Young Scholars Workshop on
Inverse Problems,Imaging and PDEs
Southern University of Science and Technology, Shenzhen, China
Mar. 25 27, 2017
Venue: Room 706, Service Center for Teaching and Research（教学科研服务中心706会议室）
Organizing Committee:
LI Jingzhi, Southern University of Science and Technology
LI Xiaofei, Southern University of Science and Technology
LIU Hongyu, Hong Kong Baptist University
Contact: LI Xiaofei（李晓菲） xiaofeilee@hotmail.com 13266572769
Friday, March 24, 2017 

12:0024:00 
Hotel Checkin: Guest House（专家公寓） 
17:3019:00 
Dinner at Faculty Restaurant（教工餐厅） 


Day 1: Saturday, March 25, 2017 

07:0008:10 
Breakfast at Faculty Restaurant（教工餐厅） 
08:3009:00 
Check in for the Meeting （Room 706） 
Morning Session 1 Chair: LIU Hongyu 

09:0009:30 
CAI Yongyong, Beijing Computational Science Research Center Nonrelativistic limit of the nonlinear Dirac equation and its numerical methods. 

09:3010:00 
CHEN Junqing, Tsinghua University A direct imaging method for inverse electromagnetic scattering problem in waveguide. 

10:0010:30 
Tea break and group photo taking 

10:3011:00 
DENG Youjun, Central South University Simultaneous recovery of an internal current and the surrounding medium in Maxwell's system. 

11:0011:30 
GONG Rongfang, Nanjing University of Aeronautics and Astronautics A modified coupled complex boundary method for an inverse chromatography problem. 

11:3012:00 
GUO Ling, Shanghai Normal University Stochastic collocation methods via nonconvex minimizations and its applications in UQ. 

12:0014:00 
Lunch 

Afternoon Session 2 Chair: LI Xiaofei 

14:0014:30 
GUO Yukun, Harbin Institute of Technology Fourier method for the inverse source problem with multifrequency farfield data. 

14:3015:00 
JI Xia, Institute of Computational Math, CAS A multicorrection method for the source identification problem. 

15:0015:30 
JIANG Daijun, Central China Normal University Quadratic convergence of LM method for parabolic inverse Robin problems and DDMs for convex minimizations. 

15:3016:00 
Tea break 

16:0016:30 
XIAO Jingni, Hong Kong Baptist University On Electromagnetic Scattering from a Penetrable Corner 

16:3017:00 
XIE Feng, Shanghai Jiao Tong University MHD Boundary layers in Sobolev spaces without monotonicity. 

17:0017:30 
XU Zhenli, Shanghai Jiao Tong University Ion distribution near layered dielectric media 

17:3019:00 
Dinner 



Day 2: Sunday, March 26, 2017 

Morning Session 3 Chair: LI Jingzhi 

07:0008:30 
Breakfast at Faculty Restaurant（教工餐厅） 

09:0009:30 
LAI Junjiang, Minjiang University Some numerical experiments for anomalous localized resonance of the elastostatic system 

09:3010:00 
LI Hongjie, Hong Kong Baptist University On anomalous localized resonance for the elastostatic system 

10:0010:15 
Tea break 

10:1510:45 
LI Jinglai, Shanghai Jiao Tong University Bayesian inference and uncertainty quantification for infinite dimensional inverse problems 

10:4511:15 
LIU Keji, Shanghai University of Finance and Economics Direct recovery of wavepenetrable scatterers in a stratified ocean waveguide. 

11:1511:45 
LIU Xiaodong, Institute of Applied Math, CAS Recovery of an embedded obstacle and its surrounding medium by formallydetermined scattering data. 

11:4514:00 
Banquet 

Afternoon Session 4 Chair: LI Jinhong 

14:0014:30 
WANG Haibing, Southeast University Solvability of interior transmission problem for the heat equation with applications. 

14:3015:00 
WANG Yuliang, Hong Kong Baptist University Electromagnetic interior transmission eigenvalue problem for inhomogeneous media containing obstacles and its applications to near cloaking. 

