Numerical absorbing boundary conditions for the wave equation.

*(English)*Zbl 0654.65083Summary: 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.

##### MSC:

65N99 | Numerical methods for partial differential equations, boundary value problems |

35L05 | Wave equation |