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| 美国阿拉巴马大学赵山教授学术报告 |
| 发布时间： 2018-06-11 浏览次数： 617 |
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题目：发展空间二阶精度的交替方向隐式算法求解三维抛物界面问题 报告人：赵山 教授 美国阿拉巴马大学数学系 主持人： 杨辉 教授 时间：2018年6月12日 15：00 地点：数学与统计学院会议室（博学楼416-1） 参加人：学院教师、研究生和高年级本科生 报告摘要： In this talk, we will present a novel alternating direction implicit (ADI) method for solving three-dimensional (3D) parabolic interface problems with discontinuous jumps and complex interfaces. The ADI scheme is a powerful finite difference method for solving diffusion equations, due to its stability and efficiency. However, it suffers from a serious accuracy reduction in space for interface problems with different materials and nonsmooth solutions. To restore the second order accuracy, physical interface conditions that describe jumps of the function and its flux have to be enforced in the spatial discretization. To this end, a non-orthogonal local coordinate system is constructed in the proposed matched ADI method, to decouple 3D jump conditions into essentially one-dimensional (1D) ones along the Cartesian directions. These 1D conditions can then be incorporated into the ADI central difference discretization. In time discretization, the matched ADI method is found to be of first order and stable in various experiments. In space discretization, the matched ADI method achieves the second order accuracy based on simple Cartesian grids for various irregularly-shaped surfaces and spatial–temporal dependent jumps. Fast algebraic solvers for perturbed tridiagonal systems are developed so that the matched ADI method is as efficient as the fastest implicit scheme based on the geometrical multigrid for solving 3D parabolic equations, in the sense that its complexity in each time step scales linearly with respect to the spatial degree of freedom N, i.e., O(N). Therefore, the proposed matched ADI method provides a very promising tool for solving 3D parabolic interface problems. 报告人简介：赵山教授于1987年至1993年在贵阳六中初中部和高中部学习. 1997年在兰州大学数学系毕业取得学士学位, 2003年在新加坡国立大学计算科学系取得博士学位. 2003年至2006年在美国密歇根州立大学进行博士后研究. 从2006年至今, 在美国阿拉巴马大学数学系任教，先后担任助理教授，副教授。他于2015年提前晋升为数学系正教授。赵教授现在指导5名博士生。 赵山教授在分子生物学，计算电磁学，工程计算等交叉学科开展了包括数学建模，数值分析，和算法创新在内的一系列基础研究工作，已做出很多受到国际同行认可的创新性学术成就；现已发表了50余篇SCI 杂志论文。根据Google Scholar索引，他的论文被同行引用了超过1500次。赵山教授的研究得到了美国国家科学基金的多项资助, 曾多次为美国国家科学基金担任基金函评和会评专家。赵山教授担任多家国际期刊的责任编委，编委，或客席编委，他也曾为50余家国际期刊担任论文评审人. 赵山教授的更多资料可在他的个人主页找到:  http://szhao.people.ua.edu/.欢迎全校感兴趣的广大师生参加！ |
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