Solving 3D magnetohydrostatics with RBF-FD: Applications to the solar corona

• DOI: 10.1016/j.jcp.2022.111214
• Publication Date: 2022-04-07T15:23:23Z
• Authors: Nat H. Mathews; Natasha Flyer; Sarah E. Gibson
• Keywords: Overdetermined system; Forcing (mathematics); Solver; Basis function

We present a novel magnetohydrostatic numerical model that solves directly for the force-balanced magnetic field in solar corona. This is constructed with Radial Basis Function Finite Differences (RBF-FD), specifically 3D polyharmonic splines plus polynomials, as core discretization. set of PDEs particularly difficult to solve since limit forcing going zero it becomes ill-posed multitude solutions. For equal there are no numerically tractable finite forcing, ability converge onto physically viable solution delicate will be demonstrated. The static force-balance equations hyperbolic nature, information travels along characteristic surfaces, yet they require an elliptic type solver approach sparse overdetermined ill-conditioned system. As example, we reconstruct highly nonlinear analytic designed represent long-lived structures observed