Time Domain Solution of Maxwell’s Equations Using Faber Polynomials

Approximations based on Faber polynomials for the numerical solution of Maxwell's equations in the time domain are investigated. The exponential convergence properties of the Faber polynomials allow to construct highly accurate time propagation schemes with time steps exceeding the Courant-Friedrichs-Lewy stability limit by several orders of magnitude. Additional material models, such as Drude and Lorentz models, and, moreover, perfectly matched layers to truncate the computational domain are included using additional differential equations. A novel approach to approximate the spectrum of the system matrix is introduced to enable the Faber polynomial expansions for arbitrary device models.