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Drawing Large Graphs by multilevel Maxent-Stress Optimization

IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS 2018年第5期24卷 1814-1827页

作者： Meyerhenke, Henning Noellenburg, Martin Schulz, Christian KIT Inst Theoret Informat D-76131 Karlsruhe Germany TU Wien Algorithms & Complex Grp A-1040 Vienna Austria Univ Vienna Dept Comp Sci A-1010 Vienna Austria Karlsruhe Inst Technol D-76131 Karlsruhe Germany

Drawing large graphs appropriately is an important step for the visual analysis of data from real-world networks. Here we present a novel multilevel algorithm to compute a graph layout with respect to the maxent-stress metric proposed by Gansner et al. (2013) that combines layout stress and entropy. As opposed to previous work, we do not solve the resulting linear systems of the maxent-stress metric with a typical numerical solver. Instead we use a simple local iterative scheme within a multilevel approach. To accelerate local optimization, we approximate long-range forces and use shared-memory parallelism. Our experiments validate the high potential of our approach, which is particularly appealing for dynamic graphs. In comparison to the previously best maxent-stress optimizer, which is sequential, our parallel implementation is on average 30 times faster already for static graphs (and still faster if executed on a single thread) while producing a comparable solution quality.

关键词： Graph layout algorithm engineering multilevel algorithm

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Fast Illinois Solver Code (FISC)

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IEEE ANTENNAS AND PROPAGATION MAGAZINE 1998年第3期40卷 27-34页

作者： Song, JM Lu, CC Chew, WC Lee, SW Univ Illinois Dept Elect & Comp Engn Ctr Comp Electromagnet Urbana IL 61801 USA Demaco Inc Champaign IL 61820 USA

FISC (Fast Illinois Solver Code), co-developed by the Center for Computational Electromagnetics, University of Illinois, and DEMACO, is designed to compute the RCS of a target described by a triangular-facet file. The problem is formulated using the Method of Moments (MoM), where the Rao, Wilton, and Glisson basis functions are used. The resultant matrix equation is solved iteratively by the Conjugate Gradient (CG) method. The multilevel Fast Multipole algorithm (MLFMA) is used to speed up the matrix-vector multiply in the CG method. The complexities for both the CPU time per iteration and the memory requirements are of O(N log N), where N is the number of unknowns. A 2.4-million unknown problem is solved in a few hours on the SGI GRAY Origin 2000 at NCSA of the University of Illinois at Urbana-Champaign.

关键词： radar cross sections electromagnetic scattering integral equations Method of Moments fast multipole multilevel algorithm

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A multilevel BCG-FFT method for the analysis of a microstrip antenna and array

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MICROWAVE AND OPTICAL TECHNOLOGY LETTERS 2000年第1期27卷 20-23页

作者： Wang, CF Jin, JM Li, LW Kooi, PS Leong, MS Natl Univ Singapore Dept Elect & Comp Engn Singapore 119260 Singapore Univ Illinois Ctr Computat Electromagnet Dept Elect & Comp Engn Urbana IL 61801 USA

The biconjugate gradient-fast Fourier transform (BCG-FFT) method is a very efficient and useful technique to analyze microstrip antennas and arrays. In order to increase the efficiency of the BCG-FFT method by reducing the number of iterations a multilevel BCG-FFT method is constructed using the idea of multigrid methods. The analysis of microstrip antennas and arrays illustrates that the multilevel BCG-FFT method has good accuracy and is much faster than the BCG-FFT method. (C) 2000 John Wiley & Sons, Inc.

关键词： BCG-FFT method multilevel algorithm microstrip antenna MPIE

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A FAFFA-MLFMA algorithm for electromagnetic scattering

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 2002年第11期50卷 1641-1649页

作者： Chew, WC Cui, TJ Song, JM Univ Illinois Ctr Computat Electromagnet Dept Elect & Comp Engn Urbana IL 61801 USA Iowa State Univ Dept Elect & Comp Engn Ames IA 50011 USA

Based on the multilevel fast multipole algorithm (MLFMA), an efficient method is proposed to accelerate the solution of the combined field integral equation in electromagnetic scattering and radiation, where the fast far-field approximation (FAFFA) is combined with MLFMA. The translation between groups in MLFMA is expensive because spherical Hankel functions and Legendre polynomials are involved and the translator is defined on an Eward sphere with many (k) over cap directions. When two groups are in the far-field region, however, the translation can be greatly simplified by FAFFA where only a single k direction is involved in the translator. The condition for using FAFFA and the way to efficiently incorporate FAFFA with MLFMA are discussed. Complexity analysis illustrates that the computational cost in FAFFA-MLFMA can be asymptotically cut by half compared to the conventional MLFMA. Numerical results are given to verify the efficiency of the algorithm.

关键词： electromagnetic scattering far-field approximation fast multipole integral equation method of moments (MoM) multilevel algorithm

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On a multilevel approach for the two dimensional Navier-Stokes equations with finite elements

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS 1998年第1-4期27卷 241-258页

作者： Calgaro, C Debussche, A Laminie, J Univ Paris 11 F-91405 Orsay France CNRS F-91405 Orsay France

We study if the multilevel algorithm introduced in Debussche et al. (Theor: Comput. Fluid Dynam., 7, 279-315 (1995)) and Dubois et al. (J. Sci. Comp., 8, 167-194 (1993)) for the 2D Navier-Stokes equations with periodic boundary conditions and spectral discretization can be generalized to more general boundary conditions and to finite elements. We first show that a direct generalization, as in Calgaro et al. (Appl. Numer. Math., 21, 1-40 (1997)), for the Burgers equation, would not be very efficient. We then propose a new approach where the domain of integration is decomposed in subdomains. This enables us to define localized small-scale components and we show that, in this context, there is a good separation of scales. We conclude that all the ingredients necessary for the implementation of the multilevel algorithm are present. (C) 1998 John Wiley & Sons, Ltd.

