Model Order Reduction by Proper Orthogonal Decomposition

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.

arXiv admin note: substantial text overlap with arXiv:1701.05054

References in corpus (1)

• A-posteriori snapshot location for POD in optimal control of linear parabolic equations

Cited by in corpus (3)

• Memory embedded non-intrusive reduced order modeling of non-ergodic flows
• Model Order Reduction in Neuroscience
• Reduced order modelling of nonlinear cross-diffusion systems