Direct and Inverse Problems for PDEs with Random Coefficients - Abstract

Sochala, Pierre

Methods based on level set polynomial chaos expansion for uncertain stiff problem with applications to fluid flows

We propose an alternative approach of the non intrusive stochastic spectral method for uncertain stiff problem. The principle of our approach is to decompose the level sets of a preconditioning quantity of interest. This method is more accurate and less expensive than the classical approach. An adaptive choice of the level set furnishes an approximation minimizing the space error interpolation. The reduction of the number of model evaluation due to the regularity of the level set widely exceeds the additional computational cost induced in the post-processing phase. We apply the method to subsurface flows especially for infiltration test cases with uncertain hydraulic conductivity, initial and boundary conditions. Homogeneous and heterogeneous soils are considered with log-uniform or log-normal distribution and a sensitivity analysis is performed to evaluate the influence of each stochastic parameter.