For several decades Brownian dynamics of polymers has attracted rising interest among physicists, chemists, material scientists and engineers. Many processes of crucial importance especially in biophysics are well-known to be governed by the Brownian dynamics of polymers.
Computer simulations have become increasingly popular in order to study this dynamics. For such simulations Brownian dynamics is usually modeled by means of a stochastic partial differential equation. The polymers subject to this dynamics are usually modeled as a chain of beads and rods in order to account for structural mechanics. So called bead-spring- and bead-rod-models together with an explicit time integration scheme are especially popular. However, there is a number of drawbacks of such models, especially with respect to numerical stability and a missing sound theoretical foundation.
In this talk we introduce a new approach for the numerical simulation of Brownian dynamics of polymers by means of the so called finite element method. We show the extensions necessary for non-linear finite beam elements in order capture Brownian polymer dynamics and discuss the advantages of this approach over other model, especially bead-spring- and bead-rod-models. We demonstrate the efficiency of the method by means of several numerical examples with respect to biophysics. Finally we give a brief outlook how the finite element approach for Brownian polymer dynamics could be exploited to understand phenomena such as mechanics of the cytoskeleton or cell motility.