A rapidly converging domain decomposition algorithm for a time delayed parabolic problem with mixed type boundary conditions exhibiting boundary layers.

Abstract

[EN] A rapidly converging domain decomposition algorithm is introduced for a time delayed parabolic problem with mixed type boundary conditions exhibiting boundary layers. Firstly, a space-time decomposition of the original problem is considered. Subsequently, an iterative process is proposed, wherein the exchange of information to neighboring subdomains is accomplished through the utilization of piecewise-linear interpolation. It is shown that the algorithm provides uniformly convergent numerical approximations to the solution. Our analysis utilizes some novel auxiliary problems, barrier functions, and a new maximum principle result. More importantly, we showed that only one iteration is needed for small values of the perturbation parameter.