Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/67444
Title: Global energy-tracking identities and global energy-tracking splitting FDTD schemes for the Drude Models of Maxwell's equations in three-dimensional metamaterials
Authors: Li, WS
Liang, D
Lin, YP 
Keywords: Drude models of Maxwell's equations in metamaterials
GET-S-FDTD
Optimal error estimates
Second order in time and space
Superconvergence
Three dimensions
Global energy-tracking identities
Unconditional stability
Issue Date: May-2017
Publisher: John Wiley & Sons
Source: Numerical methods for partial differential equations, May 2017, v. 33, no. 3, p. 763-785 How to cite?
Journal: Numerical methods for partial differential equations 
Abstract: In this article, we study the Drude models of Maxwell's equations in three-dimensional metamaterials. We derive new global energy-tracking identities for the three dimensional electromagnetic problems in the Drude metamaterials, which describe the invariance of global electromagnetic energy in variation forms. We propose the time second-order global energy-tracking splitting FDTD schemes for the Drude model in three dimensions. The significant feature is that the developed schemes are global energy-preserving, unconditionally stable, second-order accurate both in time and space, and computationally efficient. We rigorously prove that the new schemes satisfy these energy-tracking identities in the discrete form and the discrete variation form and are unconditionally stable. We prove that the schemes in metamaterials are second order both in time and space. The superconvergence of the schemes in the discrete H-1 norm is further obtained to be second order both in time and space. Their approximations of divergence-free are also analyzed to have second-order accuracy both in time and space. Numerical experiments confirm our theoretical analysis results.
URI: http://hdl.handle.net/10397/67444
ISSN: 0749-159X
DOI: 10.1002/num.22122
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