## Section: Application Domains

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

Participants : Emmanuel Agullo, Mikko Byckling, Mathieu Chanaud, Luc Giraud, Abdou Guermouche, Yohan Lee-Tin-Yien, Stojce Nakov, Jean Roman, Xavier Vasseur.

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.

For the solution of large systems arsing from PDE discretization, the geometric full multigrid technique based on a few levels in the grid hierarchy and an efficient parallel sparse direct solver on the coarsest level can be considered. Originally developped for 3D Maxwell solution in collaboration with CEA-CESTA, the approach can be extended to other application fields.

Many 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 such as implicit time tepping schemes or inverse iterations. Many of the numerical approaches and possible outcoming software are well suited to tackle these challenging problems.

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 .

The efficient solution of linear systems strongly relies 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).