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Reduced Basis Approximation and Error Bounds for Potential Flows in Parametrized Geometries

Published online by Cambridge University Press:  20 August 2015

Gianluigi Rozza
Gianluigi Rozza*
Affiliation:
Massachusetts Institute of Technology, Department of Mechanical Engineering, Room 3-264, 77 Massachusetts Avenue, Cambridge MA, 02142-4307, USA Modelling and Scientific Computing, Ecole Polytechnique Fédérale de Lausanne, Station 8-MA, CH 1015, Lausanne, Switzerland
*
*Corresponding author.Email:rozza@mit.edu

Abstract

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In this paper we consider (hierarchical, Lagrange) reduced basis approximation and a posteriori error estimation for potential flows in affinely parametrized geometries. We review the essential ingredients: i) a Galerkin projection onto a low-dimensional space associated with a smooth “parametric manifold” in order to get a dimension reduction; ii) an efficient and effective greedy sampling method for identification of optimal and numerically stable approximations to have a rapid convergence; iii) an a posteriori error estimation procedure: rigorous and sharp bounds for the linear-functional outputs of interest and over the potential solution or related quantities of interest like velocity and / or pressure; iv) an Offline-Online computational decomposition strategies to achieve a minimum marginal computational cost for high performance in the real-time and many-query (e.g., design and optimization) contexts. We present three illustrative results for inviscid potential flows in parametrized geometries representing a Venturi channel, a circular bend and an added mass problem.

Keywords

65Y2076B9935Q3565N15Reduced basis approximationerror boundspotential flowsGalerkin methoda posteriori error estimationparametrized geometries
Type
Review Article
Information
Communications in Computational Physics , Volume 9 , Issue 1 , January 2011 , pp. 1 - 48
Copyright
Copyright © Global Science Press Limited 2011

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