### A large-stepsize integrator for charged particle dynamics in a strong nonhomogeneous magnetic field

**Title: **A large-stepsize integrator for charged particle dynamics in a strong nonhomogeneous magnetic field

**Time:** 15:00--16:00 on September 11, 2024

**Meeting Room: **Math Building 2-3 Room

**Speaker: **Christian Lubich, University of Tuebingen, Germany

**Abstract:** Xiao and Qin [Computer Physics Comm., 265:107981, 2021] 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. An analysis can be based on comparing the modulated Fourier expansions of the exact and numerical solutions, which furthermore gives insight into the appearance of the unusual additional term in the numerical method, which makes it an inconsistent method as the stepsize goes to zero but allows to use it successfully with sufficiently large stepsizes. Numerical experiments illustrate and complement the theoretical results. The talk is based on joint work with Yanyan Shi [BIT Numer. Math., 63:14, 2023].

**Introduction: **Christian Lubich is a professor and head of Numerical Analysis Groups at the University of Tuebingen, Germany. His research concerns with mathematical analysis, numerical analysis, differential equation, exponential integrator and numerical stability. He is an expert on numerical analysis of time-dependent problems, including ordinary/partial differential equations and evolutionary integral equations. His recent research interests include dynamical low-rank approximation of high-dimensional matrix and tensor differential equations with applications to quantum dynamics and plasma physics, highly oscillatory problems, stable numerical interior-exterior coupling of wave equations, and the numerical analysis of geometric evolution equations. He is a famous applied mathematician with many influential works. He won a SIAM Dahlquist Prize, and gave a plenary lecture at the International Congress of Mathematicians in Rio de Janeiro in 2018.