Second-order absorbing boundary conditions for the wave equation. A solution for the corner problem

The treatment of domains with corners in the problem of absorbing boundary conditions for the wave equation is very important from a practical point of view. A technical difficulty appears as soon as conditions of order greater than or equal to 2 are considered. A solution is proposed for the two-dimensional case when second-order conditions are used. This solution consists of prescribing an adequate corner condition. The problem thus obtained is analyzed theoretically and the condition is proved to be optimal. The results obtained here are illustrated by numerical simulations. Some extensions to higher-space dimensions and higher-order conditions are proposed.