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Numerical analysis and adaptive computation for solutions of elliptic problems with randomly perturbed coefficients
Author(s) -
Målqvist Axel,
Estep Donald,
Tavener Simon
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700268
Subject(s) - domain decomposition methods , piecewise , mathematics , computation , a priori and a posteriori , constant (computer programming) , perturbation (astronomy) , poisson's equation , domain (mathematical analysis) , constant coefficients , stiffness matrix , mathematical analysis , algorithm , computer science , stiffness , finite element method , philosophy , physics , epistemology , quantum mechanics , thermodynamics , programming language , structural engineering , engineering
We develop a reliable efficient method for computing solutions to the Poisson equation a with randomly perturbed coefficient. We assume the perturbation to be piecewise constant and use a non‐overlapping domain decomposition algorithm, where the domains coincides with regions where the perturbation is constant, to solve the equations. On each sub‐domain we use an truncated Neumann series to approximate the inverse of the local stiffness matrix. By doing so we can solve for all samples simultaneously in a very efficient way. We derive a posteriori error estimates and construct an adaptive algorithm to tune the method parameters automatically. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)