Connecting waveform relaxation convergence properties to the a-stability of multirate integration methods

Application of the waveform relaxation algorithm to the differential-algebraic equations generated by problems in circuit and semiconductor device simulation have demonstrated that the method often contracts uniformly in time. In addition, instabilities in the underlying multirate integration method have not been observed. In this paper, it is proved that multirate A-stability and waveform relaxation uniform contractivity are connected, and use the result to show that the first and second-order backward-difference based multirate methods are A-stable when applied to block diagonally-dominant problems. © 1991, MCB UP Limited