Comparison of parallel implementation of some multi-level Schwarz methods for singularly perturbed parabolic problems

Parallel multi-level algorithms combining a time discretization and an overlapping domain decomposition technique are applied to the numerical solution of singularly perturbed parabolic problems. Two methods based on the Schwarz alternating procedure are considered: a two-level method with auxiliary “correcting” subproblems as well as a three-level method with auxiliary “predicting” and “correcting” subproblems. Moreover, modifications of the methods using time extrapolation on subdomain interfaces are investigated. The emphasis is given to the description of the algorithms as well as their computer realization on a distributed memory multiprocessor computer. Numerical experiments illustrate the performance of the algorithms on parallel environment and their behaviour with respect to the critical parameters, such as the perturbation parameter and the size of the auxiliary subdomains.