学术报告

沈捷学术报告

阅读次数:1840

 题目:Efficient and Accurate Numerical Methods for Solving Fractional PDEs

报告人:沈捷 教授(长江学者、千人计划,普渡大学、厦门大学)

地点:致远楼101室

时间:2018年3月15日(周四)15:00-16:00

Abstract: We present efficient and accurate numerical methods for fractional Laplacian equations and for time-fractional diffusion equations. For fractional Laplacian problem in bounded domains, we adopt the Caffarelli-Silvestre extension which transforms the fractional Laplacian equation in d-dimension into an equivalent system with local derivatives in (d+1)-dimension. We develop an efficient numerical method based on the generalized Laguerre approximation in the extended direction and usual (FEM or spectral) approximation in the original domain. Moreover, we enrich the spectral approximation space by using leading singular functions associated with the extended $y$-direction so that high-accuracy can be achieved despite the singularity of extended problem at $y=0$. For time-fractional diffusion equations, we can adopt a similar approach used for the extended problem of the fractional Laplacian. However, an essential difficulty arises as the time-fractional operator is not self-adjoint which makes the diagonalization process very ill conditioned. We shall propose a novel approach to overcome this difficulty.

简历:沈捷,美国普渡大学数学系和厦门大学数学科学学院教授,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,1987年获得法国巴黎十一大学博士学位,之后在印第安纳大学从事博士后研究。1991年起在宾夕法尼亚州立大学任教,2002年转至普渡大学任教。2008年沈捷教授获得富布赖特奖,2009年被授予教育部“长江学者”讲座教授,2010年入选国家“千人计划”,2017年当选美国数学会会士。沈捷教授主要从事偏微分方程数值解研究,特别在谱方法数值分析理论和科学计算方面有杰出贡献,目前已在Numer. Math., Math. Comp. , SIAM J. Numer. Anal., SIAM J. Sci. Comput.等国际著名期刊上发表学术论文200余篇。

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