An Optimal Solver for Linear Systems Arising from Stochastic FEM Approximation of Diffusion Equations with Random Coefficients

DOI10.1137/15M1017740zbMath1398.65284OpenAlexW2316640217MaRDI QIDQ5741180

Pranjal, David J. Silvester

Publication date: 22 July 2016

Published in: SIAM/ASA Journal on Uncertainty Quantification (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/15m1017740

zbMATH Keywords

iterative solversa posteriori error analysisoptimal preconditioningminresstochastic Galerkin approximationparametric operator equationsPDEs with random data

Mathematics Subject Classification ID

Probabilistic methods, particle methods, etc. for boundary value problems involving PDEs (65N75) Monte Carlo methods (65C05) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Asymptotic expansions of solutions to PDEs (35C20) PDEs with randomness, stochastic partial differential equations (35R60) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

Related Items (3)

CBS constants \& their role in error estimation for stochastic Galerkin finite element methods ⋮ Multifidelity Monte Carlo Estimation with Adaptive Low-Fidelity Models ⋮ Balanced iterative solvers for linear nonsymmetric systems and nonlinear systems with PDE origins: efficient black-box stopping criteria

Uses Software

• Matlab
• ALEA

Cites Work

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• Solution of Sparse Indefinite Systems of Linear Equations
• Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations
• Preconditioning and convergence in the right norm
• Solution of stochastic partial differential equations using Galerkin finite element techniques

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