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multilevel fast multipole algorithm for elastic wave scattering by large three-dimensional objects

JOURNAL OF COMPUTATIONAL PHYSICS 2009年第3期228卷 921-932页

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

multilevel fast multipole algorithm (MLFMA) is developed for solving elastic wave scattering by large three-dimensional (3D) objects. Since the governing set of boundary integral equations (BIE) for the problem includes both compressional and shear waves with different wave numbers in one medium, the double-tree structure for each medium is used in the MLFMA implementation. When both the object and Surrounding media are elastic, four wave numbers in total and thus four FMA trees are involved. We employ Nystrom method to discretize the BIE and generate the corresponding matrix equation. The MLFMA is used to accelerate the solution process by reducing the complexity of matrix-vector product from O(N-2) to O(NlogN) in iterative solvers. The multiple-tree structure differs from the single-tree frame in electromagnetics (EM) and acoustics. and greatly complicates the MLFMA implementation due to the different definitions for well-separated groups in different FMA trees. Our Nystrom method has made use of the cancellation of leading terms in the series expansion of integral kernels to handle hyper singularities in near terms. This feature is kept in the MLFMA by seeking the common near patches in different FMA trees and treating the involved near terms synergistically. Due to the high cost of the multiple-tree structure, Our numerical examples show that we can only solve the elastic wave scattering problems with 0.3-0.4 millions of unknowns on our Dell Precision 690 workstation using one core. (c) 2008 Published by Elsevier Inc.

关键词： multilevel fast multipole algorithm Elastic wave scattering Boundary integral equation

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multilevel fast multipole algorithm Enhanced Characteristic Mode Solver for Large-Scale Objects

Multilevel Fast Multipole Algorithm Enhanced Characteristic ...

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IEEE-Antennas-and-Propagation-Society International Symposium on Antennas and Propagation / USNC/URSI National Radio Science Meeting

作者： Cheng, Guang Shang Wang, Chao-Fu Natl Univ Singapore Temasek Labs Singapore Singapore

ISBN: (纸本)9781538671023

Typically, the characteristic mode (CM) analysis is based on the electric field integral equation (EFIE) and the characteristic modes are calculated numerically using the method of moments (MoM). The high computational complexity of conventional MoM approach hinders large-scale CM analysis in the practical engineering application. In this paper, the conventional multilevel fast multipole algorithm (MLFMA) is embedded into the implicitly restarted Arnoldi method (IRAM), an iterative eigenvalue solver to solve standard complex eigenvalue problem, which provides an appealing possibility for the CM analysis of electrically large complex objects.

关键词： characteristic mode analysis electric field integral equation multilevel fast multipole algorithm implicitly restarted Arnoldi method

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Efficient analysis of dielectric radomes using multilevel fast multipole algorithm with CRWG basis

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Journal of Systems Engineering and Electronics 2008年第1期19卷 81-87页

作者： Que Xiaofeng Nie Zaiping Hu Jun School of Electronic Engineering Univ. of Electronic Science and Technology of China Chengdu 610054 P. R. China

A full-wave analysis of the electromagnetic problem of a three-dimensional （3-D） antenna radiating through a 3-D dielectric radome is preserued. The problem is formulated using the Poggio-Miller-Chang-Harrington- Wu（PMCHW） approach for homogeneous dielectric objects and the electric field integral equation for conducting objects. The integral equations are discretized by the method of moment （MoM）, in which the conducting and dielectric surface/interfaces are represented by curvilinear triangular patches and the unknown equivalent electric and magnetic currents are expanded using curvilinear RWG basis functions. The resultant matrix equation is then solved by the multilevel fast multipole algorithm （MLFMA） and fast far-field approximation （FAFFA） is used to further accelerate the computation. The radiation patterns of dipole arrays in the presence of radomes are presented. The numerical results demonstrate the accuracy and versatility of this method.

关键词： multilevel fast multipole algorithm antenna radome curvilinear RWG basis PMCHW formulation fast far-field approximation.

