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

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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Main Authors: Chen, Hongbin, Sheng, Changtao, Wang, Li-Lian
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2022
Subjects:
Science::Mathematics
Integral Fractional Laplacian
Fractional Stiffness Matrix
Online Access:https://hdl.handle.net/10356/160942
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-1609422022-08-08T05:02:49Z On explicit form of the FEM stiffness matrix for the integral fractional Laplacian on non-uniform meshes Chen, Hongbin Sheng, Changtao Wang, Li-Lian School of Physical and Mathematical Sciences Science::Mathematics Integral Fractional Laplacian Fractional Stiffness Matrix 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. 2022-08-08T05:02:49Z 2022-08-08T05:02:49Z 2021 Journal Article Chen, H., Sheng, C. & Wang, L. (2021). On explicit form of the FEM stiffness matrix for the integral fractional Laplacian on non-uniform meshes. Applied Mathematics Letters, 113, 106864-. https://dx.doi.org/10.1016/j.aml.2020.106864 0893-9659 https://hdl.handle.net/10356/160942 10.1016/j.aml.2020.106864 2-s2.0-85095917026 113 106864 en Applied Mathematics Letters © 2020 Elsevier Ltd. All rights reserved.
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Science::Mathematics
Integral Fractional Laplacian
Fractional Stiffness Matrix
spellingShingle Science::Mathematics
Integral Fractional Laplacian
Fractional Stiffness Matrix
Chen, Hongbin
Sheng, Changtao
Wang, Li-Lian
On explicit form of the FEM stiffness matrix for the integral fractional Laplacian on non-uniform meshes
description 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.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Chen, Hongbin
Sheng, Changtao
Wang, Li-Lian
format Article
author Chen, Hongbin
Sheng, Changtao
Wang, Li-Lian
author_sort Chen, Hongbin
title On explicit form of the FEM stiffness matrix for the integral fractional Laplacian on non-uniform meshes
title_short On explicit form of the FEM stiffness matrix for the integral fractional Laplacian on non-uniform meshes
title_full On explicit form of the FEM stiffness matrix for the integral fractional Laplacian on non-uniform meshes
title_fullStr On explicit form of the FEM stiffness matrix for the integral fractional Laplacian on non-uniform meshes
title_full_unstemmed On explicit form of the FEM stiffness matrix for the integral fractional Laplacian on non-uniform meshes
title_sort on explicit form of the fem stiffness matrix for the integral fractional laplacian on non-uniform meshes
publishDate 2022
url https://hdl.handle.net/10356/160942
_version_ 1743119573212725248

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