Exponential energy-preserving methods for charged-particle dynamics in a strong and constant magnetic field

Wang, Bin

doi:10.1016/j.cam.2019.112617

Cited by 18 publications

(6 citation statements)

References 30 publications

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“…4 Modulated Fourier expansions and proof of Theorem 2.1 Theorem 2.1 will be proved by comparing the modulated Fourier expansions of the exact and numerical solutions. Modulated Fourier expansions have previously been used in the analysis of numerical methods for oscillatory differential equations, see [7,12] and numerous further papers, and lately also for charged-particle dynamics in a strong magnetic field [9,10,11,20,21]. Incidentally, modulated Fourier expansions (though not under this name) were used for studying the gyration of charged particles by Kruskal [14] as early as 1958.…”

Section: Order Of Accuracymentioning

confidence: 99%

On a large-stepsize integrator for charged-particle dynamics

Lubich¹,

Shi²

2022

Preprint

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Xiao and Qin [Computer Physics Comm., 265:107981, 2021] recently proposed a remarkably simple modification of the Boris algorithm to compute the guiding centre of the highly oscillatory motion of a charged particle with step sizes that are much larger than the period of gyrorotations. They gave strong numerical evidence but no error analysis. This paper provides an analysis of the large-stepsize modified Boris method in a setting that has a strong non-uniform magnetic field and moderately bounded velocities, considered over a fixed finite time interval. The error analysis is based on comparing the modulated Fourier expansions of the exact and numerical solutions, for which the differential equations of the dominant terms are derived explicitly. Numerical experiments illustrate and complement the theoretical results.

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Section: Order Of Accuracymentioning

confidence: 99%

On a large-stepsize integrator for charged-particle dynamics

Lubich¹,

Shi²

2022

Preprint

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“…In order to handle this restriction, various novel methods with improved accuracy or uniform accuracy have been studied in recent years for CPD under a strong magnetic field with 0 < ε ≪ 1. An exponential energy-preserving integrator was formulated in [43] for (1.4) in a strong uniform magnetic field and uniform second order accuracy can be derived. In order to improve the asymptotic behaviour of the Boris method as ε → 0, two filtered Boris algorithms were developed and analysed in [26] under the maximal ordering scaling [7,36], i.e.…”

Section: Introductionmentioning

confidence: 99%

Semi-discretization and full-discretization with optimal accuracy for charged-particle dynamics in a strong nonuniform magnetic field

Wang¹,

Jiang²

2022

Preprint

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The aim of this paper is to formulate and analyze numerical discretizations of chargedparticle dynamics (CPD) in a strong nonuniform magnetic field. A strategy is firstly performed for the two dimensional CPD to construct the semi-discretization and full-discretization which have optimal accuracy. This accuracy is improved in the position and in the velocity when the strength of the magnetic field becomes stronger. This is a better feature than the usual so called "uniformly accurate methods". To obtain this refined accuracy, some reformulations of the problem and twoscale exponential integrators are incorporated, and the optimal accuracy is derived from this new procedure. Then based on the strategy given for the two dimensional case, a new class of uniformly accurate methods with simple scheme is formulated for the three dimensional CPD in maximal ordering case. All the theoretical results of the accuracy are numerically illustrated by some numerical tests.

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“…Unfortunately, these effective methods do not conserve the energy (2) exactly. In order to get energy-preserving (EP) methods for CPD, an exponential energy-preserving integrator was recently developed in [37] for (1) under a uniform magnetic field B. Moreover recently, first-order splitting energy-preserving methods were researched in [40] with a rigorous error analysis and high-order splitting EP methods were considered in [26] but without convergence analysis.…”

Section: Introductionmentioning

confidence: 99%

Geometric continuous-stage exponential energy-preserving integrators for charged-particle dynamics in a magnetic field from normal to strong regimes

Li¹,

Wang²

2021

Preprint

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This paper is concerned with geometric exponential energy-preserving integrators for solving charged-particle dynamics in a magnetic field from normal to strong regimes. We firstly formulate the scheme of the methods for the system in a uniform magnetic field by using the idea of continuous-stage methods, and then discuss its energy-preserving property. Moreover, symmetric conditions and order conditions are analysed. Based on those conditions, we propose two practical symmetric continuous-stage exponential energy-preserving integrators of order up to four. Then we extend the obtained methods to the system in a nonuniform magnetic field and derive their properties including the symmetry, convergence and energy conservation. Numerical experiments demonstrate the efficiency of the proposed methods in comparison with some existing schemes in the literature.

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Exponential energy-preserving methods for charged-particle dynamics in a strong and constant magnetic field

Cited by 18 publications

References 30 publications

On a large-stepsize integrator for charged-particle dynamics

On a large-stepsize integrator for charged-particle dynamics

Semi-discretization and full-discretization with optimal accuracy for charged-particle dynamics in a strong nonuniform magnetic field

Geometric continuous-stage exponential energy-preserving integrators for charged-particle dynamics in a magnetic field from normal to strong regimes

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