Overview 

"同一物理定律的不同的数学表述，尽管在物理上是等价的，但实际并不等效。"- 冯康

"Different mathematical representations of the same physical law, while equivalent in physics, are not necessarily equivalent in practice。" - Feng Kang

Structure-preserving schemes and fast solvers for multiphysics systems

Structure-preserving discretisations are numerical schemes that reflect important algebraic, geometric, or topological features of the underlying continuous problem. Examples of such structures include conservation laws, dissipation laws, the symplecticity of the flow map (a geometric property shared by all Hamiltonian systems),  physical constraints (such as the solenoidality of the magnetic field), and topological invariants (such as helicity for ideal fluids). Therefore, it is essential to preserve those structures for high-fidelity numerical simulations. 

Designing an efficient solver for large-scale simulation and extremely physical testing problems (e.g. large Reynolds numbers) in a multiphysics problem is essential. The aim is to use efficient preconditioning techniques to design robust solvers which are independent of discretisation and physical parameters. 

In my view, the numerical analyst is the one who works between the infinite-dimensional space and the finite-dimensional space. When I work in the infinite-dimensional space, the beauty of abstraction attracts me. While I am in the finite-dimensional space, the practical motivates me. Therefore, I am interested in the finite element exterior calculus, structure-preserving scheme and preconditioning of solving partial differential equations. The tension between the pure and the applied is the core of my wok. 

多物理场问题之保结构数值离散与快速求解器

夫保结构离散者，数值算法之要义也。其旨在摹仿连续问题之本质，使代数、几何、拓扑之理不失其真。守恒与耗散、流映射之辛性，皆哈密顿系统之常理；磁场之无散、流体之螺旋，亦物理与拓扑之所系。故欲得高精之数值模拟，必当护其结构，不可损也。

若夫多物理场之复杂系统，或极端物理之试验，如高雷诺数之流体，其求解之法，尤需迅捷而稳健。唯善用预条件之术，使算法不拘于离散与参数，方可高效自如。

余以为数值分析者，实架桥于无限与有限之间也。处于无限维之境，则理趣精微，美不胜收；立于有限维之域，则计算所需，迫于实用。是以余志在有限元外形式、保结构之法，及偏微分方程之预处理术焉。纯理与应用之张弛，乃吾业之本心也。

Current Research

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Research interests:

• Structure-preservation finite element discretisations.

• Finite element exterior calculus.

• Magnetohydrodynamics, Electromagnetism and Fluid dynamics. 

• Preconditioning techniques and fast solvers development.  

Publication

1. Mingdong He, Patrick Farrell, Kaibo Hu, Boris Andrews (2025): Topology-preserving discretization for the magneto-frictional equations arising in the Parker conjecture. 

2. Junyi Zhao, Ziyang Zheng, Yunchuan Huang, Mingdong He, Jon Chapman, Mauro Pasta (2025): Impact of Concentration-Dependent Transport Properties on Concentration Gradients. 

Past Research

The University of Nottingham 2020-2022