A Framework for Scheduling Multi-rate Circuit Simulation

This paper presents a theoretical framework for scheduling of subcircuit simulation in a multirate simulation environment. We show that event-driven simulation, selective-trace, and latency are subsumed by this framework. We assume that the circuit to be simulated is partitioned into subcircuits and that the dependency relations can be expressed as a directed acyclic graph. Each subcircuit predicts its own stepsize, and we assume that a subcircuit can be simulated over some step only when all its inputs are known over that step. It is possible to show that the problem of scheduling the subcircuits subject to these constraints to minimize the amount of memory used to store intermediate voltages is NP-Complete [NV88]. We therefore propose a greedy algorithm that at each step in the schedule, simulates the subcircuit that requires the minimal amount of memory. The algorithm has been implemented in the circuit simulator XPSIM, and the performance improvement due to the scheduling technique is demonstrated on a number of circuits. Extensions of the approach to cyclic dependency graphs using the method of waveform relaxation are discussed in a section on future work.