Abstract
This paper is concerned with the development of methods for constructing stable artificial boundary conditions for wavelike equations in a general and automatic way. The one-dimensional problem of a semi-infinite, inhomogeneous, elastic bar is studied here as a prototype situation. For this problem a family of efficient artificial boundary conditions is obtained using geometrical optics in the Laplace transform domain for generating outgoing solutions, together with a stability criterion based on energy integrals to insure that the resulting artificial boundaries are dissipative. Numerical examples illustrate the efficacy of this approach. The paper also includes some remarks about the extension of the proposed method to a more general two-dimensional situation.
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