On explicit form of the FEM stiffness matrix for the integral fractional Laplacian on non-uniform meshes. (March 2021)

• Record Type: Journal Article
• Authors: Chen, Hongbin; Sheng, Changtao; Wang, Li-Lian
• Is Part Of: Applied mathematics letters. Volume 113(2021)
• Publication Date: 2021-03
• Subjects: Integral fractional Laplacian -- Fractional stiffness matrix -- Graded mesh -- Condition number; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2020.106864
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: We derive exact form of the piecewise-linear finite element stiffness matrix on general non-uniform meshes for the integral fractional Laplacian operator in one dimension, where the derivation is accomplished in the Fourier transformed space. With such an exact formulation at our disposal, we are able to numerically study some intrinsic properties of the fractional stiffness matrix on some commonly used non-uniform meshes (e.g., the graded mesh), in particular, to examine their seamless transition to those of the usual Laplacian.