High order interpolation of magnetic fields with vector potential reconstruction for particle simulations

Beznosov, O.; Bonilla, J.; Tang, X. -Z.; Wimmer, G. A.

doi:10.1016/j.cpc.2025.109770

High order interpolation of magnetic fields with vector potential reconstruction for particle simulations

Journal Article · Tue Jul 29 00:00:00 EDT 2025 · Computer Physics Communications

DOI:https://doi.org/10.1016/j.cpc.2025.109770· OSTI ID:2574841

^[1]; Bonilla, J. ^[1]; Tang, X. -Z. ^[1]; Wimmer, G. A. ^[1]

Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

We propose a method for interpolating divergence-free continuous magnetic fields via vector potential reconstruction using Hermite interpolation, which ensures high-order continuity for applications requiring adaptive, high-order ordinary differential equation (ODE) integrators, such as the Dormand-Prince method. The method provides C(m) continuity and achieves high-order accuracy, making it particularly suited for particle trajectory integration and Poincaré section analysis under optimal integration order and timestep adjustments. Through numerical experiments, we demonstrate that the Hermite interpolation method preserves volume and continuity, which are critical for conserving toroidal canonical momentum and magnetic moment in guiding center simulations, especially over long-term trajectory integration. Furthermore, we analyze the impact of insufficient derivative continuity on Runge-Kutta schemes and show how it degrades accuracy at low error tolerances, introducing discontinuity-induced truncation errors. Lastly, we demonstrate performant Poincaré section analysis in two relevant settings of field data collocated from finite element meshes.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: National Energy Research Scientific Computing Center (NERSC); USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Basic Energy Sciences (BES). Scientific User Facilities (SUF)

Grant/Contract Number:: 89233218CNA000001; AC02-05CH11231

OSTI ID:: 2574841

Report Number(s):: LA-UR--24-33348

Journal Information:: Computer Physics Communications, Journal Name: Computer Physics Communications Vol. 316; ISSN 0010-4655

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (26)

