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作者： Manouchehr Takrimi Bilkent University

学位级别：博士

fast multipole method (FMM) in computational physics and its multilevel ver- sion, i. e., multilevel fast multipole algorithm (MLFMA) in computational elec- tromagnetics are among the best known methods to solve integral equations (IEs) in the frequency-domain. MLFMA is well-accepted in the computational electromagnetic (CEM) society since it provides a full-wave solution regarding Helmholtz-type electromagnetics problems. This is done by discretizing proper integral equations based on a predetermined formulation and solving them nu- merically with O(N log N) complexity, where N is the number of unknowns. In this dissertation, we present two broadband and efficient methods in the context of MLFMA, one for surface integral equations (SIEs) and another for volume integral equations (VIEs), both of which are capable of handling large multiscale electromagnetics problems with a wide dynamic range of mesh sizes. By invoking a novel concept of incomplete-leaf tree structures, where only the overcrowded boxes are divided into smaller ones for a given population threshold, a versatile method for both types of IEs has been achieved. Regarding SIEs, for geometries containing highly overmeshed local regions, the proposed method is always more efficient than the conventional MLFMA for the same accuracy, while it is always more accurate if the efficiency is comparable. Regarding VIEs, for inhomoge- neous dielectric objects possessing variable mesh sizes due to different electrical properties, in addition to obtaining similar results from the proposed method, a reduction in the storage is also achieved. Several canonical and also real-life examples are provided to demonstrate the superior efficiency and accuracy of the proposed algorithm in comparison to the conventional MLFMA.

关键词： multilevel fast multipole algorithm Integral equations Incomplete-leaf tree

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LARGE-SCALE SOLUTIONS OF ELECTROMAGNETICS PROBLEMS USING THE multilevel fast multipole algorithm AND PHYSICAL OPTICS

LARGE-SCALE SOLUTIONS OF ELECTROMAGNETICS PROBLEMS USING THE...

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作者： Mert Hidayetoglu Bilkent University

学位级别：硕士

Integral equations provide full-wave (accurate) solutions of Helmholtz-type elec- tromagnetics problems. The multilevel fast multipole algorithm (MLFMA) dis- cretizes the equations and solves them numerically with O(NLogN) complexity, where N is the number of unknowns. For solving large-scale problems, MLFMA is parallelized on distributed-memory architectures. Despite the low complexity and parallelization, the computational requirements of MLFMA solutions grow immensely in terms of CPU time and memory when extremely-large geometries (in wavelengths) are involved. The thesis provides computational and theoreti- cal techniques for solving large-scale electromagnetics problems with lower com- putational requirements. One technique is the out-of-core implementation for reducing the required memory via employing disk space for storing large data. Additionally, a pre-processing parallelization strategy, which eliminates mem- ory bottlenecks, is presented. Another technique, MPI+OpenMP paralleliza- tion, uses distributed-memory and shared-memory schemes together in order to maintain the parallelization efficiency with high number of processes/threads. The thesis also includes the out-of-core implementation in conjunction with the MPI+OpenMP parallelization. With the applied techniques, full-wave solutions involving up to 1.3 billion unknowns are achieved with 2 TB memory. Physical optics is a high-frequency approximation, which provides fast solutions of scat- tering problems with O(N) complexity. A parallel physical optics algorithm is presented in order to achieve fast and approximate solutions. Finally, a hybrid integral-equation and physical-optics solution methodology is introduced.

关键词： Integral equations multilevel fast multipole algorithm physical optics electromagnetic scattering parallel computing out-of-core method

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SOLUTIONS OF NOVEL POTENTIAL-BASED FORMULATIONS USING THE multilevel fast multipole algorithm

SOLUTIONS OF NOVEL POTENTIAL-BASED FORMULATIONS USING THE MU...

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作者： UGUR MERIC GUR MIDDLE EAST TECHNICAL UNIVERSITY

学位级别：硕士

In this thesis, recently introduced potential-based formulations that are based on di- rect usage of magnetic vector and electric scalar potentials, instead of the equivalent field-based formulations, are investigated. These new potential-based formulations can alleviate the well-known low-frequency breakdowns. Therefore, these formula- tions can be useful in providing the solution of a plethora of problems in future and emerging technologies that are difficult to analyze via standard solvers. The aim of this thesis is to combine potential formulations with special low-frequency imple- mentations of the multilevel fast multiple algorithm (MLFMA) to tackle with finely discretized problems. Thesis also includes the explanation of low-frequency breakdown mechanisms. In ad- dition to the known breakdown of the electric-field integral equation, a hidden break- down of the potential integral equations (PIEs) is shown. A remedy with the cost of an additional integral equation is proposed. All explanations for the low-frequency breakdown are supported with numerical results. Among low-frequency stable implementations of MLFMA, two methods are imple- mented for PIEs. One of them is MLFMA based on multipoles without diagonaliza- tion. In this method, classical aggregation, translation, and disaggregation procedures in MLFMA are realized without plane-wave expansion. The other one is recently pro- posed MLFMA implementation with approximate diagonalization. In this method, diagonalization is realized approximately with scaled spherical and plane waves. Ac- curacy and efficiency of the implementations are shown with numerical results.

