Approximating and preconditioning the stiffness matrix in the GoFD approximation of the fractional Laplacian

W Huang, J Shen - arXiv preprint arXiv:2407.07199, 2024 - arxiv.org
In the finite difference approximation of the fractional Laplacian the stiffness matrix is
typically dense and needs to be approximated numerically. The effect of the accuracy in …

A study on fractional centered difference scheme for high-dimensional integral fractional Laplacian operator with {ω}-circulant preconditioner

LK Chou, W Qu, YY Huang, SL Lei - Mathematics and Computers in …, 2024 - Elsevier
Fundamental properties for the coefficients of a second-order finite difference approximation
of the fractional Laplacian in d≥ 2 dimensions are derived in this paper. The obtained decay …

Meshfree finite difference solution of homogeneous Dirichlet problems of the fractional Laplacian

J Shen, B Shi, W Huang - Communications on Applied Mathematics and …, 2024 - Springer
A so-called grid-overlay finite difference method (GoFD) was proposed recently for the
numerical solution of homogeneous Dirichlet boundary value problems (BVPs) of the …