A diagonal translation operator for the fast evaluation of two-dimensional transient wave fields

Accurate and efficient techniques for analyzing linear transient wave phenomena are of significant interest to many disciplines. Although integral equation based methods for analyzing two-dimensional (2D) transient phenomena have been studied extensively in the past they all suffer from a high computational complexity, which limits their application to practical problems. To accelerate the integral equation based analysis of three dimensional transient scattering phenomena, our group developed the three-dimensional plane wave time domain (PWTD) algorithm (Ergin et al., 1998). In this paper, we extend our previous work from three to two dimensions and propose a novel 2D PWTD algorithm that relies on a diagonal translation operator for the efficient evaluation of 2D wave fields. When used in conjunction with a marching-on-in-time (MOT) scheme, this algorithm drastically accelerates the integral equation based analysis of 2D transient scattering phenomena.