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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Analysis of a finite element PML approximation for the three dimensional time-harmonic Maxwell problem


Authors: James H. Bramble and Joseph E. Pasciak
Journal: Math. Comp. 77 (2008), 1-10
MSC (2000): Primary 78M10, 65F10, 65N30
Published electronically: September 18, 2007
MathSciNet review: 2353940
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Abstract: In our paper [Math. Comp. 76, 2007, 597-614] we considered the acoustic and electromagnetic scattering problems in three spatial dimensions. In particular, we studied a perfectly matched layer (PML) approximation to an electromagnetic scattering problem. We demonstrated both the solvability of the continuous PML approximations and the exponential convergence of the resulting solution to the solution of the original acoustic or electromagnetic problem as the layer increased.

In this paper, we consider finite element approximation of the truncated PML electromagnetic scattering problem. Specifically, we consider approximations which result from the use of Nédélec (edge) finite elements. We show that the resulting finite element problem is stable and gives rise to quasi-optimal convergence when the mesh size is sufficiently small.


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Additional Information

James H. Bramble
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368.
Email: bramble@math.tamu.edu

Joseph E. Pasciak
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368.
Email: pasciak@math.tamu.edu

DOI: http://dx.doi.org/10.1090/S0025-5718-07-02037-6
PII: S 0025-5718(07)02037-6
Keywords: Maxwell's equations, Helmholtz equation, time-harmonic acoustic and electromagnetic scattering, div-curl systems, PML layer
Received by editor(s): September 11, 2006
Received by editor(s) in revised form: January 24, 2007
Published electronically: September 18, 2007
Additional Notes: This work was supported in part by the National Science Foundation through grant No. 0311902.
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.