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)


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.


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


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  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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