Abstract
Discretisation of the integral equations of acoustic scattering yields a system of linear equations with full coefficient matrices. In recent years a number of fast algorithms for the solution of this system have been proposed. In this paper we present a complete analysis for a fast multipole method for the Helmholtz equation. A one-level diagonal form of the multipole method is applied to a hypersingular integral equation arising from 2d scattering theory. The error of the approximation is analysed and the results used to establish the complexity of the method.
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Amini, S., Profit, A.T.J. Analysis of a Diagonal Form of the Fast Multipole Algorithm for Scattering Theory. BIT Numerical Mathematics 39, 585–602 (1999). https://doi.org/10.1023/A:1022331021899
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DOI: https://doi.org/10.1023/A:1022331021899