A domain decomposition method of stochastic PDEs: An iterative solution techniques using a two-level scalable preconditioner

Recent advances in high performance computing systems and sensing technologies motivate computational simulations with extremely high resolution models with capabilities to quantify uncertainties for credible numerical predictions. A two-level domain decomposition method is reported in this investig...

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Bibliographic Details
Published in:Journal of computational physics Vol. 257; no. Part A; pp. 298 - 317
Main Authors: Subber, Waad, Sarkar, Abhijit
Format: Journal Article
Language:English
Published: United States Elsevier Inc 15.01.2014
Subjects:
ALGORITHMS
Balancing domain decomposition by constraints
CHAOS THEORY
Coarsening
Computation
Computer simulation
DECOMPOSITION
Domain decomposition method
Domain decomposition methods
ELASTICITY
ENGINEERING
FINITE ELEMENT METHOD
IMPLEMENTATION
ITERATIVE METHODS
MATHEMATICAL METHODS AND COMPUTING
Neumann–Neumann preconditioner
Numerical prediction
PARTIAL DIFFERENTIAL EQUATIONS
Polynomial chaos expansion
POLYNOMIALS
POROUS MATERIALS
Schur complement system
Solvers
Stochastic finite element method
Stochastic PDEs
STOCHASTIC PROCESSES
Stochasticity
Domain decomposition method
Balancing domain decomposition by constraints
Stochastic PDEs
Neumann–Neumann preconditioner
Stochastic finite element method
Polynomial chaos expansion
Schur complement system
ISSN:0021-9991, 1090-2716
Online Access:Get full text
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Summary:Recent advances in high performance computing systems and sensing technologies motivate computational simulations with extremely high resolution models with capabilities to quantify uncertainties for credible numerical predictions. A two-level domain decomposition method is reported in this investigation to devise a linear solver for the large-scale system in the Galerkin spectral stochastic finite element method (SSFEM). In particular, a two-level scalable preconditioner is introduced in order to iteratively solve the large-scale linear system in the intrusive SSFEM using an iterative substructuring based domain decomposition solver. The implementation of the algorithm involves solving a local problem on each subdomain that constructs the local part of the preconditioner and a coarse problem that propagates information globally among the subdomains. The numerical and parallel scalabilities of the two-level preconditioner are contrasted with the previously developed one-level preconditioner for two-dimensional flow through porous media and elasticity problems with spatially varying non-Gaussian material properties. A distributed implementation of the parallel algorithm is carried out using MPI and PETSc parallel libraries. The scalabilities of the algorithm are investigated in a Linux cluster.
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ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2013.08.058