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parallel SOLUTION OF DENSE LINEAR-SYSTEMS USING DIAGONALIZATION METHODS

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 1987年第3-4期22卷 249-270页

作者： COSNARD, M ROBERT, Y TRYSTRAM, D ECOLE CENT PARIS F-92295 CHATENAY MALABRYFRANCE

We study the parallel implementation of two diagonalization methods for solving dense linear systems: the well known Gauss-Jordan method and a new one introduced by Huard. The number of arithmetic operations performed by the Huard method is the same as for Gaussian elimination, namely 2n3/3, less than for the Jordan method, namelyn3. We introduce parallel versions of these methods, compare their performances and study their complexity. We assume a shared memory computer with a number of processorspof the order ofn, the size of the problem to be solved, We show that the best parallel version for Jordan's method is by rows whereas the best one for Huard's method is by columns. Our main result states that for a small number of processors the parallel Huard method is faster than the parallel Jordan method and slower otherwise. The separation is obtained forp= 0.44n.

关键词： parallel numerical algorithms linear system solver Jordan method diagonalization methods parallel computational complexity G.10 F.2.1

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parallel ADAPTIVE FULL-MULTIGRID METHODS ON MESSAGE-BASED MULTIPROCESSORS

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parallel COMPUTING 1986年第4期3卷 269-287页

作者： HOPPE, HC MUHLENBEIN, H Gesellschaft für Mathematik und Datenverarbeitung D-5205 Sankt Augustin Fed. Rep. Germany

This paper explores the macro data flow approach for solving numerical applications on distributed memory systems. We discuss the problems of this approach with a sophisticated ‘real life’ algorithm—the adaptive full multigrid method. It is shown that the nonnumeric parts of the algorithm—the initialization, the termination and the mapping of processes to processors—are very important for the overall performance. To avoid unnecessary global synchronization points we propose to use the distributed supervisors. We compare this solution with more centralized algorithms. The performance evaluation is done for nearest neighbour and bus connected multiprocessors using a simulation systems.

关键词： Adaptive full-multigrid method message-based multiprocessor parallel numerical algorithms macro data-flow technique distributed memory systems

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Performance of preconditioners for the distributed vector finite-element time-domain algorithm

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IEEE TRANSACTIONS ON MAGNETICS 2005年第5期41卷 1716-1719页

作者： Nicolas, A Nicolas, L Vollaire, C Butrylo, B Ecole Cent Lyon CNRS UMR 5005 Ctr Genie Elect Lyon F-69134 Ecully France Bialystok Tech Univ Fac Elect Engn PL-15351 Bialystok Poland

This paper deals with some aspects of performance of the symmetric successive over-relaxation preconditioner in a distributed environment. The details of distributed formulation of the preconditioner are presented. Some performance metrics are compared and discussed for the message passing interface implementation of the algorithm. The properties of the solver are estimated for concurrent three-dimensional formulation of the finite-element time-domain method. The analyzed benchmark models are approximated by tetrahedral first order Whitney elements.

关键词： Edge elements finite-element (FE) method iterative solver parallel numerical algorithms time-domain algorithm

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parallel algorithms for Large-Scale Nanoelectronics Simulations Using NESSIE

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JOURNAL OF COMPUTATIONAL ELECTRONICS 2004年第3-4期3卷 363-366页

作者： Polizzi, Eric Sameh, Ahmed Purdue Univ Dept Comp Sci W Lafayette IN 47907 USA

Large-scale computational problems are encountered when one attempts to realize high degree of detail and realism in the simulation of quantum transport in nanodevices. These problems can be addressed using novel parallel algorithms that are ideally suited for high-end computing platforms. This article has two objectives: (i) the description of the transport model and the associated computational challenges within the multidimensional finite element simulator NESSIE, and (ii) the presentation of a new strategy for handling the transport problem and solving the banded linear systems that arise from the Green (or wave) function approach.

关键词： NEGF quantum transport modeling computational nanoelectronics parallel numerical algorithms

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numerical integration of Maxwell's full-vector equations in nonlinear focusing media

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PHYSICA D-NONLINEAR PHENOMENA 2003年第1-4期184卷 352-375页

作者： Bennett, PM Aceves, A Univ New Mexico Dept Math & Stat Albuquerque NM 87131 USA Comp Sci Corp Vicksburg MS 39180 USA

In this paper, we present results of parallel numerical simulations on Maxwell's equations. The parallel code is used to study the effect of the instantaneous focusing nonlinearity upon dispersionless pulse propagation in bulk dielectric. Indications are given of the development of shocks on the optical carrier wave and upon the pulse envelope. We then use the code to study focusing and collapse of optical pulses at anomalously dispersive frequencies. We examine the effect of varying the focusing of the light by varying the intensity as a way to compensate linear dispersion. We demonstrate blow up of sufficiently intense short pulses at finite propagation distances, and we show numerically that the location of blow up depends nontrivially upon the intensity of the light. (C) 2003 Elsevier B.V. All rights reserved.

