[IMS Seminar] Mesh Generation Based on Computational Conformal Geometry

ON2023-12-07TAG: ShanghaiTech UniversityCATEGORY: Lecture

Topic: Mesh Generation Based on Computational Conformal Geometry
Speaker: Professor LEI Na, International School of Information and Software, Dalian University of Technology (DLUT)

Date and time: 13:30–14:30, December 8

Venue: Room S408 of IMS


Generating  meshes with regular structure plays a fundamental role in CAD/CAE.  Regular hexahedral mesh generation is called the holy grid problem in  computational mechanics. Intensive research efforts have been spent on  it for tens of years. Although there are many heuristic methods in  practice, the theoretic foundation still remains widely open. Recently,  we have established a theoretic framework for quadrilateral mesh  generation based on conformal geometry. Basically, we have discovered  the intrinsic relation between quad-meshes and meromorphic differentials  on Riemann surfaces. It can answer many fundamental problems. For  examples, it can show the existence of quad-meshes with special  properties, estimate the dimension of quad-meshes with constraints,  specify the geometric relations among the singular vertices of  quad-meshes. More importantly, it gives a simple algorithm for high  quality quad-mesh generation based on Abel-Jacobi theorems. Furthermore,  the quad-meshes based on Strebel differential can leads to hexahedral  mesh generation for volumes.


Dr. LEI Na is a professor and doctoral supervisor at the International  School of Information and Software, Dalian University of Technology. Her  research interest is applying the theories and methods of modern  differential geometry and algebraic geometry to solve problems in the  fields of engineering and medicine, mainly focusing on computational  conformal geometry, computational topology, symbolic computing and their  application in computer graphics, computer vision, geometric modeling  and medical imaging. She has presided the National key research and  development plan projects, key projects of the National Natural Science  Foundation of China, and many other important projects, with a total  funding of more than 20 million yuan. Her academic achievements have  been introduced at international conferences many times by Fields  Medalists or academicians of the National Academy of Sciences; the  intellectual property rights obtained have been transformed in the  industry. Served as the first committee member from Asia at IMR, the top  international conference in the field of mesh generation. Won the Best  Paper Award at the World Congress of Chinese Mathematicians.