## Section: Application Domains

### Application framework customers of high performance linear algebra solvers

We are currenlty collaborating with various research groups involved in geophysics, electromagnetics and structural mechanics. For all these application areas, the current bottleneck is the solution of huge sparse linear systems often involving multiple right-hand sides either available simultaneously or given in sequence. The robustness, efficiency and scalability of the numerical tools designed in Section 3.3 will be preliminary investigated in the parallel simulation codes of these partners.

More precisely, BRGM and TOTAL simulations require the solutions of
huge linear systems with many right-hand sides given simultaneously.
We notice that the collaborative work with TOTAL will also address the
use of `GPU` for intensive numerical kernels in the Reverse Time
Migration process for seismic imaging.

The CEA-CESTA simulation codes need the solution with simultaneous right-hand sides but also with right-hand sides given in sequence. The first situation arises in RCS calculations, but is generic in many parametric studies, while the second one comes from the nature of the solver that is based on a multiplicative Schwarz approach. The subproblems are solved several times in sequence. Many of the numerical approaches and possible outcoming software are well suited to tackle these challenging problems.

Research activities related to EDF and developed in the framework of the ANR
SOLSTICE project have already stimulated interactions between members of
the former `ScAlApplix` INRIA project team and members of the Parallel
Algorithms team of CERFACS. These research activities have concerned
direct and iterative solution methods for linear systems and eigenvalue
computations. A major focus was on the efficient use of parallel
sparse direct solution methods for large scale applications in
structural mechanics in both in-core and out-of-core environments. These
solution methods have been already integrated in the Code_Aster
structural mechanics code developed at EDF. The use of hybrid
solution methods will be investigated in structural mechanic applications and also
in other different applications of interest for EDF such as neutronics or fluid mechanics.

On more academic sides, some ongoing collaborations with other INRIA EPIs will be continued and others will be started. In collaboration with the NACHOS INRIA project team, we will continue to investigate the use of efficient linear solvers for the solution of the Maxwell equations in the time and frequency domains where discontinuous Galerkin discretizations are considered. Additional funding will be sought out in order to foster this research activity in connection with actions described in Section 3.3 .

Jointly with the MAGIQUE3D INRIA project team, we intend to collaborate to design parallel efficient simulation codes for sismic wave propagation at the Earth scale where various huge linear systems have to be solved on large parallel platforms. The forseen numerical techniques will be based on a mixed spectral finite element approach coupled with some boundary element techniques. The efficient solution of such problem will strongly rely on the activities described in Section 3.2 (e.g. complex load balancing problem) and in Section 3.3 (for the various parallel linear algebra kernels).