Krylov projection methods for linear Hamiltonian systems

TL;DR

This paper investigates Krylov projection methods for large sparse linear Hamiltonian systems, focusing on energy preservation and structure-preserving model reduction, with applications to Hamiltonian PDEs.

Contribution

It provides an analysis of geometric properties and energy preservation in Krylov methods, connecting them to structure-preserving model reduction techniques.

Findings

Krylov methods can preserve energy in Hamiltonian systems

The methods are effective for Hamiltonian PDEs

Connections to structure-preserving model reduction are established

Abstract

We study geometric properties of Krylov projection methods for large and sparse linear Hamiltonian systems. We consider in particular energy preservation. We discuss the connection to structure preserving model reduction. We illustrate the performance of the methods by applying them to Hamiltonian PDEs.