報(bào) 告 人：林文偉 教授
報(bào)告題目：Volumetric Stretch Energy Minimization and its Associated Optimal Mass Transport with Applications
報(bào)告時(shí)間：2023年9月22日（周五）下午04:00
報(bào)告地點(diǎn)：靜遠(yuǎn)樓1506學(xué)術(shù)報(bào)告廳
主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院
報(bào)告人簡(jiǎn)介：
林文偉，南京應(yīng)用數(shù)學(xué)中心副主任，計(jì)算幾何及應(yīng)用項(xiàng)目組負(fù)責(zé)人，臺(tái)灣陽明交通大學(xué)終身講座教授，博士生導(dǎo)師。1986年獲得德國 Bielefeld大學(xué)應(yīng)用數(shù)學(xué)博士，曾擔(dān)任臺(tái)灣陽明交通大學(xué)應(yīng)用數(shù)學(xué)系系主任、丘成桐中心執(zhí)行主任。2023年8月起任南京應(yīng)用數(shù)學(xué)中心副主任。長期從事大規(guī)模矩陣計(jì)算、保結(jié)構(gòu)加倍算法、Maxwell 方程計(jì)算、最優(yōu)化控制理論及算法、3D計(jì)算共形幾何及其在醫(yī)學(xué)影像上的應(yīng)用、混沌加密系統(tǒng)的理論及應(yīng)用等領(lǐng)域的研究，主持多項(xiàng)臺(tái)灣科技部門自然科學(xué)重大領(lǐng)航研究計(jì)劃及國際間（美國、德國、澳洲等）合作項(xiàng)目。1995年和2002年分別獲得臺(tái)灣科技部門杰出研究獎(jiǎng)，2004年獲得臺(tái)灣教育部門學(xué)術(shù)獎(jiǎng)，2007年獲得臺(tái)灣教育部門講座獎(jiǎng)，2019年獲得第八屆世界華人數(shù)學(xué)家大會(huì)陳省身獎(jiǎng)。2008年至今任SIAM Matrix Anal. Appl.雜志編委，2010年至今任Elec.Trans. Numer. Anal.雜志編委，2016年至今任Annals Math. Sci. Appl.雜志主編。在SIMAX, SISC, SIIMS, SINUM, NM, MC, JCP，IP, CPC, ACM TOMS 等國際一流期刊發(fā)表學(xué)術(shù)論文200余篇，并在SIAM Fundamentals of Algorithms出版學(xué)術(shù)專著1本。
報(bào)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.