Uncertainty Quantification for PDEs with Anisotropic Random Diffusion

Tractability of the Quasi-Monte Carlo Quadrature with Halton Points for Elliptic Pdes with Random Diffusion

This article is dedicated to the computation of the moments of the solution to stochastic partial differential equations with log-normal distributed diffusion coefficient by the Quasi-Monte Carlo method. Our main result is the polynomial tractability for the QuasiMonte Carlo method based on the Halton sequence. As a by-product, we obtain also the strong tractability of stochastic partial differ...

WEIGHTED REDUCED ORDER METHODS FOR PARAMETRIZED PDEs IN UNCERTAINTY QUANTIFICATION PROBLEMS

Nonlinear Diffusion Pdes

The main theory behind nonlinear diffusion models is to use nonlinear PDEs to create a scale space representation that consists of gradually simplified images where some image features such as edges are maintained or even enhanced. The earliest nonlinear diffusion model proposed in image processing is the so-called anisotropic diffusion1 by Perona and Malik [2]. In their formulation, they repla...

Anisotropic transport and diffusion of elastic waves in random media

We discuss the influence of material anisotropy on the possible depolarization and diffusion of elastic waves in randomly heterogeneous media. Anisotropy is considered at two levels. The first one is related to the constitutive law of random materials, which may be handled by a random matrix theory for the elasticity tensor. The second level is related to the correlation structure of these rand...

Sensitivity and Uncertainty Quantification of Random Distributed Parameter Systems

As simulation continues to replace experimentation in the design cycle, the need to quantify uncertainty in model parameters and its effect on simulation results becomes critical. While intelligent sampling methods, such as sparse grid collocation, have expanded the class of random systems that can be simulated with uncertainty quantification, the statistical characterization of the model param...