Nonoverlapping Schwarz Waveform Relaxation Algorithm for a Class of Time-Fractional Heat Equations

2017 ◽  
Vol 151 (1-4) ◽  
pp. 231-240
Author(s):  
Shu-Lin Wu ◽  
Guo-Cheng Wu
Keyword(s):  
Waveform Relaxation ◽  
Heat Equations ◽  
Relaxation Algorithm ◽  
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.

scholarly journals Schwarz Waveform Relaxation for Heat Equations with Nonlinear Dynamical Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Shu-Lin Wu
Keyword(s):  
Boundary Conditions ◽  
Domain Decomposition ◽  
Domain Decomposition Method ◽  
Linear Convergence ◽  
Decomposition Methods ◽  
Waveform Relaxation ◽  
Heat Equations ◽  
Nonlinear Dynamical ◽  
Schwarz Waveform Relaxation ◽  
Dynamical Boundary Conditions

We are interested in solving heat equations with nonlinear dynamical boundary conditions by using domain decomposition methods. In the classical framework, one first discretizes the time direction and then solves a sequence of state steady problems by the domain decomposition method. In this paper, we consider the heat equations at spacetime continuous level and study a Schwarz waveform relaxation algorithm for parallel computation purpose. We prove the linear convergence of the algorithm on long time intervals and show how the convergence rate depends on the size of overlap and the nonlinearity of the nonlinear boundary functions. Numerical experiments are presented to verify our theoretical conclusions.

Sign in / Sign up

Export Citation Format

Share Document