Mixed Finite-Element Time-Domain Method for Transient Maxwell Equations in Doubly Dispersive Media

A Stable and Efficient Direct Time Integration of the Vector Wave Equation in the Finite-Element Time-Domain Method for Dispersive Media

“…Taking the Laplace transform of it and converting it into the -domain using a bilinear transformation given by (9) we obtain where (10) and . To implement in the time domain in an efficient manner, an implementation approach named the direct transport II is borrowed from digital signal processing community [9], which involves (11) where are auxiliary variables. The variable at is given by (12) It should be noted that is an auxiliary variable utilized to simplify explanation of the algorithm.…”

“…The variable at is given by (12) It should be noted that is an auxiliary variable utilized to simplify explanation of the algorithm. One can substitute it in (11) and eliminate it, if it is not desired. To apply the above-mentioned procedure to (4), we first map (8) to the -domain, which results in…”

“…where the update equations for the auxiliary variables can be cast as (11). Having substituted (23) in (18a), we obtain (24) where and .…”

“…• In the case of the mixed formulation [10], it is easy to include the medium dispersion and both conditionally and unconditionally stable (US) formulations have been introduced [11], [12]. However, in order to avoid using an auxiliary (complementary) mesh, a combination of 1-form and 2-form discretizations has to be utilized.…”

A Study on Unconditionally Stable FDTD Methods for the Modeling of Metamaterials

“…A variant of such material responses that is also of interest can be provided by zero-index media, where permittivity and permeability are simultaneously (close to) zero at a critical frequency [6]- [8].…”