Transparent boundary conditions for the wave equation in the square domain

The paper is devoted to constructing of Transparent Boundary Conditions (TBC) for the wave equation in the square domain. The idea of the method consists in reducing the problem in a domain with non-smooth boundary to the problem with infinitely smooth boundary. It uses an auxiliary region, partly overlapping with the original area – “domain of interest”. In the auxiliary field calculations are carried out in the space of Fourier coefficients, which significantly reduces the computational cost of the auxiliary problem. Sofronov’s Transparent Boundary Conditions are put on the outside, circular, boundary of the auxiliary domain. Results of test calculations to demonstrate the accuracy and stability of the proposed method are presented. It is shown that solutions of the initial-boundary problem with TBC tends to the corresponding solutions of the Cauchy problem as square of the grid step size as it tends to zero without increasing of the computational domain.