关键词： Surface Integral Equations Potential Formulations Low-frequency Break-down multilevel fast multipole algorithm

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Computational study of scattering of a zero-order Bessel beam by large nonspherical homogeneous particles with the multilevel fast multipole algorithm

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JOURNAL OF OPTICS 2017年第12期19卷 125606-125606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 CAEP Software Ctr High Performance Numer Simulat Beijing 100088 Peoples R China Inst Appl Phys & Computat Math Beijing 100094 Peoples R China Univ & INSA Rouen CNRS Normandie Univ CORIAUMR 6614 Ave UnivBP 12 F-76801 St Etienne Du Rouvray France

Computation of scattering of shaped beams by large nonspherical particles is a challenge in both optics and electromagnetics domains since it concerns many research fields. In this paper, we report our new progress in the numerical computation of the scattering diagrams. Our algorithm permits to calculate the scattering of a particle of size as large as 110 wavelengths or 700 in size parameter. The particle can be transparent or absorbing of arbitrary shape, smooth or with a sharp surface, such as the Chebyshev particles or ice crystals. To illustrate the capacity of the algorithm, a zero order Bessel beam is taken as the incident beam, and the scattering of ellipsoidal particles and Chebyshev particles are taken as examples. Some special phenomena have been revealed and examined. The scattering problem is formulated with the combined tangential formulation and solved iteratively with the aid of the multilevel fast multipole algorithm, which is well parallelized with the message passing interface on the distributed memory computer platform using the hybrid partitioning strategy. The numerical predictions are compared with the results of the rigorous method for a spherical particle to validate the accuracy of the approach. The scattering diagrams of large ellipsoidal particles with various parameters are examined. The effect of aspect ratios, as well as half-cone angle of the incident zero-order Bessel beam and the off-axis distance on scattered intensity, is studied. Scattering by asymmetry Chebyshev particle with size parameter larger than 700 is also given to show the capability of the method for computing scattering by arbitrary shaped particles.

关键词： scattering large non spherical particle Bessel beam multilevel fast multipole algorithm

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An Efficient Parallel multilevel fast multipole algorithm for Large-scale Scattering Problems

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APPLIED COMPUTATIONAL ELECTROMAGNETICS SOCIETY JOURNAL 2010年第4期25卷 381-387页

作者： Hu Fangjing Nie Zaiping Hu Jun Univ Elect Sci & Technol China Sch Elect Engn Chengdu 610054 Peoples R China

In this paper, we present an efficient parallel multilevel fast multipole algorithm (MLFMA) for three dimensional scattering problems of large-scale objects. Several parallel implantation tricks are discussed and analyzed. Firstly, we propose a method that reduces truncation number without loss of accuracy. Furthermore, a matrix-sliced technique, allowing data in the memory transforming into the hard disk, is applied here, in order to solve the problem of extremely large targets. Finally, a transition level scheme is adopted to improve the parallel efficiency. We demonstrate the capability of our code by considering a sphere of 220 lambda discretized with 48,879,411 unknowns and a square patch of 200 lambda discretized with 10,150,143 unknowns. The bi-static RCS is calculated within 41.5 GB memory for the first object and 14.7 GB for the second one.

关键词： parallel algorithm RCS calculation multilevel fast multipole algorithm electromagnetic scattering

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Efficient matrix filling of multilevel simply sparse method via multilevel fast multipole algorithm

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RADIO SCIENCE 2011年第5期46卷 [np]页

作者： Jiang, Zhaoneng Xu, Yuan Chen, Ru-shan Fan, Zhenhong Ding, Dazhi Nanjing Univ Sci & Technol Dept Commun Engn Nanjing 210094 Jiangsu Peoples R China

In this paper, an improved multilevel simply sparse method (MLSSM) is proposed for solving electromagnetic scattering problems that are formulated using the electric field integral equation approach. Previously, the matrix filling procedure of the conventional MLSSM is based on the adaptive cross approximation (ACA) method. Although the ACA is more efficient than direct filling, it requires a longer filling time for the far-field matrix than that of the multilevel fast multipole algorithm (MLFMA). Three problems with moderate electrical sizes are used to demonstrate that the far-field matrix filling memory of the ACA is also higher than that of the MLFMA. Hence, the MLFMA is utilized to reduce both the far-field matrix filling time and memory of the conventional MLSSM. Since the MLSSM recompresses the far-field interaction matrix of the MLFMA, the matrix-vector multiplication of the proposed method is more efficient than that of the MLFMA. Numerical results are presented to demonstrate the accuracy and efficiency of the proposed method.

