On the Numerical Solution of Many-Body Contact Dynamics Problems Formulated as Complementarity Problems

This contribution is concerned with the modeling and simulation of many-body dynamics problems. In such problems, the solution method has to routinely handle millions of unknowns when, for instance, investigating granular dynamics related phenomena. Given the size of these problems, the scope of tractable applications may be limited by computational efficiency and/or computational accuracy. This scenario has been found to be the case when the equations of motion embed a differential variational inequality (DVI) problem that captures frictional/contact interactions between rigid and/or flexible bodies. As the size of the system increases, the speed and quality of the numerical solution may decrease. This contribution describes an alternative numerical method, called the Gradient Projected Minimum Residual or GPMINRES method, which demonstrates better scalability and performance (in terms of solution speed and accuracy) than methods commonly used to solve problems posed in this manner.