Computational complexity and implementation of two-level plane wave time domain algorithm for scalar wave equation

Integral equation based techniques, such as the method of moments (MOM), have been widely used to analyze time harmonic surface scattering phenomena. Unfortunately, time domain counterparts of the MOM, often referred to as marching-on-in-time (MOT) schemes, have historically received scant attention. Classical MOT schemes (i) have long been conceived as intrinsically unstable, and (ii) suffer from a high computational complexity. It is well-known that the computational complexity of the MoM can be reduced by the fast multipole method. A similar time domain algorithm, namely the plane wave time domain (PWTD) algorithm, has been introduced. The PWTD algorithm is designed to be used in tandem with the conventional MOT scheme in either a two-level or a multilevel setting. This paper describes the practical implementation of the two-level scheme and demonstrates the reduction in computational complexity achieved by using the PWTD algorithm. Although the PWTD scheme is applicable to a variety of integral equations arising from the analysis of wave phenomena, this paper illustrates its application in the context of scalar wave scattering from surfaces on which Neumann boundary conditions are enforced-a problem of interest in many disciplines.