surface integral equation (VSIE) to solve the electromagnetic scattering/radiation of composite conductor-dielectric objects. It is found that the explicit enforcement of CC in VSIE may be inaccurate if the involved conductor is infinitesimally thin, but it works well for the composite structures that only contain conductors with closed surfaces. Anew combined field integral equation-volume integral equation with enforced CC (CC-CFIE-VIE) is then proposed, and a convenient way to embed it into the context of the multilevel fast multipole algorithm is also provided. Numerical results show that CC-CFIE-VIE not only reduces the overall memory usage and the CPU time of a single iteration, but also decreases the number of iterations to reach desired accuracy.

关键词： Continuity condition (CC) method of moments (MoM) multilevel fast multipole algorithm volume-surface integral equation

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Efficient solution of the electric-field integral equation using the iterative LSQR algorithm

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IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS 2008年第1期7卷 36-39页

作者： Ergul, Ozgur Gurel, Levent Bilkent Univ Dept Elect & Elect Engn TR-06800 Bilkent Turkey Bilkent Univ Computat Electromagnet Res Ctr TR-06800 Bilkent Turkey

In this letter, we consider iterative solutions of the three-dimensional electromagnetic scattering problems formulated by surface integral equations. We show that solutions of the electric-field integral equation (EFIE) can be improved by employing an iterative least-squares QR (LSQR) algorithm. Compared to many other Krylov subspace methods, LSQR provides faster convergence and it becomes an alternative choice to the time-efficient no-restart generalized minimal residual (GMRES) algorithm that requires large amounts of memory. Improvements obtained with the LSQR algorithm become significant for the solution of large-scale problems involving open surfaces that must be formulated using EFIE, which leads to matrix equations that are usually difficult to solve iteratively, even when the matrix-vector multiplications are accelerated via the multilevel fast multipole algorithm.

关键词： iterative algorithms least-squares QR algorithm multilevel fast multipole algorithm scattering problems

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Approximate Stable Diagonalization of the Green's Function for Low Frequencies

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IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS 2014年 13卷 1054-1056页

作者： Ergul, Ozgur Karaosmanoglu, Bariscan Middle E Tech Univ Dept Elect & Elect Engn TR-06800 Ankara Turkey

We present an approximate diagonalization of the Green's function that is stable at arbitrarily short distances with respect to wavelength. The diagonalization is based on scaled spherical functions and plane waves, where a scaling factor is used to stabilize special functions with small arguments. Optimization of the scaling factor leads to accurate diagonalizations, which can be used to implement the multilevel fast multipole algorithm for low-frequency problems.

关键词： Diagonalization Green's function multilevel fast multipole algorithm low-frequency breakdown

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Implementation and experiments of a hybrid algorithm of the MLFMA-enhanced FE-BI method for open-region inhomogeneous electromagnetic problems

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 2002年第2期50卷 163-167页

作者： Sheng, XQ Yung, EKN City Univ Hong Kong Dept Elect Engn Hong Kong Hong Kong Peoples R China

Although the computational complexity of the finite-element boundary-integral (FE-BI) method is significantly reduced by the multilevel fast multipole algorithm (MLFMA), this MLFMA-enhanced FE-BI solution experiences a very slow convergence for some complex inhomogeneous problems. In this paper, a hybrid algorithm, combining direct methods with iterative methods, is designed to speed up the rate of convergence of this MLFMA-enhanced FE-BI solution. This hybrid algorithm is efficiently implemented with the aid of a newly developed package, SuperLU, of the LU decomposition solver. Numerical experiments are performed for a coated Northrop wing to demonstrate the efficiency of this hybrid algorithm. More importantly, the thorough investigation of the numerical experiments clearly shows the better accuracy, stability, and robustness of this hybrid algorithm over the conventional algorithms.

关键词： finite-element boundary-internal method inhomogencous multilevel fast multipole algorithm

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Single-Source Equivalence Principle algorithm for the Analysis of Complex Structures

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IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS 2014年 13卷 1255-1258页

作者： Shao, Hanru Hu, Jun Chew, Weng Cho UESTC Sch Elect Engn Chengdu 611731 Peoples R China Univ Illinois Dept Elect & Comp Engn Urbana IL 61801 USA

In this letter, a novel single-source equivalence principle algorithm is presented. In the traditional equivalence principle algorithm (EPA), double sources, which are equivalence electric and magnetic currents, are constructed on the equivalence surface to replace the currents of the enclosed scatterers. According to the extinction theorem, electric current is related to magnetic current. Therefore, only electric or magnetic current, called single-source, is the final unknown on the equivalence surface. The accuracy of two kinds of single-source EPA is investigated. Multi-level fast multipole algorithm (MLFMA) is used to accelerate the couplings between equivalence surfaces. Numerical results demonstrate the accuracy and efficiency of the proposed method.

关键词： Domain decomposition equivalence principle algorithm integral equation multilevel fast multipole algorithm periodic array

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Electromagnetic Analysis for Conductive Media Based on Volume Integral Equations

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 2014年第12期62卷 6228-6235页

作者： Tong, Mei Song Zhang, Jie Wang, Peng Cheng Zhang, Jian Tongji Univ Coll Elect & Informat Engn Shanghai 200092 Peoples R China

Accurate electromagnetic (EM) analysis for conductive media requires to consider the finite conductivity of the media. Although the problems can be formulated by surface integral equations (SIEs) with an approximate surface impedance, we treat the conductive media as penetrable objects and use volume integral equations (VIEs) to exactly describe their EM features. The VIEs are solved by a point-matching scheme which does not rely on any basis and testing functions and allows the use of nonconforming meshes. Since the VIEs are well-conditioned in general and the integral kernels are free of material parameters, the scheme is flexible to accommodate a wide range of skin depth. Moreover, when the skin depth is small, we can only discretize the skin domain with a current distribution to reduce the cost. For large conductive media, we also incorporate the scheme with the multilevel fast multipole algorithm (MLFMA) to accelerate the solution. Typical numerical examples are presented to illustrate the scheme and its effectiveness has been validated.

关键词： Conductive media electromagnetic analysis multilevel fast multipole algorithm point-matching method volume integral equations

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fast integral equation solvers in computational electromagnetics of complex structures

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ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2003年第8期27卷 803-823页

作者： Chew, WC Chao, HY Cui, TJ Lu, CC Ohnuki, S Pan, YC Song, JM Velamparambil, S Zhao, JS Univ Illinois Ctr Computat Electromagnet Urbana IL 61801 USA Univ Illinois Dept Elect & Comp Engn Electromagnet Lab Urbana IL 61801 USA Southeast Univ Dept Radio Engn State Key Lab Millimeter Waves Ctr Computat Electromagnet Nanjing 210096 Peoples R China Univ Kentucky Dept Elect Engn Lexington KY 40506 USA Intel Corp Log Technol Dev Microproc Design Grp Hillsboro OR 97124 USA Iowa State Univ Dept Elect & Comp Engn Ames IA 50011 USA Ansoft Corp Boulder CO 80303 USA Madmax Opt Inc Hamden CT 06518 USA

This paper reviews the recent progress of fast integral equation solvers at the Center for Computational Electromagnetics and Electromagnetics laboratory, University of Illinois at Urbana-Champaign. We will demonstrate the ability to solve a variety of electromagnetic problems for complex structures and low-frequency structures as well as large scale scattering problems with over 10 million unknowns. (C) 2003 Elsevier Ltd. All rights reserved.

关键词： computational electromagnetics fast integral equation solvers multilevel fast multipole algorithm

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