Parallel Schwarz methods for convection-dominated semilinear diffusion problems
Journal of Computational and Applied Mathematics
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Domain decomposition algorithms based on the Schwarz alternating method are applied to the numerical solution of a singularly perturbed semilinear elliptic problem. The emphasis is given to the description of the algorithms (multidomain Schwarz alternating method and two-level Schwarz method) as well as their computer realization on a distributed memory multiprocessor computer. Numerical experiments related to a model problem illustrate the performance of the algorithms on parallel environment as well as their behavior with respect to the critical parameters, such as the perturbation parameter, the amount of overlapping, and sizes of subdomains. Application of the two-level Schwarz method to a model semiconductor problem is also discussed.