Parallel projected Gauss-Seidelsolver for large-scale granular matter : Examining the physics of the parallel solver and development of amultigrid solver

Granular matter is found everywhere in nature and some examples include sand, rice,coee beans and iron ore pellets. Many dierent methods exists for simulating granularmatters using computers. In the scope of this thesis a physics engine called AgX Dynamicsfrom Algoryx Simulation AB is used to investigate and further develop methodsinvolving the discrete element method. During the rst half of 2013 a parallel solverfor the projected Gauss-Seidel method was implemented in AgX in order to speed upthe simulation time of simulations involving granular materials. In this thesis projectit is shown that the behaviour of the physics of this parallel solver is identical to theserial solver. Secondly this thesis works on the development of a multigrid solver forthe Gauss-Seidel method. Multigrid in this context means that the particle systemis partitioned in space. Each partition is then merged into a rigid body and contactforces between these rigid bodies is solved to machine precision using a direct solver.The forces from this direct solve is then used when solving the internal part of thepartitions using an iterative projected Gauss-Seidel method. The motivation for developinga multigrid method is to achieve faster convergence and even more speed-upof the solver. Numerical experiments has been performed on a 1D column and a 3Dsilo. The results show high potential of the method and the one-dimensional columnbehaves closer to a direct solver than an iterative solver. The thesis was done for UMIT Research Lab, Umea University and Algoryx SimulationAB