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Sunday, July 26, 2020 | History

1 edition of Parallel direct Poisson and biharmonic solvers found in the catalog.

Parallel direct Poisson and biharmonic solvers

Ahmed Sameh

Parallel direct Poisson and biharmonic solvers

by Ahmed Sameh

  • 100 Want to read
  • 3 Currently reading

Published by Dept. of Computer Science, University of Illinois at Urbana-Champaign in Urbana, Illinois .
Written in English

    Subjects:
  • Numerical solutions,
  • Biharmonic equations,
  • Poisson"s equation,
  • Data processing,
  • Parallel processing (Electronic computers)

  • Edition Notes

    Statementby A. H. Sameh, S. C. Chen, and D. J. Kuck
    SeriesReport (University of Illinois at Urbana-Champaign. Dept. of Computer Science) -- no. 684, Report (University of Illinois at Urbana-Champaign. Dept. of Computer Science) -- no. 684.
    ContributionsChen, Shyh-ching, 1944- author, Kuck, David J. author, University of Illinois at Urbana-Champaign. Dept. of Computer Science
    Classifications
    LC ClassificationsQA76 .I4 no. 684, QA377 .I4 no. 684
    The Physical Object
    Pagination18 p. ;
    Number of Pages18
    ID Numbers
    Open LibraryOL25454051M
    OCLC/WorldCa1286705

    Anal., 21 (), pp. –], a method was introduced for solving Poisson’s or the biharmonic equation on an irregular region by making use of an integral equation formulation. Because fast solvers were used to extend the solution to an enclosing rectangle, this method avoided many of the standard problems associated with integral by: A Fast Domain Decomposition High Order Poisson Solver Article (PDF Available) in Journal of Scientific Computing 14(3) September with 44 Reads How we measure 'reads'.

    The concept of using a radial basis function to solve Poisson equations and biharmonic equations has been researched by Mai-Duy et al.,,,,,,,,,. Haar wavelets are made up of pairs of piecewise constant functions and mathematically the simplest orthonormal wavelets with a compact by:   A fast algorithm is developed for the parallel numerical solution of the first biharmonic boundary value problem on a rectangular region with N2 interior grid points. The parallel computer considered is of SIMD type. The iterative procedure where one iteration consists in solving two transformed Poisson equations with relaxation is used. This approach allows one to apply the direct Cited by: 2.

    vi CONTENTS The Convection Diffusion Equation 50 Finite Difference Methods veloped solver may, with no additional e ort, be run on supercomputers using thousands of processors. Complete solvers are shown for the linear Poisson and biharmonic problems, as well as the nonlinear and time-dependent Ginzburg-Landau equation. 1. INTRODUCTION The spectral Galerkin method, see, e.g., Shen [1] or Kopriva [2], combines.


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Parallel direct Poisson and biharmonic solvers by Ahmed Sameh Download PDF EPUB FB2

Parallel Poisson and Biharmonic solvers. Abstract. In this paper we develop direct and iterative algorithms for the solution of finite difference approximations of the Poisson and Biharmonic equations on a square, using a number of arithmetic units in by: Lotti, G.

and Vajtersic, M. (), The application of VLSI Poisson solvers to the biharmonic problem, Parallel Computing, 18, pp. 11– zbMATH CrossRef Google Scholar [9] Mclaurin, J.W. (), A general coupled equation approach for solving the biharmonic boundary value problem, SIAM J.

: Marián Vajteršic. The modified cyclic reduction parallel Poisson solver (n = 7). IP X 4 -- X 5 6 ~g 7 Applying VLSI Poisson solvers to the biharmonic problem 15 4.

VLS. Poisson solvers We can proceed with a description of the VLSI implementation of both the algorithms of the preceding by: 7. () The application of VLSI poisson solvers to the biharmonic problem. Parallel Computing() Application of domain decomposition techniques in large-scale fluid flow by: A parallel perturbed biharmonic solver 3.

A PERTURBED BIHARMONIC SOLVER Let us consider the perturbed biharmonic equation. V4u+d:u=f in R, deR, (3) where R is the unit square with the boundary conditions u(x, y) = 0 and u,(x, y) = 0 for (x, y) ~ fiR, and u,(x, y) is the outward normal derivative at the : G.

Lotti. Two methods for solving the biharmonic equation are compared. One method is direct, using eigenvalue-eigenvector decomposition.

The other method is iterative, solving a Poisson equation directly at each by: 1. We present fast methods for solving Laplace’s and the biharmonic equations on irregular regions with smooth boundaries. The methods used for solving both equations make use of fast Poisson solvers on a rectangular region in which the irregular region is embedded.

