2026 Spring
The seminar of this semester is organized by Jiamao Wu and Zhuangao He, and co-organized by the graduate student union in the School of Mathematical Sciences at Fudan. This section is partially sponsored by Shanghai Key Laboratory for Contemporary Applied Mathematics.
2026-03-05 16:10:00 - 17:00:00 @ Rm 1801, Guanghua East Tower
[poster]
- Title:
Time-Splitting Methods for the Dirac Equation in the Semiclassical Regime
- Speaker: He Wang (Fudan University)
- Advisor: Jia Yin (Fudan University)
Abstract: Click to expand
Currently, several finite difference methods are used to solve the
Dirac equation in the semiclassical regime. However, finite
difference methods have certain limitations in terms of accuracy
and stability. The CNFD method, often employed to enhance
stability, usually requires solving large linear systems, leading
to significant computational costs. In this work, we conduct a
rigorous analysis of the numerical error for the time-splitting
methods applied to the Dirac equation in the semiclassical region.
The dimensionless parameter $\epsilon \in (0,1]$, representing the
reduced Planck constant, causes the solution field to exhibit
rapid oscillations with characteristic wavelengths of order
$O(\epsilon)$. We demonstrate that both $S_1$ and $S_2$ schemes
preserve total mass conservation in a discrete sense. Furthermore,
we establish error estimates for the time-splitting methods,
clearly describing how the approximation error varies with time
resolution $\tau$, spatial discretization step $h$, and the
parameter $\epsilon$. We also derive error bounds for physical
observables, and through numerical experiments, we validate the
reliability of the error estimates.
Past Presentations
