Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Advances in Engineering Software - Special issue on large-scale analysis, design and intelligent synthesis environments
Preconditioning techniques for large linear systems: a survey
Journal of Computational Physics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
High-Order Collocation Methods for Differential Equations with Random Inputs
SIAM Journal on Scientific Computing
Journal of Computational Physics - Special issue: Uncertainty quantification in simulation science
A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
SIAM Journal on Numerical Analysis
Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations (Lecture Notes in Computational Science and Engineering)
SIAM Journal on Numerical Analysis
An algebraic theory for primal and dual substructuring methods by constraints
Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
Numerical Methods for Stochastic Computations: A Spectral Method Approach
Numerical Methods for Stochastic Computations: A Spectral Method Approach
Iterative Solvers for the Stochastic Finite Element Method
SIAM Journal on Scientific Computing
A Kronecker Product Preconditioner for Stochastic Galerkin Finite Element Discretizations
SIAM Journal on Scientific Computing
Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients
Computing and Visualization in Science
Domain decomposition of stochastic PDEs: a novel preconditioner and its parallel performance
HPCS'09 Proceedings of the 23rd international conference on High Performance Computing Systems and Applications
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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.