Selective Evaluation of RHS during Multi-Rate Simulation

Abstract

Modeling across physical domains can lead to coupledsystems that operate on different time scales.Moreover, spatially discretized models can have dynamicbehavior on only a small portion of the whole system, whilethat portion might move over time.With a single rate solver like DASSL, the step size isrestricted to fast dynamics of a few states while theothers could do much larger time steps, degrading theoverall simulation speed.Recent development of the Generic Bi-rate ODE (GBODE)solver within the OpenModelica simulation environmentaddresses these models.It allows for adaptive partitioning of slow and fast statesand progresses these partitions with different time steps.However, substantial performance improvements were not yetobserved, in part because of the rigid evaluation structureof the generated code.During each small step only the derivatives of fast statesare required, but all derivatives are computed.This paper demonstrates the use of selective equationevaluation to reduce the computational cost of multi-rateintegration as shown on a scalable example of a distributedheating system.Further uses for selective evaluation during the simulationprocess are discussed and a complexity analysis is given.