01261nas a2200157   4500008004100000245008800041210006900129300001200198490000700210520069300217100002200910700001700932700002000949700002100969856011300990       2021                        eng d00aHierarchical model reduction techniques for flow modeling in a parametrized setting0 aHierarchical model reduction techniques for flow modeling in a p  a267-2930 v193 a<p>In this work we focus on two different methods to deal with parametrized partial differential equations in an efficient and accurate way. Starting from high fidelity approximations built via the hierarchical model reduction discretization, we consider two approaches, both based on a projection model reduction technique. The two methods differ for the algorithm employed during the construction of the reduced basis. In particular, the former employs the proper orthogonal decomposition, while the latter relies on a greedy algorithm according to the certified reduced basis technique. The two approaches are preliminarily compared on two-dimensional scalar and vector test cases.</p>1 aZancanaro, Matteo1 aBallarin, F.1 aPerotto, Simona1 aRozza, Gianluigi  uhttps://math.sissa.it/publication/hierarchical-model-reduction-techniques-flow-modeling-parametrized-setting00473nas a2200121   4500008004100000245004900041210004900090300001000139490000700149100002000156700002100176856015400197       2020                        eng d00aSpecial Issue on Reduced Order Models in CFD0 aSpecial Issue on Reduced Order Models in CFD  a91-920 v341 aPerotto, Simona1 aRozza, Gianluigi  uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85084258805&doi=10.1080%2f10618562.2020.1756497&partnerID=40&md5=d9316aad9ba95f244e07379318ebbcba01658nas a2200157   4500008004100000245009100041210006900132300001200201490000800213520106300221100001701284700001701301700002001318700002101338856014101359       2019                        eng d00aA POD-selective inverse distance weighting method for fast parametrized shape morphing0 aPODselective inverse distance weighting method for fast parametr  a860-8840 v1173 a<p>Efficient shape morphing techniques play a crucial role in the approximation of partial differential equations defined in parametrized domains, such as for fluid-structure interaction or shape optimization problems. In this paper, we focus on inverse distance weighting (IDW) interpolation techniques, where a reference domain is morphed into a deformed one via the displacement of a set of control points. We aim at reducing the computational burden characterizing a standard IDW approach without significantly compromising the accuracy. To this aim, first we propose an improvement of IDW based on a geometric criterion that automatically selects a subset of the original set of control points. Then, we combine this new approach with a dimensionality reduction technique based on a proper orthogonal decomposition of the set of admissible displacements. This choice further reduces computational costs. We verify the performances of the new IDW techniques on several tests by investigating the trade-off reached in terms of accuracy and efficiency.</p>1 aBallarin, F.1 aD'Amario, A.1 aPerotto, Simona1 aRozza, Gianluigi  uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85056396233&doi=10.1002%2fnme.5982&partnerID=40&md5=6aabcbdc9a0da25e36575a0ebfac034f