This series of workshops aim to promote research exchange and strengthen collaboration between active researchers working in the area of scientific computing from both the Hong Kong Baptist University and the Shanghai Jiao Tong University. 

Venue: FSC1217 Fong Shu Chuen Library,
Ho Sin Hang Campus 

Organizing Committee: 
Jianguo Huang, Shanghai Jiao Tong University
Hongyu Liu, Hong Kong Baptist University
Michael KwokPo Ng, Hong Kong Baptist University


Sponsors: 
Department of Mathematics, HKBU
Hong Kong Research Grants Council


Participants: 
Xinlin Cao, Hong Kong Baptist University
Weiyang Ding, Hong Kong Baptist University
Huaian Diao Northeast Normal University
Jinyan Fan, Shanghai Jiao Tong University
Jun Fan, Hong Kong Baptist University
Jianguo Huang, Shanghai Jiao Tong University
Felix Kwok, Hong Kong Baptist University
Ling Leevan, Hong Kong Baptist University
Hongjie Li, Hong Kong Baptist University
Lizhi Liao, Hong Kong Baptist University
Hongyu Liu, Hong Kong Baptist University
Shiqi Ma, Hong Kong Baptist University
Michael Ng Hong Kong Baptist University
Yuliang Wang, Hong Kong Baptist University
Xianchao Wang, Hong Kong Baptist University
Jingni Xiao, Hong Kong Baptist University
Zhenli Xu, Shanghai Jiao Tong University
Wenjun Ying, Shanghai Jiao Tong University
Lei Zhang, Shanghai Jiao Tong University


Program (Details in pdf) 
Day 1: Friday, April 20, 2018 
12:0013:30 
Lunch at Renfrew Restaurant 
13:3014:00 
Registration 
14:0014:10 
Openning Remark 
Afternoon Session 
14:1014:55 
Ling Leevan
Recents on Kernel Based Approximation Methods
This talk begins with an introduction of kernel methods and will cover some popular numerical methods for solving PDEs including asymmetric collocation and meshfree finite difference methods.

14:5515:40 
Jinyan Fan
Monotonically positive matrices
A matrix A is monotonically positive (MP) if there exists a matrix U such that A =UU^T and each column of U is monotonically nonincreasing or nondecreasing. We propose a semidefinite algorithm for checking whether or not a matrix is MP. If it is not MP, a certificate for it can be obtained; if it is MP, an MPdecomposition can be obtained. Some computational experiments are presented to show how to do this.

15:4016:10 
Tea Break 
16:1016:55 
Lizhi Liao
Computational Issues in the Interior Point Approach
In this talk, we will discuss and address the computational issues in many interior point algorithms. We will start by addressing some convergent interior point methods and continuous trajectories. Then some numerical difficulties and challenges resulting from these methods and trajectories will be raised and discussed. Some preliminary numerical results on certain numerical algorithms will be also reported.

16:5517:40 
Weiyang Ding
Computing the pSpectral Radii of Uniform Hypergraphs with Applications
The pspectral radius of a uniform hypergraph covers many important concepts, such as Lagrangian and spectral radius of the hypergraph, and is crucial for solving spectral extremal problems of hypergraphs. In this talk, we establish a spherically constrained maximization model and propose a firstorder conjugate gradient algorithm to compute the pspectral radius of a uniform hypergraph (CSRH). By the semialgebraic nature of the adjacency tensor of a uniform hypergraph, CSRH is globally convergent and obtains the global maximizer with a high probability. When computing the spectral radius of the adjacency tensor of a uniform hypergraph, CSRH outperforms existing approaches. Furthermore, CSRH is competent to calculate the pspectral radius of a hypergraph with millions of vertices and to approximate the Lagrangian of a hypergraph. Finally, we show that the CSRH method is capable of ranking realworld data set based on solutions generated by the pspectral radius model.

