Sparse wavelet approximations to transient space-time electromagnetic wave fields

Abstract

The purpose of this contribution is to introduce a method for constructing sparse, efficient, accurate and reliable representations of large-scale, discretely sampled transient space-time electromagnetic wave fields, through the use of sparse wavelet approximations. The sparse wavelet approximations are achieved by performing a three step computational process that involves a forward Fast Wavelet Transform (FWT) step, a wavelet coefficient truncation step, and an inverse FWT (IFWT) step. Numerical results that demonstrate the applicability and versatility of the approach are provided. Rigorous error analyses are also provided to demonstrate the accuracy of the method.