Energy-based model order reduction for linear stochastic Galerkin systems of second order

2023/07/10 by Roland Pulch, Pulch, Roland · 1 citation
Decision Sciences · Mathematics · Physics and Astronomy · #37H05 #65L05 #93D30 #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods for differential equations #Probabilistic and Robust Engineering Design

paper · pdf · doi:10.48550/arxiv.2307.04519

openalex publication_date 2023/07/10 · openalex created_date 2023/07/12 · openalex updated_date 2026/07/28

Abstract

We consider a second-order linear system of ordinary differential equations (ODEs) including random variables. A stochastic Galerkin method yields a larger deterministic linear system of ODEs. We apply a model order reduction (MOR) of this high-dimensional linear dynamical system, where its internal energy represents a quadratic quantity of interest. We investigate the properties of this MOR with respect to stability, passivity, and energy dissipation. Numerical results are shown for a system modelling a mass-spring-damper configuration.

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