Efficient Numerical Methods for Integral Fractional Laplacian in Multiple Dimensions


主讲人:盛长滔  上海财经大学讲师




主讲人介绍:盛长滔,上海财经大学,博士,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。

内容介绍:PDEs involving integral fractional Laplacian in multiple dimensions pose  significant numerical challenges due to the nonlocality and singularity of the  operator. In this talk, we demonstrate that spectral methods using the  generalised Hermite functions with their adjoint can lead to diagonal stiffness  matrix for fractional Laplacian in R^d. We also demonstrate that the  bi-orthogonal Fourier-like mapped Chebyshev basis under the Dunford-Taylor  formulation of the fractional Laplacian operator. For fractional Laplacian in  bounded domain, we shall report our recent attempts towards fast and accurate  semi-analytic computation of the underlying fractional stiffness matrix. We show  that for the rectangular or L-shaped domains, each entry of FEM stiffness matrix  associated with the tensorial rectangular elements can be expressed explicitly  by some one-dimensional integrals, which can be evaluated accurately. The key is  to implementing the FEM in the Fourier transformed space.