TY - JOUR T1 - Weighted Reduced Order Methods for Parametrized Partial Differential Equations with Random Inputs JF - PoliTO Springer Series Y1 - 2019 A1 - L. Venturi A1 - D. Torlo A1 - F. Ballarin A1 - Gianluigi Rozza AB -

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.

UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85084009379&doi=10.1007%2f978-3-030-04870-9_2&partnerID=40&md5=446bcc1f331167bbba67bc00fb170150 ER -