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High-frequency asymptotics for the numerical solution of the Helmholtz equation

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Authors
Kim, Seongjai; Shin, Changsoo; Keller, Joseph B.
Issue Date
2005-02-08
Publisher
Elsevier
Citation
Appl. Math. Lett. 18 (2005) 797-804
Keywords
The Helmholtz equationHigh-frequency asymptoticsCumulative amplitudeTraveltimeGrid frequency
Abstract
It is often noted that the Helmholtz equation is extremely difficult to solve, in particular, for high-frequency
solutions for heterogeneous media. Since stability for second-order discretization methods requires one to choose
at least 10–12 grid points per wavelength, the discrete problem on the possible coarsest mesh is huge. In a realistic
simulation, one is required to choose 20–30 points per wavelength to achieve a reasonable accuracy; this problem
is hard to solve. This article is concerned with the high-frequency asymptotic decomposition of the wavefield for
an efficient and accurate simulation for the high-frequency numerical solution of the Helmholtz equation. It has
been numerically verified that the new method is accurate enough even when one chooses 4–5 grid points per
wavelength.
ISSN
0893-9659
Language
English
URI
http://hdl.handle.net/10371/6118
DOI
https://doi.org/10.1016/j.aml.2004.07.027
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College of Engineering/Engineering Practice School (공과대학/대학원)Dept. of Energy Systems Engineering (에너지시스템공학부)Journal Papers (저널논문_에너지시스템공학부)
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