A partitioning algorithm for the parallel solution of differential-algebraic equations by waveform relaxation

Waveform relaxation is a natural method for the solution of large systems of differential-algebraic equations (DAEs), particularly in cases when the variables exhibit multirate behavior and latency. The performance of this method depends heavily on the ability to partition the equations into weakly coupled subsystems. With that in mind, in this paper we present a new multilevel partitioning algorithm which can achieve this for a general class of equations. The algorithm is based on successive applications of epsilon decomposition to the Jacobian which arises in the numerical solution of the equations. A variety of experimental results are provided to evaluate the performance of this method.