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【6月26日】数学学术讲座(共5场)

信息来源:统计与数学学院 发布时间:2019-06-17

      报告题目1: Numerical Simulations of Water Wave Phenomena
      主讲人:
 陈敏Purdue University
      时间:2019年6月26日(周三)8:00 a.m.
      地点:北院卓远楼305
      主办单位:统计与数学学院

      摘要:In this talk, I’ll present numerical simulations of Water Wave Phenomena and compare results with laboratory experiments and field data.

      主讲人简介:
      陈敏,教授,1982年毕业于北京大学计算数学专业,现任教于美国普渡大学(Purdue University)。

      报告题目2: Positivity preserving schemes for Wasserstein gradient flows. Wasserstein
      主讲人:沈捷(Purdue University
      时间:2019年6月26日(周三)8:50 a.m.
      地点:北院卓远楼305
      主办单位:统计与数学学院

      摘要:I will present a general strategy to construct efficient energy stable and positivity preserving schemes for a class of Wasserstein gradient flows, such as the Poisson-Nernst-Planck (PNP) equation and Keller-Segel equation, whose solution remain to be positive. 

       主讲人简介:
       沈捷,美国普渡大学数学系教授、国际著名数值计算和分析专家。1982年毕业于北京大学计算数学专业,随后赴法国巴黎十一大学研究数值分析,师从国际著名数学大师R.TEMAM,1987年获得博士学位后赴美在Indiana University从事博士后研究。1991年起在宾西法尼亚州立大学任教,2002年转至普渡大学。2008年沈捷教授因在微分方程研究中的卓越贡献获得富布赖特奖,2009年度被授予教育部“长江学者”讲座教授,2010年成为中央第三批“千人计划”入选学者(厦门大学)。沈捷教授长期从事偏微分方程数值解的研究,尤其在谱方法和投影法上有很多杰出的工作,在SIAM.J.Numer.Anal., SIAM.J.Sci.Comput., Numer.Math.,Math.Comp.等国际著名期刊上发表学术论文200余篇。

      报告题目3:Construction of H^2(curl) conforming elements and their application
      主讲人:张智民(北京计算科学研究中心)
      时间:2019年6月26日(周三)9:40 a.m.
      地点:北院卓远楼305
      主办单位:统计与数学学院

      摘要:In 1980 and 1986, Nedelec proposed $H(curl)$-conforming elements to solve electromagnetic equations that contains the “curl” operator. It is more or less as the $H^1$-conforming elements (or $C^0$ elements) for elliptic equations that contains the “grad” operator. As is well known in the finite element method literature, in order to solve 4th-order elliptic equations such as the bi-harmonic equation, $H^2$-conforming elements (or $C^1$-elements) were developed. Recently, there have been some research in solving electromagnetic equations which involve four “curl” operators. Hence, construction of $H(curl curl)$-conforming elements becomes necessary. In this work, we construct $H(curl curl)$-conforming elements for rectangular and triangular meshes and apply them to solve quad-curl equations as well as related eigenvalue problems. 

      主讲人简介:
      张智民,教授,1982年7月获中国科技大学基础数学专业学士学位,1985年1月获中国科技大学计算数学专业硕士学位,1991年7月获美国马里兰大学博士学位。现任美国韦恩州立大学终身教授及北京计算科学研究中心教授,2010年被聘为教育部长江学者讲座教授,2010被邀请在世界华人数学家大会做45分钟报告,获查尔斯H.格申森杰出教师研究员奖等多项奖励。

      报告题目4:Time-Fractional Allen-Cahn Equations: Analysis and Numerical
      主讲人:
杨将博士(南方科技大学)
      时间:2019年6月26日(周三)10:30 a.m.
      地点:北院卓远楼305
      主办单位:统计与数学学院

      摘要:In this work, we consider a time-fractional Allen-Cahn equation, where the conventional first order time derivative is replaced by a Caputo fractional derivative with order $/alpha/in(0,1)$. First, the well-posedness and (limited) smoothing property are systematically analyzed, by using the maximal $L^p$ regularity of fractional evolution equations and the fractional Gr/"onwall's inequality. We also show the maximum principle like their conventional local-in-time counterpart. Precisely, the time-fractional equation preserves the property that the solution only takes value between the wells of the double-well potential when the initial data does the same. Second, after discretizing the fractional derivative by backward Euler convolution quadrature, we develop several unconditionally solvable and stable time stepping schemes, i.e., convex splitting scheme, weighted convex splitting scheme and linear weighted stabilized scheme. Meanwhile, we study the discrete energy dissipation property (in a weighted average sense), which is important for gradient flow type models, for the two weighted schemes. Finally, by using a discrete version of fractional Gr/"onwall's inequality and maximal $/ell^p$ regularity, we prove that the convergence rates of those time-stepping schemes are $O(/tau^/alpha)$ without any extra regularity assumption on the solution. We also present extensive numerical results to support our theoretical findings and to offer new insight on the time-fractional Allen-Cahn dynamics. 

      主讲人简介:
      杨将博士,于2010年在浙江大学数学系获数学学士学位,2014年在香港浸会大学数学系获得博士学位,现任教于南方科技大学。他的研究方向包括微分方程数值解,相场模型的数值算法及应用,非局部模型的数值算法及应用。

      报告题目5:Nested Picard Integrators for the Dirac equation in the nonrelativistic limit
      主讲人:
蔡勇勇(北京计算科学研究中心)
      时间:2019年6月26日(周三)11:20 a.m.
      地点:北院卓远楼305
      主办单位:统计与数学学院

      摘要:We present the construction and analysis of uniformly accurate nested Picard iterative integrators (NPI) for the Dirac equation in the nonrelativistic limit involving a dimensionless parameter inversely proportional to the speed of light. To overcome the difficulty induced by the rapid temporal oscillation, we present the construction of several NPI methods which are uniformly first-, second- and third-order convergent in time. The NPI method can be extended to arbitrary higher order in time with optimal and uniform accuracy. The implementation of the second order NPI method will be demonstrated and analyzed.

      主讲人简介:
      蔡勇勇,北京计算科学研究中心,在北京大学获得学士、硕士学位,在新加坡国立大学获得博士学位,国家“青年千人计划”入选者。在数值分析与科学计算、多相流数值计算方法等研究领域取得了许多创造性成果,在SIAM J. on Applied Math.,SIAM J. Numer. Anal.,J. Comput. Phys. ,Phys. Rev. A,Math. Comp.等顶尖学术期刊发表论文20余篇。
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