An Approach to Parallel Simulation of Ordinary Differential Equations

Abstract

Cyber-physical systems (CPS) represent a class of complex engineered systems where functionality and behavior emerge through the interaction between the computational and physical domains. Simulation provides design engineers with quick and accurate feedback on the behaviors generated by their designs. However, as systems become more complex, simulating their behaviors becomes computation all complex. But, most modern simulation environments still execute on a single thread, which does not take advantage of the processing power available on modern multi-core CPUs. This paper investigates methods to partition and simulate differential equation-based models of cyber-physical systems using multiple threads on multi-core CPUs that can share data across threads. We describe model partitioning methods using fixed step and variable step numerical in-tegration methods that consider the multi-layer cache structure of these CPUs to avoid simulation performance degradation due to cache conflicts. We study the effectiveness of each parallel simu-lation algorithm by calculating the relative speedup compared to a serial simulation applied to a series of large electric circuit models. We also develop a series of guidelines for maximizing performance when developing parallel simulation software intended for use on multi-core CPUs.