Accuracy conditions for the numerical computation of waves
The Helmholtz equation (..delta..+K/sup 2/n/sup 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, 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)/sup -1/, is not sufficient to determine the accuracy of a given discretization. For example, the quantity K/sup 3/h/sup 2/ is shown to determine the accuracy in the L/sup 2/ norm for a second-order discretization method applied to several propagation models.
- Research Organization:
- Exxon Corporate Research, Annandale, New Jersey 08801
- DOE Contract Number:
- AC02-76CH00016
- OSTI ID:
- 5510887
- Journal Information:
- J. Comput. Phys.; (United States), Vol. 59:3
- Country of Publication:
- United States
- Language:
- English
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