Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
Modeling uncertainty in flow simulations via generalized polynomial chaos
Journal of Computational Physics
Uncertainty propagation using Wiener-Haar expansions
Journal of Computational Physics
Multi-resolution analysis of wiener-type uncertainty propagation schemes
Journal of Computational Physics
High-Order Collocation Methods for Differential Equations with Random Inputs
SIAM Journal on Scientific Computing
An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
Journal of Computational Physics
Karhunen-Loève approximation of random fields by generalized fast multipole methods
Journal of Computational Physics - Special issue: Uncertainty quantification in simulation science
Sparse grid collocation schemes for stochastic natural convection problems
Journal of Computational Physics
Parametric uncertainty analysis of pulse wave propagation in a model of a human arterial network
Journal of Computational Physics
A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
SIAM Journal on Numerical Analysis
Numerical approach for quantification of epistemic uncertainty
Journal of Computational Physics
Journal of Computational Physics
Efficient enforcement of far-field boundary conditions in the Transformed Field Expansions method
Journal of Computational Physics
Stochastic Galerkin methods for elliptic interface problems with random input
Journal of Computational and Applied Mathematics
Galerkin Methods for Stochastic Hyperbolic Problems Using Bi-Orthogonal Polynomials
Journal of Scientific Computing
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We discuss in this paper efficient solvers for stochastic diffusion equations in random media. We employ generalized polynomial chaos (gPC) expansion to express the solution in a convergent series and obtain a set of deterministic equations for the expansion coefficients by Galerkin projection. Although the resulting system of diffusion equations are coupled, we show that one can construct fast numerical methods to solve them in a decoupled fashion. The methods are based on separation of the diagonal terms and off-diagonal terms in the matrix of the Galerkin system. We examine properties of this matrix and show that the proposed method is unconditionally stable for unsteady problems and convergent for steady problems with a convergent rate independent of discretization parameters. Numerical examples are provided, for both steady and unsteady random diffusions, to support the analysis.