Author(s)

H. Voss

Abstract

Solving a rational eigenvalue problem in fluid- structure interaction H. Voss Section of Mathematics, TU Hamburg-Harburg, D-21071- Hamburg, Germany Abstract In this paper we consider a rational eigenvalue problem governing the vibrations of a tube bundle immersed in an inviscid compressible fluid. Taking advantage of eigensolutions of appropriate sparse linear eigenproblems the large nonlinear eigenvalue problem is projected to a much smaller one which is solved by inverse iteration. 1 Introduction Vibrations of a tube bundle immersed in an inviscid compressible fluid are governed under some simplifying assumptions by an elliptic eigenvalue problem with non-local boundary conditions which can be transformed to a rational eigenvalue problem. Discretizing this problem by finite elements one obtains a rational matrix eigenvalue problem T(X)x:=-Ax+XBx+cjx = 0 where the matrices A, B and Cj are symmetric and positive (semi-) definite, and they are typically large and sparse. For linear sparse eigenvalue problems one gets approximations to eigenvalues and eigenvectors by projection methods where a sequence of low dimensional spaces Vk is constructed by the Lanczos process or the Jacobi- Davidson method, e.g., and taking advantage of shift-and-invert or rational

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