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