LUPOD: Collocation in POD via LU decomposition

Rapun Banzo, Maria Luisa and Terragni, F. and Vega de Prada, J.M. (2017). LUPOD: Collocation in POD via LU decomposition. "Journal of Computational Physics", v. 335 ; pp. 1-20. ISSN 0021-9991. https://doi.org/10.1016/j.jcp.2017.01.005.

Description

Title: LUPOD: Collocation in POD via LU decomposition
Author/s:
  • Rapun Banzo, Maria Luisa
  • Terragni, F.
  • Vega de Prada, J.M.
Item Type: Article
Título de Revista/Publicación: Journal of Computational Physics
Date: 2017
ISSN: 0021-9991
Volume: 335
Subjects:
Freetext Keywords: Proper orthogonal decomposition; Singular value decomposition; Collocation points; Reduced order models; Galerkin projection
Faculty: E.T.S. de Ingeniería Aeronáutica y del Espacio (UPM)
Department: Matemática Aplicada a la Ingeniería Aeroespacial
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

A collocation method is developed for the (truncated) POD of a set of snapshots. In other words, POD computations are performed using only a set of collocation points, whose number is comparable to the number of retained modes, in a similar fashion as in collocation spectral methods. Intending to rely on simple ideas which, moreover, are consistent with the essence of POD, collocation points are computed via the LU decomposition with pivoting of the snapshot matrix. The new method is illustrated in simple applications in which POD is used as a data-processing method. The performance of the method is tested in the computationally efficient construction of reduced order models based on POD plus Galerkin projection for the complex Ginzburg–Landau equation in one and two space dimensions.

Funding Projects

TypeCodeAcronymLeaderTitle
Government of SpainTRA2013-45808-RUnspecifiedUnspecifiedSimulación eficiente de sistemas aeronáuticos
Government of SpainMTM2014-56948-C1-PUnspecifiedUnspecifiedModelos híbridos para bio y nanosistemas
Government of SpainMTM2014-56948-C2-2-PUnspecifiedUnspecifiedModelos híbridos para bio y nanosistemas

More information

Item ID: 50239
DC Identifier: http://oa.upm.es/50239/
OAI Identifier: oai:oa.upm.es:50239
DOI: 10.1016/j.jcp.2017.01.005
Official URL: https://www.sciencedirect.com/science/article/pii/S0021999117300153
Deposited by: Memoria Investigacion
Deposited on: 05 Jun 2019 11:39
Last Modified: 05 Jun 2019 11:39
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