Tricubic interpolation in three dimensions Lekien, F.; Marsden, J. International Journal for Numerical Methods in Engineering, Vol. 63, Issue 3 https://doi.org/10.1002/nme.1296	journal	January 2005
The ∇·B=0 Constraint in Shock-Capturing Magnetohydrodynamics Codes Tóth, Gábor Journal of Computational Physics, Vol. 161, Issue 2 https://doi.org/10.1006/jcph.2000.6519	journal	July 2000
Hyperbolic Divergence Cleaning for the MHD Equations Dedner, A.; Kemm, F.; Kröner, D. Journal of Computational Physics, Vol. 175, Issue 2 https://doi.org/10.1006/jcph.2001.6961	journal	January 2002
Hermite-Discontinuous Galerkin Overset Grid Methods for the Scalar Wave Equation Beznosov, Oleksii; Appelö, Daniel Communications on Applied Mathematics and Computation, Vol. 3, Issue 3 https://doi.org/10.1007/s42967-020-00075-5	journal	August 2020
A family of embedded Runge-Kutta formulae Dormand, J. R.; Prince, P. J. Journal of Computational and Applied Mathematics, Vol. 6, Issue 1 https://doi.org/10.1016/0771-050X(80)90013-3	journal	March 1980
A new discretization methodology for diffusion problems on generalized polyhedral meshes Brezzi, Franco; Lipnikov, Konstantin; Shashkov, Mikhail Computer Methods in Applied Mechanics and Engineering, Vol. 196, Issue 37-40 https://doi.org/10.1016/j.cma.2006.10.028	journal	August 2007
A multilevel multiscale mimetic (M3) method for two-phase flows in porous media Lipnikov, K.; Moulton, J. D.; Svyatskiy, D. Journal of Computational Physics, Vol. 227, Issue 14 https://doi.org/10.1016/j.jcp.2008.03.029	journal	July 2008
Mimetic finite difference method for the Stokes problem on polygonal meshes Beirão da Veiga, L.; Gyrya, V.; Lipnikov, K. Journal of Computational Physics, Vol. 228, Issue 19 https://doi.org/10.1016/j.jcp.2009.06.034	journal	October 2009
Mimetic finite difference method Lipnikov, Konstantin; Manzini, Gianmarco; Shashkov, Mikhail Journal of Computational Physics, Vol. 257 https://doi.org/10.1016/j.jcp.2013.07.031	journal	January 2014
Structure preserving transport stabilized compatible finite element methods for magnetohydrodynamics Wimmer, Golo A.; Tang, Xian-Zhu Journal of Computational Physics, Vol. 501 https://doi.org/10.1016/j.jcp.2024.112777	journal	March 2024
A mimetic discretization method for linear elasticity Beirão Da Veiga, Lourenco ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 44, Issue 2 https://doi.org/10.1051/m2an/2010001	journal	January 2010
Volume preserving integrators for solenoidal fields on a grid Finn, John M.; Chacón, Luis Physics of Plasmas, Vol. 12, Issue 5 https://doi.org/10.1063/1.1889156	journal	May 2005
Passive runaway electron suppression in tokamak disruptions Smith, H. M.; Boozer, A. H.; Helander, P. Physics of Plasmas, Vol. 20, Issue 7 https://doi.org/10.1063/1.4813255	journal	July 2013
A divergence-free constrained magnetic field interpolation method for scattered data Yang, M.; del-Castillo-Negrete, D.; Zhang, G. Physics of Plasmas, Vol. 30, Issue 3 https://doi.org/10.1063/5.0138905	journal	March 2023
Avalanche mechanism for runaway electron amplification in a tokamak plasma McDevitt, Christopher J.; Guo, Zehua; Tang, Xian-Zhu Plasma Physics and Controlled Fusion, Vol. 61, Issue 5 https://doi.org/10.1088/1361-6587/ab0d6d	journal	April 2019
Hermite methods for hyperbolic initial-boundary value problems Goodrich, John; Hagstrom, Thomas; Lorenz, Jens Mathematics of Computation, Vol. 75, Issue 254 https://doi.org/10.1090/S0025-5718-05-01808-9	journal	December 2005
Generation of finite difference formulas on arbitrarily spaced grids Fornberg, Bengt Mathematics of Computation, Vol. 51, Issue 184 https://doi.org/10.1090/S0025-5718-1988-0935077-0	journal	January 1988
A unified approach for handling convection terms in finite volumes and mimetic discretization methods for elliptic problems da Veiga, L. B.; Droniou, J.; Manzini, G. IMA Journal of Numerical Analysis, Vol. 31, Issue 4 https://doi.org/10.1093/imanum/drq018	journal	December 2010
Runaway electron current reconstitution after a nonaxisymmetric magnetohydrodynamic flush McDevitt, Christopher J.; Tang, Xian-Zhu Physical Review E, Vol. 108, Issue 4 https://doi.org/10.1103/PhysRevE.108.L043201	journal	October 2023
Hamiltonian theory of guiding-center motion Cary, John R.; Brizard, Alain J. Reviews of Modern Physics, Vol. 81, Issue 2 https://doi.org/10.1103/RevModPhys.81.693	journal	May 2009
Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media No authors listed IEEE Transactions on Antennas and Propagation, Vol. 14, Issue 3 https://doi.org/10.1109/TAP.1966.1138693	journal	May 1966
Convergence Analysis of the Mimetic Finite Difference Method for Elliptic Problems Cangiani, Andrea; Manzini, Gianmarco; Russo, Alessandro SIAM Journal on Numerical Analysis, Vol. 47, Issue 4 https://doi.org/10.1137/080717560	journal	January 2009
Hermite Methods for the Scalar Wave Equation Appelö, Daniel; Hagstrom, Thomas; Vargas, Arturo SIAM Journal on Scientific Computing, Vol. 40, Issue 6 https://doi.org/10.1137/18M1171072	journal	January 2018
A New Discretely Divergence-Free Positivity-Preserving High-Order Finite Volume Method for Ideal MHD Equations Ding, Shengrong; Wu, Kailiang SIAM Journal on Scientific Computing, Vol. 46, Issue 1 https://doi.org/10.1137/23M1562081	journal	January 2024
Globally divergence-free DG scheme for ideal compressible MHD Balsara, Dinshaw S.; Kumar, Rakesh; Chandrashekar, Praveen Communications in Applied Mathematics and Computational Science, Vol. 16, Issue 1 https://doi.org/10.2140/camcos.2021.16.59	journal	January 2021
A Comparative Study of Divergence Cleaning Methods of Magnetic Field in the Solar Coronal Numerical Simulation Zhang, Man; Feng, Xueshang Frontiers in Astronomy and Space Sciences, Vol. 3 https://doi.org/10.3389/fspas.2016.00006	journal	March 2016

Similar Records

Numerical integrators for Lagrangian oceanography

Journal Article · Mon Nov 30 19:00:00 EST 2020 · Geoscientific Model Development (Online) · OSTI ID:2325358

IMEX-a :

Technical Report · Wed May 01 00:00:00 EDT 2013 · OSTI ID:1089990

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
97 MATHEMATICS AND COMPUTING
Divergence-free magnetic fields
Guiding center motion
High-order interpolation
Particle simulations
Poincaré section analysis

High order interpolation of magnetic fields with vector potential reconstruction for particle simulations

Citation Formats

References (26)

Similar Records

Related Subjects