Two-scale exponential integrators with uniform accuracy for three-dimensional charged-particle dynamics under strong magnetic field
CoRR(2023)
摘要
The numerical simulation of three-dimensional charged-particle dynamics (CPD)
under strong magnetic field is challenging. In this paper, we introduce a new
methodology to design two-scale exponential integrators for three-dimensional
CPD whose magnetic field's strength is inversely proportional to a
dimensionless parameter $0<\varepsilon \ll 1$. By dealing with the transformed
form of three-dimensional CPD, we linearize the magnetic field and put the rest
part in a nonlinear function which can be shown to be small. Based on which and
the proposed two-scale exponential integrators, a class of novel integrators is
formulated. The corresponding uniform accuracy over
$\mathcal{O}(1/\varepsilon^{\beta})$ time interval is
$\mathcal{O}(\varepsilon^{r\beta} h^r)$ for the $r$-th order integrator with
the time stepsize $h$, $r=1,2,3,4$ and $0<\beta<1$. A rigorous proof of this
error bound is presented and a numerical test is performed to illustrate the
error behaviour of the proposed integrators.
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