Dynamical model reduction method for solving parameter-dependent dynamical systems
Abstract
We propose a projection-based model order reduction method for the solution of parameter-dependent dynamical systems. The proposed method relies on the construction of time-dependent reduced spaces generated from evaluations of the solution of the full-order model at some selected parameters values. The approximation obtained by Galerkin projection is the solution of a reduced dynamical system with a modified flux which takes into account the time dependency of the reduced spaces. An a posteriori error estimate is derived and a greedy algorithm using this error estimate is proposed for the adaptive selection of parameters values. The resulting method can be interpreted as a dynamical low-rank approximation method with a subspace point of view and a uniform control of the error over the parameter set.
Cite
@article{arxiv.1604.05706,
title = {Dynamical model reduction method for solving parameter-dependent dynamical systems},
author = {Marie Billaud-Friess and Anthony Nouy},
journal= {arXiv preprint arXiv:1604.05706},
year = {2019}
}