34 citations · 39 across the 11 of their papers we have counts for
11 papers
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…
Sparse Spectral-Galerkin Method on An Arbitrary Tetrahedron Using Generalized Koornwinder Polynomials
Lueling Jia, Huiyuan Li, Zhimin Zhang
In this paper, we propose a sparse spectral-Galerkin approximation scheme for solving the second-order partial differential equations on an arbitrary tetrahedron. Generalized Koorn…
H()-conforming quadrilateral spectral element method for quad-curl problems
Lixiu Wang, Weikun Shan, Huiyuan Li +1
In this paper, we propose an -conforming quadrilateral spectral element method to solve quad-curl problems. Starting with generalized Jacobi polynomials, we first…
Vectorial ball Prolate spheroidal wave functions with the divergence free constraint
Jing Zhang, Guidoum Ikram, Huiyuan Li
In this paper, we introduce one family of vectorial prolate spheroidal wave functions of real order on the unit ball in , which satisfy the divergence free constraint,…
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…
Jacobi-Galerkin spectral method for eigenvalue problems of Riesz fractional differential equations
Lizhen Chen, Zhiping Mao, Huiyuan Li
An efficient Jacobi-Galerkin spectral method for calculating eigenvalues of Riesz fractional partial differential equations with homogeneous Dirichlet boundary values is proposed i…
Ball Prolate Spheroidal Wave Functions In Arbitrary Dimensions
Jing Zhang, Huiyuan Li, Li-Lian Wang +1
In this paper, we introduce the prolate spheroidal wave functions (PSWFs) of real order on the unit ball in arbitrary dimension, termed as ball PSWFs. They are eigenfunction…
Optimal error estimates for Chebyshev approximations of functions with limited regularity in fractional Sobolev-type spaces
Wenjie Liu, Li-Lian Wang, Huiyuan Li
In this paper, we introduce a new theoretical framework built upon fractional Sobolev-type spaces involving Riemann-Liouville (RL) fractional integrals/derivatives, which is natura…
Spectral-Galerkin Approximation and Optimal Error Estimate for Stokes Eigenvalue Problems in Polar Geometries
Jing An, Huiyuan Li, Zhimin Zhang
In this paper we propose and analyze spectral-Galerkin methods for the Stokes eigenvalue problem based on the stream function formulation in polar geometries. We first analyze the…
A fully diagonalized spectral method using generalized Laguerre functions on the half line
Fu-jun Liu, Zhong-qing Wang, Huiyuan Li
A fully diagonalized spectral method using generalized Laguerre functions is proposed and analyzed for solving elliptic equations on the half line. We first define the generalized…
Efficient Spectral and Spectral Element Methods for Eigenvalue Problems of Schrödinger Equations with an Inverse Square Potential
Huiyuan Li, Zhimin Zhang
In this article, we study numerical approximation of eigenvalue problems of the Schrödinger operator . There are three stages in our investi…