Parallel two-level Schwarz methods for singularly perturbed elliptic problems

Schwarz domain decomposition methods are developed for the numerical solution of singularly perturbed elliptic problems. Three variants of a two-level Schwarz method with interface subproblems are investigated both theoretically and from the point of view of their computer realization on a distributed memory multiprocessor computer. Numerical experiments illustrate their parallel performance as well as their behavior with respect to the critical parameters such as the perturbation parameter, the size of the interface subdomains and the number of parallel processors. Application of one of the methods to a model problem with an interior layer of complex geometry is also discussed. This revised version was published online in June 2006 with corrections to the Cover Date.