By studying the superlinear convergence of waveform relaxation method on finite time intervals, it has formerly been shown, by using the theory of quasinilpotent operators, that the convergence properties are largely determined by the graph properties of the splitting. In this paper, we show how the directed graphs associated to the decomposition are modified when overlapping splittings are used. In particular, we explain how overlapping should be used in order to best accelerate convergence of the iteration method.
@Article{ Miekkala_1998aa,
abstract = {<P>By studying the superlinear convergence of waveform relaxation method on finite time intervals, it has formerly been shown, by using the theory of quasinilpotent operators, that the convergence properties are largely determined by the graph properties of the splitting. In this paper, we show how the directed graphs associated to the decomposition are modified when overlapping splittings are used. In particular, we explain how overlapping should be used in order to best accelerate convergence of the iteration method.</P>},
author = {Miekkala, Ulla},
doi = {10.1016/S0377-0427(97)00224-0},
file = {Miekkala_1998aa.pdf},
journal = {Journal of Computational and Applied Mathematics},
keywords = {waveform-relaxation,overlapping,cosimulation,splitting,convergence},
langid = {english},
number = {2},
pages = {349--361},
title = {Remarks on waveform relaxation method with overlapping splittings},
volume = {88},
year = {1998},
shortjournal = {J. Comput. Appl. Math.}
}