Comparison of parallel implementation of some multi-level Schwarz methods for singularly perturbed parabolic problems
The authors consider a two-dimensional parabolic equation with small diffusion coefficient (but without convection terms!) and propose an overlapping Schwarz method for its solution. Whereas for theoretical details like exponential convergence they refer to unpublished work of the first author, in this paper the algorithms and numerical results are presented: an implicit Euler method for time discretization, a Bakhvalov-type grid for spatial discretization, and the Schwarz iteration on 2 or 3 levels. For the parallelization on a distributed memory multiprocessor, the message passing interface library is used. The authors conclude that it is more effective to solve some of the subproblems on the overlapping regions on coarser grids and employing time extrapolation.
scientific article; zbMATH DE number 1326098