Efficient low dimensional modelling based on POD and residual estimates

Rapun Banzo, Maria Luisa and Terragni, Filippo and Vega De Prada, Jose Manuel (2015). Efficient low dimensional modelling based on POD and residual estimates. In: "Workshop on Numerical Techniques for Computation Speedup", 2-4 Feb 2015, Biarritz, Francia. pp. 1-28.

Description

Title: Efficient low dimensional modelling based on POD and residual estimates
Author/s:
  • Rapun Banzo, Maria Luisa
  • Terragni, Filippo
  • Vega De Prada, Jose Manuel
Item Type: Presentation at Congress or Conference (Other)
Event Title: Workshop on Numerical Techniques for Computation Speedup
Event Dates: 2-4 Feb 2015
Event Location: Biarritz, Francia
Title of Book: Workshop on Numerical techniques for computation speedup: towards real-time simulation
Date: 2015
Subjects:
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

An adaptive low dimensional model is considered to simulate time dependent dynamics in nonlinear dissipative systems governed by partial differential equations. The method combines "on the fly" a standard numerical solver and a much more computationally inexpensive Galerkin system. The latter is constructed by projecting the governing equations onto adapting sets of POD modes, resulting from snapshots computed by the numerical solver. The strategy is based on a truncation error estimate and a residual estimate, designed to control the truncation error and the mode truncation instability, respectively. These estimates support the selection of the appropriate time intervals in which the numerical solver is run to first construct and then update, on demand, the POD modes. Furthermore, in order to reduce the computational effort needed at the outset to generate the initial POD subspace, some mode libraries are taken into account. Such libraries may either be generic (e.g., constructed from orthogonal polynomials) or result from different, former simulations.

More information

Item ID: 42556
DC Identifier: http://oa.upm.es/42556/
OAI Identifier: oai:oa.upm.es:42556
Official URL: http://ntcs2015.estia.fr/
Deposited by: Memoria Investigacion
Deposited on: 28 Apr 2017 09:37
Last Modified: 28 Apr 2017 09:37
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