题目: An Efficient Spectral Method for Solving PDEs in Torus Pipe Geometries

主讲人：孔德松 博士后

时间：2026年06月03日（星期三）10:00 —11:30

地点：理学院楼308

主办单位：理学院

主讲人简介：

孔德松博士于2023年毕业于中南大学，指导老师是向淑晃教授，攻读博士学位期间受国家留学基金委资助前往新加坡南洋理工大学进行联合培养，合作导师王立联教授。2023年至今在宁波东方理工大学做博士后，合作导师沈捷教授。孔德松博士的主要研究方向是奇异函数的逼近理论、复杂区域和非标准几何上的高效算法研究，以及发展型方程的时空谱方法研究。其博士学位论文获得湖南省优秀博士学位论文，至今已在Mathematics of Computation, Journal of Scientific Computing, Advances in Computational Mathematics等计算数学国际知名期刊发表学术论文多篇。

摘要：

We develop an efficient spectral method for partial differential equations posed in torus pipe geometries, formulated in orthogonal toroidal-poloidal coordinates. Starting from the weak formulation of the underlying elliptic problems, we identify and analyze the pole conditions induced by coordinate singularities, and construct a spectral-Galerkin scheme whose basis functions intrinsically satisfy these conditions. The proposed framework is further extended to eigenvalue problems and to the incompressible Navier--Stokes equations via a scalar auxiliary variable (SAV) formulation combined with a consistent splitting time discretization. Extensive numerical experiments demonstrate the efficiency, spectral accuracy, and robustness of the method for a range of problems in torus geometries.