#### A high order solver for the Grad-Shafranov free boundary problem

###### Ponente(s): Tonatiuh Sanchez Vizuet, Antoine Cerfon, Manuel Solano, Evan Toler

###### In magnetic confinement fusion devices, the equilibrium configuration of a plasma is determined by the balance between the hydrostatic pressure in the fluid and the magnetic forces generated by an array of external coils and the plasma itself. The equilibrium configuration is determined by the solution to a nonlinear elliptic partial differential equation. However, since the location of the plasma is not known a priori, the domain of definition of the PDE must be determined as a problem unknown leading to a free boundary problem. In this talk we will discuss some recent advances in and interior/exterior iterative solution strategy. Computationally, this involves the coupling of a hybridizable discontinuous Galerkin solver for the solution of the problem inside the assumed plasma domain and a boundary integral equation solver for the solution of the exterior problem, and a minimization step. This is joint work with Antoine Cerfon (NYU), Manuel Solano (University of ConcepciĆ³n, Chile) and Evan Toler (NYU).