58 citations · 196 across the 26 of their papers we have counts for
27 papers
Deterministic-Statistical Approach for an Inverse Acoustic Source Problem using Multiple Frequency Limited Aperture Data
Yanfang Liu, Zhizhang Wu, Jiguang Sun +1
We propose a deterministic-statistical method for an inverse source problem using multiple frequency limited aperture far field data. The direct sampling method is used to obtain a…
Regular Convergence and Finite Element Methods for Eigenvalue Problems
Bo Gong, Jiguang Sun
Regular convergence, together with various other types of convergence, has been studied since the 1970s for the discrete approximations of linear operators. In this paper, we consi…
FE-Holomorphic Operator Function Method for Nonlinear Plate Vibrations with Elastically Added Masses
Xiangying Pang, Jiguang Sun, Zhimin Zhang
Vibrations of structures subjected to concentrated point loads have many applications in mechanical engineering. Experiments are expensive and numerical methods are often used for…
Local estimators and Bayesian inverse problems with non-unique solutions
Jiguang Sun
The Bayesian approach is effective for inverse problems. The posterior density distribution provides useful information of the unknowns. However, for problems with non-unique solut…
A deterministic-statistical approach to reconstruct moving sources using sparse partial data
Yanfang Liu, Yukun Guo, Jiguang Sun
We consider the reconstruction of moving sources using partial measured data. A two-step deterministic-statistical approach is proposed. In the first step, an approximate direct sa…
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…
A Novel Computational Method for Band Structures of Dispersive Photonic Crystals
Wenqiang Xao, Jiguang Sun
We propose a new method to compute band structures of dispersive photonic crystals. It can treat arbitrarily frequency-dependent, lossy or lossless materials. The band structure pr…
Finite Element Calculation of Photonic Band Structures for Frequency Dependent Materials
Wenqiang Xiao, Bo Gong, Jiguang Sun +1
We consider the calculation of the band structure of frequency dependent photonic crystals. The associated eigenvalue problem is nonlinear and it is challenging to develop effectiv…
A priori and a posteriori error estimates for the quad-curl eigenvalue problem
Lixiu Wang, Qian Zhang, Jiguang Sun +1
In this paper, we propose a new family of H(curl^2)-conforming elements for the quad-curl eigenvalue problem in 2D. The accuracy of this family is one order higher than that in [32…
A Multilevel Spectral Indicator Method for Eigenvalues of Large Non-Hermitian Matrices
Ruihao Huang, Jiguang Sun, Chao Yang
Recently a novel family of eigensolvers, called spectral indicator methods (SIMs), was proposed. Given a region on the complex plane, SIMs first compute an indicator by the spectra…
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…
Finite Element Approximation of the Modified Maxwell's Stekloff Eigenvalues
Bo Gong, Jiguang Sun, Xinming Wu
The modified Maxwell's Stekloff eigenvalue problem arises recently from the inverse electromagnetic scattering theory for inhomogeneous media. This paper contains a rigorous analys…
Finite Element Approximation of Transmission Eigenvalues for Anisotropic Media
Bo Gong, Jiguang Sun, Tiara Turner +1
The transmission eigenvalue problem arises from the inverse scattering theory for inhomogeneous media and has important applications in many qualitative methods. The problem is pos…
A new finite element approach for the Dirichlet eigenvalue problem
Wenqiang Xiao, Bo Gong, Jiguang Sun +1
In this paper, we propose a new finite element approach, which is different than the classic Babuska-Osborn theory, to approximate Dirichlet eigenvalues. The Dirichlet eigenvalue p…
Limited Aperture Inverse Scattering Problems using Bayesian Approach and Extended Sampling Method
Zhaoxiang Li, Zhiliang Deng, Jiguang Sun
Inverse scattering problems have many important applications. In this paper, given limited aperture data, we propose a Bayesian method for the inverse acoustic scattering to recons…
Extended sampling method for inverse elastic scattering problems using one incident wave
J Liu, X. Liu, J. Sun
We consider the inverse elastic scattering problems using the far field data due to one incident plane wave. A simple method is proposed to reconstruct the location and size of the…
An inverse medium problem using Stekloff eigenvalues and a Bayesian approach
Juan Liu, Yanfang Liu, Jiguang Sun
This paper studies the reconstruction of Stekloff eigenvalues and the index of refraction of an inhomogeneous medium from Cauchy data. The inverse spectrum problem to reconstruct S…
Revisiting the Jones eigenproblem in fluid-structure interaction
Sebastián Domínguez, Nilima Nigam, Jiguang Sun
The Jones eigenvalue problem first described by D.S. Jones in 1983 concerns unusual modes in bounded elastic bodies: time-harmonic displacements whose tractions and normal componen…
Extended Sampling Method in Inverse Scattering
Juan Liu, Jiguang Sun
A new sampling method for inverse scattering problems is proposed to process far field data of one incident wave. As the linear sampling method, the method sets up ill-posed integr…
Spectral Indicator Method for A Non-selfadjoint Steklov Eigenvalue Problem
Juan Liu, Jiguang Sun, Tiara Turner
We propose an efficient numerical method for a non-selfadjoint Steklov eigenvalue problem. The Lagrange finite element is used for discretization. The convergence is proved using t…
Computation of Transmission Eigenvalues for Elastic Waves
Xia Ji, Peijun Li, Jiguang Sun
The goal of this paper is to develop numerical methods computing a few smallest elasticity transmission eigenvalues, which are of practical importance in inverse scattering theory.…
Fast acoustic source imaging using multi-frequency sparse data
Ala Alzaalig, Guanghui Hu, Xiaodong Liu +1
We consider the acoustic source imaging problems using multiple frequency data. Using the data of one observation direction/point, we prove that some information (size and location…
Data recovery: from limited-aperture to full-aperture
Xiaodong Liu, Jiguang Sun
The inverse scattering problems have been popular for the past thirty years. While very successful in many cases, progress has lagged when only {\em limited-aperture} measurement i…
Direct and Inverse Elastic Scattering From Anisotropic Media
Gang Bao, Guanghui Hu, Jiguang Sun +1
Assume a time-harmonic elastic wave is incident onto a penetrable anisotropic body embedded into a homogeneous isotropic background medium. We propose an equivalent variational for…