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
Abstract:
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.
Biography:
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.