Some Incipient Techniques For Improving Efficiency in Computational Mechanics

Models encountered in computational physics and engineering, in particular computational mechanics, usually involve too many degrees of freedom, too many simulation time-steps, too many iterations (non-linear models, optimization or inverse identification), too many particles (in atomistic descriptions) or simply excessive simulation time (for example when simulation in real time is envisaged). Some examples of those scenarios are encountered in computational chemistry involving large time scale differences (reaction versus diffusion), direct numerical simulation of fluid flows (analysis of turbulence), kinetic theory descriptions of solid and fluids (including complex fluids) that usually involve multi-dimensional models with the associated curse of dimensionality problematic, virtual surgery, mechanical systems involving localized behavior, ... In our former works (see [1] and the references therein) some new strategies of model reduction and computational time saving have been proposed. In what follows the main ideas of those techniques are revisited. 2 GENERAL FORM OF THE PROBLEM