Weighted Reduced Order Methods for Parametrized Partial Differential Equations with Random Inputs

Francesco Ballarin, Luca Venturi, Davide Torlo, Gianluigi Rozza

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

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.
Original languageEnglish
Title of host publicationUncertainty modeling for engineering applications
Pages27-40
Number of pages14
DOIs
Publication statusPublished - 2019

Publication series

NamePOLITO SPRINGER SERIES

Keywords

  • uncertainty quantification
  • weighted reduced order models

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