Restarting projection methods for rational eigenproblems arising in fluid‐solid vibrations

Abstract

For nonlinear eigenvalue problems T(λ)x = 0 satisfying a minmax characterization of its eigenvalues iterative projection methods combined with safeguarded iteration are suitable for computing all eigenvalues in a given interval. Such methods hit their limitations if a large number of eigenvalues is required. In this paper we discuss restart procedures which are able to cope with this problem, and we evaluate them for a rational eigenvalue problem governing vibrations of a fluid‐solid structure.

Key words:

• nonlinear eigenvalue problem
• iterative projection method
• Arnoldi method
• minmax characterization
• restart
• fluid‐solid structure