Journal
SIAM JOURNAL ON NUMERICAL ANALYSIS
Volume 45, Issue 2, Pages 666-697Publisher
SIAM PUBLICATIONS
DOI: 10.1137/050642137
Keywords
domain decomposition; waveform relaxation; Schwarz methods; time parallelism
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We study in this paper a new class of waveform relaxation algorithms for large systems of ordinary differential equations arising from discretizations of partial differential equations of advection reaction diffusion type. We show that the transmission conditions between the subsystems have a tremendous influence on the convergence speed of the waveform relaxation algorithms, and we identify transmission conditions with optimal performance. Since these optimal transmission conditions are expensive to use, we introduce a class of local transmission conditions of Robin type, which approximate the optimal ones and can be used at the same cost as the classical transmission conditions. We determine the transmission conditions in this class with the best performance of the associated waveform relaxation algorithm. We show that the new algorithm is well posed and converges much faster than the classical one. We illustrate our analysis with numerical experiments.
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