Essential molecular dynamics: Progress in a new algorithmic approach

Recently, the author -- together with his co-authors Michael Dellnitz, Oliver Junge, and Christof Schütte -- developed a new algorithmic approach to molecular dynamics, which is based on the computation of almost invariant sets of Hamiltonian systems. In this approach, only well-conditioned short term subtrajectories in lieu of ill-posed long term trajectories (which are typically used in Monte Carlo simulations) are exploited. The aim is to directly compute averages of physical observables, comformations and conformational changes - informations that are actually desired by computational chemistry. Mathematically speaking, such informations come out of the computation of the invariant measures and sets (corresponding to the dominant eigenvalue 1 and infinite relaxation time) and almost invariant measures and sets (corresponding to eigenmodes for eigenvalues close to 1 and therefore finite, but "large" relaxation times). An adaptive multilevel box method or subdivision technique is presented, which helps to solve the arising stochastic eigenvalue problem "fast". The basic concepts of the new algorithm and recent speed-ups will be presented.