Wavelet-Based Methods to Partition Multibody Systems with Contact in Dynamic Simulation

The performance of physics simulation of multibody systems with contact can be enhanced by viewing the system as being composed of subsystems of bodies, and solving the dynamics of these subsystems in parallel. This approach to partition a system into subsystems, known as substructuring, is often based on topological information, such as the connectivity of a body in the system. However, substructuring based on topology may generate a potentially large number of equivalent decompositions, especially in highly symmetric systems, thus requiring a way to choose one partition over another. We propose that augmenting a topology-based partitioning scheme with dynamical information about the interactions between bodies may provide speedups by including temporal information about the constraint relationships between bodies. The simulation of multibody systems with contact typically exhibit non-stationary and multiscale interactions, which suggests a subsystem can be defined as a collection of bodies which have complex interactions with each other. We define complexity by introducing a novel metric based on the spread of time scales from a wavelet analysis of constraints between bodies. We show that for systems where purely topological information about the interaction between bodies is redundant, including dynamical information not only removes redundancy, but also can achieve significant computational speedups. Our results highlight the versatility of using dynamical information to look at large-scale structure in multibody simulations.