Physica D - Special issue originating from the 18th Annual International Conference of the Center for Nonlinear Studies, Los Alamos, NM, May 11&mdash ;15, 1998
Modeling uncertainty in flow simulations via generalized polynomial chaos
Journal of Computational Physics
Stochastic Solutions for the Two-Dimensional Advection-Diffusion Equation
SIAM Journal on Scientific Computing
Beyond Wiener---Askey Expansions: Handling Arbitrary PDFs
Journal of Scientific Computing
Numerical studies of the stochastic Korteweg-de Vries equation
Journal of Computational Physics
Uncertainty quantification of limit-cycle oscillations
Journal of Computational Physics - Special issue: Uncertainty quantification in simulation science
Predicting shock dynamics in the presence of uncertainties
Journal of Computational Physics - Special issue: Uncertainty quantification in simulation science
Journal of Computational Physics
Stochastic spectral methods for efficient Bayesian solution of inverse problems
Journal of Computational Physics
Stochastic Computational Fluid Mechanics
Computing in Science and Engineering
Sparse grid collocation schemes for stochastic natural convection problems
Journal of Computational Physics
Inversion of Robin coefficient by a spectral stochastic finite element approach
Journal of Computational Physics
Finite Elements in Analysis and Design
Journal of Computational Physics
The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications
Journal of Computational Physics
Generalized spectral decomposition for stochastic nonlinear problems
Journal of Computational Physics
Efficient stochastic Galerkin methods for random diffusion equations
Journal of Computational Physics
A stochastic multiscale framework for modeling flow through random heterogeneous porous media
Journal of Computational Physics
Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems
Journal of Computational Physics
Journal of Computational Physics
A least-squares approximation of partial differential equations with high-dimensional random inputs
Journal of Computational Physics
Padé-Legendre approximants for uncertainty analysis with discontinuous response surfaces
Journal of Computational Physics
A domain adaptive stochastic collocation approach for analysis of MEMS under uncertainties
Journal of Computational Physics
Journal of Computational Physics
Polynomial chaos representation of spatio-temporal random fields from experimental measurements
Journal of Computational Physics
Linear quadratic regulation of systems with stochastic parameter uncertainties
Automatica (Journal of IFAC)
Multi-element probabilistic collocation method in high dimensions
Journal of Computational Physics
IROS'09 Proceedings of the 2009 IEEE/RSJ international conference on Intelligent robots and systems
Numerical approach for quantification of epistemic uncertainty
Journal of Computational Physics
Using polynomial chaos to compute the influence of multiple random surfers in the PageRank model
WAW'07 Proceedings of the 5th international conference on Algorithms and models for the web-graph
Time-dependent generalized polynomial chaos
Journal of Computational Physics
A non-adapted sparse approximation of PDEs with stochastic inputs
Journal of Computational Physics
SIAM Journal on Scientific Computing
Structural and Multidisciplinary Optimization
Uncertainty investigations in nonlinear aeroelastic systems
Journal of Computational and Applied Mathematics
A Posteriori Error Analysis of Stochastic Differential Equations Using Polynomial Chaos Expansions
SIAM Journal on Scientific Computing
Multiscale Stochastic Preconditioners in Non-intrusive Spectral Projection
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
Error Estimates for the ANOVA Method with Polynomial Chaos Interpolation: Tensor Product Functions
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Bayesian inference with optimal maps
Journal of Computational Physics
Wave scattering by randomly shaped objects
Applied Numerical Mathematics
Numerical schemes for dynamically orthogonal equations of stochastic fluid and ocean flows
Journal of Computational Physics
Multiparameter Spectral Representation of Noise-Induced Competence in Bacillus Subtilis
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Journal of Computational Physics
Uncertainty quantification in hybrid dynamical systems
Journal of Computational Physics
Simplex stochastic collocation with ENO-type stencil selection for robust uncertainty quantification
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Extended stochastic FEM for diffusion problems with uncertain material interfaces
Computational Mechanics
Subcell resolution in simplex stochastic collocation for spatial discontinuities
Journal of Computational Physics
A stochastic Galerkin method for the Euler equations with Roe variable transformation
Journal of Computational Physics
Journal of Computational Physics
Grid and basis adaptive polynomial chaos techniques for sensitivity and uncertainty analysis
Journal of Computational Physics
Hi-index | 31.63 |
We formulate a Multi-Element generalized Polynomial Chaos (ME-gPC) method to deal with long-term integration and discontinuities in stochastic differential equations. We first present this method for Legendre-chaos corresponding to uniform random inputs, and subsequently we generalize it to other random inputs. The main idea of ME-gPC is to decompose the space of random inputs when the relative error in variance becomes greater than a threshold value. In each subdomain or random element, we then employ a generalized polynomial chaos expansion. We develop a criterion to perform such a decomposition adaptively, and demonstrate its effectiveness for ODEs, including the Kraichnan-Orszag three-mode problem, as well as advection-diffusion problems. The new method is similar to spectral element method for deterministic problems but with h-p discretization of the random space.