3 papers
math.NA2024
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…
math.NA2023
A highly efficient and accurate divergence-free spectral method for curl-curl equation in two and three dimensions
Lechang Qin, Changtao Sheng, Zhiguo Yang
In this paper, we present a fast divergence-free spectral algorithm (FDSA) for the curl-curl problem. Divergence-free bases in two and three dimensions are constructed by using the…
math.NA2023
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…