TY - JOUR
T1 - Convergence Analysis of Yee Schemes for Maxwell's Equations in Debye and Lorentz Dispersive Media
AU - Bokil , V. A.
AU - Gibson , N. L.
JO - International Journal of Numerical Analysis and Modeling
VL - 4
SP - 657
EP - 687
PY - 2014
DA - 2014/11
SN - 11
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/546.html
KW - Maxwell's equations, Debye, Lorentz dispersive materials, Yee, FDTD method, energy decay, convergence analysis.
AB - <p style="text-align: justify;">We present discrete energy decay results for the Yee scheme applied to Maxwell&#39;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 in a nondispersive dielectric. However, energy decay for the
Maxwell-Debye and Maxwell-Lorentz models indicate that the Yee schemes are dissipative. The
energy decay results are then used to prove the convergence of the Yee schemes for the dispersive
models. We also show that the Yee schemes preserve the Gauss divergence laws on its discrete
mesh. Numerical simulations are provided to illustrate the theoretical results.</p>