[en] The developments presented make it economically feasible to use a time-explicit numerical code to perform thermomechanical simulations of quasi-static systems that incorporate physically small source regions (or centers of activity) in a relatively large space. A nuclear waste repository in a geological medium is an example of such a system. The technique developed make it possible to eliminate two major restrictions that explicit-finite difference codes generally have that can considerably limit their efficiency. The technique is a time-step optimization method called pseudo-time steps (PTS). This report describes the motivation, derivation, and implementation of the PTS method