An explicit multiscale pseudo orbit-averaging time integration algorithm

Maxwell H. Rosen; Manaure Francisquez; Gregory W. Hammett

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arXiv · 2604.00121

An explicit multiscale pseudo orbit-averaging time integration algorithm

Maxwell H. Rosen·Manaure Francisquez·Gregory W. Hammett

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Abstract

We present an explicit multiscale algorithm for solving differential equations for problems with high-frequency modes that can be averaged over by separating and scaling the fast and slow dynamics within a single equation. We introduce a phased time integrator for cases where the boundaries of dynamical scales are known: one phase solves the unmodified equation, while the other freezes part of phase-space and slows down the evolution of the fast dynamics. This algorithm is applied to reduced kinetic models of plasmas in magnetic mirrors, which feature a distinct boundary between a region dominated by rapid particle transit and a region characterized by slow collisions. Two representative model problems are presented that decompose the dynamics of the magnetic mirror into a simpler, computationally inexpensive form. The model problems demonstrate a speedup by a factor of order $\omega / \nu_c$, where $\omega$ is the fast oscillation frequency and $\nu_c$ is the slow damping rate. This is a 30,000$\times$ speedup for a case of practical interest.

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BibTeX RIS

Maxwell H. Rosen, Manaure Francisquez, Gregory W. Hammett. 2026-03-31. An explicit multiscale pseudo orbit-averaging time integration algorithm. https://arxiv.org/abs/2604.00121

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