报 告 人：盛长滔讲师 上海财经大学
报告题目：EfficientNumerical Methods for Integral Fractional Laplacian in Multiple Dimensions
报告时间：2021年5月29日（周六）上午10:20
报告地点：静远楼204学术报告厅
主办单位：数学与统计学院、科学技术研究院
报告人简介：
盛长滔，上海财经大学，讲师，研究方向为偏微分方程数值方法，主要包括谱方法及其应用。2018年于厦门大学获得博士学位，2018年12月至2021年1月在新加坡南洋理工大学从事博士后研究。目前为止，在SIAM J. Numer. Anal., Math. Comp., J. Sci. Comput., 等知名国内外期刊上发表SCI论文10余篇。
报告摘要：
PDEs involving integralfractional Laplacian in multiple dimensions pose significant numericalchallenges due to the nonlocality and singularity of the operator. In thistalk, we demonstrate that spectralmethods using the generalised Hermite functions with their adjoint can lead todiagonal stiffness matrix for fractional Laplacian in R^d. We also demonstratethat the bi-orthogonal Fourier-like mapped Chebyshev basis under theDunford-Taylor formulation of the fractional Laplacian operator. For fractionalLaplacian in bounded domain, we shall report our recent attempts towards fastand accurate semi-analytic computation of the underlying fractional stiffnessmatrix. We show that for the rectangular or L-shaped domains, each entry of FEMstiffness matrix associated with the tensorial rectangular elements can beexpressed explicitly by some one-dimensional integrals, which can be evaluatedaccurately. The key is to implementing the FEM in the Fourier transformedspace.
邀请人：陈升