关键词： multilevel algorithm 2D Navier-Stokes equations finite element large eddy simulations long time integration

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Noise reduction algorithm for glueball correlators

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PHYSICS LETTERS B 2014年 736卷 415-420页

作者： Majumdar, Pushan Mathur, Nilmani Mondal, Sourav Indian Assoc Cultivat Sci Dept Theoret Phys Kolkata India Tata Inst Fundamental Res Dept Theoret Phys Bombay 400005 Maharashtra India

We present an error reduction method for obtaining glueball correlators from Monte Carlo simulations of SU(3) lattice gauge theory. We explore the scalar and tensor channels at three different lattice spacings. Using this method we can follow glueball correlators to temporal separations even up to 1 fermi. We estimate the improvement over the naive method and compare our results with existing computations. (C) 2014 The Authors. Published by Elsevier B.V.

关键词： Glueball mass Error reduction multilevel algorithm

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Some multilevel decoupled algorithms for a mixed navier-stokes/darcy model

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ADVANCES IN COMPUTATIONAL MATHEMATICS 2018年第1期44卷 115-145页

作者： Cai, Mingchao Huang, Peiqi Mu, Mo Morgan State Univ Dept Math 1700 E Cold Spring Ln Baltimore MD 21251 USA Nanjing Forestry Univ Dept Appl Math Nanjing 210037 Jiangsu Peoples R China Hong Kong Univ Sci Technol Dept Math Kowloon Hong Kong Peoples R China

In this work, several multilevel decoupled algorithms are proposed for a mixed Navier-Stokes/Darcy model. These algorithms are based on either successively or parallelly solving two linear subdomain problems after solving a coupled nonlinear coarse grid problem. Error estimates are given to demonstrate the approximation accuracy of the algorithms. Experiments based on both the first order and the second order discretizations are presented to show the effectiveness of the decoupled algorithms.

关键词： Fluid flow coupled with porous media flow Darcy law Navier-Stokes equations Interface coupling multilevel algorithm Decoupling Linearization

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Thin-stratified medium fast-multipole algorithm for solving microstrip structures

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES 1998年第4期46卷 395-403页

作者： Zhao, JS Chew, WC Lu, CC Michielssen, E Song, JM Univ Illinois Dept Elect & Comp Engn Ctr Computat Electromagnet Electromagnet Lab Urbana IL 61801 USA Demaco Inc Champaign IL 61820 USA

An accurate and efficient technique called the thin-stratified medium fast-multipole algorithm (TSM-FMA) is presented for solving integral equations pertinent to electromagnetic analysis of microstrip structures, which consists of the full-wave analysis method and the application of the multilevel fast multipole algorithm (MLFMA) to thin stratified structures, In this approach, a new form of the electric-field spatial-domain Green's function is developed in a symmetrical form which simplifies the discretization of the integral equation using the method of moments (MoM). The patch mag be of arbitrary shape since their equivalent electric currents are modeled with subdomain triangular patch basis functions, TSM-FMA is introduced to speed up the matrix-vector multiplication which constitutes the major computational cost in the application of the conjugate gradient (CG) method, TSM-FMA reduces the central processing unit (CPU) time per iteration to O(N log N) for sparse structures and to O(N) for dense structures, from O(N-3) for the Gaussian elimination method and O(N-3) per iteration for the CG method, The memory requirement for TSM-FMA also scales as O(N log N) for sparse structures and as O(N) for dense structures, Therefore, this approach is suitable for solving large-scale problems on a small computer.

关键词： fast multipole integral equation method of moments microstrip multilevel algorithm

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Hierarchical Interpolation algorithm for Fast Born Approximation Analysis of Scattering by Electrically Large Objects

Hierarchical Interpolation Algorithm for Fast Born Approxima...

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IEEE International Conference on Microwaves, Antennas, Communications and Electronic Systems (COMCAS)

作者： Elbaz, E. Brick, Y. Ben Gurion Univ Negev Sch Elect & Comp Engn IL-8410501 Beer Sheva Israel

ISBN: (纸本)9780738146720

An algorithm for the fast computation of Born approximation scattered field integral for electrically large lowcontrast inhomogeneous targets is presented. The algorithm takes advantage of the integrand's phase in order to efficiently sample partial the contributions to the scattered field, in both the source and observer coordinates. These contributions are gradually interpolated and aggregated, with appropriate phase factors, in a multilevel fashion, in order to obtain the total field integral, sampled at a desired density. This reduces the cost of field integrations by three orders of the scatterer's electrical length. For the far-field and incident plane wave scenario, the computations are further simplified and reduced to that of a single scalar component.

关键词： Wave scattering Born approximation fast methods multilevel algorithm

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Spectral document clustering algorithms with different data structures

Spectral document clustering algorithms with different data ...

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International Conference on Scientific Computing

作者： Oliveira, S Seok, SC Univ Iowa Dept Comp Sci Iowa City IA 52242 USA

ISBN: (纸本)1932415629

Spectral document clustering methods construct sparse word-document matrix W to measure the difference or similarity of documents. It may produce a dense similarity matrix S with W-T X W. We presented a multilevel algorithm on S in [9]. The spectral clustering algorithms on S work well when the size of the dataset is not too big. However, the multiplication for S takes too much time even with efficient sparse multiplication. In this paper, we present a variant of the algorithm on W and investigate two algorithms with computational experiments.

关键词： document clustering multilevel algorithm spectral method data mining

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