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A parallel hierarchical blocked adaptive cross approximation algorithm

INTERNATIONAL JOURNAL OF HIGH PERFORMANCE COMPUTING APPLICATIONS 2020年第4期34卷 394-408页

作者： Liu, Yang Sid-Lakhdar, Wissam Rebrova, Elizaveta Ghysels, Pieter Li, Xiaoye Sherry Lawrence Berkeley Natl Lab Computat Res Div Scalable Solvers Grp Berkeley CA 94720 USA Lawrence Berkeley Natl Lab Computat Res Div Berkeley CA 94720 USA Univ Calif Los Angeles Dept Math Los Angeles CA 90024 USA

This article presents a low-rank decomposition algorithm based on subsampling of matrix entries. The proposed algorithm first computes rank-revealing decompositions of submatrices with a blocked adaptive cross approximation (BACA) algorithm, and then applies a hierarchical merge operation via truncated singular value decompositions (H-BACA). The proposed algorithm significantly improves the convergence of the baseline ACA algorithm and achieves reduced computational complexity compared to the traditional decompositions such as rank-revealing QR. Numerical results demonstrate the efficiency, accuracy, and parallel scalability of the proposed algorithm.

关键词： Adaptive cross approximation singular value decomposition rank-revealing decomposition parallelization multilevel algorithms

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Fast Computation of Born-Approximated Multistatic Scattering

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IEEE TRANSACTIONS ON ULTRASONICS FERROELECTRICS AND FREQUENCY CONTROL 2021年第12期68卷 3637-3645页

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

An algorithm for the fast computation of multistatic scattering patterns, produced by low-contrast inhomogeneous volumetric objects, which satisfy the Born approximation assumption, is presented. The algorithm relies on hierarchical interpolation and aggregation of optimally sampled phase-compensated partial contributions to the scattered field integral. The Born approximation enables the efficient simultaneous computation for ranges of incident and observation angles, as well as excitation frequencies. This leads to a reduction in the asymptotic computational complexity by several polynomial orders of the problem's acoustical size. The algorithm's error controllability and favorable computation time are demonstrated via representative examples.

关键词： Scattering Approximation algorithms Nonhomogeneous media Interpolation Integral equations Frequency control Observers Fast methods multilevel algorithms wave scattering

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A two-scale method for radiative heat transfer in non-grey absorbing and emitting media

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JOURNAL OF NUMERICAL MATHEMATICS 2007年第1期15卷 59-79页

作者： Seaid, M. AG Technomath Fachbereich Math D-67663 Kaiserslautern Germany

Multiscale radiative heat transfer (RHT) problems are formulated and methods to approximate their numerical solutions are developed. We focus on RHT problems in participating media with heterogeneous optical properties leading to both optically thick and thin regimes within the same media spectrum. By introducing a diffusive scale and using an asymptotic expansion in the RHT equations we formulate the simplified P-N approximations. The optical spectrum is decomposed in wavelength bands and the RHT equations are solved for bands with low absorption while the simplified P-N equations are solved for bands with high absorption. The hybrid models solve the multiscale RHT more accurately than the simplified PN approximations and with a computational costs less than using the full RHT solver. Accuracy and effectiveness of the proposed models are demonstrated on three-dimensional RHT problems arising in combustion systems.

关键词： radiative heat transfer simplified P-N approximations multiscale problems discrete-ordinate method multilevel algorithms non-grey gases combustion systems

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multilevel hypergraph partitioning: Applications in VLSI domain

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IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS 1999年第1期7卷 69-79页

作者： Karypis, G Aggarwal, R Kumar, V Shekhar, S Univ Minnesota Dept Comp Sci & Engn Minneapolis MN 55455 USA Lattice Semiconductor Corp Milpitas CA 95131 USA

