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Parallel solution of eigenvalue problems in acoustics on the Distributed Array Processor (DAP)

  • A. Polster
Namerical Algorithms (Session 3.2)
Part of the Lecture Notes in Computer Science book series (LNCS, volume 237)

Abstract

The paper deals with the parallel solution of the partial differential equation -Δu=u in an 2− or 3-dimensional domain on the Distributed Arrary Processor (DAP). We want to find the eigenfunctions corresponding to the two or three smallest eigenvalues. A discretisation leads to a system of linear equations AxBx, A,BR nxn ,x ε R n , A and B large and sparse.

λ and x are determined by minimising the Rayleigh quotient \(f(x) = \frac{{(x,Ax)}}{{(x,Bx)}}\)using a modified conjugate gradient method. We describe the implementation of the algorithm and show how to generate the linear systems automatically for arbitrary domains. We show results of 2− and 3− dimensional calculations, where we looked for the resonance swings in the interior of a car by solving linear systems with up to 263144 unknowns.

Keywords

PDE Rayleigh Quotient Conjugate Gradient Method DAP arbitrary domains 3-dimensional calculations 

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References

  1. [BRAD]
    W.W. Bradbury and R. Fletcher. New Iterative Methods for Solution of the Eigenproblem; Numer. Math. 9 (1966), 256–267.Google Scholar
  2. [SCHW]
    H.R. Schwarz: Methode der finiten Elemente; Teubner (Studienbuch Mathematik): Stuttgart 1980.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • A. Polster
    • 1
  1. 1.Universität Erlangen IMMD 7ErlangenWest Germany

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