Abstract
We investigate the long time behavior of two unsplit PML methods for the absorption of electromagnetic waves. Computations indicate that both methods suffer from a temporal instability after the fields reach a quiescent state. The analysis reveals that the source of the instability is the undifferentiated terms of the PML equations and that it is associated with a degeneracy of the quiescent systems of equations. This highlights why the instability occurs in special cases only and suggests a remedy to stabilize the PML by removing the degeneracy. Computational results confirm the stability of the modified equations and is used to address the efficacy of the modified schemes for absorbing waves.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Engquist, B., and Majda, A. (1977). Absorbing boundary conditions for the numerical solution of waves. Math. Comp. 31, 629–651.
Bayliss, A., and Turkel, E. (1980). Radiation boundary conditions for wave-like equations. Comm. Pure Appl. Math. 23, 707–725.
Givoli, D. (1991). Nonreflecting boundary conditions. J. Comput. Phys. 94, 1–29.
Grote, M., and Keller, J. (1996). Nonreflecting boundary conditions for time dependent scattering. J. Comput. Phys. 127, 52–81.
Tsynkov, S. V. (1998). Numerical solution of problems on unbounded domains. Appl. Numer. Math. 27, 465–532.
Hagstrom, T. (1999). Radiation boundary conditions for the numerical simulation of waves. Acta Numerica 8, 47–106.
Berenger, J. P. (1994). A perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys. 114, 185–200.
Berenger, J. P. (1996). Three-dimensional perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys. 127, 363–379.
Hu, F. Q. (1996). On absorbing boundary conditions for linearized Euler equations by a perfectly matched layer. J. Comput. Phys. 129, 201–219.
Chew, W. C., and Liu, Q. H. (1996). Perfectly matched layers for elastodynamics: A new absorbing boundary condition. J. Comput. Acoust. 4, 341–349.
Abarbanel, S., and Gottlieb, D. (1997). A mathematical analysis of the PML method. J. Comput. Phys. 134, 357–363.
Hesthaven, J. S. (1998). On the analysis and construction of perfectly matched layers for the linearized Euler equations. J. Comput. Phys. 142, 129–147.
Gedney, S. D. (1996). Anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices. IEEE Trans. Antennas Propagat. 44, 1630–1639.
Ziolkowski, R. W. (1997). Time-derivative Lorenz material model based absorbing boundary conditions. IEEE Trans. Antennas Propagat. 45, 1530–1535.
Abarbanel, S., and Gottlieb, D. (1998). On the construction and analysis of absorbing layers in CEM. Appl. Numer. Math. 27, 331.
Hardin, J. C., Ristorcelli, J. R., and Tam, C. K. W. (eds.) (1995). ICASE/LaRC Workshop on Benchmark Problems in Computational Aeroacoustics (CAA), NASA CP 3300, NASA Langley Research Center, Virginia.
Abarbanel, S., Gottlieb, D., and Hesthaven, J. S. (1999). Well-posed perfectly matched layers for advective acoustics. J. Comput. Phys. 154, 266–283.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Abarbanel, S., Gottlieb, D. & Hesthaven, J.S. Long Time Behavior of the Perfectly Matched Layer Equations in Computational Electromagnetics. Journal of Scientific Computing 17, 405–422 (2002). https://doi.org/10.1023/A:1015141823608
Issue Date:
DOI: https://doi.org/10.1023/A:1015141823608