Signal-Flow Based Runge-Kutta Methods for the Simulation of Complex Networks
For engineers simulating large circuits or networks with multirate behavior, this method accelerates simulation without significant accuracy loss.
The paper introduces signal-flow based Runge-Kutta methods that exploit system latency and periodic behavior to speed up simulation of complex networks, achieving up to 80-90% reduction in active equations for latent parts.
Complex dynamical networks appear in a wide range of physical, biological, and engineering systems. The coupling of subsystems with varying time scales often results in multirate behavior. During the simulation of highly integrated circuits, for example, only a few elements underlie changing signals whereas the major part -- usually up to 80 or even 90 per cent -- remains latent. Standard integration schemes discretize the entire circuit with a single step size which is mainly limited by the accuracy requirements of the rapidly changing subcircuits. It is of a particular interest to speed up the simulation without a significant loss of accuracy. By exploiting the latency of the system, only a fraction of the equations has to be formulated and solved at a given time point. Günther and Rentrop suggest that multirate strategies must be based both on the numerical information of the integration scheme and on the topology of the circuit. In this paper, we will introduce a directed graph describing the interdependency of the underlying system and propose Runge--Kutta methods which utilize the signal flow of the system in order to identify and exploit inactive regions. Furthermore, we describe an extension of these methods to identify and exploit periodic subsystems.