受6163银河线路检测中心国际合作处及数学系邀请，南卡罗莱纳大学王宏教授将于近日来访我系并做系列报告，欢迎感兴趣的师生来参加，下面是报告的详细信息。 报告题目1：Anomalous diffusion and fractional PDEs 报告时间： 2016 年7月30日下午14：00 报告地点：数学系会议室（格物楼503） 报告摘要: Fractional diffusion equations provide an adequate and accurate description of transport processes that exhibit anomalous diffusion that is characterized by an inverse power law detail decaying behavior of the corresponding probability density function. These processes range from the signaling of biological cells, anomalous electrodiffusion in nerve cells, foraging behavior of animals, and electrochemistry among other applications. In the talk we will go over the underlying physics and derivation of FPDEs, based on fractional calculus and stochastic analysis. 报告题目2：Fast numerical methods for FPDEs 报告时间： 2016 年7月30日下午15：00 报告地点：数学系会议室（格物楼503） 报告摘要: Computationally, because of the nonlocal property of fractional differential operators, the numerical methods for FPDEs often generate dense coefficient matrices. consequently, these methods often require computational work of O(N3) to invert per time step and memory of O(N2) for where N is the number of unknowns. In this talk we go over the development of faithful and efficient numerical methods for space-fractional partial differential equations, without resorting to any lossy compression, but rather by exploring the structure of the coefficient matrices. These methods have computational cost of O(N log2 N) per time step and memory of O(N), while retaining the same accuracy and approximation property of the underlying numerical methods.
报告题目3：Mathematical issues in the analysis of FPDEs 报告时间：2017年7月31日上午9:00 报告地点：格物楼503 报告摘要：Because of the nonlocal nature of fractional differential operators, FPDEs present new mathematical difficulties that have not been encountered in the context of integer-order PDEs. These include the loss of coercivity of the Galerkin formulation for variable-coefficient problems, non-existence of the weak solution to inhomogeneous Dirichlet boundary-boundary value problems, and low regularity (the solution to homogeneous Dirichlet boundary-value problem of a one-dimensional fractional PDE with constant coefficient and source term is not in the Sobolev space $H^1$). In this talk we will address these issues and report our recent progress in this direction. 报告题目4：An indirect method for FPDEs 报告时间：2017年7月31日上午10:00 报告地点：格物楼503 报告摘要：As we showed in the presentation (3), smooth coefficients and domain cannot guarantee the existence of a smooth solution to FPDEs. Hence, traditional high-order numerical methods do not necessarily yield high-order convergence rates in the context of FPDEs. In this talk we present an indirect numerical approach to generate high-order approximations to FPDEs under the assumption of smooth coefficients but without assuming artificially the smoothness of the true solution.
报告人简介：王宏，美国南卡罗来纳大学数学系终身教授，分别于1981年和1984年获山东大学数学学士学位和计算数学硕士学位，1992年获美国怀俄明大学数学博士学位。主要从事油气田勘探开发、环境污染的预测与治理和二氧化碳埋存等领域的数学模型、数值模拟与大规模科学计算的理论及应用方面的研究；迄今为止已在SIAM J Numer. Anal.、SIAM Sci. Comput.、J Comput Phys、Numer. Methods PDEs和IMA J. Numer. Anal.等国际权威学术杂志发表论文百余篇。王宏教授还是Numer. Methods PDEs、Computing and Visualization in Sciences、Intl J. Numer. Anal. Modeling等国际知名杂志的编委。王宏教授的研究得到了美国国家自然科学基金会、挪威自然科学基金会、南卡州以及世界排名前列的石油公司等的多项基金资助。 | 
