QMC methods for high dimensional Fokker-Planck equations

In order to determine the dynamic behavior of dilute polymeric liquids, we use the standard bead-spring model of polymer chains and describe the solvent interaction with a stochastic differential equation in the limit of neglectable inertia. Since the state of a bead-spring chain is given by the collection of all connecting vectors between the beads, a chain with 21 beads, for example, leads to a 60-dimensional state space. Instead of solving a coupled system of 60 stochastic differential equations, one can alternatively try to solve a Fokker-Planck equation for the probability density of the random process on a 60-dmensional space.

In this project, we employ quasi Monte-Carlo (QMC) methods for the solution of the Fokker-Planck equation. The hope is that the better convergence properties of QMC methods compared to Monte-Carlo (MC) methods in the case of integration problems carry over to this situation.