Parallel schwarz methods : Algebraic construction of coarse problems, implementation and testing

The paper describes domain decomposition methods of the Schwarz type with coarse problems constructed algebraically by aggregation of unknowns. The description includes a new method with no overlap of subdomains and interfaces on the coarse grid. Implementation issues are discussed for all the methods and their comparison is made on a model elasticity problem. Special attention is given to nonsymmetric hybrid preconditioners. A parallel implementation of the additive Schwarz method is tested on a 3D elasticity problem, employing a Beowulf cluster.