- Autor
- Kimeswenger, Arno
- Steinbach, Olaf
- Unger, Gerhard
- TitelCoupled finite and boundary element methods for fluid-solid interaction eigenvalue problems
- Datei
- DOI10.1137/13093755x
- Persistent Identifier
- Erschienen inSIAM Journal on Numerical Analysis
- Band52
- Erscheinungsjahr2014
- Heft5
- Seiten2400-2414
- LicenceCC BY
- ISSN1095-7170
- Download Statistik186
- Peer ReviewJa
- AbstractWe analyze the approximation of a vibro-acoustic eigenvalue problem for an elas- tic body which is submerged in a compressible inviscid fluid in ℝ³. As model the time-harmonic elastodynamic and the Helmholtz equation are used and are coupled in a strong sense via the standard transmission conditions on the interface between the solid and the fluid. Our approach is based on a coupling of the field equations for the solid with boundary integral equations for the fluid. The coupled formulation of the eigenvalue problem leads to a nonlinear eigenvalue problem with respect to the eigenvalue parameter since the frequency occurs nonlinearly in the used bound- ary integral operators for the Helmholtz equation. The nonlinear eigenvalue problem and its Galerkin discretization are analyzed within the framework of eigenvalue prob- lems for Fredholm operator-valued functions where convergence is shown and error estimates are given. For the numerical solution of the discretized nonlinear matrix eigenvalue problem the contour integral method is a reliable method which is demon- strated by some numerical examples.
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