Paper Info
Title
A fast method for the solution of the Helmholtz equation
Abstract
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 complex-valued 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.
Year
DOI
Venue
2011
10.1016/j.jcp.2011.01.015
J. Comput. Physics
Keywords
Field
DocType
fast method,computational performance,helmholtz,complex-valued advection-diffusion-reaction equation,wave equation,efficient solution algorithm,fourier analysis,multiplicative decomposition,advection–diffusion,helmholtz equation,numerical result,fast multigrid method,numerical solution,analytical plane wave,multigrid,frequency domain,multigrid method,plane waves
Mathematical optimization,Characteristic equation,Stiff equation,Mathematical analysis,Helmholtz free energy,Weak solution,Helmholtz equation,Electromagnetic wave equation,Wave equation,Partial differential equation,Mathematics
Journal
Volume
Issue
ISSN
230
12
Journal of Computational Physics
Citations 
PageRank 
References 
17
0.91
8
Authors
2
Name
Order
Citations
PageRank
Eldad Haber134233.21
Scott MacLachlan2788.09