On explicit form of the FEM stiffness matrix for the integral fractional Laplacian on non-uniform meshes

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 ab...

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Bibliographic Details
Main Authors: Chen, Hongbin, Sheng, Changtao, Wang, Li-Lian
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2022
Subjects:
Online Access:https://hdl.handle.net/10356/160942
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Institution: Nanyang Technological University
Language: English
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Summary: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.