In this paper, we present a new hypergraph-partitioning algorithm that is based on the multilevel paradigm. In the multilevel paradigm, a sequence of successively coarser hypergraphs is constructed, A bisection of the smallest hypergraph is computed and it is used to obtain a bisection of the original hypergraph by successively projecting and refining the bisection to the next level finer hypergraph. We have developed new hypergraph coarsening strategies within the multilevel framework. We evaluate their performance both in terms of the size of the hyperedge cut on the bisection, as well as on the run time for a number of very large scale integration circuits. Our experiments show that our multilevel hypergraph-partitioning algorithm produces high-quality partitioning in a relatively small amount of time. The quality of the partitionings produced by our scheme are on the average 6%-23% better than those produced by other state-of-the-art schemes. Furthermore, our partitioning algorithm is significantly faster, often requiring CIO times less time than that required by the other schemes. Our multilevel hypergraph-partitioning algorithm scales very well for large hypergraphs, Hypergraphs with over 100 000 vertices can be bisected in a few minutes on today's workstations. Also, on the large hypergraphs, our scheme outperforms other schemes (in hyperedge cut) quite consistently with larger margins (9%-30%).

关键词： circuit partitioning hypergraph partitioning multilevel algorithms

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multilevel cooperative search for the circuit/hypergraph partitioning problem

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IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS 2002年第6期21卷 685-693页

作者： Ouyang, M Toulouse, M Thulasiraman, K Glover, F Deogun, JS Synopsys Inc Mountain View CA 94043 USA Univ Manitoba Dept Comp Sci Winnipeg MB R3T 2N2 Canada Univ Oklahoma Sch Comp Sci Norman OK 73019 USA Univ Mississippi Sch Business Adm Hearin Ctr Enterprise Sci University MS 38677 USA Univ Nebraska Dept Comp Sci & Engn Lincoln NE 68588 USA

The objectives in this paper are twofold: design an approach for the netlist partitioning problem using the cooperative multilevel search paradigm introduced by Toulouse et aL and study the effectiveness of this paradigm for solving combinatorial optimization problems, in particular, those arising in the very large scale integration (VLSI) computer-aided design (CAD) area. The authors present, a cooperative multilevel search algorithm CoMHP and describe a parallel implementation on the SGI O2000 system. Experiments on ISPD98 benchmark suite of circuits show, for four-way and eight-way partitioning, a reduction of 3% to 15% in the size of hyperedge cuts compared to those obtained by hMETIS. Bisections of hypergraphs based on the algorithm also outperform hMETIS, although more modestly. The authors present experimental results to demonstrate that the cooperation scheme plays a key role in the performance of CoMHP. In fact, the improvement in the quality of the solutions produced by CoMHP is to a large extent independent of the partitioners used in the implementation of CoMHP. The experimental results also demonstrate the effectiveness of the cooperative multilevel search paradigm for solving the netlist partitioning problem and show that the cooperative multilevel search strategy can be used as a paradigm for designing effective solution techniques for combinatorial optimization problems such as those arising in the VLSI CAD area.

关键词： combinatorial optimization cooperative search graph partitioning multilevel algorithms VLSI physical design

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Nonuniform Polar Grid Algorithm for Fast Field Evaluation

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IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS 2002年 1卷 142-145页

作者： Boag, Amir Michielssen, Eric Brandt, Achi Tel Aviv Univ Dept Phys Elect IL-69978 Tel Aviv Israel Univ Illinois Dept Elect & Comp Engn Urbana IL 61801 USA Weizmann Inst Sci Dept Comp Sci & Appl Math IL-76100 Rehovot Israel

A novel algorithm to efficiently compute time-harmonic fields produced by known two-dimensional source constellations is proposed. The algorithm relies on domain decomposition and comprises two steps to be repeated for each subdomain. In the first step, phase, and amplitude compensated fields, produced by currents residing within each subdomain are computed over a sparse set of points surrounding the observation domain. During the second step, total fields in the observer domain are evaluated by interpolation, phase and amplitude restoration and aggregation of subdomain fields. The proposed approach is applied to the fast iterative analysis of scattering phenomena using the method of moments.

