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  • 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
  • ZugriffsrechteCC-BY
  • Download Statistik146
  • 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.