Reduced order models based on local POD plus Galerkin projection

Rapun Banzo, Maria Luisa and Vega de Prada, José Manuel (2010). Reduced order models based on local POD plus Galerkin projection. "Journal of Computational Physics", v. 229 (n. 8); pp. 3046-3063. ISSN 0021-9991. https://doi.org/10.1016/j.jcp.2009.12.029.

Description

Title: Reduced order models based on local POD plus Galerkin projection
Author/s:
  • Rapun Banzo, Maria Luisa
  • Vega de Prada, José Manuel
Item Type: Article
Título de Revista/Publicación: Journal of Computational Physics
Date: April 2010
ISSN: 0021-9991
Volume: 229
Subjects:
Freetext Keywords: Low dimensional models; Surrogate models; Low dimensional dynamics; Proper orthogonal decomposition
Faculty: E.T.S.I. Aeronáuticos (UPM)
Department: Fundamentos Matemáticos de la Tecnología Aeronáutica [hasta 2014]
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

A method is presented to accelerate numerical simulations on parabolic problems using a numerical code and a Galerkin system (obtained via POD plus Galerkin projection) on a sequence of interspersed intervals. The lengths of these intervals are chosen according to several basic ideas that include an a priori estimate of the error of the Galerkin approximation. Several improvements are introduced that reduce computational complexity and deal with: (a) updating the POD manifold (instead of calculating it) at the end of each Galerkin interval; (b) using only a limited number of mesh points to calculate the right hand side of the Galerkin system; and (c) introducing a second error estimate based on a second Galerkin system to account for situations in which qualitative changes in the dynamics occur during the application of the Galerkin system. The resulting method, called local POD plus Galerkin projection method, turns out to be both robust and efficient. For illustration, we consider a time-dependent Fisher-like equation and a complex Ginzburg–Landau equation.

More information

Item ID: 6110
DC Identifier: http://oa.upm.es/6110/
OAI Identifier: oai:oa.upm.es:6110
DOI: 10.1016/j.jcp.2009.12.029
Official URL: http://www.elsevier.com/locate/jcp
Deposited by: Memoria de Investigacion 2
Deposited on: 21 Feb 2011 10:55
Last Modified: 20 Apr 2016 14:44
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