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
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
Computational Modeling of Uncertainty in Time-Domain Electromagnetics
SIAM Journal on Scientific Computing
Numerical Methods for Differential Equations in Random Domains
SIAM Journal on Scientific Computing
Stochastic analysis of transport in tubes with rough walls
Journal of Computational Physics - Special issue: Uncertainty quantification in simulation science
A fictitious domain approach to the numerical solution of PDEs in stochastic domains
Numerische Mathematik
A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
SIAM Journal on Numerical Analysis
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We propose a new methodology for the evaluation of the scattered radiation by objects of uncertain shape. The uncertainties are handled by treating them as random fields. The analysis is not restricted to small geometric variations, such as in modeling of rough surfaces. Due to its efficiency and accuracy we employ the Stochastic Galerkin method. We combine this later method with a specially suited domain decomposition procedure, with which we obtain a spectrally global convergence rate. The key idea is to split the equation system with respect to the spatial position of the boundaries, and consider the interface fields as the unknown quantities. This approach preserves the governing equations, allowing us to obtain the projections of the classical integral representation of the solution. The original unbounded domain of interest is transformed to a bounded domain, while the far-field radiation condition is automatically satisfied. Discretization is accomplished by standard numerical integration, which coincides with a collocation scheme. We conclude by showing the inherent connection of the integral representation to the formulation of the problem in terms of boundary integrals.