Schemes and Estimates for the Long-Time Numerical Solution of Maxwell's Equations for Lorentz Metamaterials
Year: 2015
International Journal of Numerical Analysis and Modeling, Vol. 12 (2015), Iss. 2 : pp. 343–365
Abstract
We consider time domain formulations of Maxwell's equations for the Lorentz model for metamaterials. The field equations are considered in two different forms which have either six or four unknown vector fields. In each case we use arguments tuned to the physical laws to derive data-stability estimates which do not require Gronwall's inequality. The resulting estimates are, in this sense, sharp. We also give fully discrete formulations for each case and extend the sharp data-stability to these. Since the physical problem is linear it follows (and we show this with examples) that this stability property is also reflected in the constants appearing in the a priori error bounds. By removing the exponential growth in time from these estimates we conclude that these schemes can be used with confidence for the long-time numerical simulation of Lorentz metamaterials.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2015-IJNAM-493
International Journal of Numerical Analysis and Modeling, Vol. 12 (2015), Iss. 2 : pp. 343–365
Published online: 2015-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Maxwell's equations Lorentz model metamaterial Galerkin and mixed finite element method long-time integration time stepping.