Mixing Snapshots and Fast Time Integration of PDEs

Rapun Banzo, Maria Luisa and Terragni, Filippo and Vega de Prada, José Manuel (2011). Mixing Snapshots and Fast Time Integration of PDEs. In: "IV International Conference on Computational Methods for Coupled Problems in Science and Engineering COUPLED PROBLEMS 2011", 20/06/2011 - 22/06/2011, Kos Island, Grecia. pp. 861-873.

Description

Title: Mixing Snapshots and Fast Time Integration of PDEs
Author/s:
  • Rapun Banzo, Maria Luisa
  • Terragni, Filippo
  • Vega de Prada, José Manuel
Item Type: Presentation at Congress or Conference (Article)
Event Title: IV International Conference on Computational Methods for Coupled Problems in Science and Engineering COUPLED PROBLEMS 2011
Event Dates: 20/06/2011 - 22/06/2011
Event Location: Kos Island, Grecia
Title of Book: Proceedings of IV International Conference on Computational Methods for Coupled Problems in Science and Engineering COUPLED PROBLEMS 2011
Date: 2011
Subjects:
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 local proper orthogonal decomposition (POD) plus Galerkin projection method was recently developed to accelerate time dependent numerical solvers of PDEs. This method is based on the combined use of a numerical code (NC) and a Galerkin sys- tem (GS) in a sequence of interspersed time intervals, INC and IGS, respectively. POD is performed on some sets of snapshots calculated by the numerical solver in the INC inter- vals. The governing equations are Galerkin projected onto the most energetic POD modes and the resulting GS is time integrated in the next IGS interval. The major computa- tional e®ort is associated with the snapshots calculation in the ¯rst INC interval, where the POD manifold needs to be completely constructed (it is only updated in subsequent INC intervals, which can thus be quite small). As the POD manifold depends only weakly on the particular values of the parameters of the problem, a suitable library can be con- structed adapting the snapshots calculated in other runs to drastically reduce the size of the ¯rst INC interval and thus the involved computational cost. The strategy is success- fully tested in (i) the one-dimensional complex Ginzburg-Landau equation, including the case in which it exhibits transient chaos, and (ii) the two-dimensional unsteady lid-driven cavity problem

More information

Item ID: 12976
DC Identifier: http://oa.upm.es/12976/
OAI Identifier: oai:oa.upm.es:12976
Official URL: http://congress.cimne.com/coupled2011/frontal/default.asp
Deposited by: Memoria Investigacion
Deposited on: 12 Dec 2012 14:55
Last Modified: 21 Apr 2016 12:16
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