Sanchez-Vizuet: The hybridizable discontinuous Galerkin method: an application to plasma equilibrium in fusion reactors

In axisymmetric fusion reactors, the equilibrium magnetic configuration can be expressed in terms of the solution to a semi-linear elliptic equation. Solving this problem efficiently, quickly and with high precision is important for the design of reactors, and for real time monitoring of plasmas in experimental settings. The Hybridizable Discontinuous Galerkin is a numerical solution strategy which, based in a weak formulationof the equation. It turns the global problem in a set of local subproblems that can be solved in parallel; the global solution is obtained by ”glueing” the local solutions. This strategy can have a high order of approximation and itis very robust with respect to geometric properties of the domain. We will introduce the problem of magnetic confinement and use it to develop the ideas behind the Discontinuous Galerkin Method.