scholarly journals Parallel Schwarz Waveform Relaxation Algorithm for an N-dimensional semilinear heat equation

2014 ◽  
Vol 48 (3) ◽  
pp. 795-813 ◽  
Author(s):  
Minh-Binh Tran
Keyword(s):  
Heat Equation ◽  
Waveform Relaxation ◽  
Relaxation Algorithm ◽  
Semilinear Heat Equation ◽  
Schwarz Waveform Relaxation

scholarly journals Schwarz waveform relaxation algorithm for heat equations with distributed delay

2016 ◽  
Vol 20 (suppl. 3) ◽  
pp. 659-667
Author(s):  
Shu-Lin Wu
Keyword(s):  
Numerical Computation ◽  
Distributed Delay ◽  
Computation Time ◽  
Analytic Solutions ◽  
Transmission Conditions ◽  
Waveform Relaxation ◽  
Heat Equations ◽  
Relaxation Algorithm ◽  
Schwarz Waveform Relaxation ◽  
The One

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.

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