Multiple steady states for characteristic initial value problems
Applied Numerical Mathematics - Special issue in honor of Milt Rose's sixtieth birthday
Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Nested multivariate Padé approximants
ICCAM '96 Proceedings of the seventh international congress on Computational and applied mathematics
Generalized multivariate Pade´ approximants
Journal of Approximation Theory
Multivariate Padé approximation
Journal of Computational and Applied Mathematics - Special issue on numerical analysis in the 20th century vol. 1: approximation theory
Multi-resolution analysis of wiener-type uncertainty propagation schemes
Journal of Computational Physics
Uncertainty analysis for the steady-state flows in a dual throat nozzle
Journal of Computational Physics
Analysis of Some Padé--Chebyshev Approximants
SIAM Journal on Numerical Analysis
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
Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures
SIAM Journal on Scientific Computing
Padé-Legendre Interpolants for Gibbs Reconstruction
Journal of Scientific Computing
Measures of agreement between computation and experiment: validation metrics
Journal of Computational Physics - Special issue: Uncertainty quantification in simulation science
A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Uncertainty Quantification given Discontinuous Model Response and a Limited Number of Model Runs
SIAM Journal on Scientific Computing
Journal of Computational Physics
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
Hi-index | 31.46 |
A novel uncertainty propagation method for problems characterized by highly non-linear or discontinuous system responses is presented. The approach is based on a Pade-Legendre (PL) formalism which does not require modifications to existing computational tools (non-intrusive approach) and it is a global method. The paper presents a novel PL method for problems in multiple dimensions, which is non-trivial in the Pade literature. In addition, a filtering procedure is developed in order to minimize the errors introduced in the approximation close to the discontinuities. The numerical examples include fluid dynamic problems characterized by shock waves: a simple dual throat nozzle problem with uncertain initial state, and the turbulent transonic flow over a transonic airfoil where the flight conditions are assumed to be uncertain. Results are presented in terms of statistics of both shock position and strength and are compared to Monte Carlo simulations.