10月27日 五室第330期研讨会（邀请报告）

报告题目：1.Multiscale Numerical Methods for Plasmas: Asymptotic-Preserving Solvers and Sparse-Grid Particle-in-Cell Schemes

          2.Vlasov方程的一种守恒型级联半拉格朗日方法

报 告 人：Dr.Fabrice Deluzet¹ （Institut de Mathématiques de Toulouse）

          杨畅² 教授 （哈尔滨工业大学）

主 持 人：叶磊 研究员

时    间：2026年10月27日（星期二）下午14:00-15:30

地    点：五室 224会议室

报告1

报告摘要：

This talk presents two families of numerical methods addressing the multiscale nature of plasma simulations.The first part deals with fluid models of magnetized plasmas. Strong magnetic fields lead to highly anisotropic problems, for which standard discretizations become ill-conditioned and lose accuracy. Asymptotic-preserving (AP) schemes remain accurate from weak to very strong fields, as illustrated on magnetically confined low-temperature plasmas. The approach extends to fluid models facing several singular limits at once: quasi-neutrality, drift and anisotropy. A new method for building reference solutions is also introduced to validate numerical schemes in realistic magnetic configurations, including X-point singularities.

The second part addresses particle-in-cell (PIC) methods, whose cost is driven by statistical noise. Sparse-grid reconstructions reduce this noise dramatically specifically  in a 3D-3V benchmark. Efficient CPU and GPU implementations and high-order variants will be presented. The talk concludes with a hierarchical B-spline formulation enabling adaptive refinement and more general geometries.

报告人简介：

Fabrice Deluzet，Senior CNRS Research Engineer, Institut de Mathématiques de Toulouse (IMT).Fabrice Deluzet is a senior CNRS research engineer at the Institut de Mathématiques de Toulouse. His research lies at the interface of applied mathematics, high-performance computing and plasma physics. It focuses on multiscale numerical methods for fluid and kinetic plasma models. These methods address singular regimes such as strong magnetization, quasi-neutrality breakdown, drift limits and fluid limits.His work covers two main areas. The first is asymptotic-preserving solvers for strongly anisotropic problems, which remain accurate and efficient however strong the magnetic field. The second is sparse-grid particle-in-cell methods (Sparse-PIC), including hierarchical and adaptive variants he has developed, which sharply reduce the noise and cost of kinetic simulations.

报告2

报告摘要：

针对等离子体动理学模拟，我们发展了守恒级联半拉格朗日格式求解Vlasov方程。该方法源于大气科学，通过逐维重映射实现高效质量守恒输运。我们给出了该格式的精度分析，指出其二阶精度及误差来源，并设计了保自由流修正和极值原理限制器，以提升守恒性与稳定性。数值结果涵盖线性输运、回旋中心模型及相对论Vlasov-Maxwell系统，展示了方法在长期模拟中的优异表现。与现有半拉格朗日格式对比，本方法在无散速度场下能更精确地维持能量等物理不变量，兼具高保真度与良好并行可扩展性，为动理学方程数值求解提供了新思路。

报告2报告人简介：

杨畅，哈尔滨工业大学数学学院教授、博士生导师，法国里尔科技大学博士。研究方向聚焦于等离子体物理中的多尺度与强各向异性问题的数学建模、渐近保持算法及高效数值模拟，同时开展生物学中的反应扩散模型研究。研究成果发表于《SIAM Journal on Scientific Computing》《Multiscale Modeling & Simulation》《Journal of Computational Physics》等权威期刊。目前主持国家自然科学基金项目，致力于托卡马克偏滤器等离子体的多尺度算法研究。

欢迎感兴趣的老师同学参加！