Spectral-domain decomposition methods for the solution of acoustic and elastic wave equations

A new spectral-domain decomposition method is presented for acoustic and elastodynamic wave propagation in 2-D heterogeneous media. Starting from a variational formulation of the problem, two different approaches are proposed for the spatial discretization: a mixed Fourier-Legendre and a full Legendre collocation. The matching conditions at subdomain interfaces are carefully analyzed, and the stability and efficiency of time-advancing schemes are investigated. The numerical validation with some significant test cases illustrates the accuracy, flexibility, and robustness of our methods. These allow the treatment of complex geometries and heterogeneous media while retaining spectral accuracy.