TY - JOUR

T1 - On accuracy conditions for the numerical computation of waves

AU - Bayliss, A.

AU - Goldstein, C. I.

AU - Turkel, E.

N1 - Funding Information:
* The submitted manuscript has been authored under Contract DE-AC02-76CHOOO16w ith the U.S. Department of Energy. Accordingly, the U.S. Government’s right to retain a nonexclusive, royalty-free license in and the copyright covering, this paper, for govetmental purposes, is acknowledged. t Author partially supported by the National Aeronautics and Space Administration under NASA Contract NASl-17130 while the author was in residence at ICASE, NASA Langley Research Center.

PY - 1985/7

Y1 - 1985/7

N2 - The Helmholtz equation (Δ+K2n2)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, 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 K3h2 is shown to determine the accuracy in the L2 norm for a second-order discretization method applied to several propagation models.

AB - The Helmholtz equation (Δ+K2n2)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, 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 K3h2 is shown to determine the accuracy in the L2 norm for a second-order discretization method applied to several propagation models.

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U2 - 10.1016/0021-9991(85)90119-6

DO - 10.1016/0021-9991(85)90119-6

M3 - Article

AN - SCOPUS:0000350889

SN - 0021-9991

VL - 59

SP - 396

EP - 404

JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 3

ER -