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Title: Schemes and estimates for the long-time numerical solution of Maxwell’s equations for Lorentz metamaterials
Authors: Shaw, S
Li, J
Keywords: Maxwell's equations;Lorentz model;Metamaterial;Galerkin and mixed nite element method;Long-time integration;Time stepping
Issue Date: 2015
Publisher: Wuhan University and Institute for Scientific Computing and Information
Citation: International Journal of Numerical Analysis and Modeling, 12(2): 343 - 365, (2015)
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.
ISSN: 1705-5105
Appears in Collections:Dept of Mathematics Research Papers

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