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 integration 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 simulation 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.

Modeling and simulation of large-scale systems: A systematic comparison of modeling paradigms

“…The results of a prototype implementation showed that the use of GPU speeds up the simulations by a factor of five. Carl and Biswas [35] investigated methods to partition and simulate differential equation-based models of cyber-physical systems (using a subset of Modelica) using multiple threads on multi-core CPUs;…”

Parallel Integration Algorithm and Its Usage for a Practical Simulation of Spacecraft Attitude Motion

“…This issue also applies to existing simulation tools that are used to simulation complex dynamic systems, for example, cyber-physical systems. 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 (Carl & Biswas, 2016). The usage of a bundle of multiple parallel processes or threads that are not consistent with an architecture of the multi-core processors also can be a cause of an inefficient exploitation of the multi-core processors and even can lead to a loss of operating speed compared to non multi-core processors.…”

“…Majid, Mehrkanoon and Othman (2010) employed MPI technology for their parallel block method for solving large systems of ODEs. In (Carl & Biswas, 2016) the multi-threaded implementation in C++ has developed for parallel solution of ODEs on a multi-core CPUs. Approaches to parallel solution of the ODEs on the GPUs are given in (Al-Omari, Arnold, Taha & Schuttler, 2013;Ahnert, Demidov, & Mulansky, 2014).…”