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.

Weighted Reduced Order Methods for Parametrized Partial Differential Equations with Random Inputs / Venturi, Luca; Torlo, Davide; Ballarin, Francesco; Rozza, Gianluigi. - (2019), pp. 27-40. [10.1007/978-3-030-04870-9_2]

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

Venturi, Luca;Torlo, Davide;Ballarin, Francesco
;
Rozza, Gianluigi
2019-01-01

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.
2019
Uncertainty modeling for engineering applications
27
40
https://doi.org/10.1007/978-3-030-04870-9_2
https://arxiv.org/abs/1805.00828
Venturi, Luca; Torlo, Davide; Ballarin, Francesco; Rozza, Gianluigi
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/87854
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