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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Numerical absorbing boundary conditions for the wave equation


Author: Robert L. Higdon
Journal: Math. Comp. 49 (1987), 65-90
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 first-order, one-dimensional 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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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1987-0890254-1
PII: S 0025-5718(1987)0890254-1
Keywords: Absorbing boundary conditions, wave equation, initial-boundary value problems
Article copyright: © Copyright 1987 American Mathematical Society