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Domain decomposition of stochastic PDEs: Theoretical formulations
Author(s) -
Sarkar Abhijit,
Benabbou Nabil,
Ghanem Roger
Publication year - 2008
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.2431
Subject(s) - domain decomposition methods , discretization , decomposition , probabilistic logic , domain (mathematical analysis) , decomposition method (queueing theory) , mathematics , schur complement , complement (music) , mortar methods , mathematical optimization , partial differential equation , computer science , algorithm , finite element method , mathematical analysis , discrete mathematics , ecology , biochemistry , statistics , physics , eigenvalues and eigenvectors , chemistry , quantum mechanics , complementation , biology , gene , thermodynamics , phenotype
We present a novel theoretical framework for the domain decomposition of uncertain systems defined by stochastic partial differential equations. The methodology involves a domain decomposition method in the geometric space and a functional decomposition in the probabilistic space. The probabilistic decomposition is based on a version of stochastic finite elements based on orthogonal decompositions and projections of stochastic processes. The spatial decomposition is achieved through a Schur‐complement‐based domain decomposition. The methodology aims to exploit the full potential of high‐performance computing platforms by reducing discretization errors with high‐resolution numerical model in conjunction to giving due regards to uncertainty in the system. The mathematical formulation is numerically validated with an example of waves in random media. Copyright © 2008 John Wiley & Sons, Ltd.