A note on windowing for the waveform relaxation method

摘要

The technique of windowing has often been used in the implementation of the waveform relaxation method for solving ordinary differential equations and time-dependent partial differential equations. Its efficiency depends upon the operator splitting and the coupling of the subsystems involved. For two model problems, estimates for the window length and convergence rate for the early phase of the iteration are derived. The effectiveness of windowing is then investigated, leading to some suggestions for the use of windowing. The discussions are supported by the computational results.