关键词： Acoustic scattering electromagnetic scattering fast algorithms integral equations multilevel algorithms

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multilevel fast physical optics algorithm for radiation from non-planar apertures

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 2005年第6期53卷 2064-2072页

作者： Boag, A Letrou, C Tel Aviv Univ Sch Elect Engn IL-69978 Tel Aviv Israel INT GET CNRS UMR 5157Lab SAMOVAR F-91011 Evry France

A novel multilevel algorithm for computing the radiation patterns of nonplanar aperture antennas over a range of observation angles is presented. The proposed technique is directly applicable to reflector and lens antennas as well as to radomes. The multilevel computational sequence is based on a hierarchical decomposition of the. radiating aperture and comprises two main steps. First, computation of the radiation patterns of all subapertures of the finest level over a very coarse angular grid. Second, multilevel aggregation of the radiation patterns of neighboring subapertures into the final pattern of the whole aperture via a phase compensated interpolation. The multilevel algorithm attains computational complexity comparable to that of the fast Fourier transform based techniques while avoiding their limitations.

关键词： computation time fast algorithms lens antennas multilevel algorithms physical optics radomes reflector antennas

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MULTIGRID METHODS FOR DISCRETE FRACTIONAL SOBOLEV SPACES

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 2019年第2期41卷 A948-A972页

作者： Baerland, Trygve Kuchta, Miroslav Mardal, Kent-andre Univ Oslo Dept Math N-0316 Oslo Norway

Coupled multiphysics problems often give rise to interface conditions naturally formulated in fractional Sobolev spaces. Here, both positive and negative fractionality are common. When designing efficient solvers for discretizations of such problems it would therefore be useful to have a preconditioner for the fractional Laplacian. In this work, we develop an additive multigrid preconditioner for the fractional Laplacian with positive fractionality and show a uniform bound on the condition number. For the case of negative fractionality, we reuse the preconditioner developed for the positive fractionality and left-right multiply a regular Laplacian with a preconditioner with positive fractionality to obtain the desired negative fractionality. Implementational issues are out-lined in detail as the differences between the discrete operators and their corresponding matrices must be addressed when realizing these algorithms in code. We finish with some numerical experiments verifying the theoretical findings.

关键词： fractional Laplacian multilevel algorithms operator preconditioning

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multilevel strategies for parametric shape optimization in aerodynamics

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EUROPEAN JOURNAL OF COMPUTATIONAL MECHANICS 2008年第1-2期17卷 149-168页

作者： Abou El Majd, Badr Desideri, Jean-Antoine Duvigneau, Regis INRIA Opale Project Team 2004 Route LuciolesBP 93 F-06902 Sophia Antipolis France

The essential numerical features of multilevel strategies developed for parametric shape optimization are reviewed. These methods employ nested parameterization supports of either shape, or shape deformation, and the classical process of degree elevation resulting in exact geometrical data transfer from coarse to fine representations. The algorithms mimick classical multigrid strategies and are found very effective in terms of convergence acceleration. In particular, for a drag reduction problem involving a three-dimensional Eulerian transonic flow simulated by an unstructured-grid finite-volume method, the complete algorithm is found to be noticeably superior to the natural algorithm simply based on progressive degree elevation.

关键词： optimum shape design compressible aerodynamics finite-volume methods shape parameterization multilevel algorithms

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A combined steepest descent-fast multipole algorithm for the fast analysis of three-dimensional scattering by rough surfaces

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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 1998年第3期36卷 738-748页

作者： Jandhyala, V Michielssen, E Balasubramaniam, S Chew, WC Univ Illinois Dept Elect & Comp Engn Ctr Computat Electromagnet Urbana IL 61801 USA

A new technique, the steepest descent-fast multipole method (SDFMM), is developed to efficiently analyze scattering from perfectly conducting random rough surfaces. Unlike other prevailing methods, this algorithm has linear computational complexity and memory requirements, making it a suitable candidate for analyzing scattering from large rough surfaces as well as for carrying out Monte Carlo simulations. The method exploits the quasiplanar nature of rough surfaces to efficiently evaluate the dyadic Green's function for multiple source and observation points. This is achieved through a combination of a Sommerfeld steepest descent integral and a multilevel fast multipole-like algorithm based on inhomogeneous plane wave expansions. The fast evaluation of the dyadic Green's function dramatically speeds up the iterative solution of the integral equation for rough surface scattering, Several numerical examples are presented to demonstrate the efficacy and accuracy of the method in analyzing scattering from extremely large finite rough surfaces.

关键词： fast-multipole methods integral equations multilevel algorithms rough surface scattering

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