报告题目：Volumetric Stretch Energy Minimization and Optimal Mass Transport with Applications
报告摘要：Volumetric stretch energy has been widely applied to the computation of volume-/mass-preserving parameterizations of simply connected tetrahedral mesh models M. However, this approach still lacks theoretical support. In this talk, we provide a theoretical foundation for volumetric stretch energy minimization (VSEM) to show that a map is a precise volume-/mass-preserving parameterization from M to a region of a specified shape if and only if its volumetric stretch energy reaches 3|M|/2, where |M| is the total mass of M. We use VSEM to compute an \epsilon-volume-/mass-preserving map f* from M to a unit ball, where \epsilon is the gap between the energy of f* and 3|M|/2. In addition, we prove the efficiency of the VSEM algorithm with guaranteed asymptotic R-linear convergence. Furthermore, based on the VSEM algorithm, we propose a projected gradient method for the computation of the \epsilon-volume-/mass-preserving optimal mass transport map with a guaranteed convergence rate of O(1/m) and combined with Nesterov-based acceleration, the guaranteed convergence rate becomes O(1/m^2). Numerical experiments are presented to justify the theoretical convergence behavior for various examples drawn from known benchmark models. Moreover, these numerical experiments show the effectiveness of the proposed algorithm, particularly in the processing of 3D medical MRI brain images.
报告人简介：林文伟，台湾阳明交通大学终身讲座教授，博士生导师，目前任南京应用数学中心副主任及 B 项目组负责人。1986 年获得德国 Bielefeld 大学应用数学博士，曾担任台湾阳明交通大学应用数学系系主任、丘成桐中心执行主任。长期从事大规模矩阵计算、保结构加倍算法、Maxwell 方程计算、最优化控制理论及算法、3D 计算共形几何及其在医学影像上的应用、混沌加密系统的理论及应用等领域的研究，主持多项台湾科技部门自然科学重大领航研究计划及国际间（美国、德国、澳洲等）合作项目。1995 年和 2002 年分别获得台湾科技部门杰出研究奖，2004 年获得台湾教育部门学术奖，2007 年获得台湾教育部门讲座奖，2019 年获得第八届世界华人数学家大会陈省身奖。2008年 至今任 SIAM Matrix Anal. Appl. 杂志编委，2010 年至今任 Elec. Trans. Numer. Anal. 杂志编委，2016 年至今任 Annals Math. Sci. Appl. 杂志主编。在 SIMAX, SISC, SIIMS, SINUM, NM, MC, JCP，IP, CPC, ACM TOMS 等国际一流期刊发表学术论文 200 余篇，并在 SIAM Foundaments of Algorithms 出版学术专著 1 本。
报告时间：2024/04/25 19:30-20:30
报告地点：腾讯会议：464-806-110
