Parallel Domain Decomposition Strategies for Stochastic Elliptic Equations Part B: Accelerated Monte Carlo Sampling with Local PC Expansions

DOI10.1137/17M1132197zbMath1417.65163OpenAlexW2882991384MaRDI QIDQ3174781

Omar M. Knio, Andres Contreras, Bert J. Debusschere, Francesco Rizzi, Paul Mycek, Olivier P. Le Maître

Publication date: 18 July 2018

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/17m1132197

zbMATH Keywords

domain decompositionMonte Carlo methodpolynomial chaos expansionstochastic elliptic equations

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Parallel numerical computation (65Y05) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) PDEs with randomness, stochastic partial differential equations (35R60) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55)

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Cites Work

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• Convergence of quasi-optimal stochastic Galerkin methods for a class of PDES with random coefficients
• High-dimensional adaptive sparse polynomial interpolation and applications to parametric PDEs
• Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients
• Convergence rates of best \(N\)-term Galerkin approximations for a class of elliptic SPDEs
• A two level domain decomposition preconditioner based on local Dirichlet-to-Neumann maps
• Multi-level Monte Carlo finite element method for elliptic PDEs with stochastic coefficients
• Generalized spectral decomposition for stochastic nonlinear problems
• A generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations
• Robust and efficient methods for stochastic finite element analysis using Monte Carlo simulation
• A multigrid solver for two-dimensional stochastic diffusion equations.
• Finite elements for elliptic problems with stochastic coefficients
• A stochastic projection method for fluid flow. II: Random process
• A two-level domain decomposition method for the iterative solution of high frequency exterior Helmholtz problems
• Addressing the curse of dimensionality in SSFEM using the dependence of eigenvalues in KL expansion on domain size
• Generalized spectral decomposition method for solving stochastic finite element equations: invariant subspace problem and dedicated algorithms
• Model Reduction Based on Proper Generalized Decomposition for the Stochastic Steady Incompressible Navier--Stokes Equations
• ON THE OPTIMAL POLYNOMIAL APPROXIMATION OF STOCHASTIC PDES BY GALERKIN AND COLLOCATION METHODS
• Parallel Domain Decomposition Strategies for Stochastic Elliptic Equations. Part A: Local Karhunen--Loève Representations
• Local Polynomial Chaos Expansion for Linear Differential Equations with High Dimensional Random Inputs
• Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics
• Spectral Methods for Uncertainty Quantification
• A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
• A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
• The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
• Dirichlet–Dirichlet Domain Decomposition Methods for Elliptic Problems
• Uncertainty propagation in CFD using polynomial chaos decomposition
• An Explicit Representation of a Stationary Gaussian Process
• A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
• Solution of stochastic partial differential equations using Galerkin finite element techniques