A fast method for the solution of the Helmholtz equation

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A fast method for the solution of the Helmholtz equation
In this paper, we consider the numerical solution of the Helmholtz equation, arising from the study of the wave equation in the frequency domain. The approach proposed here differs from those recently considered in the literature, in that it is based on a decomposition that is exact when considered analytically, so the only degradation in computational performance is due to discretization and roundoff errors. In particular, we make use of a multiplicative decomposition of the solution of the Helmholtz equation into an analytical plane wave and a multiplier, which is the solution of a complexvalued advection-diffusion-reaction equation. The use of fast multigrid methods for the solution of this equation is investigated. Numerical results show that this is an efficient solution algorithm for a reasonable range of frequencies.
Eldad Haber, Scott MacLachlan
Added 15 Sep 2011
Updated 15 Sep 2011
Type Journal
Year 2011
Authors Eldad Haber, Scott MacLachlan
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