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Massive parallelization of multilevel fast multipole algorithm for 3-D electromagnetic scattering problems on SW26010 many-core cluster

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JOURNAL OF SUPERCOMPUTING 2024年第7期80卷 8702-8718页

作者： Liu, Xin-Duo He, Wei-Jia Yang, Ming-Lin Sheng, Xin-Qing Beijing Inst Technol Ctr Electromagnet Simulat Beijing 100081 Peoples R China

This paper presents a massively parallel approach of the multilevel fast multipole algorithm (PMLFMA) on homegrown many-core SW26010 cluster of China, noted as (SW-PMLFMA), for 3-D electromagnetic scattering problems. In this approach, the multilevel fast multipole algorithm (MLFMA) octree is first partitioned among management processing elements (MPEs) of SW26010 processors following the ternary partitioning scheme using the message passing interface (MPI). Then, the computationally intensive parts of the PMLFMA on each MPI process, matrix filling, aggregation and disaggregation are accelerated by using all the 64 computing processing elements (CPEs) in the same core group of the MPE via the Athread parallel programming model. Different parallelization strategies are designed for many-core accelerators to ensure a high computational throughput. In coincidence with the special characteristic of local Lagrange interpolation, the compressed sparse row (CSR) and the compressed sparse column (CSC) sparse matrix storage format is used for storing interpolation and anterpolation matrices, respectively, together with a specially designed cache mechanism of hybrid dynamic and static buffers using the scratchpad memory (SPM) to improve data access efficiency. Numerical results are included to demonstrate the efficiency and versatility of the proposed method. The proposed parallel scheme is shown to have excellent speedup.

关键词： multilevel fast multipole algorithm Distributed memory parallelization Many-core acceleration Electromagnetic scattering SW26010 processor

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Efficient strategy for parallelisation of multilevel fast multipole algorithm using CUDA

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IET MICROWAVES ANTENNAS & PROPAGATION 2019年第10期13卷 1554-1563页

作者： Garcia, Eliseo Delgado, Carlos Lozano, Lorena Catedra, Felipe Univ Alcala Automat Dept Alcala De Henares Spain Univ Alcala Comp Sci Dept Alcala De Henares Spain

The multilevel fast multipole algorithm is a popular technique that enables the efficient solution of the method of moments (MoM) matrix equations. In this work, the authors address the adaptation of this method to the compute unified device architecture (CUDA), a relatively new computing infrastructure provided by NVIDIA, and the authors take into account some of the limitations that appear when the geometry under analysis becomes too large to fit into the memory of graphics processing units.

关键词： method of moments computational electromagnetics parallel architectures computer graphic equipment coprocessors electromagnetic wave scattering graphics processing units efficient strategy multilevel fast multipole algorithm CUDA popular technique efficient solution moments matrix equations compute unified device architecture relatively new computing infrastructure

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Error control in the perfectly matched layer based multilevel fast multipole algorithm

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JOURNAL OF COMPUTATIONAL PHYSICS 2009年第13期228卷 4811-4822页

作者： Vande Ginste, Dries Knockaert, Luc De Zutter, Daniel Univ Ghent Dept Informat Technol B-9000 Ghent Belgium

The development of efficient algorithms to analyze complex electromagnetic structures is of topical interest. Application of these algorithms in commercial solvers requires rigorous error controllability. In this paper we focus on the perfectly matched layer based multilevel fast multipole algorithm (PML-MLFMA), a dedicated technique constructed to efficiently analyze large planar structures. More specifically the crux of the algorithm, viz. the pertinent layered medium Green functions, is under investigation. Therefore, particular attention is paid to the plane wave decomposition for 2-D homogeneous space Green functions in very lossy media, as needed in the PML-MLFMA. The result of the investigations is twofold. First, upper bounds expressing the required number of samples in the plane wave decomposition as a function of a preset accuracy are rigorously derived. These formulas can be used in 2-D homogeneous (lossy) media MLFMAs. Second, a more heuristic approach to control the error of the PML-MLFMA's Green functions is presented. The theory is verified by means of several numerical experiments. (c) 2009 Elsevier Inc. All rights reserved.

