Abstract of SOLVER3+ Project

Numerical codes used to simulate plasma turbulence typically require the solution of elliptic equations associated with the field equations. This proposal is especially geared towards applications in which such field equations evolve in time, i.e. for which the discretized problem has to be reassembled and solved at every time step. Due to the memory requirements and cpu time involved by direct methods, alternatives must be found especially for cases requiring fine grid resolution. One such an alternative is provided by the multigrid technique. In the previous project, geometrical multigrid techniques were successfully applied to the solution of the 2D Poisson equation on a Cartesian grid within a finite element formulation, demonstrating their high potential. The present project is to be considered as an extension of the previous one. We propose, first, to demonstrate the validity of a finite element geometrical multigrid approach to the solution of the Poisson equation in curvilinear coordinate systems, in particular polar coordinates. Second, we propose to apply the multigrid approach to the solution of the field equation considered by the fluid turbulence code GBS. In the long term, the proposed project may have an impact on several other turbulence codes, e.g. in treating the nonlinearity of the polarization density in the gyrokinetic codes.