On the effect of linear algebra implementations in real-time multibody system dynamics

Abstract

[Abstract] This paper compares the efficiency of multibody system (MBS) dynamic simulation codes that rely on different implementations of linear algebra operations. The dynamics of an N-loop four-bar mechanism has been solved with an index-3 augmented Lagrangian formulation combined with the trapezoidal rule as numerical integrator. Different implementations for this method, both dense and sparse, have been developed, using a number of linear algebra software libraries (including sparse linear equation solvers) and optimized sparse matrix computation strategies. Numerical experiments have been performed in order to measure their performance, as a function of problem size and matrix filling. Results show that optimal implementations can increase the simulation efficiency in a factor of 2–3, compared with our starting classical implementations, and in some topics they disagree with widespread beliefs in MBS dynamics. Finally, advices are provided to select the implementation which delivers the best performance for a certain MBS dynamic simulation.