A pseudospectral Chebychev method for the 2D wave equation with domain stretching and absorbing boundary conditions

In this paper we develop a method for the simulation of wave propagation on artificially bounded domains. The acoustic wave equation is solved at all points away from the boundaries by a pseudospectral Chebychev method. Absorption at the boundaries is obtained by applying one-way wave equations at the boundaries, without the use of damping layers. The theoretical reflection coefficient for the method is compared to theoretical estimates of reflection coefficients for a Fourier model of the problem. These estimates are confirmed by numerical results. Modification of the method by a transformation of the grid to allow for better resolution at the center of the grid reduces the maximum eigenvalues of the differential operator. Consequently, for stability the maximum timestep is O(1/N) as compared to O(1/N²) for the standard Chebychev method. Therefore, the Chebychev method can be implemented with efficiency comparable to that of the Fourier method. Moreover, numerical results presented demonstrate the superior performance of the new method.