Evaluation of failure probability via surrogate models
Journal of Computational Physics
An efficient surrogate-based method for computing rare failure probability
Journal of Computational Physics
SIAM Journal on Scientific Computing
Original articles: On the linear advection equation subject to random velocity fields
Mathematics and Computers in Simulation
Generalised Polynomial Chaos for a Class of Linear Conservation Laws
Journal of Scientific Computing
Multi-output local Gaussian process regression: Applications to uncertainty quantification
Journal of Computational Physics
A method for solving stochastic equations by reduced order models and local approximations
Journal of Computational Physics
Bayesian inference with optimal maps
Journal of Computational Physics
Error analysis of generalized polynomial chaos for nonlinear random ordinary differential equations
Applied Numerical Mathematics
Structural and Multidisciplinary Optimization
Numerical schemes for dynamically orthogonal equations of stochastic fluid and ocean flows
Journal of Computational Physics
A flexible numerical approach for quantification of epistemic uncertainty
Journal of Computational Physics
Journal of Computational Physics
Extended stochastic FEM for diffusion problems with uncertain material interfaces
Computational Mechanics
Multiphysics simulations: Challenges and opportunities
International Journal of High Performance Computing Applications
Proceedings of the International Conference on Computer-Aided Design
Uncertainty quantification for integrated circuits: stochastic spectral methods
Proceedings of the International Conference on Computer-Aided Design
Journal of Computational Physics
Stochastic collocation and stochastic Galerkin methods for linear differential algebraic equations
Journal of Computational and Applied Mathematics
High-order methods as an alternative to using sparse tensor products for stochastic Galerkin FEM
Computers & Mathematics with Applications
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The first graduate-level textbook to focus on fundamental aspects of numerical methods for stochastic computations, this book describes the class of numerical methods based on generalized polynomial chaos (gPC). These fast, efficient, and accurate methods are an extension of the classical spectral methods of high-dimensional random spaces. Designed to simulate complex systems subject to random inputs, these methods are widely used in many areas of computer science and engineering. The book introduces polynomial approximation theory and probability theory; describes the basic theory of gPC methods through numerical examples and rigorous development; details the procedure for converting stochastic equations into deterministic ones; using both the Galerkin and collocation approaches; and discusses the distinct differences and challenges arising from high-dimensional problems. The last section is devoted to the application of gPC methods to critical areas such as inverse problems and data assimilation. Ideal for use by graduate students and researchers both in the classroom and for self-study, Numerical Methods for Stochastic Computations provides the required tools for in-depth research related to stochastic computations.The first graduate-level textbook to focus on the fundamentals of numerical methods for stochastic computations Ideal introduction for graduate courses or self-study Fast, efficient, and accurate numerical methods Polynomial approximation theory and probability theory included Basic gPC methods illustrated through examples