Recursive inverse matrix algorithm in granular mechanics applications

A recursive algorithm is presented which allows to deal efficiently with overconstrained clusters of particles with variable in time interconnectivity. The algorithm is based on a numerically generated inverse matrix for the system and is given in terms of the updates if a link between any two particles is added or eliminated. The method is demonstrated for plane granular clusters comprising disks: a pile and a hopper. The efficiency and accuracy of the algorithm is investigated numerically and the results are compared with the ones obtained by the Gauss elimination algorithm. It is shown that for an 800-particle system in a hopper the computing time needed when the presented algorithm is used is 10 times less than that for the Gauss algorithm.