Numerical absorbing boundary conditions for the wave equation
Author:
Robert L. Higdon
Journal:
Math. Comp. 49 (1987), 6590
MSC:
Primary 65N05; Secondary 35L05
MathSciNet review:
890254
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Abstract: We develop a theory of difference approximations to absorbing boundary conditions for the scalar wave equation in several space dimensions. This generalizes the work of the author described in [8]. The theory is based on a representation of analytical absorbing boundary conditions proven in [8]. These conditions are defined by compositions of firstorder, onedimensional differential operators. Here the operators are discretized individually, and their composition is used as a discretization of the boundary condition. The analysis of stability and reflection properties reduces to separate studies of the individual factors. A representation of the discrete boundary conditions makes it possible to perform the analysis geometrically, with little explicit calculation.
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 B. Engquist & A. Majda, "Absorbing boundary conditions for the numerical simulation of waves," Math. Comp., v. 31, 1977, pp. 629651. MR 0436612 (55:9555)
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 B. Engquist & A. Majda, "Radiation boundary conditions for acoustic and elastic wave calculations," Comm. Pure Appl. Math., v. 32, 1979, pp. 313357. MR 517938 (80e:76041)
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 L. Halpern & L. N. Trefethen, "Wideangle oneway wave equations," J. Acoust. Soc. Amer. (To appear.) MR 965847 (89j:76076)
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 R. L. Higdon, "Initialboundary value problems for linear hyperbolic systems," SIAM Rev., v. 28, 1986, pp. 177217. MR 839822 (88a:35138)
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 R. L. Higdon, "Absorbing boundary conditions for difference approximations to the multidimensional wave equation," Math. Comp., v. 47, 1986, pp. 437459. MR 856696 (87m:65131)
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 E. L. Lindman, ""Freespace" boundary conditions for the time dependent wave equation," J. Comput. Phys., v. 18, 1975, pp. 6678.
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 L. N. Trefethen, "Instability of difference models for hyperbolic initial boundary value problems," Comm. Pure Appl. Math., v. 37, 1984, pp. 329367. MR 739924 (86f:65162)
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 L. N. Trefethen & L. Halpern, "Wellposedness of oneway wave equations and absorbing boundary conditions," Math. Comp., v. 47, 1986, pp. 421435. MR 856695 (88b:65148)
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 G.Q. Zhang, High Order Approximation of OneWay Wave Equations, Technical report, Computing Center, Academia Sinica, Beijing, China, 1984. MR 815413 (87a:65151)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198708902541
PII:
S 00255718(1987)08902541
Keywords:
Absorbing boundary conditions,
wave equation,
initialboundary value problems
Article copyright:
© Copyright 1987 American Mathematical Society
