Absorbing Boundary Conditions for Difference Approximations to the Multi-Dimensional Wave Equation

We consider the problem of constructing absorbing boundary conditions for the multi-dimensional wave equation. Here we work directly with a difference approximation to the equation, rather than first finding analytical boundary conditions and then discretizing the analytical conditions. This approach yields some simple and effective discrete conditions. These discrete conditions are consistent with analytical conditions that are perfectly absorbing at certain nonzero angles of incidence. This fact leads to a simple and general canonical form for analytical absorbing boundary conditions. The use of this form has theoretical and practical advantages.