edu.ucar.opensky::articles:25441 UCAR/NCAR - Library OpenSky Support PO Box 3000 Boulder CO 80307-3000 opensky@ucar.edu http://opensky.ucar.edu/ homepage pointOfContact 2025-12-24T20:07:37.796753 ISO 19115-2 Geographic Information - Metadata - Part 2: Extensions for Imagery and Gridded Data ISO 19115-2:2009(E) https://n2t.org/ark:/85065/d79k4fz7 Solving 3D magnetohydrostatics with RBF-FD: Applications to the solar corona 2022-08-01T00:00:00Z publication https://n2t.org/ark:/85065/d79k4fz7 https://doi.org/10.1016/j.jcp.2022.111214 Mathews, N. H. author Flyer, N. author Gibson, Sarah E. author UCAR/NCAR - Library publisher We present a novel magnetohydrostatic numerical model that solves directly for the force-balanced magnetic field in the solar corona. This model is constructed with Radial Basis Function Finite Differences (RBF-FD), specifically 3D polyharmonic splines plus polynomials, as the core discretization. This set of PDEs is particularly difficult to solve since in the limit of the forcing going to zero it becomes ill-posed with a multitude of solutions. For the forcing equal to zero there are no numerically tractable solutions. For finite forcing, the ability to converge onto a physically viable solution is delicate as will be demonstrated. The static force-balance equations are of a hyperbolic nature, in that information of the magnetic field travels along characteristic surfaces, yet they require an elliptic type solver approach for a sparse overdetermined ill-conditioned system. As an example, we reconstruct a highly nonlinear analytic model designed to represent long-lived magnetic structures observed in the solar corona. UCAR/NCAR - Library OpenSky Support PO Box 3000 Boulder CO 80307-3000 opensky@ucar.edu http://opensky.ucar.edu/ homepage pointOfContact PDF Text theme Resource Type 2016-01-01T00:00:00Z publication Copyright author(s). This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. None eng geoscientificInformation