Self-adapting absorbing boundary conditions for the wave equation

In this paper, we introduce a self-adapting absorbing boundary condition for the linear wave equation. The construction is based on a local computation of the incidence angle of the outgoing wave and on the use of the classical lowest order Engquist–Majda absorbing boundary condition. In order to obtain a good approximation of the incidence angle, we decompose adaptively the absorbing boundary into subsegments and apply locally the Fourier transformation. Numerical results illustrate the performance of the newly designed self-adapting absorbing boundary condition and show its robustness.

► We propose a self-adapting absorbing boundary condition for the linear wave equation. ► A technique to incorporate the second order Engquist–Majda absorbing boundary condition into the weak formulation is presented. ► The superiority of the proposed boundary condition over the first and second order Engquist–Majda ones is demonstrated for different angles of incidence and wave types.