Implicitly Extrapolated Geometric Multigrid on Disk-Like Domains for the Gyrokinetic Poisson Equation from Fusion Plasma Applications

Abstract The gyrokinetic Poisson equation arises as a subproblem of Tokamak fusion reactor simulations. It is often posed on disk-like cross sections the that are represented in generalized polar coordinates. On resulting curvilinear anisotropic meshes, we discretize differential by finite differences or low order elements. Using an implicit extrapolation technique similar to multigrid $$\tau $$ ? -extrapolation, approximation can be increased. This naturally integrated matrix-free geometric algorithm. Special smoothers developed deal with mesh anisotropy arising from coordinate system and grading.