Suscripción a Biblioteca: Guest
Portal Digitalde Biblioteca Digital eLibros Revistas Referencias y Libros de Ponencias Colecciones
International Journal for Uncertainty Quantification
Factor de Impacto: 4.911 Factor de Impacto de 5 años: 3.179 SJR: 1.008 SNIP: 0.983 CiteScore™: 5.2

ISSN Imprimir: 2152-5080
ISSN En Línea: 2152-5099

Acceso abierto

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2014007778
pages 225-242

A MULTI-FIDELITY STOCHASTIC COLLOCATION METHOD FOR PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS WITH RANDOM INPUT DATA

Maziar Raissi
Department of Mathematical Sciences, George Mason University, 4400 University Drive, MS: 3F2, Planetary Hall, Fairfax, Virginia 22030, USA
Padmanabhan Seshaiyer
Department of Mathematical Sciences, George Mason University, 4400 University Drive, MS: 3F2, Planetary Hall, Fairfax, Virginia 22030, USA

SINOPSIS

Over the last few years there have been dramatic advances in the area of uncertainty quantification. In particular, we have seen a surge of interest in developing efficient, scalable, stable, and convergent computational methods for solving differential equations with random inputs. Stochastic collocation (SC) methods, which inherit both the ease of implementation of sampling methods like Monte Carlo and the robustness of nonsampling ones like stochastic Galerkin to a great deal, have proved extremely useful in dealing with differential equations driven by random inputs. In this work we propose a novel enhancement to stochastic collocation methods using deterministic model reduction techniques. Linear parabolic partial differential equations with random forcing terms are analysed. The input data are assumed to be represented by a finite number of random variables. A rigorous convergence analysis, supported by numerical results, shows that the proposed technique is not only reliable and robust but also efficient.


Articles with similar content:

A HYBRID GENERALIZED POLYNOMIAL CHAOS METHOD FOR STOCHASTIC DYNAMICAL SYSTEMS
International Journal for Uncertainty Quantification, Vol.4, 2014, issue 1
Michael Schick, Vincent Heuveline
A GENERAL FRAMEWORK FOR ENHANCING SPARSITY OF GENERALIZED POLYNOMIAL CHAOS EXPANSIONS
International Journal for Uncertainty Quantification, Vol.9, 2019, issue 3
Xiu Yang, Xiaoliang Wan, Huan Lei, Lin Lin
EFFECT OF DEM UNCERTAINTY ON GEOPHYSICAL MASS FLOW VIA IDENTIFICATION OF STRONGLY COUPLED SUBSYSTEM
International Journal for Uncertainty Quantification, Vol.9, 2019, issue 6
Abani Patra, Puneet Singla, Rahul Rai, Arpan Mukherjee, Tarunraj Singh
POLYNOMIAL CHAOS FOR SEMIEXPLICIT DIFFERENTIAL ALGEBRAIC EQUATIONS OF INDEX 1
International Journal for Uncertainty Quantification, Vol.3, 2013, issue 1
Roland Pulch
VARIABLE-SEPARATION BASED ITERATIVE ENSEMBLE SMOOTHER FOR BAYESIAN INVERSE PROBLEMS IN ANOMALOUS DIFFUSION REACTION MODELS
International Journal for Uncertainty Quantification, Vol.9, 2019, issue 3
Yuming Ba, Na Ou, Lijian Jiang