Model Order Reduction by Proper Orthogonal Decomposition
Numerical Analysis
2020-08-04 v2 Numerical Analysis
Abstract
We provide an introduction to POD-MOR with focus on (nonlinear) parametric PDEs and (nonlinear) time-dependent PDEs, and PDE constrained optimization with POD surrogate models as application. We cover the relation of POD and SVD, POD from the infinite-dimensional perspective, reduction of nonlinearities, certification with a priori and a posteriori error estimates, spatial and temporal adaptivity, input dependency of the POD surrogate model, POD basis update strategies in optimal control with surrogate models, and sketch related algorithmic frameworks. The perspective of the method is demonstrated with several numerical examples.
Cite
@article{arxiv.1906.05188,
title = {Model Order Reduction by Proper Orthogonal Decomposition},
author = {Carmen Gräßle and Michael Hinze and Stefan Volkwein},
journal= {arXiv preprint arXiv:1906.05188},
year = {2020}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1701.05054