35 citations · 172 across the 30 of their papers we have counts for
31 papers
A Matrix-free Augmented High Order Compact Solver for Variable-Coefficient Biharmonic Problems
Jin Li, Kejia Pan, Xu Qian +1
We propose an augmented high-order compact finite difference method for biharmonic equations with clamped boundary conditions and variable coefficients. Standard mixed-type formula…
A Robust Helmholtz-Decomposition-Based Real Compressed Layer Method for Time-Harmonic Elastic Wave Scattering
Li-Lian Wang, Lu Zhang
Time-harmonic elastic wave scattering involves both compressional (P-) and shear (S-) waves, which propagate with different wavenumbers and polarization characteristics. The naive…
Pointwise error estimates and local superconvergence of Jacobi expansions
Shuhuang Xiang, Desong Kong, Guidong Liu +1
As one myth of polynomial interpolation and quadrature, Trefethen [30] revealed that the Chebyshev interpolation of (with ) at the Clenshaw-Curtis points exhibited…
Eigenvalue Analysis and Applications of the Legendre Dual-Petrov-Galerkin Methods for Initial Value Problems
Desong Kong, Jie Shen, Li-Lian Wang +1
In this paper, we show that the eigenvalues and eigenvectors of the spectral discretisation matrices resulted from the Legendre dual-Petrov-Galerkin (LDPG) method for the th-ord…
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…
Analysis of a Backward Euler-type Scheme for Maxwell's Equations in a Havriliak-Negami Dispersive Medium
Yubo Yang, Li-Lian Wang, Fanhai Zeng
For the Maxwell's equations in a Havriliak-Negami (H-N) dispersive medium, the associated energy dissipation law has not been settled at both continuous level and discrete level. I…
Optimal error estimates for Legendre expansions of singular functions with fractional derivatives of bounded variation
Wenjie Liu, Li-Lian Wang, Boying Wu
We present a new fractional Taylor formula for singular functions whose Caputo fractional derivatives are of bounded variation. It bridges and ``interpolates" the usual Taylor form…
On time-domain NRBC for Maxwell's equations and its application in accurate simulation of electromagnetic invisibility cloaks
Bo Wang, Zhiguo Yang, Lilian Wang +1
In this paper, we present analytic formulas of the temporal convolution kernel functions involved in the time-domain non-reflecting boundary condition (NRBC) for the electromagneti…
A Truly Exact and Optimal Perfect Absorbing Layer for Time-harmonic Acoustic Wave Scattering Problems
Zhiguo Yang, Li-Lian Wang, Yang Gao
In this paper, we design a truly exact and optimal perfect absorbing layer (PAL) for domain truncation of the two-dimensional Helmholtz equation in an unbounded domain with bounded…
An Efficient Iterative Method for Solving Multiple Scattering in Locally Inhomogeneous Media
Ziqing Xie, Rui Zhang, Bo Wang +1
In this paper, an efficient iterative method is proposed for solving multiple scattering problem in locally inhomogeneous media. The key idea is to enclose the inhomogeneity of the…
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…
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…
An accurate spectral method for Maxwell equations in Cole-Cole dispersive media
Can Huang, Li-lian Wang
In this paper, we propose an accurate numerical means built upon a spectral-Galerkin method in spatial discretization and an enriched multi-step spectral-collocation approach in te…
Calculation of SPH and VSH Expansions
Bo Wang, Li-Lian Wang, Ziqing Xie
We present in this paper a spectrally accurate numerical method for computing the spherical/vector spherical harmonic expansion of a function/vector field with given (elemental) no…
Uniform bounds and asymptotics of Generalized Gegenbauer functions of fractional degree
Wenjie Liu, Li-Lian Wang
The generalised Gegenbauer functions of fractional degree (GGF-Fs), denoted by (right GGF-Fs) and (left GGF-Fs) with $λ>-…
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…
Laguerre Functions and Their Applications to Tempered Fractional Differential Equaitons on Infinite Intervals
Sheng Chen, Jie Shen, Lilian Wang
Tempered fractional derivatives originated from the tempered fractional diffusion equations (TFDEs) modeled on the whole space R (see [23]). For numerically solving TFDEs, two kind…
Seamless Integration of Global Dirichlet-to-Neumann Boundary Condition and Spectral Elements for Transformation Electromagnetics
Zhiguo Yang, Li-Lian Wang, Zhijian Rong +2
In this paper, we present an efficient spectral-element method (SEM) for solving general two-dimensional Helmholtz equations in anisotropic media, with particular applications in a…
Well-Conditioned Fractional Collocation Methods Using Fractional Birkhoff Interpolation Basis
Yujian Jiao, Li-Lian Wang, Can Huang
The purpose of this paper is twofold. Firstly, we provide explicit and compact formulas for computing both Caputo and (modified) Riemann-Liouville (RL) fractional pseudospectral di…
Generalized Jacobi Functions and Their Applications to Fractional Differential Equations
Sheng Chen, Jie Shen, Li-Lian Wang
In this paper, we consider spectral approximation of fractional differential equations (FDEs). A main ingredient of our approach is to define a new class of generalized Jacobi func…
Accurate Simulation of Ideal Circular and Elliptic Cylindrical Invisibility Cloaks
Zhiguo Yang, Li-Lian Wang
The coordinate transformation offers a remarkable way to design cloaks that can steer electromagnetic fields so as to prevent waves from penetrating into the {\em cloaked region} (…
On -Convergence of PSWFs and A New Well-Conditioned Prolate-Collocation Scheme
Li-Lian Wang, Jing Zhang, Zhimin Zhang
The first purpose of this paper is to provide a rigorous proof for the nonconvergence of -refinement in -approximation by the PSWFs, a surprising convergence property that w…