## Section: Software

### MaPHyS

`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 SectionÂ
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 SectionÂ
3.3 .