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Polynomial chaos representation of a stochastic preconditioner
Author(s) -
Desceliers Christophe,
Ghanem Roger,
Soize Christian
Publication year - 2005
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1382
Subject(s) - polynomial chaos , preconditioner , convergence (economics) , polynomial , mathematics , chaos (operating system) , monte carlo method , sampling (signal processing) , representation (politics) , mathematical optimization , algebra over a field , computer science , iterative method , mathematical analysis , pure mathematics , law , statistics , computer security , filter (signal processing) , politics , political science , economics , computer vision , economic growth
A method is developed in this paper to accelerate the convergence in computing the solution of stochastic algebraic systems of equations. The method is based on computing, via statistical sampling, a polynomial chaos decomposition of a stochastic preconditioner to the system of equations. This preconditioner can subsequently be used in conjunction with either chaos representations of the solution or with approaches based on Monte Carlo sampling. In addition to presenting the supporting theory, the paper also presents a convergence analysis and an example to demonstrate the significance of the proposed algorithm. Copyright © 2005 John Wiley & Sons, Ltd.