THERMAL SCIENCE

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Shu-Lin Wu

SCHWARZ WAVEFORM RELAXATION ALGORITHM FOR HEAT EQUATIONS WITH DISTRIBUTED DELAY

ABSTRACT
Heat equations with distributed delay are a class of mathematic models that has wide applications in many fields. Numerical computation plays an important role in the investigation of these equations, because the analytic solutions of partial differential equations with time delay are usually unavailable. On the other hand, duo to the delay property, numerical computation of these equations is time-consuming. To reduce the computation time, we analyze in this paper the Schwarz waveform relaxation algorithm with Robin transmission conditions. The Robin transmission conditions contain a free parameter, which has a significant effect on the convergence rate of the Schwarz waveform relaxation algorithm. Determining the Robin parameter is therefore one of the top-priority matters for the study of the Schwarz waveform relaxation algorithm. We provide new formula to fix the Robin parameter and we show numerically that the new Robin parameter is more efficient than the one proposed previously in the literature.
KEYWORDS
Schwarz waveform relaxation, heat equation, distributed delay, parameter optimization, convergence analysis
PAPER SUBMITTED: 2016-02-01
PAPER REVISED: 2016-03-11
PAPER ACCEPTED: 2016-03-22
PUBLISHED ONLINE: 2016-09-24
DOI REFERENCE: https://doi.org/10.2298/TSCI16S3659W
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2016, VOLUME 20, ISSUE Supplement 3, PAGES [S659 - S667]
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Schwarz waveform relaxation algorithm for heat equations with distributed delay

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