Suscripción a Biblioteca: Guest
Portal Digitalde Biblioteca Digital eLibros Revistas Referencias y Libros de Ponencias Colecciones
International Journal for Uncertainty Quantification
Factor de Impacto: 3.259 Factor de Impacto de 5 años: 2.547 SJR: 0.417 SNIP: 0.8 CiteScore™: 1.52

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
Xiaoliang Wan, Huan Lei, Xiu Yang, Lin Lin
Order Reduction for Large-Scale Finite Element Models: A Systems Perspective
International Journal for Multiscale Computational Engineering, Vol.3, 2005, issue 3
William Gressick, John T. Wen, Jacob Fish
COMPARISON OF LINEARIZATION AND GRAPH CLUSTERING METHODS FOR UNCERTAINTY QUANTIFICATION OF LARGE SCALE DYNAMICAL SYSTEMS
International Journal for Uncertainty Quantification, Vol.7, 2017, issue 1
Abani K. Patra, Puneet Singla, Rahul Rai, Arpan Mukherjee, Tarunraj Singh
ON TWO-SCALE ANALYSIS OF HETEROGENEOUS MATERIALS BY MEANS OF THE MESHLESS FINITE DIFFERENCE METHOD
International Journal for Multiscale Computational Engineering, Vol.14, 2016, issue 2
Sławomir Milewski, Irena Jaworska