On Computational Strategies within Molecular Dynamics Simulation

Present-day computational mathematics tries to overcome the boundaries beset by time (of calculation) and space (of memory allocation). To this end, novel computational strategies have been developed in order to devise efficient numerical algorithms. One of these is based on the partial relaxation of the mathematical constraints defining the calculation. We illustrate how such a strategy, which we shall refer to as approximate computational complexity, has found many successful applications in the molecular dynamics simulation of condensed-matter model systems. This strategy has also been diffusely applied to abstract theories to an extent that one can even recognize the birth of a novel form of theory that, while not describing the real world, has nonetheless a legitimate existence on a computer.