報告題目一：On the convergence of a two-level preconditioned Jacobi-Davidson method for eigenvalue problems
報告時間⛑️：2019年11月22日14:00-14:40
報告地點👉🏻：必一体育平台二樓會議室
報告人：許學軍
報告人簡介: 國家傑出青年基金獲得者，同濟大學數學科學必一院長，曾任中國計算數學學會常務理事、秘書長🫸🏿，國家973項目小組負責人🫲🏻，中國數學會理事👨🏻🦳🤸🏻♂️，中國工業和應用數學會理事⁉️。曾獲得過中科院優秀博士後稱號和中國數學會鐘家慶數學獎🧗🏼，以及中科院數學與系統科學研究院十大重大科研進展獎（2007）和中科院數學與系統科學研究院突出科研成果獎（2008）。在SIAM J. Numer. Anal.🤦🧘🏼，Numer. Math.等計算數學重要學術期刊上發表論文100余篇🏪。
報告摘要：In this talk, we shall give a rigorous theoretical analysis of the two-level preconditioned Jacobi-Davidson method for solving the large scale discrete elliptic eigenvalue problems, which was essentially proposed by Zhao, Hwang, and Cai in 2016. Focusing on eliminating the error components in the orthogonal complement space of the target eigenspace, we find that the method could be extended to the case of the 2m th order elliptic operator (m = 1, 2). By choosing a suitable coarse space, we prove that the method holds a good scalability and we obtain the error reduction γ in each iteration, where C is a constant independent of the mesh size h and the diameter of subdomains H, δ = c[1-C(δ2m-1)/(H2m-1)] is the overlapping size among the subdomains, and c → 1 decreasingly as H → 0. Moreover, the method does not need any assumption between H and h. Numerical results supporting our theory are given.
報告題目二🔢：Interpolation and Expansion on Orthogonal Polynomials
報告時間：2019年11月22日14:40-15:20
報告地點🙃：必一体育平台二樓會議室
報告人🫴🏼：向淑晃
報告人簡介✧：湖南省計算數學與應用軟件學會理事長，中南大學教授，博士生導師🧖🏻。主要從事高振蕩問題數值計算、矩陣理論及計算、線性互補問題👅、新古典主義數值分析等領域的研究。主持國家自然科學基金面上項目多項。在SIAM J. Numer. Anal.🛸，SIAM Sci. Comput.🈷️，Math. Program 等國內外重要學術期刊發表論文100余篇◼️👌🏼。
報告摘要🛏：The convergence rates on polynomial interpolation in most cases are estimated by Lebesgue constants. These estimates may be overestimated for some special points of sets for functions of limited regularities. In this talk, new formulas on the convergence rates are considered. Moreover, new and optimal asymptotics on the coefficients of functions of limited regularity expanded in forms of Jacobi and Gegenbauer polynomial series are presented. All of these asymptotic analysis are optimal. Numerical examples illustrate the perfect coincidence with the estimates.
報告題目三：Spectral methods for some problems having low regularity solutions
報告時間：2019年11月22日15:20-16:00
報告地點🧛🏽♀️🧜🏿♂️：必一体育平台二樓會議室
報告人🤚🏿：許傳炬
報告人簡介：福建省閩江學者特聘教授，廈門大學博士生導師。主要研究方向：偏微分方程數值分析，計算流體力學，反常擴散問題理論及計算。主持多項國家自然科學基金, 參加973項目、國家自然科學基金重點項目等🫅🏿。在SIAM J. Numer. Anal., SIAM J. Sci. Comput., Math. Comput.等計算數學重要學術期刊上發表論文100余篇。2003年獲福建省科技進步二等獎✳️✷，是國際計算數學頂級期刊SIAM J. Sci. Comput.的編委。
報告摘要🏌🏿♂️：In this talk we will present a new spectral method for a class of equations with non-smooth solutions. The proposed method makes use of the fractional polynomials, also known as Muntz polynomials. We first present some basic approximation properties of the Muntz polynomials, including error estimates for the weighted projection and interpolation operators. Then we will show how to construct efficient spectral methods by using the Muntz polynomials. A detailed convergence analysis will be provided. The potential application of this method covers a large number of problems, including classical elliptic equations, integro-differential equations with weakly singular kernels, fractional differential equations, and so on.
報告題目四♍️🧑🏼🦰：Virtual element methods for elliptic variational inequalities of the second kind
報告時間👩🦽：2019年11月22日16:00-16:40
報告地點：必一体育平台二樓會議室
報告人🏊🏼：黃建國
報告人簡介：上海交通大學教授，博士生導師👐🏿，中國計算數學會理事👩🏻⚖️。長期從事偏微分方程數值解♒️，組合彈性結構問題的數學模型和有限元方法，反問題數值解等的研究工作🧑🧒🧒。在SIAM J. Numer. Anal., SIAM J. Sci. Comput., Math. Comput. 等計算數學重要學術期刊上發表論文100余篇。先後主持多項國家自然科學基金項目，參加973項目等🥛。
報告摘要🙌🏼：In this talk, we are concerned with virtual element methods for solving elliptic variational inequalities (EVIs) of the second kind. First, a general framework is provided for the numerical solution of the EVIs and for its error analysis. Then virtual element methods are applied to solve two representative EVIs: a simplified friction problem and a frictional contact problem. Optimal order error estimates are derived for the virtual element solutions of the two representative EVIs, including the effects of numerical integration for the non-smooth term in the EVIs. A fast solver is introduced to solve the discrete problems. Several numerical examples are included to show the numerical performance of the proposed methods. This is a joint with Fang Feng from Shanghai Jiao Tong University and Weimin Han from University of Iowa.