Analysis of a fast method for solving the high frequency Helmholtz equation in one dimension
type: Item
instance of: scholarly article
title: Analysis of a fast method for solving the high frequency Helmholtz equation in one dimension
zbMATH Open document ID: 1260.65067
author: Jelena Popovic
author: Olof Runborg
published in: BIT
publication date: 2011-10-11T00:00:00Z
review text: Based on wave splitting, the authors introduce a fast method for computing the solution of the high frequency Helmholtz equation in a bounded one-dimensional domain with a variable wave speed function. The Helmholtz equation is split into one-way wave equations with source functions which are solved iteratively for a given tolerance. The source functions depend on the wave speed function and on the solutions of the one-way wave equations from the previous iteration. The solution of the Helmholtz equation is then approximated by the sum of the one-way solutions at every iteration. To improve the computational cost, the source functions are thresholded and in the domain where they are equal to zero, the one-way wave equations are solved with geometrical optics with a computational cost independent of the frequency. Convergence of the algorithm is proved in one dimension. Numerical experiments indicate that the growth rate of the computational cost is much slower than a direct method.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 65L20
zbMATH DE Number: 5956843
zbMATH Keywords: Helmholtz equation
zbMATH Keywords: high frequency
zbMATH Keywords: wave splitting
zbMATH Keywords: one-dimensional domain
zbMATH Keywords: wave equations
zbMATH Keywords: convergence
zbMATH Keywords: algorithm
zbMATH Keywords: numerical experiments
reviewed by: Sebastian Aniţa
MaRDI profile type: Publication
full work available at URL: s10543-011-0315-7
OpenAlex ID: W1985319925
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DOI: 10.1007/S10543-011-0315-7
description: scientific article; zbMATH DE number 5956843