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2010

Analysis of a finite PML approximation to the three dimensional elastic wave scattering problem

8 years 9 months ago
Analysis of a finite PML approximation to the three dimensional elastic wave scattering problem
We consider the application of a perfectly matched layer (PML) technique to approximate solutions to the elastic wave scattering problem in the frequency domain. The PML is viewed as a complex coordinate shift in spherical coordinates which leads to a variable complex coefficient equation for the displacement vector posed on an infinite domain (the complement of the scatterer). The rapid decay of the PML solution suggests truncation to a bounded domain with a convenient outer boundary condition and subsequent finite element approximation (for the truncated problem). We prove existence and uniqueness of the solutions to the infinite domain and truncated domain PML equations (provided that the truncated domain is sufficiently large). We also show exponential convergence of the solution of the truncated PML problem to the solution of the original scattering problem in the region of interest. We then analyze a Galerkin numerical approximation to the truncated PML problem and prove that it ...
James H. Bramble, Joseph E. Pasciak, Dimitar Trene
Added 20 May 2011
Updated 20 May 2011
Type Journal
Year 2010
Where MOC
Authors James H. Bramble, Joseph E. Pasciak, Dimitar Trenev
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