Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
The Hermite spectral method for Gaussian-type functions
SIAM Journal on Scientific Computing
Spectral Polynomial Chaos Solutions of the Stochastic Advection Equation
Journal of Scientific Computing
Uncertainty propagation using Wiener-Haar expansions
Journal of Computational Physics
Multi-resolution analysis of wiener-type uncertainty propagation schemes
Journal of Computational Physics
Stochastic Power Grid Analysis Considering Process Variations
Proceedings of the conference on Design, Automation and Test in Europe - Volume 2
Uncertainty analysis for the steady-state flows in a dual throat nozzle
Journal of Computational Physics
Using stochastic analysis to capture unstable equilibrium in natural convection
Journal of Computational Physics
An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
Journal of Computational Physics
Stochastic analysis of interconnect performance in the presence of process variations
Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design
Wiener Chaos expansions and numerical solutions of randomly forced equations of fluid mechanics
Journal of Computational Physics
Journal of Computational Physics - Special issue: Uncertainty quantification in simulation science
Uncertainty estimation and prediction for interdisciplinary ocean dynamics
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
A stochastic variational multiscale method for diffusion in heterogeneous random media
Journal of Computational Physics
Statistical model order reduction for interconnect circuits considering spatial correlations
Proceedings of the conference on Design, automation and test in Europe
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
Stochastic extended Krylov subspace method for variational analysis of on-chip power grid networks
Proceedings of the 2007 IEEE/ACM international conference on Computer-aided design
Finite Elements in Analysis and Design
Journal of Computational Physics
Robust stability and performance analysis using polynomial chaos theory
Proceedings of the 2007 Summer Computer Simulation Conference
Variational capacitance modeling using orthogonal polynomial method
Proceedings of the 18th ACM Great Lakes symposium on VLSI
Journal of Computational Physics
Building Blocks for Computer Vision with Stochastic Partial Differential Equations
International Journal of Computer Vision
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
Statistical modeling and analysis of chip-level leakage power by spectral stochastic method
Proceedings of the 2009 Asia and South Pacific Design Automation Conference
Journal of Computational Physics
Numerical analysis of the Burgers' equation in the presence of uncertainty
Journal of Computational Physics
Statistical modeling and analysis of chip-level leakage power by spectral stochastic method
Integration, the VLSI Journal
Linear quadratic regulation of systems with stochastic parameter uncertainties
Automatica (Journal of IFAC)
Performance evaluation of generalized polynomial chaos
ICCS'03 Proceedings of the 2003 international conference on Computational science
Uncertainty propagation using polynomial chaos and centre manifold theories
ISPRA'10 Proceedings of the 9th WSEAS international conference on Signal processing, robotics and automation
A joint diagonalisation approach for linear stochastic systems
Computers and Structures
WSEAS TRANSACTIONS on SYSTEMS
Time-dependent generalized polynomial chaos
Journal of Computational Physics
Efficient solution for Galerkin-based polynomial chaos expansion systems
Advances in Engineering Software
Variational capacitance extraction and modeling based on orthogonal polynomial method
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Efficient stochastic structural analysis using Guyan reduction
Advances in Engineering Software
Kernel principal component analysis for stochastic input model generation
Journal of Computational Physics
Mathematics and Computers in Simulation
Galerkin Methods for Stochastic Hyperbolic Problems Using Bi-Orthogonal Polynomials
Journal of Scientific Computing
Epidemic models with random coefficients
Mathematical and Computer Modelling: An International Journal
Wave scattering by randomly shaped objects
Applied Numerical Mathematics
Error analysis of generalized polynomial chaos for nonlinear random ordinary differential equations
Applied Numerical Mathematics
Statistical extraction and modeling of inductance considering spatial correlation
Analog Integrated Circuits and Signal Processing
Uncertainty quantification in hybrid dynamical systems
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Uncertainty quantification for integrated circuits: stochastic spectral methods
Proceedings of the International Conference on Computer-Aided Design
A one-time truncate and encode multiresolution stochastic framework
Journal of Computational Physics
An adaptive ANOVA-based PCKF for high-dimensional nonlinear inverse modeling
Journal of Computational Physics
Grid and basis adaptive polynomial chaos techniques for sensitivity and uncertainty analysis
Journal of Computational Physics
Hi-index | 31.57 |
We present a new algorithm to model the input uncertainty and its propagation in incompressible flow simulations. The stochastic input is represented spectrally by employing orthogonal polynomial functionals from the Askey scheme as trial basis to represent the random space. A standard Galerkin projection is applied in the random dimension to obtain the equations in the weak form. The resulting system of deterministic equations is then solved with standard methods to obtain the solution for each random mode. This approach can be considered as a generalization of the original polynomial chaos expansion, first introduced by Wiener [Am. J. Math. 60 (1938) 897]. The original method employs the Hermite polynomials (one of the 13 members of the Askey scheme) as the basis in random space. The algorithm is applied to micro-channel flows with random wall boundary conditions, and to external flows with random freestream. Efficiency and convergence are studied by comparing with exact solutions as well as numerical solutions obtained by Monte Carlo simulations. It is shown that the generalized polynomial chaos method promises a substantial speed-up compared with the Monte Carlo method. The utilization of different type orthogonal polynomials from the Askey scheme also provides a more efficient way to represent general non-Gaussian processes compared with the original Wiener-Hermite expansions.