ANALYSIS OF THE PERFECTLY MATCHED LAYER PROBLEMS FOR TIME DEPENDENT MAXWELL EQUATIONS

Lung-An Ying (P. R. China)

Received January 6, 2008

References:

[1] S. Abarbanel and D. Gottlieb, A mathematical analysis of the PML method, J. Comput. Phys. 134 (1997), 357-363. [2] D. Appelo, T. Hagstrom and G. Kreiss, Perfectly matched layers for hyperbolic systems: general formulation, well-posedness, and stability, SIAM J. Appl. Math. 67(1) (2006), 1-23. [3] G. Bao and H. Wu, Convergence analysis of the perfectly matched layer problems for time-harmonic Maxwell’s equations, SIAM J. Numer. Anal. 43(5) (2005), 2121-2143. [4] E. Bécache and P. Joly, On the analysis of Berenger’s perfectly matched layers for Maxwell’s equations, M2AN 36(1) (2002), 87-119. [5] J. P. Berenger, A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys. 114 (1994), 185-200. [6] J. P. Berenger, Perfectly matched layer for the FDTD solution of wave-structure interaction problems, IEEE Trans. Antennas Propagat. 44 (1996), 110-117. [7] J. P. Berenger, Three dimensional perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys. 127 (1996), 363-379. [8] J. P. Berenger, Numerical reflection from FDTD-PMLs: a comparison of the split PML with the unsplit and CFS PMLs, IEEE Trans. Antennas Propagat. 50(3) (2002), 258-265. [9] J. H. Bramble and J. E. Pasciak, Analysis of a finite PML approximation for the three dimensional time-harmonic Maxwell and acoustic scattering problems, Math. Comp., to appear. [10] Z. Chen and X. Liu, An adaptive perfectly matched layers technique for time-harmonic scattering problems, SIAM J. Numer. Anal., to appear. [11] Z. Chen and H. Wu, An adaptive finite element method with perfectly matched absorbing layers for the wave scattering by periodic structures, SIAM J. Numer. Anal. 41 (2003), 799-826. [12] W. Chew and W. Weedon, A 3d perfectly matched medium for modified Maxwell's equations with stretched coordinates, Microwave Opt. Techno. Lett. 13(7) (1994), 599-604. [13] F. Collino and P. B. Monk, The perfectly matched layer in curvilinear coordinates, SIAM J. Sci. Comput. 19 (1998), 2061-2090. [14] N. Fang and L.-A. Ying, Stability analysis of Berenger PML method, preprint. [15] T. Hagstron and S. Lau, Radiation boundary conditions for Maxwell’s equation: a review of accurate time-domain formulations, J. Comp. Math. 25(3) (2007), 305-336. [16] P. Petropoulos, Reflectionless sponge layers as absorbing boundary conditions for the numerical solution of Maxwell’s equations in rectangular, cylindrical and spherical coordinates, SIAM J. Appl. Math. 60 (2000), 1037-1058. [17] L.-A. Ying, Numerical Methods for Exterior Problems, World Scientific, Singapore, 2006.

Keywords and phrases: Maxwell’s equation, perfectly matched layer, initial-boundary value problem, well posed.