We present a novel strategy for minimizing the numerical dispersion error in edge discretizations of the time-domain electric vector wave equation on square meshes based on the mimetic finite difference (MFD) method. We compare this strategy, called M-adaptation, to two other discretizations, also based on square meshes. One is the...
We present discrete energy decay results for the Yee scheme applied to Maxwell's equations in Debye and Lorentz dispersive media. These estimates provide stability conditions for the Yee scheme in the corresponding media. In particular, we show that the stability conditions are the same as those for the Yee scheme...
We study the stability properties of, and the phase error present in, a finite element scheme for Maxwell’s
equations coupled with a Debye or Lorentz polarization model. In one dimension we consider a second order
formulation for the electric field with an ordinary differential equation for the electric polarization added...