# Structured eigenvalue methods for the computation of corner singularities in anisotropic elastic structures

## Prof. Dr. Volker Mehrmann

Jan. 22, 2002, 3:30 p.m. T 811

We study the computation of 3D vertex singularities of anisotropic elastic structures. The singularities are described by eigenpairs of a corresponding operator pencil on a subdomain of the sphere. The solution approach is to introduce a modified quadratic eigenvalue problem which consists of two self-adjoint, positive definite sesquilinear forms and a skew-Hermitian form. This eigenvalue problem is discretized by the finite element method. The resulting quadratic matrix eigenvalue problem is then solved with the Skew Hamiltonian Implicitly Restarted Arnoldi method (SHIRA) which is specifically adapted to the structure of this problem. Some numerical examples are given that show the performance of this approach.

(Joint work with Thomas Apel and David Watkins).