Martin Heida, WIAS Berlin, & Marcus Weber, Zuse Institut Berlin

"What is... SQRA discretization of the Fokker-Planck equation?"

Estimating the probability of rare events with the help of sampling methods is a difficult problem area of our CRC 1114. Particularly in the field of molecular simulations, it is important to know the rate at which chemical complexes are formed or dissociate. In SQRA (square root approximation), these type of processes are discretized by a finite volume operator in the state space where the transition rates between "neighboring" states of the system are estimated in a special mathematical way. The resulting SQRA operator has good qualitative (high dimension) and quantitative (low dimension) convergence properties. It is related to the known exponential fitting scheme (Scharfetter-Gummel) but imposes less difficulties in the proof of convergence. However, we can show that these two methods are asymptotically equivalent.