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

Bramble, James; Pasciak, Joseph

doi:10.1090/S0025-5718-07-02037-6

Analysis of a finite element PML approximation for the three dimensional time-harmonic Maxwell problem
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by James H. Bramble and Joseph E. Pasciak PDF

Math. Comp. 77 (2008), 1-10 Request permission

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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