Error estimates of some splitting schemes for charged-particle dynamics under strong magnetic field

by   Bin Wang, et al.

In this work, we consider the error estimates of some splitting schemes for the charged-particle dynamics under a strong magnetic field. We first propose a novel energy-preserving splitting scheme with computational cost per step independent from the strength of the magnetic field. Then under the maximal ordering scaling case, we establish for the scheme and in fact for a class of Lie-Trotter type splitting schemes, a uniform (in the strength of the magnetic field) and optimal error bound in the position and in the velocity parallel to the magnetic field. For the general strong magnetic field case, the modulated Fourier expansions of the exact and the numerical solutions are constructed to obtain a convergence result. Numerical experiments are presented to illustrate the error and energy behaviour of the splitting schemes.



There are no comments yet.


page 1

page 2

page 3

page 4


A filtered Boris algorithm for charged-particle dynamics in a strong magnetic field

A modification of the standard Boris algorithm, called filtered Boris al...

Long term analysis of splitting methods for charged-particle dynamics

In this paper, we rigorously analyze the energy, momentum and magnetic m...

Uniformly accurate methods for three dimensional Vlasov equations under strong magnetic field with varying direction

In this paper, we consider the three dimensional Vlasov equation with an...

Large-stepsize integrators for charged-particle dynamics over multiple time scales

The Boris algorithm, a closely related variational integrator and a newl...

Magnetically actuated artificial microswimmers as mobile microparticle manipulators

Micro-scale swimming robots have been envisaged for many medical applica...

Scattering and uniform in time error estimates for splitting method in NLS

We consider the nonlinear Schrödinger equation with a defocusing nonline...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.