15:0015:30 
XIE Chunjing, Shanghai Jiao Tong University Steady subsonic Euler flows in nozzles or past a body 

15:3016:00 
Tea break 

16:0016:30 
YANG Jiaqing, Xi’an Jiao tong University Inverse obstacle scattering in a twolayered medium with locally rough surfaces. 

16:3017:00 
YING Wenjun, Shanghai Jiao Tong University A simple method for computing singular or nearly singular integrals on closed surfaces 

17:0017:30 
ZHANG Haiwen, Institute of Applied Math, CAS A direct imaging method for inverse scattering problem by unbounded rough surfaces: the case of incident point sources. 

17:3019:00 
Dinner 

Day 3: Monday, March 27, 2017 

Session 5 

07:0008:30 
Breakfast at Faculty Restaurant（教工餐厅） 
09:0011:30 
Group discussion 
12:00 
Departure 
Participants
CAI Yongyong (Beijing Computational Science Research Center) 
CAO Xinlin (Hong Kong Baptist University) 
CHEN Junqing (Tsinghua University) 
DENG Youjun (Central South University) 
GONG Rongfang (Nanjing University of Aeronautics and Astronautics) 
GUO Ling (Shanghai Normal University) 
GUO Yukun (Harbin Institute of Technology) 
JI Xia (Institute of Computational Math, CAS) 
JIANG Daijun (Central China Normal University) 
LAI Junjiang (Minjiang University) 
LI Hongjie (Hong Kong Baptist University) 
LI Jinhong (Qilu University of Technology) 
LI Jinglai (Shanghai Jiao Tong University) 
LI Jingzhi (Southern University of Science and Technology) 
LI Xiaofei (Southern University of Science and Technology) 
LIU Hongyu (Hong Kong Baptist University) 
LIU Keji (Shanghai University of Finance and Economics) 
LIU Xiaodong (Institute of Applied Math, CAS) 
Ma Shiqi (Hong Kong Baptist University) 
WANG Haibing (Southeast University) 
WANG Yong (Institute of Applied Math, CAS) 
WANG Yuliang (Hong Kong Baptist University) 
XIAO Jingni (Hong Kong Baptist University) 
XIE Chunjing (Shanghai Jiao Tong University) 
XIE Feng (Shanghai Jiao Tong University) 
XU Zhenli (Shanghai Jiao Tong University) 
YANG Jiaqing (Xi’an Jiaotong University) 
YING Wenjun (Shanghai Jiao Tong University) 
ZHANG Haiwen (Institute of Applied Math, CAS) 
ZENG Fang (Chong Qing University) 
Traffic Information
By Metro: Tanglang Station塘朗站, Huanzhong Line (环中线); School gate 1 (一号门)is 500m from Exit D of Tanglang Metro Station
By Bus: SUSTech Station(南方科技大学站), Line M369, 43, 74, 81
Taxi: South University of Science and Technology, Tanglang（塘朗）, Nanshan District
Address: No 1088, Xueyuan Rd., Xili, Nanshan District, Shenzhen, Guangdong, China 518055
Hotel Information and Checkin
l Guest House（专家公寓）
l Front Desk Telephone：86075588015773
l Show your ID card or passport for hotel checkin
Abstracts
1. CAI Yongyong, Beijing Computational Science Research Center
Title: Nonrelativistic limit of the nonlinear Dirac equation and its numerical methods
Abstract: We consider the nonlinear Dirac equation in the nonrelativistic limit regime, involving a small parameter inversely proportional to the speed of light. The nonlinear Dirac equation converges to the nonlinear Schroedinger equation in the nonrelativistic limit. By a careful analysis, we obtain a semirelativistic limit of the nonlinear Dirac equation, which enables a design of uniformly accurate multiscale numerical method. The major difficulty of the problem is that the solution has a rapid oscillation in time depending on the small parameter.
2. CHEN Junqing, Tsinghua University
Title: A direct imaging method for inverse electromagnetic scattering problem in waveguide
Abstract: I will talk about a direct imaging method based on reverse time migration (RTM) algorithm for imaging extended targets using electromagnetic waves at a fixed frequency in the rectangular waveguide. The imaging functional is defined as the imaginary part of the crosscorrelation of the Green function for Helmholtz equation and the backpropagated electromagnetic field. The resolution of our RTM method for penetrable extended targets is studied by virtue of HelmholtzKirchhoff identity in the rectangular domain, which implies that the imaging functional always peaks in the target. Numerical examples are provided to demonstrate the powerful imaging quality and confirm our theoretical results.
3. DENG Youjun, Central South University
Title: Simultaneous recovery of an internal current and the surrounding medium in Maxwell's system
Abstract: We consider the inverse problem of recovering both an unknown electric current and the surrounding electromagnetic parameters of a medium from boundary measurements. This inverse problem arises in brain imaging. We show that we can recover both the source and the electromagnetic parameters if these are piecewise constant and the current source is invariant in a fixed direction or a harmonic function.
4. GONG Rongfang, Nanjing University of Aeronautics and Astronautics
Title: A
