MaPHyS (Massivelly Parallel Hybrid Solver) is a software package whose proptotype was initially developed in the framework of the PhD thesis of Azzam Haidar (CERFACS) and futher consolidated thanks to the ANR-CIS Solstice funding. This parallel linear solver couples direct and iterative approaches. The underlying idea is to apply to general unstructured linear systems domain decomposition ideas developed for the solution of linear systems arising from PDEs. The interface problem, associated with the so called Schur complement system, is solved using a block preconditioner with overlap between the blocks that is referred to as Algebraic Additive Schwarz. To cope with the possible lack of coarse grid mechanism that enables one to keep constant the number of iterations when the number of blocks is increased, the solver exploits two levels of parallelism (between the blocks and within the treatment of the blocks). This enables us to exploit a large number of processors with a moderate number of blocks which ensures a reasonable convergence behaviour.
The current prototype code will be further consolidated to end-up with a high performance software package to be made freely available to the scientific community. In that respect, an additional support has been obtained in the framework of the INRIA technologic development actions; 24 man-month engineer (Yohan Lee-Tin-Yien) have been allocated to this software activity. The roadmap for this software development is well defined; it should enable us to have interfaces with various graph partitioning packages at the end of the first year and interfaces with most of the parallel sparse direct solvers at the end of the second year. The MaPHyS package is very much a first outcome of the research activity described in Section 3.3 . Finally, MaPHyS is a preconditioner that can be used to speed-up the convergence of any Krylov subspace method. We forsee to either embed in MaPHyS some Krylov solvers or to release them as standalone packages, in particular for the block variants that will be some outcome of the studies discussed in Section 3.3 .