They also both use an integral equation formulation of the problem where the integral equations are Cited by: Stage 1: (Parallel among all processors) After each processor 1 Poisson Solver for Multiprocessors matrix of T and by:   A direct method is developed for the discrete solution of Poisson's equation on a rectangle.

The algorithm proposed is of the class of marching methods. The idea is to generalize the classical Cramer's method using Chebyshev matrix polynomials formalism. This results in the solution ofN independent diagonal system of linear equations in the eigenvector coordinate Cited by: 2.

Poisson Solvers William McLean Ap Return to Math/Math Common Material. 1 Introduction Many problems in applied mathematics lead to a partial di erential equation of the form 2aru+ bru+ cu= f in.

(1) Here, is an open subset of Rd for d= 1, 2 or 3, the coe cients a, band ctogether with the source term fare given functions on File Size: KB. This algorithm is more effective than Gaussian elimination with pivoting, Gram-Schmidt, or Householder's reduction, since A.H.

Sameh, D.J. Kuck/Parallel direct linear system solvers - A survey 7 6 8 5 7 9 4 6 8 10 3 5 7 9 11 2 4 6 8 10 12 1 3 5 7 9 11 13 F(Givens) = (1/n) compared to = (1/n log 2n) for the by: Full text of "Fast parallel iterative solution of Poisson's and the biharmonic equations on irregular regions" See other formats Computer Science Department TECHNICAL REPORT Fast Parallel Iterative Solution of Poisson's and the Biharmonic Equations on Irregular Regions A.

Mayo A. Greenbaum Technical Report January NEW YORK UNIVERSITY C 03 C. Parallel direct Poisson solver for discretisations with one Fourier diagonalisable direction Article in Journal of Computational Physics (12) June with 34 Reads.

A fast solver for the Stokes equations with distributed forces in complex geometries 1 George Biros, Lexing Ying, and Denis Zorin “The Fast Solution of Poisson’s and the Biharmonic Equations on Irregular Regions”, SIAM As parallel computation is necessary to solve realistic problems with sufficient accuracy.

‘The application of VLSI Poisson solvers to the biharmonic problem’, Parallel Computing 18 () 11– zbMATH CrossRef Google Scholar [16] Mead, C. and Conway, L.: Introduction to VLSI Systems, Addison-Wesley, Reading, Author: Marián Vajteršic.

PoisFFT – A free parallel fast Poisson solver. This pap er presents the free softw are implementation of a fast direct solver.

for the P oisson equation in 1. The first problem concerns solving the discretized Poisson equation with Dirichlet boundary conditions. Parallel direct as well as iterative methods have been already examined for solving this model problem on various architectures.

Among the direct methods, e.g., parallel schemes for. This IMA Volume in Mathematics and its Applications PARALLEL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS is based on the proceedings of a workshop with the same title. The work­ shop was an integral part of the IMA program on "MATHEMAT­ ICS IN HIGH-PERFORMANCE COMPUTING." I would like to.

In addition, the code uses the "blktri" direct solver found in the FISHPACK library to solve the Poisson equation in 2D. Is there a parallel version of the "blktri" subroutine or a similar direct solver that has parallel capabilities. I've searched on the internet for parallel direct Poisson solvers but the closest thing I found are these two: 1.

The overall goals of this project are to parallelize an existing serial code (C/C++) for a multigrid poisson equation solver using MPI and to study the performance and scalability of the resulting implementation. This will require the parallelization of two key components in the solver: 1.

classical iterative methods 2. geometric multigridFile Size: KB. Abstract. We present a fast parallel solution method for the Poisson equation on irregular domains.

Due to a simple embedding method using harmonic polynomial approximation, a dominant part of the computation becomes solving one Poisson problem on a by: 3.A Fast Direct Solver for the Biharmonic Problem 3 a typical computing time of the solver for a × grid is ten seconds on a PC. Finally, let us mention the work [29] for a comprehensivehistory of the biharmonic problem in two dimensions.

2. Notation. Finite difference operators. We consider a square Ω = (0,L)2 with a.A survey of the parallel performance and accuracy of Poisson solvers for electronic structure calculations Pablo Garc a-Risue no~ 1,2,3, Joseba Alberdi-Rodriguez 4,5, Micael J.

T. Oliveira 6, Xavier Andrade 7, Michael Pippig 8, Javier Muguerza 4, Agustin Arruabarrena 4, and Angel Rubio 5,9 1 Institut fur Physik, Humboldt Universit at zu Berlin, Zum grossen.