Naslov
New contributions to the theory and practice of the Discrete Empirical Interpolation Method

Autori
Drmač, Zlatko ; Ipsen, Ilze ; Gugercin, Serkan ; Saibaba, Arwind

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

Skup
Householder Symposium XX

Mjesto i datum
Blacksburg (VA), Sjedinjene Američke Države, 18.06.2017. - 23.06.2017

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
discrete empirical interpolation, model order reduction

Sažetak
This presentation discusses recent new contributions to the theory and practice of the DEIM. Both the matrix theoretical and computational (application oriented) aspects of the method are considered. - The theoretical error bound of the DEIM oblique projection is substantially improved by deploying strong rank revealing QR factorization in the Q-DEIM formulation of the index selection. It is shown in that we can obtain $c\leq \sqrt{; ; ; 1+\eta^2 r(m-r)}; ; ; $, where $\eta$ is a tunable parameter, e.g. $\eta=\sqrt{; ; ; m}; ; ; $. - Using the theory of projections, the canonical structure of the DEIM oblique projection is revealed in detail - in a suitably constructed orthonormal basis, its matrix representation is block diagonal with the diagonal blocks of sizes $1\times 1$ and $2\times 2$. This allows closer look at the structure of the error and provides further insights. - Further, DEIM is formulated in a general, weighted inner product, defined by a symmetric positive definite matrix $W$, and the interpolation property is generalized via linear functionals. This puts weighted DEIM ($W$-DEIM) in a more natural framework where the POD Galerkin projection is formulated in a discretization of a suitable energy inner product in which Galerkin projection preserves underlying physical properties. Also, as a special case of $W$-DEIM, we have DGEIM, a discrete version of the Generalized Empirical Interpolation Method (GEIM). - Finally, we reveal interesting connections between the Gappy POD, DEIM and clustering methods.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA