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Optimal interpolation of translation operator in multilevel fast multipole algorithm

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 2006年第12期54卷 3822-3826页

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

Lagrange interpolation of the translation operator in the three-dimensional multilevel fast multipole algorithm (MLFMA) is revisited. Parameters of the interpolation, namely, the number of interpolation points and the oversampling factor, are optimized for controllable error. Via optimization, it becomes possible to obtain the desired level of accuracy with the minimum processing time.

关键词： Lagrange interpolation multilevel fast multipole algorithm translation operator

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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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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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Error analysis of the multilevel fast multipole algorithm

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IEICE TRANSACTIONS ON ELECTRONICS 2006年第11期E89C卷 1676-1681页

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

The computational error of the multilevel fast multipole algorithm is studied. The error convergence rate, achievable minimum error, and error bound are investigated for various element distributions. We will discuss the boundary between the large and small buffer cases in terms of machine precision. The needed buffer size to reach double precision accuracy will be clarified.

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

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Highly efficient hybrid method for monostatic scattering by objects on a rough surface

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IET MICROWAVES ANTENNAS & PROPAGATION 2010年第10期4卷 1597-1604页

作者： Zhang, X-Y Sheng, X-Q Beijing Inst Technol Sch Informat Sci & Technol Ctr Electromagnet Simulat Beijing 100081 Peoples R China

A highly efficient hybrid method is proposed for computing scattering by objects above a rough surface. A special treatment is designed and applied to the conventional hybrid method of the Kirchhoff approach (KA) and the method of moments (MoMs) to speed up the computation of the interaction between the objects and the rough surface. To further improve efficiency, the multilevel fast multipole algorithm (MLFMA) and the fast far-field approximation (FAFFA) are employed in the hybrid KA-MoM method. The accuracy and efficiency of the proposed method are validated by numerical experiments.

关键词： monostatic scattering Electromagnetic wave propagation rough surface multilevel fast multipole algorithm MLFMA Kirchhoff approach Electromagnetic waves: theory fast far-field approximation electromagnetic wave scattering FAFFA method of moments Numerical analysis MoM Numerical approximation and analysis

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A Broadband Stable and Efficient Addition Theorem for the Two-Dimensional Helmholtz equation

A Broadband Stable and Efficient Addition Theorem for the Tw...

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2010 IEEE International Symposium Antennas and Propagation/CNC-USNC/URSI Radio Science Meeting

作者： Bogaert, I. De Zutter, D. Cools, K. Fostier, J. Michiels, B. Peeters, J. Univ Ghent Dept Informat Technol INTEC B-9000 Ghent Belgium

ISBN: (纸本)9781424449682

Boundary integral equations are the principal tools for efficiently simulating electromagnetic fields in structures with piecewise constant material parameters. A specific trait of boundary integral equations is that the Green function of the Helmholtz equation appears as the integration kernel. Hence, discretizing a boundary integral equation leads to a dense linear system. Many such acceleration schemes exist, for example the renowned multilevel fast multipole algorithm (MLFMA).The MLFMA is based on an addition theorem that decomposes the Green function into a superposition of propagating plane waves. This decomposition is then used to evaluate the interactions between entire groups of basis functions, in contrast to evaluating the interactions between all the individual basis functions. Unfortunately, the MLFMA addition theorem is numerically unstable when the groups become significantly smaller than the wavelength. This phenomenon is called the low-frequency breakdown of the MLFMA and prevents the efficient simulation of structures with a lot of subwavelength geometrical detail.

关键词： Green function Green's function methods Helmholtz equations MLFMA addition theorem boundary integral equations boundary integral equations broadband stable theorem computational electromagnetics dense linear system electromagnetic fields electromagnetic fields electromagnetic wave propagation integration integration kernel linear systems low-frequency breakdown multilevel fast multipole algorithm piecewise constant material parameters propagating plane waves subwavelength geometrical detail two-dimensional Helmholtz equation

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Near Interaction Preconditioner Using Overlapped Localizing Local Global Solution Modes

Near Interaction Preconditioner Using Overlapped Localizing ...

