ABSTRACT

This article reviews some of the recent developments in numerical methods for simulations of transient acoustic and elastic wave propagation in multidimensional inhomogeneous media. Starting from the more conventional finite difference methods, it focuses on the artificial absorbing boundary conditions proposed to truncate the computation domain and on the order of accuracy in the numerical schemes. Since Berenger proposed the so-called perfectly matched layer (PML) to absorb electromagnetic waves, the PML has been developed both for scalar acoustic and vector elastic waves. This material absorbing boundary condition provides much more effective absorption of outgoing waves at the computational edge, and is becoming increasingly important in finite-difference time-domain (FDTD) methods. More recently, the PML material has made possible the highly accurate Fourier pseudospectral time-domain (PSTD) method possible for nonperiodic problems. As a result, large-scale problems of unprecedented size can now be solved with the available supercomputers. Future directions of research in the nonuniform PSTD algorithm are also discussed.