Model transitions and optimization problem in multi-flexible-body systems: Application to modeling molecular systems

This paper presents an efficient algorithm for the simulation of multi-flexible-body systems undergoing discontinuous changes in model definition. The equations governing the dynamics of the transitions from a higher to a lower fidelity model and vice versa are formulated through imposing/removing certain constraints on/from the system model. The issue of the non-uniqueness of the results associated with the transition from a lower to a higher fidelity model may be handled by solving an optimization problem. This optimization problem is subjected to the satisfaction of the constraint imposed by the generalized impulse-momentum equations. The divide-and-conquer algorithm (DCA) is applied to formulate the jumps in the system states resulting from the model transition. The DCA formulation in its basic form is both time and processor optimal and results in linear and logarithmic complexity when implemented in serial and parallel with O(n) processors, respectively. As such, its application can reduce the effective computational cost of formulating and solving the optimization problem in the transitions to the finer models. The principal aspects of the mathematics for the algorithm implementation is developed and numerical examples are provided to validate the method.