6 papers
Optimal convergence of local discontinuous Galerkin methods for convection-diffusion equations
Wenjie Liu, Ruiyi Xie, Li-Lian Wang +1
The local discontinuous Galerkin (LDG) method proposed by Castillo et al. [Math. Comp.,~71 (238): 455-478, 2002] has been shown to be an efficient approach for solving convect…
Solving PDEs on Surfaces of Pipe Geometries Using New Coordinate Transformations and High-order Compact Finite Differences
Shuaifei Hu, Yujian Jiao, Desong Kong +1
We introduce suitable coordinate systems for pipes and their variants that allow us to transform partial differential equations (PDEs) on the pipe surfaces or in the solid pipes in…
PODNO: Proper Orthogonal Decomposition Neural Operators
Zilan Cheng, Zhongjian Wang, Li-Lian Wang +1
In this paper, we introduce Proper Orthogonal Decomposition Neural Operators (PODNO) for solving partial differential equations (PDEs) dominated by high-frequency components. Build…
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…
An Efficient Spectral Trust-Region Deflation Method for Multiple Solutions
Lin Li, Lilian Wang, Huiyuan Li
It is quite common that a nonlinear partial differential equation (PDE) admits multiple distinct solutions and each solution may carry a unique physical meaning. One typical approa…
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…