Mathematical Modeling and Analysis
Mathematical Modeling and Analysis
Extended Magnetohydrodynamics (XMHD) is a highly coupled, nonlinear PDE system characterized by multiple physical phenomena that span a very large range of length and time scales. Numerically, XMHD results in very ill-conditioned algebraic systems, which require implicit time stepping for efficiency, and spatial adaptivity to resolve dynamically forming thin layers. We summarize our progress towards fully implicit 3D XMHD using Newton-Krylov methods, and towards the implementation of fully implicit adaptive mesh refinement.
