## Section: New Results

### Resolution of the quasi-neutrality equation

Participant : Nicolas Crouseilles.

In reference [39] , different parallel algorithms are proposed for the numerical resolution of the quasi-neutrality equation in the GYSELA code. A set of benchmarks on a parallel machine has permitted to evaluate the performance of the different versions of the quasi-neutrality solver. In particular, in [40] , these improvements are combined with memory optimization which enable a scalability of the GYSELA code up to $64k$ cores.

In [20] , a new discretization scheme of the gyrokinetic quasi-neutrality equation is proposed. It is based on Isogeometric Analysis; the IGA which relies on NURBS functions, seems to accommodate arbitrary coordinates and the use of complicated computation domains. Moreover, arbitrary high order degree of basis functions can be used. Here, this approach is successfully tested on elliptic problems like the quasi-neutrality equation.