01267nas a2200145   4500008004100000245010200041210006900143300001000212520067900222100001600901700001400917700001700931700002100948856015200969       2019                        eng d00aWeighted Reduced Order Methods for Parametrized Partial Differential Equations with Random Inputs0 aWeighted Reduced Order Methods for Parametrized Partial Differen  a27-403 a<p>In this manuscript we discuss weighted reduced order methods for stochastic partial differential equations. Random inputs (such as forcing terms, equation coefficients, boundary conditions) are considered as parameters of the equations. We take advantage of the resulting parametrized formulation to propose an efficient reduced order model; we also profit by the underlying stochastic assumption in the definition of suitable weights to drive to reduction process. Two viable strategies are discussed, namely the weighted reduced basis method and the weighted proper orthogonal decomposition method. A numerical example on a parametrized elasticity problem is shown.</p>1 aVenturi, L.1 aTorlo, D.1 aBallarin, F.1 aRozza, Gianluigi  uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85084009379&doi=10.1007%2f978-3-030-04870-9_2&partnerID=40&md5=446bcc1f331167bbba67bc00fb17015001436nas a2200145   4500008004100000245011100041210006900152300001400221490000600235520085400241100001401095700001701109700002101126856014301147       2018                        eng d00aStabilized weighted reduced basis methods for parametrized advection dominated problems with random inputs0 aStabilized weighted reduced basis methods for parametrized advec  a1475-15020 v63 a<p>In this work, we propose viable and eficient strategies for stabilized parametrized advection dominated problems, with random inputs. In particular, we investigate the combination of the wRB (weighted reduced basis) method for stochastic parametrized problems with the stabilized RB (reduced basis) method, which is the integration of classical stabilization methods (streamline/upwind Petrov-Galerkin (SUPG) in our case) in the ofine-online structure of the RB method. Moreover, we introduce a reduction method that selectively enables online stabilization; this leads to a sensible reduction of computational costs, while keeping a very good accuracy with respect to high-fdelity solutions. We present numerical test cases to assess the performance of the proposed methods in steady and unsteady problems related to heat transfer phenomena.</p>1 aTorlo, D.1 aBallarin, F.1 aRozza, Gianluigi  uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85058246502&doi=10.1137%2f17M1163517&partnerID=40&md5=6c54e2f0eb727cb85060e988486b8ac8