Volume 9, Issue 1
Reduced Basis Approximation and Error Bounds for Potential Flows in Parametrized Geometries

Gianluigi Rozza

Commun. Comput. Phys., 9 (2011), pp. 1-48.

Published online: 2011-09

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  • Abstract

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 lowdimensional space associated with a smooth “parametric manifold” in order to get a dimension reduction; ii) an efficient and effective greedy sampling method for identifi- cation of optimal and numerically stable approximations to have a rapid convergence; iii) an a posteriori error estimation procedure: rigorous and sharp bounds for the linearfunctional 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.

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@Article{CiCP-9-1, author = {Gianluigi Rozza}, title = {Reduced Basis Approximation and Error Bounds for Potential Flows in Parametrized Geometries}, journal = {Communications in Computational Physics}, year = {2011}, volume = {9}, number = {1}, pages = {1--48}, abstract = {

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 lowdimensional space associated with a smooth “parametric manifold” in order to get a dimension reduction; ii) an efficient and effective greedy sampling method for identifi- cation of optimal and numerically stable approximations to have a rapid convergence; iii) an a posteriori error estimation procedure: rigorous and sharp bounds for the linearfunctional 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.100310.260710a}, url = {http://global-sci.org/intro/article_detail/cicp/7489.html} }
TY - JOUR T1 - Reduced Basis Approximation and Error Bounds for Potential Flows in Parametrized Geometries AU - Gianluigi Rozza JO - Communications in Computational Physics VL - 1 SP - 1 EP - 48 PY - 2011 DA - 2011/09 SN - 9 DO - http://dor.org/10.4208/cicp.100310.260710a UR - https://global-sci.org/intro/cicp/7489.html KW - AB -

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 lowdimensional space associated with a smooth “parametric manifold” in order to get a dimension reduction; ii) an efficient and effective greedy sampling method for identifi- cation of optimal and numerically stable approximations to have a rapid convergence; iii) an a posteriori error estimation procedure: rigorous and sharp bounds for the linearfunctional 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.

Gianluigi Rozza. (1970). Reduced Basis Approximation and Error Bounds for Potential Flows in Parametrized Geometries. Communications in Computational Physics. 9 (1). 1-48. doi:10.4208/cicp.100310.260710a
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