2024/07/09 by Luis Chacòn, Chacon, Luis
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Geomagnetism and Paleomagnetism Studies #Magnetic confinement fusion research #Numerical Analysis (math.NA) #Plasma Physics (physics.plasm-ph) #Solar and Space Plasma Dynamics
paper · pdf · doi:10.48550/arxiv.2407.07031
openalex publication_date 2024/07/09 · openalex created_date 2024/07/11 · openalex updated_date 2026/07/28
We propose an optimally performant fully implicit algorithm for the Hall magnetohydrodynamics (HMHD) equations based on multigrid-preconditioned Jacobian-free Newton-Krylov methods. HMHD is a challenging system to solve numerically because it supports stiff fast dispersive waves. The preconditioner is formulated using an operator-split approximate block factorization (Schur complement), informed by physics insight. We use a vector-potential formulation (instead of a magnetic field one) to allow a clean segregation of the problematic ∇ × ∇ × operator in the electron Ohm's law subsystem. This segregation allows the formulation of an effective damped block-Jacobi smoother for multigrid. We demonstrate by analysis that our proposed block-Jacobi iteration is convergent and has the smoothing property. The resulting HMHD solver is verified linearly with wave propagation examples, and nonlinearly with the GEM challenge reconnection problem by comparison against another HMHD code. We demonstrate the excellent algorithmic and parallel performance of the algorithm up to 16384 MPI tasks in two dimensions.