Multiscale Computations for Kinetic and Related Problems

Multiscale control variate methods for kinetic equations with random inputs

Lorenzo Pareschi

University of Ferrara

Kinetic equations play a major rule in modeling large systems of interacting particles. Uncertainties may be due to various reasons, like lack of knowledge on the microscopic interaction details or incomplete informations at the boundaries. These uncertainties, however, contribute to the curse of dimensionality and the development of efficient numerical methods is a challenge. In this paper we consider the construction of novel Monte Carlo methods for such problems which, thanks to a multi-scale control variate approach, are capable to reduce the variance of standard Monte Carlo techniques. Generalization to the case of multiple control variates are also discussed.