Research研究
My research builds mathematically robust bridges from CAD geometry to simulation: high-quality spline parameterizations that let a single model be both designed and analyzed, together with the fast, reliable methods that make this practical for complex and industrial problems. 我的研究致力于在 CAD 几何与仿真之间架起数学上稳健的桥梁：构造高质量的样条参数化，使同一套模型既可用于设计又可直接用于分析，并发展使之在复杂与工业问题中切实可行的快速、可靠方法。
Analysis-Suitable Parameterization for IGA面向 IGA 的分析适用参数化
A bijective, high-quality map from a parameter domain to the physical geometry is the foundation of isogeometric analysis. I develop optimization-based and PDE-based constructions that guarantee a strictly positive Jacobian (injectivity) and control element quality — so a single spline model serves both design and simulation, with no mesh conversion and no foldovers.
从参数域到物理几何的双射、高质量映射是等几何分析的基础。我发展了基于优化与基于 PDE的构造方法，保证 Jacobian 严格为正（单射性）并控制单元质量——使同一套样条模型同时服务于设计与仿真，无需网格转换、无翻转。
Volumetric (Trivariate) Parameterization三维（体）参数化
Engineering parts are three-dimensional. I extend analysis-suitable parameterization to trivariate volumetric spline models, producing watertight, regular interiors for solids with non-trivial shape and topology — the geometric input that downstream 3D simulation actually needs.
工程部件是三维的。我将分析适用参数化拓展到三变量（体）样条模型，为形状与拓扑非平凡的实体生成无缝、正则的内部——这正是后续三维仿真真正需要的几何输入。
Multi-Patch & Multi-Sided Parameterization多片与多边参数化
Complex domains can rarely be mapped from a single square. I construct multi-patch and multi-sided parameterizations with consistent interfaces, including boundary parameter matching with Schwarz–Christoffel tools, to assemble reliable IGA models of intricate geometries.
复杂区域很难由单个正方形映射得到。我构造具有一致交界的多片与多边参数化，并结合 Schwarz–Christoffel 工具进行边界参数匹配，从而拼装出复杂几何的可靠 IGA 模型。
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Fast Solvers — Preconditioned Anderson Acceleration快速求解器 —— 预处理 Anderson 加速
The nonlinear PDEs behind high-quality parameterization can be slow and fragile to solve with Newton-type iterations. I introduced a preconditioned Anderson acceleration framework — with diagonal, block-diagonal and full-Jacobian preconditioners and a delayed-update strategy — that converges far faster and more robustly while avoiding expensive Newton solves.
高质量参数化背后的非线性 PDE 用 Newton 类迭代求解往往又慢又脆弱。我提出了一套预处理 Anderson 加速框架（含对角、块对角、全 Jacobian 预处理及延迟更新策略），在避免昂贵 Newton 求解的同时收敛更快、更稳健。
Industrial Structured Meshing for Twin-Screw Machines双螺杆机械的工业结构化网格生成
With industry, I generate fast, robust structured spline meshes for the intermeshing rotors of twin-screw compressors and expanders — geometry that deforms continuously as the rotors turn. This work received the ICSM 2024 Best Paper Award and underpins the SplineMesh / SCORG™ toolchain.
我与工业界合作，为双螺杆压缩机/膨胀机相互啮合的转子（随转动连续变形的几何）生成快速、稳健的结构化样条网格。该工作获 ICSM 2024 最佳论文奖，并支撑 SplineMesh / SCORG™ 工具链。
Metal Additive Manufacturing金属增材制造
Thermal modeling of laser powder bed fusion (LPBF) is dominated by steep, fast-moving gradients that conventional FEM resolves only at prohibitive cost. I work on a semi-analytical isogeometric framework that splits the temperature field into an analytical point-source solution and a spline-based correction enforcing the boundary conditions — giving accurate part-scale thermal histories on complex CAD geometries with large speed-ups (up to 258×) over conventional FEM.
激光粉末床熔融（LPBF）的热建模充满陡峭、快速移动的温度梯度，传统有限元只能以高昂代价求解。我参与的半解析等几何框架将温度场分解为解析点源解与基于样条、施加边界条件的修正场——在复杂 CAD 几何上给出准确的零件级热历史，并较传统有限元最高提速 258 倍。
Emerging Directions新兴方向
I am extending these ideas to large-deformation fluid–structure interaction (recasting mesh motion as successive domain parameterization) and the isogeometric lattice Boltzmann method for flows over curved boundaries.
我正将这些思想拓展到大变形流固耦合（将网格运动重构为连续的区域参数化）与面向曲边界流动的等几何格子玻尔兹曼方法。