On the matching of eigensolutions to parametric partial differential equations

TL;DR

This paper introduces a new algorithm for tracking eigenvalues in parametric eigenvalue problems, supported by a POD reduced order model example, enhancing numerical approximation methods.

Contribution

The paper presents a novel algorithm for matching eigenvalues in parametric PDEs, improving numerical approximation techniques.

Findings

Effective eigenvalue tracking algorithm demonstrated

Application to POD reduced order model shown

Enhanced accuracy in parametric eigenvalue approximation

Abstract

In this paper a novel numerical approximation of parametric eigenvalue problems is presented. We motivate our study with the analysis of a POD reduced order model for a simple one dimensional example. In particular, we introduce a new algorithm capable to track the matching of eigenvalues when the parameters vary.