Seminar| Institute of Mathematical Sciences
Time: Friday, December 8th, 2023 , 13:30-14:30
Speaker: Na Lei, International School of Information and Software, Dalian University of Technology
雷娜，大连理工大学国际信息与软件学院教授，博士生导师，国家杰出青年基金获得者。 研究方向为：应用现代微分几何和代数几何的理论与方法解决工程及医学领域的问题，主要聚焦于计算共形几何、计算拓扑、符号计算及其在计算机图形学、计算机视觉、几何建模和医学图像中的应用。多次受邀在国际国内重要会议上做大会邀请报告和会前短课程。主持国家重点研发计划项目课题、国家自然科学基金重点项目、面上项目以及中央部委创新项目等10 余项，主持项目总经费一千余万元。学术成果多次被菲尔兹奖获得者或美国科学院院士等在国际会议上介绍；获得的知识产权在工业界得到转化。担任网格生成领域国际顶会IMR 首位来自亚洲的committee member。获得世界华人数学家大会最佳论文奖。
Dr. Na Lei 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.
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.
网格生成是CAD/CAE领域中的基本问题。结构化的六面体网格被称为计算力学中的“神圣网格”问题。数十年来，人们对其进行了大量的研究。尽管实践中有许多基于经验的工程类方法，但其理论基础仍然缺乏。在这个报告中将要介绍我们建立的基于计算共形几何的四边形网格的理论框架。我们发现了黎曼曲面上的四边形网格可以用亚纯四次微分来刻画，四边形网格的奇异点对应着亚纯微分的零点和极点，进而满足Abel-Jaboci方程。基于这些理论和Ricci flow算法，我们设计了高质量四边形网格自动生成的方法。此外，我们还发现基于Strebel 微分的四边形网格可以进一步生成六面体网格，从而可以对任意复杂拓扑的目标生成全结构化六面体网格。
