NDLI: Stabilized FEMBEM Coupling for Helmholtz Transmission Problems

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Hiptmair, R. Meury, P.
Copyright Year	2006
Abstract	We consider timeharmonic acoustic scattering at a nonsmooth penetrable object and coupled boundary element finite element schemes for its numerical simulation. Straightforward coupling approaches are haunted by instabilities at wave numbers related to interior resonances, the socalled spurious resonances. A remedy is offered by adopting the idea underlying the widely used combined field integral equations. We apply it in the form of modified trace operators. These will also feature regularizing operators to offset the lack of compactness of the doublelayer potential integral operators on nonsmooth surfaces. Caldern projectors can be defined based on the modified trace operators. Thus, Costabels approach to the symmetric coupling of domain variational formulations and boundary integral equations carries over. The modified traces guarantee uniqueness of solutions of the coupled problem, whereas regularization ensures coercivity. From this we immediately concludeasymptotic quasioptimality of a combined finite element and boundary element Galerkin discretization for all frequencies.
Starting Page	2107
Ending Page	2130
Page Count	24
File Format	PDF
ISSN	00361429
DOI	10.1137/050639958
e-ISSN	10957170
Issue Number	5
Volume Number	44
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-11-03
Access Restriction	Subscribed
Subject Keyword	Stability and convergence of numerical methods boundary integral equations acoustic scattering combined field integral equations Galerkin discretization Integral equations Boundary element methods boundary elements Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods finite elements
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Numerical Analysis Computational Mathematics

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