A pseudospectral Chebychev method for the 2D wave equation with domain stretching and absorbing boundary conditions
A new numerical method for simulation of wave propagation in artificially bounded domains is presented. The approach consists in solving the 2D acoustic wave equation \(u_{tt}= c^2(u_{xx}+ u_{yy})\) by the pseudospectral Chebychev method at all points away from the boundary of \(D= \{(x, y): 0< x< 1, 0< y< 1\}\) in conjunction with the first-order one-way wave equation \(u_t= cu_x\) at the \(x= 0\) boundary. The spatial derivatives in both above equations are approximated using the same Chebychev expansions. Integration in time is performed by a Crank-Nicolson method at the boundary and a standard discretization in time at the interior points. The numerical results presented show the superior performance of the introduced method and its efficiency comparable to that of the Fourier method.
scientific article; zbMATH DE number 881890