40 citations · 246 across the 65 of their papers we have counts for
66 papers
A highly efficient and accurate numerical method for the electromagnetic scattering problem with rectangular cavities
Peijun Li, Xiaokai Yuan
This paper presents a robust numerical solution to the electromagnetic scattering problem involving multiple multi-layered cavities in both transverse magnetic and electric polariz…
Numerical solution of the cavity scattering problem for flexural waves on thin plates: linear finite element methods
Junhong Yue, Peijun Li
Flexural wave scattering plays a crucial role in optimizing and designing structures for various engineering applications. Mathematically, the flexural wave scattering problem on a…
Stability for inverse source problems of the stochastic Helmholtz equation with a white noise
Peijun Li, Ying Liang
This paper is concerned with the stability estimates for inverse source problems of the stochastic Helmholtz equation driven by white noise. The well-posedness is established for t…
Inverse scattering of periodic surfaces with a superlens
Peijun Li, Yuliang Wang
We propose a scheme for imaging periodic surfaces using a superlens. By employing an inverse scattering model and the transformed field expansion method, we derive an approximate r…
A data-assisted two-stage method for the inverse random source problem
Peijun Li, Ying Liang, Yuliang Wang
We propose a data-assisted two-stage method for solving an inverse random source problem of the Helmholtz equation. In the first stage, the regularized Kaczmarz method is employed…
An inverse potential problem for the stochastic diffusion equation with a multiplicative white noise
Xiaoli Feng, Peijun Li, Xu Wang
This work concerns the direct and inverse potential problems for the stochastic diffusion equation driven by a multiplicative time-dependent white noise. The direct problem is to e…
A novel boundary integral formulation for the biharmonic wave scattering problem
Heping Dong, Peijun Li
This paper is concerned with the cavity scattering problem in an infinite thin plate, where the out-of-plane displacement is governed by the two-dimensional biharmonic wave equatio…
Inverse scattering for the biharmonic wave equation with a random potential
Peijun Li, Xu Wang
We consider the inverse random potential scattering problem for the two- and three-dimensional biharmonic wave equation in lossy media. The potential is assumed to be a microlocall…
An Adaptive Finite Element DtN Method for Maxwell's Equations
Gang Bao, Mingming Zhang, Xue Jiang +2
This paper is concerned with a numerical solution to the scattering of a time-harmonic electromagnetic wave by a bounded and impenetrable obstacle in three dimensions. The electrom…
A spectral boundary integral method for the elastic obstacle scattering problem in three dimensions
Heping Dong, Jun Lai, Peijun Li
In this paper, we consider the scattering of a plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in three dimensions. Based on the Helmholtz dec…
Variational Inverting Network for Statistical Inverse Problems of Partial Differential Equations
Junxiong Jia, Yanni Wu, Peijun Li +1
To quantify uncertainties in inverse problems of partial differential equations (PDEs), we formulate them into statistical inference problems using Bayes' formula. Recently, well-j…
Inverse source problems for the stochastic wave equations: far-field patterns
Jianliang Li, Peijun Li, Xu Wang
This paper addresses the direct and inverse source problems for the stochastic acoustic, biharmonic, electromagnetic, and elastic wave equations in a unified framework. The driven…
Stability for the multi-dimensional Borg--Levinson theorem of the biharmonic operator
Peijun Li, Xiaohua Yao, Yue Zhao
In this paper, we prove a conditional Hölder stability estimate for the inverse spectral problem of the biharmonic operator. The proof employs the resolvent estimate and a Weyl-typ…
An inverse random source problem for the biharmonic wave equation
Peijun Li, Xu Wang
This paper is concerned with an inverse source problem for the stochastic biharmonic operator wave equation. The driven source is assumed to be a microlocally isotropic Gaussian ra…
Direct and inverse problems for the Schrödinger operator in a three-dimensional planar waveguide
Peijun Li, Xiaohua Yao, Yue Zhao
In this paper, we study the meromorphic continuation of the resolvent for the Schrödinger operator in a three-dimensional planar waveguide. We prove the existence of a resonance-fr…
Stability for an inverse source problem of the damped biharmonic plate equation
Peijun Li, Xiaohua Yao, Yue Zhao
This paper is concerned with the stability of the inverse source problem for the damped biharmonic plate equation in three dimensions. The stability estimate consists of the Lipsch…
Inverse random potential scattering for elastic waves
Jianliang Li, Peijun Li, Xu Wang
This paper is concerned with the inverse elastic scattering problem for a random potential in three dimensions. Interpreted as a distribution, the potential is assumed to be a micr…
Stability for an inverse source problem of the biharmonic operator
Peijun Li, Xiaohua Yao, Yue Zhao
In this paper, we study for the first time the stability of the inverse source problem for the biharmonic operator with a compactly supported potential in . Firstly, t…
Stein variational gradient descent on infinite-dimensional space and applications to statistical inverse problems
Junxiong Jia, Peijun Li, Deyu Meng
In this paper, we propose an infinite-dimensional version of the Stein variational gradient descent (iSVGD) method for solving Bayesian inverse problems. The method can generate ap…
An adaptive finite element DtN method for the elastic wave scattering problem in three dimensions
Gang Bao, Peijun Li, Xiaokai Yuan
Consider the elastic scattering of an incident wave by a rigid obstacle in three dimensions, which is formulated as an exterior problem for the Navier equation. By constructing a D…
An inverse source problem for the stochastic wave equation
Xiaoli Feng, Meixia Zhao, Peijun Li +1
This paper is concerned with an inverse source problem for the stochastic wave equation driven by a fractional Brownian motion. Given the random source, the direct problem is to st…
Numerical solution of an inverse random source problem for the time fractional diffusion equation via PhaseLift
Yuxuan Gong, Peijun Li, Xu Wang +1
This paper is concerned with the inverse random source problem for a stochastic time fractional diffusion equation, where the source is assumed to be driven by a Gaussian random fi…
An inverse random source problem for the one-dimensional Helmholtz equation with attenuation
Peijun Li, Xu Wang
This paper is concerned with an inverse random source problem for the one-dimensional stochastic Helmholtz equation with attenuation. The source is assumed to be a microlocally iso…
Analysis of the time-domain PML problem for Maxwell's equations in a waveguide
Yanli Chen, Peijun Li, Xu Wang
This paper is concerned with the mathematical analysis of the time-domain electromagnetic scattering problem in an infinite rectangular waveguide. A transparent boundary condition…