Journal of Scientific Computing

, Volume 36, Issue 3, pp 351–390 | Cite as

A Legendre Pseudospectral Penalty Scheme for Solving Time-Domain Maxwell’s Equations

  • Chun-Hao Teng
  • Bang-Yan Lin
  • Hung-Chun Chang
  • Hei-Chen Hsu
  • Chien-Nan Lin
  • Ko-An Feng


In this paper we present a Legendre pseudospectral algorithm based on a tensor product formulation for solving the time-domain Maxwell equations. Our approach starts by conducting an analysis for finding well-posed boundary operators for the Maxwell equations. We then discuss equivalent characteristic boundary conditions for common physical boundary constraints. These theoretical results are then employed to construct a pseudospectral penalty scheme which is asymptotically stable at the semidiscrete level. Numerical computations based on the proposed scheme are also provided for different cases where exact solutions exist. By measuring the differences between the computed and exact solutions, we observe the expected convergence patterns of the scheme.


Spectral/pseudospectral penalty methods Multidomain formulation Maxwell’s equations 


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Chun-Hao Teng
    • 1
  • Bang-Yan Lin
    • 2
  • Hung-Chun Chang
    • 2
    • 3
    • 4
  • Hei-Chen Hsu
    • 5
  • Chien-Nan Lin
    • 1
  • Ko-An Feng
    • 1
  1. 1.Department of MathematicsNational Cheng Kung UniversityTainanTaiwan
  2. 2.Graduate Institute of Communication EngineeringNational Taiwan UniversityTaipeiTaiwan
  3. 3.Department of Electrical EngineeringNational Taiwan UniversityTaipeiTaiwan
  4. 4.Graduate Institute of Photonics and OptoelectronicsNational Taiwan UniversityTaipeiTaiwan
  5. 5.Institute of Atomic and Molecular ScienceAcademia SinicaTaipeiTaiwan

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