On the development of PSBLAS-based parallel two-level Schwarz preconditioners

Design and implementation issues that concern the development of a package of parallel algebraic two-level Schwarz preconditioners are discussed. The computations are based on the Parallel Sparse BLAS (PSBLAS) library. The package implements various versions of Additive Schwarz preconditioners and applies a smoothed aggregation technique to generate a coarse-level correction. The coarse matrix can be either replicated on the processors or distributed among them; the corresponding system is solved by factorization or block Jacobi sweeps, respectively. The design of the package started from a description of the preconditioners in terms of parallel basic Linear Algebra operators, in order to develop software based on standard kernels. Suitable preconditioner data structures were defined to fully exploit the existing PSBLAS functionalities; however, the implementation of the preconditioner required also an extension of the set of basic library kernels. The results of experiments carried out on different test matrices show that the package is competitive in terms of runtime efficiency.