Reduced basis approximation of parametric eigenvalue problems in presence of clusters and intersections

TL;DR

This paper explores reduced basis methods for parametric eigenvalue problems, focusing on challenges posed by eigenvalue intersections and clusters, and examines how existing techniques extend to higher frequencies.

Contribution

It analyzes the extension of reduced basis approaches to complex eigenvalue scenarios involving intersections and clusters, addressing singularities in parametric eigenvalue problems.

Findings

Reduced basis methods face challenges with eigenvalue clusters.

Singularities complicate straightforward generalizations.

Extensions to higher frequencies require specialized strategies.

Abstract

In this paper we discuss reduced order models for the approximation of parametric eigenvalue problems. In particular, we are interested in the presence of intersections or clusters of eigenvalues. The singularities originating by these phenomena make it hard a straightforward generalization of well known strategies normally used for standards PDEs. We investigate how the known results extend (or not) to higher order frequencies.