modified coupled complex boundary method for an inverse chromatography
problem
5. GUO Ling, Shanghai Normal University
Title: Stochastic collocation methods via nonconvex minimizations and its applications in UQ
Abstract: Stochastic computation has received intensive attention in recent years, due to the pressing need to conduct uncertainty quantification (UQ) in practical computing. One of the most widely used techniques in UQ is generalized polynomial chaos. In this talk, we will discuss collocation method via nonconvex minimizations for recovering sparse polynomial chaos expansions (PCE). We present several theoretical estimates regarding the recoverability for both sparse and nonsparse signals via the transformed L1 minimization. We then apply the method to sparse orthogonal polynomial approximations for stochastic collocation. Various numerical examples, including sparse polynomial functions and nonsparse analytical functions recovery, demonstrate the recoverability and efficiency of the method.
6. GUO Yukun, Harbin Institute of Technology
Title: Fourier method for the inverse source problem with multifrequency farfield data.
Abstract: This talk is concerned with an inverse source problem of determining a source term in the Helmholtz equation from multifrequency farfield measurements. Based on the Fourier series expansion, we develop a novel noniterative reconstruction method for solving the problem. A promising feature of this method is that it utilizes the data from only a few observation directions for each frequency. Theoretical uniqueness and stability analysis will be provided. Numerical experiments will be presented to illustrate the effectiveness and efficiency of the proposed method in both two and three dimensions. This is a joint work with Xianchao Wang, Deyue Zhang and Hongyu Liu.
7. JI Xia, Institute of Computational Math, CAS
Title: A multicorrection method for the source identification problem
Abstract: We design a multicorrection method for the source identification problems in which the state variable is the solution of the 2D variablecoefficient Poisson problem with full and partial observations. In this method, we replace solving the PDE constrained optimization problem on the finest finite element space by solving a series of linear boundary value problems with multigrid scheme in the corresponding series of finite element spaces and a series of PDE constrained optimization problems in the coarsest finite element space. Based on the analysis, the proposed method can obtain optimal errors with an almost optimal computational complexity.
8. JIANG Daijun, Central China Normal University
Title: Quadratic convergence of LM method for parabolic inverse Robin problems and DDMs for convex minimizations
Abstract: Consider the interior transmission problem arising in inverse boundary value problems for the heat equation with discontinuous heat conductivity. The unique solvability of this problem is justified in the following way. First, we construct the local parametrix for the interior transmission problem in the Laplace domain, by using the theory of pseudodifferential operators with a large parameter. Second, the local parametrix for the original parabolic interior transmission problem is obtained via the inverse Laplace transform. Finally, using a partition of unity, we patch all local parametrices and the fundamental solution of the heat operator to have a parametrix for the parabolic interior transmission problem, and then compensate it to get the Green function. Thus, the unique solvability of our interior transmission problem can be proved in a standard way. Based on this result, we develop a sampling method for an inverse boundary value problem for the heat equation.
9. XIAO Jingni, Hong Kong Baptist University
Title: On Electromagnetic Scattering from a Penetrable Corner
Abstract: We show that an inhomogeneous electromagnetic(EM) medium with a right corner will always scatter the incident waves, by assuming certain regularity conditions. This result implies that one cannot make such a medium with corner invisible. This is a joint work with Hongyu Liu.
10. XIE Feng, Shanghai Jiao Tong University
Title: MHD Boundary layers in Sobolev spaces without
monotonicity.
11. XU Zhenli, Shanghai Jiao Tong University
Title: Ion distribution near layered dielectric media
Abstract: We develop a fast algorithm for the ion interaction in media with layered dielectric structure, in particular, a coreshell structured sphere. The algorithm is derived by analytically solving the Green’s function, which represents the solution as an image line charge and thus it can be approximated by point charges using numerical quadrature. Based on this algorithm, we performed Monte Carlo simulations for ion structure near a coreshell dielectric nanoparticle, and observed that the ion distribution significantly depends on the dielectric ratios and the shell thickness. Monte Carlo simulations show the influence of the layered structure on the capacitance of the electric double layer.
