Reduced order adaptive models for systems of PDEs using POD

Terragni, Filippo and Rapun Banzo, Maria Luisa and Vega de Prada, José Manuel (2011). Reduced order adaptive models for systems of PDEs using POD. In: "Interdisciplinary Meeting on Mathematical Aspects of Fluid Problems", 01/04/2011 - 01/04/2011, Sevilla, España.

Description

Title: Reduced order adaptive models for systems of PDEs using POD
Author/s:
  • Terragni, Filippo
  • Rapun Banzo, Maria Luisa
  • Vega de Prada, José Manuel
Item Type: Presentation at Congress or Conference (Article)
Event Title: Interdisciplinary Meeting on Mathematical Aspects of Fluid Problems
Event Dates: 01/04/2011 - 01/04/2011
Event Location: Sevilla, España
Title of Book: Proceedings of Interdisciplinary Meeting on Mathematical Aspects of Fluid Problems
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

In this work we propose a method to accelerate time dependent numerical solvers of systems of PDEs that require a high cost in computational time and memory. The method is based on the combined use of such numerical solver with a proper orthogonal decomposition, from which we identify modes, a Galerkin projection (that provides a reduced system of equations) and the integration of the reduced system, studying the evolution of the modal amplitudes. We integrate the reduced model until our a priori error estimator indicates that our approximation in not accurate. At this point we use again our original numerical code in a short time interval to adapt the POD manifold and continue then with the integration of the reduced model. Application will be made to two model problems: the Ginzburg-Landau equation in transient chaos conditions and the two-dimensional pulsating cavity problem, which describes the motion of liquid in a box whose upper wall is moving back and forth in a quasi-periodic fashion. Finally, we will discuss a way of improving the performance of the method using experimental data or information from numerical simulations

More information

Item ID: 12975
DC Identifier: http://oa.upm.es/12975/
OAI Identifier: oai:oa.upm.es:12975
Official URL: http://www.imus.us.es/ACT/mafp2011/
Deposited by: Memoria Investigacion
Deposited on: 12 Dec 2012 15:01
Last Modified: 21 Apr 2016 12:16
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