Modular representation of asynchronous geometric integrators with support for dynamic topology

Abstract

Geometric integrators play an essential role for simulating second-order energy preserving systems, offering an alternative to the decomposition of systems into first-order Ordinary Differential Equations. This approach, although commonly used nowadays in modeling and simulation software, is not acceptable when long simulation runs are required. In this work we develop a modular representation of geometric, adaptive step-size integrators using the Heterogeneous Flow Systems Specification (HyFlow) formalism. Modularity is achieved in HyFlow through the use of an explicit definition of sampling that is treated as a first-order construct, enabling a novel representation of continuous systems and their seamless integration. We show that the HyFlow representation enables the interoperability of geometrical integrators with other families of models including, for example, conventional integrators, enhancing the ability to represent complex systems. HyFlow sampling enables geometric integrators to operate asynchronously, contributing to simulation efficiency by allowing the sampling rate to de defined independently by each component. We demonstrate that HyFlow-based geometric integrators can be used to model systems with a dynamic topology. In addition, we show that the modifying model topology at run-time can provide an effective solution to some systems exhibiting Zeno behavior.