کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
519774 867681 2012 19 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A method for solving stochastic equations by reduced order models and local approximations
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نرم افزارهای علوم کامپیوتر
پیش نمایش صفحه اول مقاله
A method for solving stochastic equations by reduced order models and local approximations
چکیده انگلیسی

A method is proposed for solving equations with random entries, referred to as stochastic equations (SEs). The method is based on two recent developments. The first approximates the response surface giving the solution of a stochastic equation as a function of its random parameters by a finite set of hyperplanes tangent to it at expansion points selected by geometrical arguments. The second approximates the vector of random parameters in the definition of a stochastic equation by a simple random vector, referred to as stochastic reduced order model (SROM), and uses it to construct a SROM for the solution of this equation.The proposed method is a direct extension of these two methods. It uses SROMs to select expansion points, rather than selecting these points by geometrical considerations, and represents the solution by linear and/or higher order local approximations. The implementation and the performance of the method are illustrated by numerical examples involving random eigenvalue problems and stochastic algebraic/differential equations. The method is conceptually simple, non-intrusive, efficient relative to classical Monte Carlo simulation, accurate, and guaranteed to converge to the exact solution.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational Physics - Volume 231, Issue 19, 1 August 2012, Pages 6495–6513
نویسندگان
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