Variationally consistent Hamiltonian model reduction

2024/04/03 by Gruber, Anthony, Tezaur, Irina · 4 citations
#65P10 #70H05 #74H15 #Dynamical Systems (math.DS) #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2404.15315

Abstract

Though ubiquitous as first-principles models for conservative phenomena, Hamiltonian systems present numerous challenges for model reduction even in relatively simple, linear cases. Here, we present a method for the projection-based model reduction of canonical Hamiltonian systems that is variationally consistent for any choice of linear reduced basis: Hamiltonian models project to Hamiltonian models. Applicable in both intrusive and nonintrusive settings, the proposed method is energy-conserving and symplectic, with error provably decomposable into a data projection term and a term measuring deviation from canonical form. Examples from linear elasticity with realistic material parameters are used to demonstrate the advantages of a variationally consistent approach, highlighting the steady convergence exhibited by consistent models where previous methods reliant on inconsistent techniques or specially designed bases exhibit unacceptably large errors.

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