12. LAI Junjiang, Minjiang University
Title: Some numerical experiments for anomalous localized resonance of the elastostatic system
Abstract: In this talk, we give some numerical experiments for anomalous localized resonance of the elastostatic system. These numerical results confirm some related anomalous localized resonance theory, such as resonance with no core and resonance for a core. We also obtain some new conclusions through these experiments. This is joint work with Hongyu Liu.
13. LI Hongjie, Hong Kong Baptist University
Title: On anomalous localized resonance for the elastostatic system
Abstract: In this talk, I will talk about our recent results on anomalous localized resonances (ALR) due to a plasmonic structure for the elastostatic system in two and three dimensions. I shall first talk about our study from a variational perspective. Then, I will discuss the ALR from a spectral perspective. Since the NeumannPoincare(NP) operator for the Lame system is not compact even if the domain has a smooth boundary, the main difficulty is to calculate the spectrum of that operator. Using the spectrum of NP operator, the occurrence and nonoccurrence of ALR will be discussed in three dimensions.
14. LI Jinglai, Shanghai Jiao Tong University
Title: Bayesian inference and uncertainty quantification for infinite dimensional inverse problems
Abstract: Bayesian inference has become increasingly popular as a tool to solve inverse problems, largely due to its ability to quantify the uncertainty in the solutions obtained. In many practical problems such as image reconstructions, the unknowns are often of infinite dimension, i.e., functions of space and/or time. Theories and methods developed for finite dimensional problems may become problematic in the infinite dimensional setting and thus new theories and methods must be developed for such problems. In this talk we shall discuss several critical issues associated with the infinite dimensional problems and some efforts made to address them. First we discuss the Maximum a Posterior (MAP) estimation in this setting and its numerical implementations. Next we introduce a nonGaussian prior for modeling functions that are subject to sharp jumps. We then present an efficient adaptive MCMC algorithm that is specifically designed for function space inference. Finally, we apply the Bayesian inference methods to a medical image reconstruction problem.
15. LIU Keji, Shanghai University of Finance and Economics
Title: Direct recovery of wavepenetrable scatterers in a stratified ocean waveguide
Abstract: We shall extend the direct sampling method for more general recovery of wavepenetrable inhomogeneous scatterers in a threedimensional stratified ocean waveguide. The proposed method is simple, straightforward and computationally efficient since no matrix inversions, optimizations or solutions of illposed linear systems are involved. Moreover, it is highly tolerant to noise and is applicable with a few scattered fields corresponding to only two or four incidences. In addition, a priori knowledge of either the number of disconnected components or the physical features of the unknown obstacles is not required by the direct sampling method. A mathematical derivation is provided for its validation and several extensive numerical experiments are shown to evaluate the effectiveness and feasibility of the newly proposed method.
16. LIU Xiaodong, Institute of Applied Math, CAS
Title: Recovery of an embedded obstacle and its surrounding medium by formallydetermined scattering data
Abstract: We consider an inverse acoustic scattering problem in simultaneously recovering an embedded obstacle and its surrounding inhomogeneous medium by formally determined far field data. It is shown that the knowledge of the scattering amplitude with a fixed incident direction and all observation angles along with frequencies from an open interval can be used to uniquely identify the embedded obstacle, soundsoft or soundhard disregarding the surrounding medium. Furthermore, if the surrounding inhomogeneous medium is from an admissible class (still general), then the medium can be recovered as well. Our argument is based on deriving certain integral identities involving the unknowns and then inverting them by certain harmonic analysis techniques. Finally, based on our theoretical study, a fast and robust sampling method is proposed to reconstruct the shape and location of the buried targets and the support of the surrounding inhomogeneities. This is a joint work with Prof. Hongyu Liu from HongKong Baptist University.
17. WANG Haibing, Southeast University
