A 3D Mesh-Free Solver for Magnetohydrostatic Simulations in the Corona

An understanding of coronal magnetism is vital to heliophysics, but typical methods to model such fields are not robust to the true complexities present in the Sun. We present a first-of-its-kind forced magnetohydrostatic numerical solver for the purpose of reconstructing coronal magnetic fields. This solver is constructed with Radial Basis Function finite differences as the core discretization, in a novel application of that method. This discretization allows the solver to use scattered datasets. We perform accurate reconstruction of a highly nonlinear analytic flux rope model, and investigate an application of the solver to the coronal magnetic field inverse problem.