28 citations · 128 across the 27 of their papers we have counts for
27 papers
High-order complete flux schemes for convection-diffusion equations on arbitrary subdivisions
Wenyu Lei, Liwei Xu, Peng Yang
We develop a novel complete flux finite volume method for convection-diffusion equations on arbitrary subdivisions in two and three dimensions. Unlike standard finite volume discre…
A model-data asymptotic-preserving neural network method based on micro-macro decomposition for gray radiative transfer equations
Hongyan Li, Song Jiang, Wenjun Sun +2
We propose a model-data asymptotic-preserving neural network(MD-APNN) method to solve the nonlinear gray radiative transfer equations(GRTEs). The system is challenging to be simula…
A highly accurate perfectly-matched-layer boundary integral equation solver for acoustic layered-medium problems
Wangtao Lu, Liwei Xu, Tao Yin +1
Based on the perfectly matched layer (PML) technique, this paper develops a high-accuracy boundary integral equation (BIE) solver for acoustic scattering problems in locally defect…
Optimal error estimates of a Crank--Nicolson finite element projection method for magnetohydrodynamic equations
Cheng Wang, Jilu Wang, Zeyu Xia +1
In this paper, we propose and analyze a fully discrete finite element projection method for the magnetohydrodynamic (MHD) equations. A modified Crank--Nicolson method and the Galer…
On the hyper-singular boundary integral equation methods for dynamic poroelasticity: three dimensional case
Lu Zhang, Liwei Xu, Tao Yin
In our previous work [SIAM J. Sci. Comput. 43(3) (2021) B784-B810], an accurate hyper-singular boundary integral equation method for dynamic poroelasticity in two dimensions has be…
On the generalized Calderón formulas for closed- and open-surface elastic scattering problems
Liwei Xu, Tao Yin
The Calderón formulas (i.e., the combination of single-layer and hyper-singular boundary integral operators) have been widely utilized in the process of constructing valid boundary…
Optimal error estimates of a second-order projection finite element method for magnetohydrodynamic equations
Cheng Wang, Jilu Wang, Zeyu Xia +1
In this paper, we propose and analyze a temporally second-order accurate, fully discrete finite element method for the magnetohydrodynamic (MHD) equations. A modified Crank--Nicols…
An extended sampling-ensemble Kalman filter approach for partial data inverse elastic problems
Zhaoxing Li, Jiguang Sun, Liwei Xu
Inverse problems are more challenging when only partial data are available in general. In this paper, we propose a two-step approach combining the extended sampling method and the…
An accurate hyper-singular boundary integral equation method for dynamic poroelasticity in two dimensions
Lu Zhang, Liwei Xu, Tao Yin
This paper is concerned with the boundary integral equation method for solving the exterior Neumann boundary value problem of dynamic poroelasticity in two dimensions. The main con…
Quality-Bayesian approach to inverse acoustic source problems with partial data
Zhaoxing Li, Yanfang Liu, Jiguang Sun +1
A quality-Bayesian approach, combining the direct sampling method and the Bayesian inversion, is proposed to reconstruct the locations and intensities of the unknown acoustic sourc…
Big-Data Clustering: K-Means or K-Indicators?
Feiyu Chen, Yuchen Yang, Liwei Xu +2
The K-means algorithm is arguably the most popular data clustering method, commonly applied to processed datasets in some "feature spaces", as is in spectral clustering. Highly sen…
An interior penalty discontinuous Galerkin method for the time-domain acoustic-elastic wave interaction problem
Yingda Cheng, Jing Huang, Xiaozhou Li +1
In this paper, we consider numerical solutions of a time domain acoustic-elastic wave interaction problem which occurs between a bounded penetrable elastic body and a compressible…
A Superconvergent Ensemble HDG Method for Parameterized Convection Diffusion Equations
Gang Chen, Liangya Pi, Liwei Xu +1
In this paper, we first devise an ensemble hybridizable discontinuous Galerkin (HDG) method to efficiently simulate a group of parameterized convection diffusion PDEs. These PDEs h…
A convergent linearized Lagrange finite element method for the magneto-hydrodynamic equations in 2D nonsmooth and nonconvex domains
Buyang Li, Jilu Wang, Liwei Xu
A new fully discrete linearized -conforming Lagrange finite element method is proposed for solving the two-dimensional magneto-hydrodynamics equations based on a magnetic pote…
A hybridizable discontinuous Galerkin method for the indefinite time-harmonic Maxwell equations
Gang Chen, Haijun Wu, Liwei Xu
In this paper, we aim to develop a hybridizable discontinuous Galerkin (HDG) method for the indefinite time-harmonic Maxwell equations with the perfectly conducting boundary in the…
A hybridizable discontinuous Galerkin method for the quad-curl problem
Gang Chen, Jintao Cui, Liwei Xu
The quad-curl problem arises in magnetohydrodynamics, inverse electromagnetic scattering and transform eigenvalue problems. In this paper we investigate a hybridizable discontinuou…
Weighted integral solvers for elastic scattering by open arcs in two dimensions
Oscar P. Bruno, Liwei Xu, Tao Yin
We present a novel approach for the numerical solution of problems of elastic scattering by open arcs in two dimensions. Our methodology relies on the composition of weighted versi…
A CDG-FE method for the two-dimensional Green-Naghdi model with the enhanced dispersive property
Maojun Li, Liwei Xu, Yongping Cheng
In this work, we investigate numerical solutions of the two-dimensional shallow water wave using a fully nonlinear Green-Naghdi model with an improved dispersive effect. For the pu…
Boundary integral equation methods for the elastic and thermoelastic waves in three dimensions
Gang Bao, Liwei Xu, Tao Yin
In this paper, we consider the boundary integral equation (BIE) method for solving the exterior Neumann boundary value problems of elastic and thermoelastic waves in three dimensio…
Numerical simulation of a coupled system of Maxwell equations and a gas dynamic model
Maohui Lyu, Weng Cho Chew, Lijun Jiang +2
It is known that both linear and nonlinear optical phenomena can be produced when the plasmon in metallic nanostructures are excited by the external electromagnetic waves. In this…
A discontinuous Galerkin method for wave propagation in orthotropic poroelastic media with memory terms
Jiangming Xie, Miao-jung Yvonne Ou, Liwei Xu
In this paper, we investigate wave propagation in orthotropic poroelastic media by studying the time-domain poroelastic equations. Both the low frequency Biot's (LF-Biot) equations…
Analysis of an interior penalty DG method for the quad-curl problem
Gang Chen, Weifeng Qiu, Liwei Xu
The quad-curl term is an essential part of the resistive magnetohydrodynamic (MHD) equation and the fourth order inverse electromagnetic scattering problem, which are both of great…
Analysis of a hybridizable discontinuous Galerkin method for the Maxwell operator
Gang Chen, Jintao Cui, Liwei Xu
In this paper, we study a hybridizable discontinuous Galerkin (HDG) method for the Maxwell operator. The only global unknowns are defined on the inter-element boundaries, and the n…
Analysis of the Fourier series Dirichlet-to-Neumann boundary condition of the Helmholtz equation and its application to finite element methods
Liwei Xu, Tao Yin
It is well known that the Fourier series Dirichlet-to-Neumann (DtN) boundary condition can be used to solve the Helmholtz equation in unbounded domains. In this work, applying such…