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2010 IEEE International Symposium Antennas and Propagation/CNC-USNC/URSI Radio Science Meeting

作者： Xu, Xin Luo, Chong Adams, Robert J. Univ Kentucky Lexington KY 40506 USA Alpha Omega Electromagnet LLC Arnold MD USA

ISBN: (纸本)9781424449682

multilevel fast multipole algorithm (MLFMA) has been widely used to expedite the iterative solution of the linear systems that arise from discretizing integral equations for electromagnetic applications. However, the slow convergence rate, or nonconvergence, of the iterative solver must be improved by either changing the underlying formulation or by using a good preconditioner. In this paper, we form an approximate inverse of the near interaction part of the system matrix and used it as a preconditioner to improve the convergence of an MLFMA based iterative solvers. The near interaction matrix is defined and filled by an existing MLFMA code, and it is factored and inverted using overlapped localizing local global solution modes (OL-LOGOS). Numerical results shows that the OL-LOGOS factored near interaction preconditioner is effective in improving the convergence rate.

关键词： convergence rate discretizing integral equations electromagnetic applications electromagnetic wave scattering iterative methods iterative solution linear systems multilevel fast multipole algorithm near interaction preconditioner overlapped localizing local global solution modes

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Computational study of scattering from healthy and diseased red blood cells

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JOURNAL OF BIOMEDICAL OPTICS 2010年第4期15卷 045004页

作者： Ergul, Ozgur Arslan-Ergul, Ayca Gurel, Levent Univ Strathclyde Dept Math & Stat Glasgow G1 1XH Lanark Scotland Univ Strathclyde Strathclyde Inst Pharm & Biomed Sci Glasgow G4 0NR Lanark Scotland Bilkent Univ Dept Elect & Elect Engn TR-06800 Ankara Turkey Bilkent Univ Computat Electromagnet Res Ctr BiLCEM TR-06800 Ankara Turkey

We present a comparative study of scattering from healthy red blood cells (RBCs) and diseased RBCs with deformed shapes. Scattering problems involving three-dimensional RBCs are formulated accurately with the electric and magnetic current combined- field integral equation and solved efficiently by the multilevel fast multipole algorithm. We compare scattering cross section values obtained for different RBC shapes and different orientations. In this way, we determine strict guidelines to distinguish deformed RBCs from healthy RBCs and to diagnose various diseases using scattering cross section values. The results may be useful for designing new and improved flow cytometry procedures. (C) 2010 Society of Photo-Optical Instrumentation Engineers. [DOI: 10.1117/1.3467493]

关键词： red blood cell electromagnetic scattering surface formulations multilevel fast multipole algorithm

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Incomplete LU Factorization Preconditioner for the Efficient Solution of Improved Electric Field Integral Equations

Incomplete LU Factorization Preconditioner for the Efficient...

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2010 International Conference on Microwave and Millimeter Wave Technology(2010国际微波与毫米波技术会议 ICMMT2010)

作者： H. H. Zhang Z. H. Fan R. S. Chen Department of Communication Engineering Nanjing University of Science and Technology Nanjing 210094

ISBN: (纸本)9781424457052

This paper is a study on the numerical solution of linear systems arising from the discretization of the improved electric field integral equation (IEFIE) for electromagnetic scattering problems. Using incomplete LU factorization preconditioner, the IEFIE is solved by generalized minimal residual iterative method in the context of the multilevel fast multipole algorithm (MLFMA). Numerical results show that the efficiency and robustness of the solution can be significantly improved by contrast with the conventional EFIE formulation.

关键词： Improved electric field integral equation incomplete LU factorization preconditioner generalized minimal residual iterative method multilevel fast multipole algorithm

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Iterative Solutions of Hybrid Integral Equations for Coexisting Open and Closed Surfaces

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 2009年第6期57卷 1751-1758页

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

We consider electromagnetics problems involving composite geometries with coexisting open and closed conductors. Hybrid integral equations are presented to improve the efficiency of the solutions, compared to the conventional electric-field integral equation. We investigate the convergence characteristics of iterative solutions of large composite problems with the multilevel fast multipole algorithm. Following a thorough study of how the convergence characteristics depends on the problem geometry, formulation, and iterative solvers, we provide concrete guidelines for efficient solutions.

关键词： Hybrid formulations iterative methods multilevel fast multipole algorithm surface integral equations

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