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Numerical absorbing boundary conditions for the wave equation. (English) Zbl 0654.65083
Summary: 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 ibid. 47, 437-459 (1986; Zbl 0609.35052). The theory is based on a representation of analytical absorbing boundary conditions. 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.

65N99 Numerical methods for partial differential equations, boundary value problems
35L05 Wave equation
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