Ridgelet-Based Implementation of Multiresolution Time Domain

The theory of ridgelet-based analysis of time-domain wave propagation and scattering is developed. Some of the advantages of using ridgelets as compared to conventional wavelets are as follows. First, ridgelets often require less expansion coefficients (unknowns) to describe the fields. Second, radiation boundary conditions can be applied naturally, and therefore one need not employ a perfectly matched layer or other absorbing boundary. Moreover, plane-wave propagation (in arbitrary directions) is easily represented. In this paper, biorthogonal ridgelets are applied as basis functions to simulate time domain electromagnetic wave propagation and several numerical examples are presented.