Adaptive POD-based low-dimensional modeling supported by residual estimates

Rapun Banzo, Maria Luisa and Terragni, Filippo and Vega de Prada, José Manuel (2015). Adaptive POD-based low-dimensional modeling supported by residual estimates. "International Journal for Numerical Methods in Engineering", v. 104 (n. 9); pp. 844-868. ISSN 0029-5981. https://doi.org/10.1002/nme.4947.

Description

Title: Adaptive POD-based low-dimensional modeling supported by residual estimates
Author/s:
  • Rapun Banzo, Maria Luisa
  • Terragni, Filippo
  • Vega de Prada, José Manuel
Item Type: Article
Título de Revista/Publicación: International Journal for Numerical Methods in Engineering
Date: 30 November 2015
ISSN: 0029-5981
Volume: 104
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 PDEs. The method combines an inexpensive POD-based Galerkin system with short runs of a standard numerical solver that provides the snapshots necessary to first construct and then update the POD modes. Switching between the numerical solver and the Galerkin system is decided ‘on the fly’ by monitoring (i) a truncation error estimate and (ii) a residual estimate. The latter estimate is used to control the mode truncation instability and highly improves former adaptive strategies that detected this instability by monitoring consistency with a second instrumental Galerkin system based on a larger number of POD modes. The most computationally expensive run of the numerical solver occurs at the outset, when the whole set of POD modes is calculated. This step is improved by using mode libraries, which may either be generic or result from former applications of the method. The outcome is a flexible, robust, computationally inexpensive procedure that adapts itself to the local dynamics by using the faster Galerkin system for the majority of the time and few, on demand, short runs of a numerical solver. The method is illustrated considering 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 SpainFIS2011–28838-C02-02UnspecifiedUnspecifiedComportamiento colectivo y estocástico en bio y nanomateriales

More information

Item ID: 41219
DC Identifier: http://oa.upm.es/41219/
OAI Identifier: oai:oa.upm.es:41219
DOI: 10.1002/nme.4947
Official URL: http://onlinelibrary.wiley.com/doi/10.1002/nme.4947/abstract
Deposited by: Memoria Investigacion
Deposited on: 30 Sep 2016 11:01
Last Modified: 30 Nov 2016 23:30
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