A partly matrix-free solver for the gyrokinetic field equation in three-dimensional geometry

In the case of adiabatic electrons the gyrokinetic field equation for the electrostatic potential includes an averaging operator acting on flux surfaces. For realistic three-dimensional configurations, as e.g. in stellarator devices, the discretisation of this integro-differential equation leads to very large nearly dense matrices (full matrix approach) which typically cannot be stored in computer memory explicitly. A low memory consuming partly matrix-free approach, based on a preconditioned iterative matrix solver, has been developed where the Helmholtz part of the field equation is used in a matrix formulation while the averaging term is treated matrix-free. For matrices which could still be stored in memory explicitly, it is demonstrated that this approach is also much faster than the full matrix approach.