5 citations · 8 across the 8 of their papers we have counts for
9 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…
FEM on nonuniform meshes for nonlocal Laplacian: Semi-analytic Implementation in One Dimension
Hongbin Chen, Changtao Sheng, Li-Lian Wang
In this paper, we compute stiffness matrix of the nonlocal Laplacian discretized by the piecewise linear finite element on nonuniform meshes, and implement the FEM in the Fourier t…
Müntz ball polynomials and Müntz spectral-Galerkin methods for singular eigenvalue problems
Xiu Yang, Li-Lian Wang, Huiyuan Li +1
In this paper, we introduce a new family of orthogonal systems, termed as the Müntz ball polynomials (MBPs), which are orthogonal with respect to the weight function: $\|x\|^{2θ+2μ…
Efficient Monte Carlo Method for Integral Fractional Laplacian in Multiple Dimensions
Changtao Sheng, Bihao Su, Chenglong Xu
In this paper, we develop a Monte Carlo method for solving PDEs involving an integral fractional Laplacian (IFL) in multiple dimensions. We first construct a new Feynman-Kac repres…
On explicit form of the FEM stiffness matrix for the integral fractional Laplacian on non-uniform meshes
Hongbin Chen, Changtao Sheng, Li-Lian Wang
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 th…
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…
Generalised Hermite spectral methods for PDEs involving integral fractional Laplacian and Schrödinger operators
Changtao Sheng, Suna Ma, Huiyuan Li +2
In this paper, we introduce two new families of generalised Hermite polynomials/functions (GHPs/GHFs) in arbitrary dimensions, and develop efficient and accurate generalised Hermit…
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:…
Fundamental Gaps of the Fractional Schrödinger Operator
Weizhu Bao, Xinran Ruan, Jie Shen +1
We study asymptotically and numerically the fundamental gap -- the difference between the first two smallest (and distinct) eigenvalues -- of the fractional Schrödinger operator (F…