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This paper compares five methods, including quasi-Monte Carlo quadrature, polynomial chaos with coefficients determined by sparse quadrature and by point collocation, radial basis function and a gradient-enhanced version of kriging, and examines their efficiency in estimating statistics of aerodynamic performance upon random perturbation to the airfoil geometry which is parameterized by independent Gaussian variables. The results show that gradient-enhanced surrogate methods achieve better accuracy than direct integration methods with the same computational cost.<\/jats:p>","DOI":"10.1137\/15m1050239","type":"journal-article","created":{"date-parts":[[2017,3,30]],"date-time":"2017-03-30T12:26:01Z","timestamp":1490876761000},"page":"334-352","source":"Crossref","is-referenced-by-count":31,"title":["Quantification of Airfoil Geometry-Induced Aerodynamic Uncertainties---Comparison of Approaches"],"prefix":"10.1137","volume":"5","author":[{"given":"Dishi","family":"Liu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alexander","family":"Litvinenko","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Claudia","family":"Schillings","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Volker","family":"Schulz","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,3,30]]},"reference":[{"key":"atypb1","unstructured":"R. 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Dwight,\n                      Discrete adjoint of the Navier-Stokes equations for aerodynamic shape optimization\n                      , in Proceedings of the 6th Conference on Evolutionary and Deterministic Methods for Design, Optimization and Control with Applications to Industrial and Societal Problems (EUROGEN 2005), Munich, 2005."},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492900000015"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492900002804"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1007\/s00158-011-0660-9"},{"key":"atypb9","first-page":"2002","volume":"2002","author":"Chung H.-S.","journal-title":"NV"},{"key":"atypb10","unstructured":"S. Dolgov, B. N. Khoromskij, A. Litvinenko, and H. G. Matthies,\n                      Computation of the response surface in the tensor train data format\n                      , preprint,arXiv:1406.2816, 2014."},{"key":"atypb11","unstructured":"T. Evans, P. Tattersall, and J. 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Knio,\n                      Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics\n                      , Springer, Dordrecht, 2010."},{"key":"atypb24","first-page":"477","author":"Litvinenko A.","year":"2010","journal-title":"Greece"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1002\/pamm.201110425"},{"key":"atypb26","doi-asserted-by":"crossref","unstructured":"A. Litvinenko, H. G. Matthies, and T. A. El-Moselhy,\n                      Sampling and low-rank tensor approximation of the response surface\n                      , in Monte Carlo and Quasi-Monte Carlo Methods 2012, Springer Proceedings in Mathematics and Statistics 65, J. Dick, F. Y. Kuo, G. W. Peters, and I. H. Sloan, eds., Springer, Berlin, 2013, pp. 535-551.","DOI":"10.1007\/978-3-642-41095-6_27"},{"key":"atypb27","unstructured":"D. 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