High order interpolation of magnetic fields with vector potential reconstruction for particle simulations
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912176004923392 |
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| author | Beznosov, Oleksii Bonilla, Jesus Tang, Xianzhu Wimmer, Golo |
| author_facet | Beznosov, Oleksii Bonilla, Jesus Tang, Xianzhu Wimmer, Golo |
| contents | 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. Finally, we demonstrate performant Poincaré section analysis in two relevant settings of field data collocated from finite element meshes |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_01523 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | High order interpolation of magnetic fields with vector potential reconstruction for particle simulations Beznosov, Oleksii Bonilla, Jesus Tang, Xianzhu Wimmer, Golo Numerical Analysis Plasma Physics 65D05 G.1.1 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. Finally, we demonstrate performant Poincaré section analysis in two relevant settings of field data collocated from finite element meshes |
| title | High order interpolation of magnetic fields with vector potential reconstruction for particle simulations |
| topic | Numerical Analysis Plasma Physics 65D05 G.1.1 |
| url | https://arxiv.org/abs/2501.01523 |