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6 papers
An Efficient Finite Element Method for Multi-dimensional Nonlocal Laplacian on Uniform Grids
Changtao Sheng, Huiyuan Li, Huifang Yuan +1
Computing the stiffness matrix for the finite element discretization of the nonlocal Laplacian on unstructured meshes is difficult, because the operator is nonlocal and can even be…
An efficient spectral-Galerkin method for fractional reaction-diffusion equations in unbounded domains
Huifang Yuan
In this work, we apply a fast and accurate numerical method for solving fractional reaction-diffusion equations in unbounded domains. By using the Fourier-like spectral approach in…
On diagonal dominance of FEM stiffness matrix of fractional Laplacian and maximum principle preserving schemes for fractional Allen-Cahn equation
Hongyan Liu, Changtao Sheng, Li-Lian Wang +1
In this paper, we study diagonal dominance of the stiffness matrix resulted from the piecewise linear finite element discretisation of the integral fractional Laplacian under globa…
Fast Fourier-like Mapped Chebyshev Spectral-Galerkin Methods for PDEs with Integral Fractional Laplacian in Unbounded Domains
Changtao Sheng, Jie Shen, Tao Tang +2
In this paper, we propose a fast spectral-Galerkin method for solving PDEs involving integral fractional Laplacian in , which is built upon two essential components:…
Rational spectral methods for PDEs involving fractional Laplacian in unbounded domains
Tao Tang, Li-Lian Wang, Huifang Yuan +1
Many PDEs involving fractional Laplacian are naturally set in unbounded domains with underlying solutions decay very slowly, subject to certain power laws. Their numerical solution…
Hermite spectral collocation methods for fractional PDEs in unbounded domains
Tao Tang, Huifang Yuan, Tao Zhou
This work is concerned with spectral collocation methods for fractional PDEs in unbounded domains. The method consists of expanding the solution with proper global basis functions…