A new scheme for the FDTD discretization of the wave equation has been
proposed. This scheme offers more control than the Yee scheme with additional
tunable parameters giving the possibility to damp high frequencies, allowing a
reduction of numerical noise as well as the numerical Cerenkov effect. It also
provides an access to multiscale electromagnetic simulation using the mesh
refinement technique when coupled with the use of the `Transmitted-wave'
boundary condition algorithm. This scheme can be seen as a generalization of
the standard Yee scheme together with various boundary conditions (second
order Engquist and Majda outgoing-wave, Berenger PML, `Transmitted-Wave') to
which it reduces for specific values of the additional parameters. This
generalization, if it gives a computationaly more expensive algorithm (small
compared to the enhancement of the capabilities), simplifies the task of the
programmer because it offers a unique algorithm for the computation of fields
inside and on the boundaries of the grids, the differentiation being
controlled by an array of parameters.