Title: Solvability of interior transmission problem for the heat equation with applications
Abstract: Consider the interior transmission problem arising in inverse boundary value problems for the heat equation with discontinuous heat conductivity. The unique solvability of this problem is justified in the following way. First, we construct the local parametrix for the interior transmission problem in the Laplace domain, by using the theory of pseudodifferential operators with a large parameter. Second, the local parametrix for the original parabolic interior transmission problem is obtained via the inverse Laplace transform. Finally, using a partition of unity, we patch all local parametrices and the fundamental solution of the heat operator to have a parametrix for the parabolic interior transmission problem, and then compensate it to get the Green function. Thus, the unique solvability of our interior transmission problem can be proved in a standard way. Based on this result, we develop a sampling method for an inverse boundary value problem for the heat equation.
18. WANG Yuliang, Hong Kong Baptist University
Title: Electromagnetic interior transmission eigenvalue problem for inhomogeneous media containing obstacles and its applications to near cloaking
Abstract: This talk is concerned with the invisibility cloaking in electromagnetic wave scattering from a new perspective. We are especially interested in achieving the invisibility cloaking by completely regular and isotropic mediums. Our study is based on an interior transmission eigenvalue problem. We propose a cloaking scheme that takes a threelayer structure including a cloaked region, a lossy layer and a cloaking shell. The target medium in the cloaked region can be arbitrary but regular, whereas the mediums in the lossy layer and the cloaking shell are both regular and isotropic. We establish that there exists an infinite set of incident waves such that the cloaking device is nearlyinvisible under the corresponding wave interrogation. The set of waves is generated from the MaxwellHerglotz approximation of the associated interior transmission eigenfunctions. We provide the mathematical design of the cloaking device and sharply quantify the cloaking performance.
19. XIE Chunjing, Shanghai Jiao Tong University
Title: Steady subsonic Euler flows in nozzles or past a body
20. YANG Jiaqing, Xi’an Jiaotong University
Title: Inverse obstacle scattering in a twolayered medium with locally rough surfaces
Abstract: In this talk, I will discuss an inverse scattering problem by an impenetrable obstacle in a twolayered medium with locally rough surfaces. The global uniqueness result on the surface, buried obstacles and the wavenumber is obtained from the knowledge of nearfield data measured only on the upperhalf space. Moreover, a sampling method is developed to numerically solve the inverse problem of recovering the local rough surface using such data. This is a join work with Dr. Jianliang Li and Prof. Bo Zhang.
21. YING Wenjun, Shanghai Jiao Tong University
Title: A simple method for computing singular or nearly singular integrals on closed surfaces
Abstract: In this talk, I will present a simple, accurate method for computing singular or nearly singular integrals on a smooth, closed surface, such as layer potentials for harmonic functions evaluated at points on or near the surface. The integral is first computed with a regularized kernel and then discretized with a new quadrature using surface points which project onto grid points in coordinate planes. Leading order terms of the regularization and discretization errors are computed from asymptotic analysis near the singular point and added to the computed value so that the result has high order accuracy. The method does not require coordinate charts on the surface or special treatment of the singularity other than the corrections. The method is accelerated by the treecode algorithm of Duan and Krasny for Ewald summation. I will also present numerical examples with different surfaces.
22. ZHANG Haiwen, Institute of Applied Math, CAS
Title: A direct imaging method for inverse scattering problem by unbounded rough surfaces: the case of incident point sources
Abstract: In this talk, we consider the inverse acoustic scattering problems by an unbounded rough surface. A direct imaging method is proposed to reconstruct the rough surfaces from Cauchy data of the scattered field for incident point sources. The performance analysis is also studied by using integral equation method. The reconstruction method is very robust to noises of measured data and works for penetrable surfaces and impenetrable surfaces with Dirichlet or impedance boundary conditions. Finally, numerical examples are carried out to illustrate that our method is fast, accurate and stable.