A new stochastic approach to transient heat conduction modeling with uncertainty

By Dongbin Xiu, G. Em Karniadakis. 2003

243 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Environmental Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d95964f3df2bcccbef734fcec93069a2bf6cad00

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In Civil and Structural Engineering

In Environmental Engineering

In Statistics and Probability

Citations in the corpus

An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations (2009, methodology): “The gPC was successfully applied to model uncertainty propagation in various applications [8] [9] [10].”
Simulation-based optimal Bayesian experimental design for nonlinear systems (2011, background): “, [52, 53, 54, 55]) including parameter estimation and inverse problems (e.”
Fast Numerical Methods for Stochastic Computations: A Review (2009, methodology): “It has been shown that the Galerkin system of equations can be decoupled for both steady diffusion [90] and unsteady diffusion [93], and the technique was analyzed rigorously in [98].”
Use of global sensitivity analysis and polynomial chaos expansion for interpretation of nonreactive transport experiments in laboratory‐scale porous media (2011, methodology): “The polynomial chaos theory was originally developed by Wiener [1938], and it has been extensively used in various engineering fields [e.g., Ghanem and Spanos, 1991; Xiu and Karniadakis, 2003; Acharjee and Zabaras, 2007].”
Polynomial chaos expansions for uncertainty propagation and moment independent sensitivity analysis of seawater intrusion simulations (2015, methodology): “Fourth, with the introduction of generalized PCEs (gPCE) (Xiu and Karniadakis, 2002, 2003a), multi-element gPCEs (Wan and Karniadakis, 2006; Prempraneerach et al., 2010) and arbitrary PCEs (aPCEs) (Oladyshkin and Nowak, 2012), PCEs can handle many probability distribution types (e.g., normal,…”
Modeling Multibody Systems with Uncertainties. Part I: Theoretical and Computational Aspects (2006, background): “Karniadakis and co-workers introduced the concept of generalized polynomial chaos, and studied extensively its use to model uncertainties in fluids, including applications such as advection and diffusion, turbulence, and flow-structure interactions [44-55].”
Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures (2006, methodology): “The convergence of gPC for the Navier–Stokes equation and the advection-diffusion equation has been studied and verified in [34, 30].”
Sparse grid collocation schemes for stochastic natural convection problems (2007, background): “Karniadakis and co-workers applied a generalized polynomial chaos expansion to model uncertainty in diffusion [11], fluid flow applications [12] and transient heat conduction problems [13].”