2011•Mathematical Methods in the Applied SciencesRequires access

Transparent boundary conditions for the wave equation—a Kirchhoff point of view

George C. Hsiao, Richard J. Weinacht

Abstract

We reduce an exterior initial boundary value problem for the wave equation in three space dimensions to an initial boundary value problem on a bounded computational domain bounded by an artificial boundary as well as the original boundary. From a Kirchhoff representation formula for the solution of wave equation in an exterior domain, we derive on the artificial boundary (exact) transparent boundary conditions that are nonlocal in space and time. These lead to local approximate transparent boundary conditions of the first and second orders. It is shown that these approximate transparent conditions are satisfied exactly for a related spherically symmetric problem. Copyright © 2012 John Wiley & Sons, Ltd.

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Key concepts: Mathematics, Boundary value problem, Bounded function, Mathematical analysis, Boundary (topology), Domain (mathematical analysis), Mixed boundary condition, Wave equation