关键词： Error controllability Green function multilevel fast multipole algorithm Perfectly matched layer Layered medium

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fast and accurate solutions of electromagnetics problems involving lossy dielectric objects with the multilevel fast multipole algorithm

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ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2012年第3期36卷 423-432页

作者： Erguel, Oezguer Univ Strathclyde Dept Math & Stat Glasgow G1 1XH Lanark Scotland

fast and accurate solutions of electromagnetic scattering problems involving lossy dielectric objects are considered. Problems are formulated with two recently developed formulations, namely, the combined-tangential formulation (CTF) and the electric and magnetic current combined-field integral equation (JMCFIE), and solved iteratively using the multilevel fast multipole algorithm (MLFMA). Iterative solutions and accuracy of the results are investigated in detail for diverse geometries, frequencies, and conductivity values. It is demonstrated that CTF solutions are significantly accelerated as the conductivity increases to moderate values and CTF becomes comparable to JMCFIE in terms of efficiency. Considering also the superior accuracy of this formulation, CTF becomes suitable for fast and accurate analysis of scattering problems involving lossy dielectric objects. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Dielectrics Surface integral equations Iterative solutions multilevel fast multipole algorithm

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fast Fourier Transform multilevel fast multipole algorithm in Rough Ocean Surface Scattering

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ELECTROMAGNETICS 2009年第7期29卷 541-552页

作者： Yang, Wei Zhao, Zhiqin Nie, Zaiping Univ Elect Sci & Technol China Sch Elect Engn Chengdu 610054 Sichuan Peoples R China

In this article, the microwave backscattering from 3-D rough sea surfaces has been numerically studied. Due to the advantages of the memory and CPU savings of the rigorous multilevel fast multipole algorithm, it was employed to calculate the radar cross-section of the sea surface at large incident angles. Usually, the sea surface can be regarded as a planar scatterer comparing the roughness height with the domain;therefore, an algorithm, called the fast Fourier transform multilevel fast multipole algorithm, was applied in the calculation of this case for a nearly planar scatterer. The difference of the fast Fourier transform multilevel fast multipole algorithm is the use of fast Fourier transform for the translation operator, which can further reduce the computational memory and the CPU time compared with the common multilevel fast multipole algorithm. In the calculation, the Thorsos window and Gaussian window were used in the azimuthal and range direction, respectively, to suppress the edge effects. This fast Fourier transform multilevel fast multipole algorithm provides a useful tool to test the effectiveness of classic analytical methods in computing the backscattering of large sea surfaces at very large incident angles. Some numerical examples are presented to test the accuracy and efficiency of the fast Fourier transform multilevel fast multipole algorithm. It shows that the results of the small perturbation method agree very well with the fast Fourier transform multilevel fast multipole algorithm results at moderate incident angles.

关键词： electromagnetic scattering rough surface multilevel fast multipole algorithm fast Fourier transform

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A Global Interpolator With Low Sample Rate for multilevel fast multipole algorithm

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 2013年第3期61卷 1291-1300页

作者： Jarvenpaa, Seppo Yla-Oijala, Pasi Aalto Univ Sch Elect Engn Dept Radio Sci & Engn Espoo 00076 Finland

A new, improved version of a global interpolator utilizing trigonometric polynomials is presented for the high-frequency multilevel fast multipole algorithm. The number of required points to sample the outgoing and incoming field patterns is low, almost half in some levels, compared with the earlier published versions. Compared with local interpolators based on Lagrange interpolating polynomials, the proposed technique performs even more favorably and reduces the number of sample points by a factor of eight. The numerical examples demonstrate that the interpolator allows full numerical accuracy control during the aggregation and disaggregation phases, regardless of the number of the levels in the octree.

关键词： Anterpolation fast Fourier transform (FFT) interpolation method of moments multilevel fast multipole algorithm

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Applying matrix rotation to the three-dimensional low-frequency multilevel fast multipole algorithm

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MICROWAVE AND OPTICAL TECHNOLOGY LETTERS 2000年第2期26卷 105-110页

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

The matrix rotation technique is applied to three-dimensional (3-D) multilevel fast multipole algorithm (MLFMA) at very low frequencies (LF) to save the storage without increasing the order of the floating-point operations. Some symmetrical properties of the translation matrices along the z-direction for the 3-D LF-MLFMA and the static MLFMA are also derived to further reduce the memory requirement Numerical results shown that the order of errors introduced by the matrix rotation is much smaller than the order of errors from the plain LF-MLFMA or plain static MLFMA. The implementation of the matrix technique does not change the precision order of the LF-MLFMA and the static MLFMA for fixed truncation of multipole expansions. (C) 2000 John Wiley & Sons, Inc.

关键词： fast algorithm multilevel fast multipole algorithm low frequencies matrix rotation

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