The Mathematical Institute, University of Oxford, Eprints Archive

Preconditioned iterative solution of the 2D Helmholtz equation

Laird, Alistair L. and Giles, M. B. (2002) Preconditioned iterative solution of the 2D Helmholtz equation. Technical Report. Unspecified. (Submitted)

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Abstract

Using a finite element method to solve the Helmholtz equation leads to a sparse system of equations which in three dimensions is too large to solve directly. It is also non-Hermitian and highly indefinite and consequently difficult to solve iteratively. The approach taken in this paper is to precondition this linear system with a new preconditioner and then solve it iteratively using a Krylov subspace method. Numerical analysis shows the preconditioner to be effective on a simple 1D test problem, and results are presented showing considerable convergence acceleration for a number of different Krylov methods for more complex problems in 2D, as well as for the more general problem of harmonic disturbances to a non-stagnant steady flow.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1216
Deposited By:Lotti Ekert
Deposited On:19 May 2011 07:39
Last Modified:19 May 2011 07:39

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