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: 0.531 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.2012003670
pages 321-339

EFFICIENT NUMERICAL METHODS FOR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS THROUGH TRANSFORMATION TO EQUATIONS DRIVEN BY CORRELATED NOISE

Ju Ming
Department of Scientific Computing, Florida State University, Tallahassee, Florida 32306-4120
Max Gunzburger
Department of Scientific Computing, Florida State University, Tallahassee, Florida 32306-4120

SINOPSIS

A procedure is provided for the efficient approximation of solutions of a broad class of stochastic partial differential equations (SPDEs), that is, partial differential equations driven by additive white noise. The first step is to transform the given SPDE into an equivalent SPDE driven by a correlated random process, specifically, the Ornstein-Uhlenbeck process. This allows for the use of truncated Karhunen-Loeve expansions and sparse-grid methods for the efficient and accurate approximation of the input stochastic process in terms of few random variables. Details of the procedure are given and its efficacy is demonstrated through computational experiments involving the stochastic heat equation and the stochastic Navier-Stokes equations.


Articles with similar content:

Reduction of Waveform Distortions in Bispectrum-Based Signal Reconstruction System
Telecommunications and Radio Engineering, Vol.61, 2004, issue 7-12
I. V. Kurbatov, P. Yu. Kostenko
SOME A PRIORI ERROR ESTIMATES FOR FINITE ELEMENT APPROXIMATIONS OF ELLIPTIC AND PARABOLIC LINEAR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS
International Journal for Uncertainty Quantification, Vol.4, 2014, issue 5
Christophe Audouze , Prasanth B. Nair
DATA ASSIMILATION FOR NAVIER-STOKES USING THE LEAST-SQUARES FINITE-ELEMENT METHOD
International Journal for Uncertainty Quantification, Vol.8, 2018, issue 5
Richard P. Dwight, Alexander Schwarz
Reduction Theory in Extrapolation Problems
Journal of Automation and Information Sciences, Vol.30, 1998, issue 2-3
V. I. Vasil'ev
A GRADIENT-BASED SAMPLING APPROACH FOR DIMENSION REDUCTION OF PARTIAL DIFFERENTIAL EQUATIONS WITH STOCHASTIC COEFFICIENTS
International Journal for Uncertainty Quantification, Vol.5, 2015, issue 1
Miroslav Stoyanov, Clayton G. Webster