scholarly journals Optimized Schwarz waveform relaxation for advection reaction diffusion equations in two dimensions

2015 ◽  
Vol 134 (3) ◽  
pp. 513-567 ◽  
Author(s):  
Daniel Bennequin ◽  
Martin J. Gander ◽  
Loic Gouarin ◽  
Laurence Halpern
Keyword(s):  
Reaction Diffusion ◽  
Two Dimensions ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Waveform Relaxation ◽  
Schwarz Waveform Relaxation

scholarly journals Schwarz waveform relaxation algorithms for semilinear reaction-diffusion equations

2010 ◽  
Vol 5 (3) ◽  
pp. 487-505 ◽  
Author(s):  
Filipa Caetano ◽  
◽  
Martin J. Gander ◽  
Laurence Halpern ◽  
Jérémie Szeftel ◽  
...  
Keyword(s):  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Waveform Relaxation ◽  
Schwarz Waveform Relaxation ◽  
Relaxation Algorithms

Quasi-Optimized Overlapping Schwarz Waveform Relaxation Algorithm for PDEs with Time-Delay

2013 ◽  
Vol 14 (3) ◽  
pp. 780-800 ◽  
Author(s):  
Shu-Lin Wu ◽  
Ting-Zhu Huang
Keyword(s):  
Time Delay ◽  
Reaction Diffusion ◽  
Transmission Condition ◽  
Reaction Diffusion Equations ◽  
Complete Analysis ◽  
Waveform Relaxation ◽  
Schwarz Waveform Relaxation ◽  
Regular Time ◽  
The One ◽  
Time Dependent Problems

AbstractSchwarz waveform relaxation (SWR) algorithm has been investigated deeply and widely for regular time dependent problems. But for time delay problems, complete analysis of the algorithm is rare. In this paper, by using the reaction diffusion equations with a constant discrete delay as the underlying model problem, we investigate the convergence behavior of the overlapping SWR algorithm with Robin transmission condition. The key point of using this transmission condition is to determine a free parameter as better as possible and it is shown that the best choice of the parameter is determined by the solution of a min-max problem, which is more complex than the one arising for regular problems without delay. We propose new notion to solve the min-max problem and obtain a quasi-optimized choice of the parameter, which is shown efficient to accelerate the convergence of the SWR algorithm. Numerical results are provided to validate the theoretical conclusions.

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