Parallel scalability study of three dimensional additive Schwarz preconditioners in non-overlapping domain decomposition

In this paper we study the parallel scalability of variants of additive Schwarz preconditioners for three dimensional non-overlapping domain decomposition methods. To alleviate the computational cost, both in terms of memory and floating-point complexity, we investigate variants based on a sparse approximation or on mixed 32- and 64-bit calculation. The robustness of the preconditioners is illustrated on a set of linear systems arising from the finite element discretization of elliptic PDEs through extensive parallel experiments on up to 1000 processors. Their efficiency from a numerical and parallel performance view point are studied.