Two-scale exponential integrators with uniform accuracy for three-dimensional charged-particle dynamics under strong magnetic field
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2023
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913507222487040 |
|---|---|
| author | Wang, Bin Miao, Zhen Jiang, Yaolin |
| author_facet | Wang, Bin Miao, Zhen Jiang, Yaolin |
| contents | The numerical simulation of three-dimensional charged-particle dynamics (CPD) under strong magnetic field is a basic and challenging algorithmic task in plasma physics. 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 and small parameter $0<\varepsilon \ll 1$. By dealing with the transformed form of three-dimensional CPD, we linearize the magnetic field and put the residual component in a new nonlinear function which is shown to be uniformly bounded. Based on this foundation and the proposed two-scale exponential integrators, a class of novel integrators is formulated and studied. The corresponding uniform accuracy of the proposed $r$-th order integrator is shown to be $\mathcal{O}(h^r)$, where $r=1,2,3,4$ and the constant symbolized by $\mathcal{O}$, the time stepsize $h$ and the computation cost are all independent of $\varepsilon$. Moreover, in the case of maximal ordering strong magnetic field, improved error bound $\mathcal{O}(\varepsilon^r h^r)$ is obtained for the proposed $r$-th order integrator. A rigorous proof of these uniform and improved error bounds is presented, and a numerical test is performed to illustrate the error and efficiency behaviour of the proposed integrators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_18615 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Two-scale exponential integrators with uniform accuracy for three-dimensional charged-particle dynamics under strong magnetic field Wang, Bin Miao, Zhen Jiang, Yaolin Numerical Analysis 65L05, 65L70, 78A35, 78M25 The numerical simulation of three-dimensional charged-particle dynamics (CPD) under strong magnetic field is a basic and challenging algorithmic task in plasma physics. 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 and small parameter $0<\varepsilon \ll 1$. By dealing with the transformed form of three-dimensional CPD, we linearize the magnetic field and put the residual component in a new nonlinear function which is shown to be uniformly bounded. Based on this foundation and the proposed two-scale exponential integrators, a class of novel integrators is formulated and studied. The corresponding uniform accuracy of the proposed $r$-th order integrator is shown to be $\mathcal{O}(h^r)$, where $r=1,2,3,4$ and the constant symbolized by $\mathcal{O}$, the time stepsize $h$ and the computation cost are all independent of $\varepsilon$. Moreover, in the case of maximal ordering strong magnetic field, improved error bound $\mathcal{O}(\varepsilon^r h^r)$ is obtained for the proposed $r$-th order integrator. A rigorous proof of these uniform and improved error bounds is presented, and a numerical test is performed to illustrate the error and efficiency behaviour of the proposed integrators. |
| title | Two-scale exponential integrators with uniform accuracy for three-dimensional charged-particle dynamics under strong magnetic field |
| topic | Numerical Analysis 65L05, 65L70, 78A35, 78M25 |
| url | https://arxiv.org/abs/2311.18615 |