zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Reduced-order modeling of time-dependent PDEs with multiple parameters in the boundary data. (English) Zbl 1121.65354
Summary: The computational approximation of solutions to nonlinear partial differential equations (PDEs) such as the Navier-Stokes equations is often a formidable task. For this reason, there is significant interest in the development of very low-dimensional models that can be used to determine reasonably accurate approximations in simulation and control problems for PDEs. Many concrete tests have been reported on in the literature that show that several classes of reduced-order models (ROMs) are effective, i.e., an accurate approximate solution can be obtained using very low-dimensional ROMs. Most of these tests involved problems for which the solution depends on only a single parameter appearing in the boundary data. The extension of the techniques used in those tests to the case of multiple parameters is not a straightforward matter. Here, we present, test, and compare two methods for treating, within the context of a class of ROMs, inhomogeneous Dirichlet-type boundary conditions that contain multiple parameters. In this study, we focus on the proper orthogonal decomposition (POD) approach to ROM; however, the issues and results discussed here in the POD context apply equally well to other ROM approaches.
65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)