High Performance Algorithms and Implementations Using Sparse and Parallelization Techniques on MBS

In this paper we will see how the efficiency of the MBS simulations can be improved in two different ways, by considering both an explicit and implicit semi-recursive formulation. The explicit method is based on a double velocity transformation that involves the solution of a redundant but compatible system of equations. The high computational cost of this operation has been drastically reduced by taking into account the sparsity pattern of the system. Regarding this, the goal of this method is the introduction of MA48, a high performance mathematical library provided by Harwell Subroutine Library. The second method proposed in this paper has the particularity that, depending on the case, between 70 and 85% of the computation time is devoted to the evaluation of forces derivatives with respect to the relative position and velocity vectors. Keeping in mind that evaluating these derivatives can be decomposed into concurrent tasks, the main goal of this paper lies on a successful and straightforward parallel implementation that have led to a substantial improvement with a speedup of 3.2 by keeping all the cores busy in a quad-core processor and distributing the workload between them, achieving on this way a huge time reduction by doing an ideal CPU usage