Molecular simulations have become an essential tool in biology, chemistry and physics. Unfortunately, they still remain computationally challenging. In this dissertation, we propose algorithms that accelerate molecular simulations by clustering particles into rigid bodies.We first study several neighbor-search algorithms for large rigid bodies, and show that hierarchy-based algorithms may provide significant speedups. Accordingly, we propose a technique to build a hierarchical representation of an arbitrary molecular graph. We show how this technique can be used in adaptive torsion-angle mechanics, a simulation method that describes molecules as articulated rigid bodies. Finally, we introduce ARPS – Adaptively Restrained Particle Simulations – a mathematically-grounded method able to switch positional degrees of freedom on and off. We propose two switching strategies, and illustrate the advantages of ARPS on various examples. In particular, we show how ARPS allow us to smoothly trade between precision and speed, and to efficiently compute correct static equilibrium properties on molecular systems.
