Antti Ojalammi: Condensed Pole Interpolation for quadratic eigenvalue problems

Abstract: We consider solving eigenvalues of QEP's on a spectral region of interest when the matrices have a common block structure. This happens in particular when using FEM and decomposing the underlying domain into two (or more) subdomains. The proposed method for this problem setting, the Condensed Pole Interpolation (CPI) method, is based on interpolation of a resolvent function related to a subdomain after some of its singularities have been removed by a spectral projection. Existing theory concerning the symmetric positive definite case is reviewed, and aspects of the numerical QEP implementation are discussed with a focus on different interpolation strategies.