Can complex systems really be simulated?

Abstract

The simulation of complex systems is important in many fields of science and in real-world applications. Such systems are composed of many interacting subsystems. There might exist different software packages for simulating the individual subsystems and co-simulation refers to the simultaneous execution of multiple interacting subsystem simulators. Simulation or co-simulation, if not designed properly, can return misleading numerical solutions (unstable numerical solutions for what is in fact a stable system or vice versa). To understand the cause of these numerical artifacts, we first propose a simple mathematical model for co-simulation, and then construct stability charts. These charts shed light on transitions between stable and unstable behaviour in co-simulation. Our goal is to understand the stability properties of the simulated and co-simulated representation of the continuous system. We will achieve this goal by expressing the trace and determinant of the discretized system in terms of the trace and determinant of the continuous system to establish stability criteria.

Inconsistent Stability of Newmark's Method in Structural Dynamics Applications

“…The results in this paper are partially based on an earlier publication on the phenomenon of inconsistent stability under co-simulation using fourth-order Runge-Kutta (RK4) [6]. In this paper we instead focus on the Newmark method [7], as it is the method of choice in the field of structural mechanics for time integration.…”

“…In this paper we instead focus on the Newmark method [7], as it is the method of choice in the field of structural mechanics for time integration. We also test the theoretical results using multiple numerical case studies, which was not the focus of [6].…”

A robust composite time integration scheme for snap-through problems

“…Instead, consistent stability should be the goal. It is possible that the real response is divergent and yet the integrator produces a stable oscillation (shown in [29]). From an engineering perspective, this case, that was so far ignored, leads to an under-conservative prediction of the response.…”

“…Unconditionally stable integrators may, when applied to complex systems with multiple equilibria, predict trajectories that are non-physical and/or greatly underestimate the severity of the response [45]. Following similar methods with those used in [29,45], a bound on the time step size can be determined to enforce the condition that the algorithm will not predict a stable response for an unstable linear system. The maximal time steps for the methods compared in this paper are shown in Fig.…”

Computational Aeroelasticity of Flying Robots with Flexible Wings

“…In the authors' novel methodology, the dynamical system is partitioned into two subsystems (the structural and aerodynamic models) that communicate with each other across the boundary of the flow field Aerial Robots -Aerodynamics, Control and Applications(the surface of the structure) in a strong way. The computational environment can be considered a strong co-simulation framework [36]. Initial steps taken in this direction are presented in reference [37].…”