Fast Q1 finite element for two-dimensional integral fractional Laplacian

Yi Yang, Jin Huang, Yifei Wang, Ting Deng and Hu Li

Applied Mathematics and Computation, 2023, vol. 443, issue C

Abstract: To investigate 2-dimensional integral fractional Laplacian, a fast Q1 finite element method is proposed based on a weighted trapezoidal rule. Different from the very limited existing finite element approximations, the singular integrals are handled numerically, but the rest of integrals can be exactly evaluated. In addition, the entries of stiffness matrix with Toeplitz structure can be efficiently expressed as c2,sh2−γ144w·e with known vectors w and e, where γ∈(2s,2] and 0Keywords: Integral fractional laplacian; Q1-Element; Toeplitz structure; Matrix-vector product; FFT-Based fast algorithm; Error analysis (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:443:y:2023:i:c:s0096300322008256

DOI: 10.1016/j.amc.2022.127757

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