Absorbing boundary conditions for difference approximations to the multi- dimensional wave equation. (English) Zbl 0609.35052

Higdon, Robert L.

Math. Comput. 47, 437-459 (1986).

The author considers the problem of constructing absorbing boundary conditions for the multidimensional wave equation. He works 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.

Reviewer: N.Maria

MSC:

35L20	Initial-boundary value problems for second-order hyperbolic equations
35A35	Theoretical approximation in context of PDEs
65M99	Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65N99	Numerical methods for partial differential equations, boundary value problems

Keywords:

absorbing boundary conditions; multidimensional wave equation; difference approximation; discrete conditions