Convergence Study of Dynamic Iteration Methods Using Compound and Multirate Discretization

摘要

For a linear model problem considered on infinite time interval, the convergence rate of the dynamic iteration method is determined by the chosen decomposition. As the main advantage of WR (Waveform Relaxation) method comes from parallel independent integration of different subsystems, the authors study the convergence rate of the discretized WR iteration when compound and multirate methods are applied. It is shown that provided that strictly stable integration methods are used, then the convergence rate is still essentially that of the underlying time continuous problem when the time step is small enough. The effect of the interpolation method used in connection with the multirate method is also discussed.