关键词： nonlinear optics parallel numerical algorithms ultrashort intense pulses Maxwell's equations anomalous dispersion instantaneous nonlinearity

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A parallel hybrid banded system solver: the SPIKE algorithm

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parallel COMPUTING 2006年第2期32卷 177-194页

作者： Polizzi, E Sameh, AH Purdue Univ Dept Comp Sci W Lafayette IN 47907 USA

This paper describes an efficient and robust hybrid parallel solver "the SPIKE algorithm" for narrow-banded linear systems. Two versions of SPIKE with their built-in-options are described in detail: the Recursive SPIKE version for handling non-diagonally dominant systems and the Truncated SPIKE version for diagonally dominant ones. These SPIKE schemes can be used either as direct solvers, or as preconditioners for outer iterative schemes. Both versions are faster than the direct solvers in ScaLAPACK on parallel computing platforms, and quite competitive in terms of achieved accuracy For handling systems that are dense within the band. (c) 2005 Elsevier B.V. All rights reserved.

关键词： banded linear systems iterative schemes numerical linear algebra parallel numerical algorithms preconditioners ScaLAPACK SPIKE

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A Comparison of Accuracy and Efficiency of parallel Solvers for Fractional Power Diffusion Problems 12th

A Comparison of Accuracy and Efficiency of Parallel Solvers ...

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12th International Conference on parallel Processing and Applied Mathematics (PPAM)

作者： Ciegis, Raimondas Starikovicius, Vadimas Margenov, Svetozar Kriauziene, Rima Vilnius Gediminas Tech Univ Sauletekis Ave 11 LT-10223 Vilnius Lithuania Bulgarian Acad Sci Inst Informat & Commun Technol Acad G Bonchev StBl 25A BU-1113 Sofia Bulgaria Vilnius Univ Inst Math & Informat Akad St 4 LT-08663 Vilnius Lithuania

ISBN: (纸本)9783319780245;9783319780238

In this paper, we construct and investigate parallel solvers for three dimensional problems described by fractional powers of elliptic operators. The main aim is to make a scalability analysis of parallel versions of several state of the art solvers. The originality of this work is that we also consider the accuracy of the selected numerical algorithms. For comparison of accuracy, we use solutions obtained solving the test problem by the Fourier algorithm. Such analysis enables to compare the efficiency of the proposed parallel algorithms depending on the required accuracy of solution and on a number of processes used in computations.

关键词： Fractional diffusion Finite volume method parallel numerical algorithms MPI Scalability Multigrid

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A parallel hybrid banded system solver: the SPIKE algorithm

A parallel hybrid banded system solver: the SPIKE algorithm

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3rd Workshop on parallel Matrix algorithms and Applications (PMAA 2004)

作者： Polizzi, E Sameh, AH Purdue Univ Dept Comp Sci W Lafayette IN 47907 USA

关键词： banded linear systems iterative schemes numerical linear algebra parallel numerical algorithms preconditioners ScaLAPACK SPIKE

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Supercomputer simulation of nonlinear problems of fluid dynamics in cores

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LOBACHEVSKII JOURNAL OF MATHEMATICS 2017年第5期38卷 958-963页

作者： Podryga, V. O. Polyakov, S. V. Puzyrkov, D. V. Russian Acad Sci Keldysh Inst Appl Math Moscow 125047 Russia

This report focuses on technology of supercomputer simulation of nonlinear processes in the cores, extracted from oil and gas production wells in order to study the properties of hydrocarbon reservoirs. One of modern approaches to solving these kind problems is to create multiphysical mathematical model of core for its study by computer methods. This approach minimizes the number of natural experiments and predicts the evolution of layers properties. Also it allows to predict oil and gas recovery of layers for a long time period. However, implementation of this technology called "virtual core" requires the following: 1) to create multiparametrical model of core as close as possible to the reality;2) to include the multicomponent and multiphase composition and complex real geometry of core in consideration;3) to develop a computational framework for modeling the seepage of multicomponent liquid and gas mixtures through the core;4) to carry out large-scale calibration calculations. In this paper, an attempt to create such a multifactor mathematical model and computational foundations for its computing and supercomputing analysis is made.

关键词： Fluid dynamics nonlinear processes in cores mathematical modeling parallel numerical algorithms supercomputer simulations

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numerical integration of Maxwell's full-vector equations in nonlinear focusing media

Numerical integration of Maxwell's full-vector equations in ...

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Conference on Complexity and Nonlinearity in Physical Systems held in Honor of Alan Newell

作者： Bennett, PM Aceves, A Univ New Mexico Dept Math & Stat Albuquerque NM 87131 USA Comp Sci Corp Vicksburg MS 39180 USA

关键词： nonlinear optics parallel numerical algorithms ultrashort intense pulses Maxwell's equations anomalous dispersion instantaneous nonlinearity

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