## Section: New Results

### Application : electrical engines simulations

Participants : Jean-Luc Dekeyser, Frédéric Guyomarc'h, Abdellatif Tinzefte, Wendell Rodrigues.

Within a collaboration with the L2EP, Abdellatif Tinzefte has started to model and program a parallel version of a Maxwell equations solver based on a Finite Element Method (FEM) formulation, and the first step of this work is defining a parallel preconditioner for the Krylov solver. The idea here is to use the Finite Integration Technique (FIT) in order to compute the electromagnetic phenomena as like the FEM but on a coarser grid. The F.I.T is efficient if the mesh is generated by hexahedron elements. With this regular mesh the obtained system is large, sparse and have some properties of regularity which can be used for the parallel computing. Thus this FIT parallel solver will be used to approach the FEM operator. The first numerical results show an excellent precision and a good acceleration for the FEM solver. Another part of this work, is to was implemented in CUDA and OpenCL as well a solver for Maxwell's equations (Finite-Element Method and a conjugate gradient). The aim is to accelerate and verify the parallel code on GPUs. The first results showed a speedup around 6 times against sequential code on CPU. Another approach uses an algorithm that explores the sparse matrix storage format (by rows and by columns). This one did not increase the speedup but it allows to evaluate the impact of different accesses to the memory.