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On accuracy conditions for the numerical computation of wavesThe Helmholtz equation (Delta + K(2)n(2))u = f with a variable index of refraction n, and a suitable radiation condition at infinity serves as a model for a wide variety of wave propagation problems. Such problems can be solved numerically by first truncating the given unbounded domain and imposing a suitable outgoing radiation condition on an artificial boundary and then solving the resulting problem on the bounded domain by direct discretization (for example, using a finite element method). In practical applications, the mesh size h and the wave number K, are not independent but are constrained by the accuracy of the desired computation. It will be shown that the number of points per wavelength, measured by (Kh)(-1), is not sufficient to determine the accuracy of a given discretization. For example, the quantity K(3)h(2) is shown to determine the accuracy in the L(2) norm for a second-order discretization method applied to several propagation models.
Document ID
19840025040
Acquisition Source
Legacy CDMS
Document Type
Contractor Report (CR)
Authors
Bayliss, A. (Exxon Corporate Research)
Goldstein, C. I. (Brookhaven National Lab.)
Turkel, E. (Tel-Aviv Univ.)
Date Acquired
September 4, 2013
Publication Date
August 1, 1984
Subject Category
Numerical Analysis
Report/Patent Number
ICASE-84-38
NAS 1.26:172433
NASA-CR-172433
Accession Number
84N33111
Funding Number(s)
CONTRACT_GRANT: NAS1-17130
PROJECT: RTOP 505-31-83-01
CONTRACT_GRANT: DE-AC02-76CH-00016
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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