Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Ten lectures on wavelets
A class of bases in L2 for the sparse representations of integral operators
SIAM Journal on Mathematical Analysis
Essential wavelets for statistical applications and data analysis
Essential wavelets for statistical applications and data analysis
A stochastic projection method for fluid flow. I: basic formulation
Journal of Computational Physics
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
A stochastic projection method for fluid flow II.: random process
Journal of Computational Physics
Adaptive solution of partial differential equations in multiwavelet bases
Journal of Computational Physics
Modeling uncertainty in flow simulations via generalized polynomial chaos
Journal of Computational Physics
Uncertainty propagation using Wiener-Haar expansions
Journal of Computational Physics
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Monte Carlo Strategies in Scientific Computing
Monte Carlo Strategies in Scientific Computing
An Equation-Free, Multiscale Approach to Uncertainty Quantification
Computing in Science and Engineering
Beyond Wiener---Askey Expansions: Handling Arbitrary PDFs
Journal of Scientific Computing
Journal of Computational Physics - Special issue: Uncertainty quantification in simulation science
Uncertainty quantification of limit-cycle oscillations
Journal of Computational Physics - Special issue: Uncertainty quantification in simulation science
Stochastic analysis of transport in tubes with rough walls
Journal of Computational Physics - Special issue: Uncertainty quantification in simulation science
Stochastic spectral methods for efficient Bayesian solution of inverse problems
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
Discontinuity detection in multivariate space for stochastic simulations
Journal of Computational Physics
Uncertainty quantification for systems of conservation laws
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
Multi-element probabilistic collocation method in high dimensions
Journal of Computational Physics
Intrusive Galerkin methods with upwinding for uncertain nonlinear hyperbolic systems
Journal of Computational Physics
Roe solver with entropy corrector for uncertain hyperbolic systems
Journal of Computational and Applied Mathematics
A non-adapted sparse approximation of PDEs with stochastic inputs
Journal of Computational Physics
SIAM Journal on Scientific Computing
Structural and Multidisciplinary Optimization
Eigenvalues of the Jacobian of a Galerkin-Projected Uncertain ODE System
SIAM Journal on Scientific Computing
A Posteriori Error Analysis of Stochastic Differential Equations Using Polynomial Chaos Expansions
SIAM Journal on Scientific Computing
Data-free inference of the joint distribution of uncertain model parameters
Journal of Computational Physics
Multiscale Stochastic Preconditioners in Non-intrusive Spectral Projection
Journal of Scientific Computing
Journal of Computational Physics
Sampling-free linear Bayesian update of polynomial chaos representations
Journal of Computational Physics
SIAM Journal on Scientific Computing
A Posteriori Error Analysis of Parameterized Linear Systems Using Spectral Methods
SIAM Journal on Matrix Analysis and Applications
Uncertainty Quantification given Discontinuous Model Response and a Limited Number of Model Runs
SIAM Journal on Scientific Computing
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)
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 one-time truncate and encode multiresolution stochastic framework
Journal of Computational Physics
A stochastic Galerkin method for the Euler equations with Roe variable transformation
Journal of Computational Physics
Grid and basis adaptive polynomial chaos techniques for sensitivity and uncertainty analysis
Journal of Computational Physics
Hi-index | 31.56 |
A multi-resolution analysis (MRA) is applied to an uncertainty propagation scheme based on a generalized polynomial chaos (PC) representation. The MRA relies on an orthogonal projection of uncertain data and solution variables onto a multi-wavelet basis, consisting of compact piecewise-smooth polynomial functions. The coefficients of the expansion are computed through a Galerkin procedure. The MRA scheme is applied to the simulation of the Lorenz system having a single random parameter. The convergence of the solution with respect to the resolution level and expansion order is investigated. In particular, results are compared to two Monte-Carlo sampling strategies, demonstrating the superiority of the MRA. For more complex problems, however, the MRA approach may require excessive CPU times. Adaptive methods are consequently developed in order to overcome this drawback. Two approaches are explored: the first is based on adaptive refinement of the multi-wavelet basis, while the second is based on adaptive block-partitioning of the space of random variables. Computational tests indicate that the latter approach is better suited for large problems, leading to a more efficient, flexible and parallelizable scheme.