[inria-00340708, v1] Stochastic spectral formulations for elliptic problems

[inria-00182436, v1] Some new simulations schemes for the evaluation of Feynman-Kac representations

We describe new variants of the Euler scheme and of the walk on spheres method for the Monte Carlo computation of Feynman-Kac representations. We optimize these variants using quantization for both source and boundary terms. Numerical tests are given on basic examples and on Monte Carlo versions of spectral methods for the Poisson equation. We especially introduce a new stochastic spectral form...

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators

Solving log-transformed random diffusion problems by stochastic Galerkin mixed finite element methods

Stochastic Galerkin finite element discretisations of PDEs with stochastically nonlinear coefficients lead to linear systems of equations with block dense matrices. In contrast, stochastic Galerkin finite element discretisations of PDEs with stochastically linear coefficients lead to linear systems of equations with block sparse matrices which are cheaper to manipulate and precondition in the f...

Multilevel Monte Carlo Finite Element Methods for Stochastic Elliptic Variational Inequalities

Multi-Level Monte-Carlo Finite Element (MLMC–FE) methods for the solution of stochastic elliptic variational inequalities are introduced, analyzed, and numerically investigated. Under suitable assumptions on the random diffusion coefficient, the random forcing function, and the deterministic obstacle, we prove existence and uniqueness of solutions of “mean-square” and “pathwise” formulations. S...

Shape-Measure Method for Solving Elliptic Optimal Shape Problems (Fixed Control Case)