Stability and superconvergence analysis of the FDTD scheme for the 2D Maxwell equations in a lossy medium

被引：0
作者：
LiPing Gao
Bo Zhang
机构：
[1] China University of Petroleum,Department of Computational and Applied Mathematics, School of Sciences
[2] Chinese Academy of Sciences,LSEC and Institute of Applied Mathematics, Academy of Mathematics and Systems Science
来源：
Science China Mathematics | 2011年 / 54卷
关键词：
Maxwell equations; finite-difference time-domain method; stability; superconvergence; perfectly electric conducting boundary conditions; energy identities; 65M06; 65M12; 65Z05;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper is concerned with the stability and superconvergence analysis of the famous finite-difference time-domain (FDTD) scheme for the 2D Maxwell equations in a lossy medium with a perfectly electric conducting (PEC) boundary condition, employing the energy method. To this end, we first establish some new energy identities for the 2D Maxwell equations in a lossy medium with a PEC boundary condition. Then by making use of these energy identities, it is proved that the FDTD scheme and its time difference scheme are stable in the discrete L2 and H1 norms when the CFL condition is satisfied. It is shown further that the solution to both the FDTD scheme and its time difference scheme is second-order convergent in both space and time in the discrete L2 and H1 norms under a slightly stricter condition than the CFL condition. This means that the solution to the FDTD scheme is superconvergent. Numerical results are also provided to confirm the theoretical analysis.
引用
收藏
页码：2693 / 2712
页数：19
相关论文
共 53 条
  • [1] Berenger J. P.(1994)A perfectly matched layer for the absorption of electromagnetic waves J Comput Phys 114 185-200
  • [2] Chen W.(2008)Energy-conserved splitting FDTD Schemes for Maxwell’s equations Numer Math 108 445-485
  • [3] Li X.(2010)Energy-conserved splitting finite difference time-domain methods for Maxwell’s equations in three dimensions SIAM J Numer Anal 108 445-485
  • [4] Liang D.(1994)A 3-D perfectly matched medium for the modified Maxwell equations with streched coordinates Micro Opt Tech Lett 7 257-260
  • [5] Chen W.(2003)Convergence analysis of a finite volume method for Maxwell’s equations in nonhomogeneous media SIAM J Numer Anal 41 37-63
  • [6] Li X.(1977)Absorbing boundary conditions for the numerical simulation of waves Math Comp 31 629-651
  • [7] Liang D.(2009)Stability analysis of FDTD to UPML for time dependent Maxwell equations Sci China Ser A 52 794-1811
  • [8] Chew W. C.(2007)The splitting finite difference time domain methods for Maxwell’s equations in two dimensions J Comput Appl Math 205 207-230
  • [9] Weedon W. H.(2008)Splitting finite difference methods on staggered grids for the three dimensional time dependent Maxwell equations Commun Comput Phys 4 405-432
  • [10] Chung E. T.(2010)Splitting multisymplectic integrators for Maxwell’s equations J Comput Phys 229 4259-4278
123456