Hybrid-Parallel Calculation Of Jacobians In Multi-Body Dynamics

Implicit integration methods are often used for numerically stiff multi-body systems in order to reduce the timestep-size. But within most implicit integration methods, the JACOBIAN of the right hand side must be calculated at every step. In case of multibody dynamics, this is the vector of generalized forces and the calculation of its JACOBIAN can be so expensive, that it often outweighs the advantage of a bigger step-size. For large systems, this task can take more than 99% of the whole simulation time, while it can be easily parallelized. In this paper, a hybrid-parallel implementation of calculating this JACOBIAN is presented With a combination of MPI and OpenMP, simulations on up to 512 cores are run. The experiments are carried out on a high-performance-computing cluster with an infiniband network. The performance of a pure MPI implementation is compared to several hybrid variants, using different numbers of OpenMP threads per process.