关键词： electromagnetic scattering multilevel fast multipole algorithm multilevel simply sparse method

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Meshless-based multilevel fast multipole algorithm for Solving Volume Integral Equations with Complex Media

Meshless-based Multilevel Fast Multipole Algorithm for Solvi...

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The 6th International Symposium on Microwave,Antenna,Propagation,and Electromagnetic Compatibility Technologies(MAPE 2015)

作者： M.S.Tong C.X.Yang M.H.Cai Q.F.Li Department of Electronic Science and Technology Tongji University

Electromagnetic(EM) problems with complex media are formulated by volume integral equations(VIEs) in the integral equation approach. The VIEs are usually solved by the method of moments(Mo M) with the Schaubert-WiltonGlisson(SWG) basis function, but the solution requires highquality conforming meshes, resulting in a high cost in geometric discretization. In this work, a point-matching meshless method is proposed to discretize the VIEs and it uses discrete points instead of meshes to represent an object domain. Also, the method chooses the current densities as the unknown functions to be solved so that the integral kernels are free of material parameters. For electrically large problems, we incorporate it with the multilevel fast multipole algorithm(MLFMA) to accelerate the solving process. Numerical examples are presented to demonstrate the method and good results have been observed

关键词： Meshless method multilevel fast multipole algorithm volume integral equation complex medium

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fast computation of RCS of 3D electrically large structure by modified multilevel fast multipole algorithm

Fast computation of RCS of 3D electrically large structure b...

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2009 IET International Radar Conference

作者： Wen Bin Hu Jun Hu Fangjing Nie Zaiping Schoolof Electronic Engineering University of Electronic Science and Technology Chengdu China

ISBN: (纸本)9781849190107

In this paper, two novel strategies are proposed to determine the multipole number of multilevel fast multipole algorithm (MLFMA). With the modified multipole number, the computation of RCS of 3D electrically large structures is realized. Compared with traditional MLFMA, The proposed methods in this paper can reduce the multipole number, CPU time and the memory requirement. Numerical results show that the modified methods have the complexity of O(N log N) both for the computation of matrix-vector multiplication and the memory requirement, thus yields more efficiency for scattering problems of 3D electrically large structures.

关键词： Modified multipole number multilevel fast multipole algorithm Radar cross section Electrically large problem Combined field integral equation

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An Efficient MLFMA Solution of Self-Dual Integral Equation for EM Analysis of Multiscale IBC Objects

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IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS 2025年第4期24卷 883-887页

作者： Wang, Pengyuan Liu, Jintong He, Mang Beijing Inst Technol Sch Integrated Circuits & Elect Beijing 100081 Peoples R China

A fast and efficient method is proposed to analyze electromagnetic (EM) scattering of multiscale objects with impedance boundary condition (IBC). The self-dual integral equation (SDIE) in combination with the mixed-potential (MiP) multilevel fast multipole algorithm (MLFMA) is used to calculate EM scattering from the IBC targets, in which the incomplete-leaf (ICL) tree structure and interpolative-decomposition (InDe) based skeletonization technique is utilized to reduce excessive memory usage imposed by multiscale IBC targets meshed with large multiscale factor (MSF). A difference matrix generated from the near-field interactions by two grouping schemes is supplemented in the sparse approximate inverse (SAI) preconditioner to speed up the convergence of the iterative solvers. Numerical experiments demonstrate the effectiveness of the presented method.

关键词： Integral equations Surface impedance Sparse matrices Accuracy Matrix decomposition Impedance MLFMA Costs Vectors Mathematical models Impedance boundary condition incomplete-leaf tree interpolative decomposition multilevel fast multipole algorithm multiscale self-dual integral equation (SDIE)

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Helmholtz and High-Frequency Maxwell multilevel fast multipole algorithms with Self-Tuning Library

Helmholtz and High-Frequency Maxwell Multilevel Fast Multipo...

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作者： Yucel, Abdulkadir C University of Michigan

学位级别：master

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