Naslov
New developments of the Discrete Empirical Interpolation Method

Autori
Drmač, Zlatko ; Gugercin, Serkan ; Peherstorfer, Benjamin ; Saibaba, Arwind

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, neobjavljeni rad, znanstveni

Skup
ILAS (International Linear Algebra Society) 2019

Mjesto i datum
Rio de Janeiro, Brazil, 08.07.2019. - 13.07.2019

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
POD, Galerkin projection, DEIM, clustering

Sažetak
In large scale modeling and simulations, the discrete empirical interpolation method (DEIM, as a discrete version of the Empirical Interpolation Method, EIM) is a powerful and versatile computational tool. When combined with the POD/Galerkin projection method in a model order reduction framework, it efficiently removes the bottleneck caused by the evaluation of the nonlinear term. Further, in the implicit POD scheme, it provides an efficient on-line approximation of the Jacobian, needed for the Newton iteration step. In essence, DEIM is an oblique interpolatory projection, which approximates the POD projection based on sparse information. In a concrete application, to preserve physical properties of the reduced model, the POD/Galerkin and the DEIM projection must be with respect to a particular weighted inner product. We present fine numerical details of the weighted DEIM, that can also be interpreted as a numerical implementation of the Generalized Empirical Interpolation Method and the more general Parametrized-Background Data-Weak approach. Further, we discuss how the concept of the DEIM projection can be interpreted as trajectories clustering method, and how to use the new point of view for further development. We emphasize the fine interplay between numerical linear algebra and pure matrix theory.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA