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://doi.org/10.4208/cicp.100310.260710a
UR - https://global-sci.org/intro/article_detail/cicp/7489.html
KW - 
AB - <p style="text-align: justify;">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 &quot;parametric manifold&quot; 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.</p>