Time-Domain Finite Element Methods for Metamaterials

  • Jichun Li
  • Yunqing Huang
Chapter
Part of the Springer Series in Computational Mathematics book series (SSCM, volume 43)

Abstract

In this chapter, we present several fully discrete mixed finite element methods for solving Maxwell’s equations in metamaterials described by the Drude model and the Lorentz model. In Sects. 3.1 and 3.2, we respectively discuss the constructions of divergence and curl conforming finite elements, and the corresponding interpolation error estimates. These two sections are quite important, since we will use both the divergence and curl conforming finite elements for solving Maxwell’s equations in the rest of the book. The material for Sects. 3.1 and 3.2 is quite classic, and we mainly follow the book by Monk (Finite element methods for Maxwell’s equations. Oxford Science Publications, New York, 2003). After introducing the basic theory of divergence and curl conforming finite elements, we focus our discussion on developing some finite element methods for solving the time-dependent Maxwell’s equations when metamaterials are involved. More specifically, in Sect. 3.3, we discuss the well posedness of the Drude model. Then in Sects. 3.4 and 3.5, we present detailed stability and error analysis for the Crank-Nicolson scheme and the leap-frog scheme, respectively. Finally, we extend our discussion on the well posedness, scheme development and analysis to the Lorentz model and the Drude-Lorentz model in Sects. 3.6 and 3.7, respectively.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jichun Li
    • 1
  • Yunqing Huang
    • 2
  1. 1.Mathematical SciencesUniversity of Nevada Las VegasLas VegasUSA
  2. 2.Xiangtan UniversityXiangtanChina, People’s Republic

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