Fast evaluation of two-dimensional transient wave fields

This paper presents a novel scheme to efficiently evaluate transient linear wave fields that are generated by two-dimensional (2D) source configuratio ns. The scheme, termed the plane wave time domain algorithm (PWTD), realize s a diagonal translation operator for 2D transient wave fields through thei r representation in terms of Hilbert transformed plane wave expansions. Num erical results are presented that validate the algorithm and demonstrate it s convergence properties. The proposed PWTD algorithm can be coupled to cla ssical 2D time domain integral equation solvers in a two-level and multilev el setting. It is shown that analysis of a 2D surface scattering phenomenon . in which sources are represented in terms of N-s spatial and N-t temporal samples, based on two-level and multilevel PWTD augmented integral equatio n solvers, requires O(N-s(1.51) N-t log N-t) and O(N-s N-t log N-s log N-t) computational resources, respectively (as opposed to O((NsNt2)-N-2) for a classical solver). Therefore, these PWTD schemes render feasible the rapid integral equation based analysis of 2D transient scattering phenomena invol ving large surfaces. (C) 2000 Academic Press.