Approximation of the Wave and Electromagnetic Diffusion Equations by Spectral Method

The aim of this paper is to describe a variational spectral solver of the three-dimensional operator (I + curl curl) which we often encounter when dealing with the Maxwell problem. We carry out a mathematical study proving the optimality of such an algorithm and we make an analysis of its complexity showing its efficiency. Finally, some applications to time-dependent partial differential equations obtained from the Maxwell model are presented.