Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Multiresolution representation of data: a general framework
SIAM Journal on Numerical Analysis
Multiresolution Schemes for the Numerical Solution of 2-D Conservation Laws I
SIAM Journal on Scientific Computing
High resolution schemes for hyperbolic conservation laws
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
Multiresolution Representation in Unstructured Meshes
SIAM Journal on Numerical Analysis
Fully adaptive multiresolution finite volume schemes for conservation laws
Mathematics of Computation
Modeling uncertainty in flow simulations via generalized polynomial chaos
Journal of Computational Physics
Uncertainty propagation using Wiener-Haar expansions
Journal of Computational Physics
Multi-resolution analysis of wiener-type uncertainty propagation schemes
Journal of Computational Physics
Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure
SIAM Journal on Scientific Computing
Beyond Wiener---Askey Expansions: Handling Arbitrary PDFs
Journal of Scientific Computing
Sparse grid collocation schemes for stochastic natural convection problems
Journal of Computational Physics
Journal of Computational Physics
A domain adaptive stochastic collocation approach for analysis of MEMS under uncertainties
Journal of Computational Physics
Multi-element probabilistic collocation method in high dimensions
Journal of Computational Physics
Time-dependent generalized polynomial chaos
Journal of Computational Physics
Quasi-Monte Carlo methods for elliptic PDEs with random coefficients and applications
Journal of Computational Physics
Journal of Computational Physics
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In this work a novel adaptive strategy for stochastic problems, inspired from the classical Harten@?s framework, is presented. The proposed algorithm allows building, in a very general manner, stochastic numerical schemes starting from a whatever type of deterministic schemes and handling a large class of problems, from unsteady to discontinuous solutions. Its formulations permits to recover the same results concerning the interpolation theory of the classical multiresolution approach, but with an extension to uncertainty quantification problems. The present strategy permits to build numerical scheme with a higher accuracy with respect to other classical uncertainty quantification techniques, but with a strong reduction of the numerical cost and memory requirements. Moreover, the flexibility of the proposed approach allows to employ any kind of probability density function, even discontinuous and time varying, without introducing further complications in the algorithm. The advantages of the present strategy are demonstrated by performing several numerical problems where different forms of uncertainty distributions are taken into account, such as discontinuous and unsteady custom-defined probability density functions. In addition to algebraic and ordinary differential equations, numerical results for the challenging 1D Kraichnan-Orszag are reported in terms of accuracy and convergence. Finally, a two degree-of-freedom aeroelastic model for a subsonic case is presented. Though quite simple, the model allows recovering some physical key aspect, on the fluid/structure interaction, thanks to the quasi-steady aerodynamic approximation employed. The injection of an uncertainty is chosen in order to obtain a complete parameterization of the mass matrix. All the numerical results are compared with respect to classical Monte Carlo solution and with a non-intrusive Polynomial Chaos method.