Numerical absorbing boundary conditions for the wave equation

Higdon, Robert L.

doi:10.1090/S0025-5718-1987-0890254-1

Numerical absorbing boundary conditions for the wave equation
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by Robert L. Higdon PDF

Math. Comp. 49 (1987), 65-90 Request permission

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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