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【北航数学论坛】Localized Exponential Time Differencing Methods: algorithms and Analysis
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报告题目:Localized Exponential Time Differencing Methods: algorithms and Analysis

报告人:鞠立力 教授,Department of Mathematics, University of South CarolinaUSA

报告时间:20191218,    1000-1100


摘要:Exponential time differencing (ETD) has been proven to be very effective for solving stiff evolution problems in the past decades due to rapid development of matrix exponential algorithms and computing capacities. While direct parallelization of the ETD methods is rarely of good efficiency due to the required data communication, the localized exponential time differencing approach was recently introduced for extreme-scale phase field simulations of coarsening dynamics, which displayed excellent parallel scalability in modern supercomputers. The main idea is to use domain decomposition techniques to reduce the size of the problem, so that one instead only solves a group of smaller-sized subdomain problems simultaneously using the locally computed products of matrix exponentials and vectors. With the diffusion equation as the model problem, we will develop and analyze some overlapping and nonoverlapping localized ETD schemes and their solution algorithms. Numerical experiments are also carried out to confirm the theoretical results. This work is to serve as the first step toward building a solid mathematical foundation for localized ETD methods.

报告人概况:鞠立力教授1995年毕业于武汉大学数学系获数学学士学位, 1998年在中国科ag平台app下载计算数学与科学工程计算研究所获得计算数学硕士学位,2002年在美国爱荷华州立大学获得应用数学博士学位。2002-2004年在美国明尼苏达大学数学与应用研究所从事博士后研究。随后进入美国南卡莱罗纳大学工作,历任数学系助理教授(20048-20088),副教授(20088-201212),及教授(20131-现在)。美国工业与应用数学学会(SIAM)成员,2008-2009年期间担任其东南大西洋分会主席。主要从事数值计算方法与分析,网格优化,非局部模型, 图像处理,深度学习, 高性能科学计算,及其在材料与地球科学中的应用等方面的研究工作。至今已发表科研论文100余篇,谷歌学术引用2800多次。主持了多项由美国国家科学基金会(NSF)和美国能源部(DOE)等联邦机构资助的科研项目。20122017年任数值分析领域国际重要学术期刊SIAM Journal on Numerical Analysis的编委。多次受邀担任美国国家科学基金会计算数学领域基金会审评议组成员。与合编辑关于合金微结构演化在“神威·太湖之光”超级计算机上的相场模拟工作入围2016年国际高性能计算应用最高奖—“戈登·贝尔”奖提名。


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