We shortly review the uncoupling-coupling method, a Markov chain
Monte Carlo based approach to compute statistical properties of systems like
medium-sized biomolecules. This technique has recently been proposed for the efficient computation of biomolecular conformations. One crucial step of UC is the
decomposition of reversible nearly uncoupled Markov chains into rapidly mixing
subchains. We show how the underlying scheme of uncoupling-coupling can also be
applied to stochastic differential equations where it can be translated into a domain
decomposition technique for partial differential equations.