18:0020:00 
Dinner at Renfrew Restaurant 
 
Day 2: Saturday, 21 April 2018 
Morning Session 
09:0009:45 
Jianguo Huang
A robust finite element method for elastic vibration problems
A robust finite element method is introduced for solving elastic vibration problems in two dimensions. The discretization in time is based on the $P_1$continuous discontinuous Galerkin (CDG) method, while the spatial discretization on the CrouziexRaviart (CR) element. It is proved that the error of the displacement (resp. velocity) in the energy norm (resp. $L^2$ norm) is bounded by $O(h+k)$ (resp. $O(h^2+k)$), where $h$ and $k$ denote the mesh sizes of the subdivisions in space and time, respectively. Under some regularity assumptions on the exact solution, the error bound is independent of the Lam\'{e} coefficients of the elastic material under discussion. Several numerical results are reported to illustrate numerical performance of the proposed method.

09:4510:30 
Zhenli Xu
Analysis and Computation for Modified PoissonNernstPlanck Equations
We develop a modified PoissonNernstPlanck model to include Coulomb manybody properties in electrolytes, which also takes the ionsize effect into account and is expected to provide more accurate prediction for ion dynamics with microscopic confinement. Asymptotic expansions are performed to remove the multiscale properties of the equations and also used to understand dielectric properties near interfaces. Furthermore, we discuss numerical strategies to solve the resulted PDEs and show numerical results to demonstrate the performance of our numerical methods.

10:3011:00 
Tea Break 
11:0011:45 
Wenjun Ying
Solution of the Biharmonic Equation with the Kernelfree Boundary Integral Method
In this talk, I will present two versions (one has secondorder accuracy and another one has fourthorder accuracy) of the kernelfree boundary integral method for the biharmonic equation on complex domains. This method is a generalization of the traditional boundary integral method. It does not need to know analytical expressions of the kernel or associated Green's function of the differential operator and evaluate boundary and volume integrals by solving equivalent simple interface problems on Cartesian grids with FFTbased fast solvers. The method has several advantages over the traditional finite element based biharmonic solvers that work with a saddlepoint formulation and unstructured grids. Numerical examples will be included to demonstrate accuracy and efficiency of the method.

11:4512:30 
Yuliang Wang
Vanishing and Localizing of Transmission Eigenfunctions near Corners/Edges
In this talk I will present our recent finding on the intrinsic geometric structure of interior transmission eigenfunctions arising in wave scattering theory. We numerically show that the aforementioned geometric structure can be very delicate and intriguing. The major findings can be roughly summarized as follows. If there is a cusp, i.e. a discontinuity of the surface tangent on the support of the underlying potential function, then the interior transmission eigenfunction vanishes near the cusp if its interior angle is less than Pi, whereas the interior transmission eigenfunction localizes near the cusp if its interior angle is bigger than Pi. Furthermore, we show that the vanishing and blowup orders are inversely proportional to the interior angle of the cusp: the sharper the corner, the higher the convergence order.

12:3014:00 
Lunch at Renfrew Restaurant 
Afternoon Session 
14:0014:45 
Lei Zhang

14:4515:30 
Jun Fan
Spectral Algorithms for Functional Linear Regression
Functional data analysis is concerned with inherently infinite dimensional data such as curves or images. It attracts more and more attentions because of its successful applications in many areas such as neuroscience and econometrics. We consider a class of regularization methods called spectral algorithms for functional linear regression within the framework of reproducing kernel Hilbert space. The proposed estimators can achieve the minimax optimal rates of convergence. Despite of the infinite dimensional nature of functional data, we show that the algorithms are easily implementable.

15:3016:00 
Tea Break 
16:0016:45 
Felix Kwok
Waveform relaxation methods: analysis and implementation
In this talk, we consider a class of domain decomposition methods, known as
waveform relaxation (WR) methods, for solving timedependent PDEs numerically on many
different processors in parallel. WR methods are distinctive in that a typical subdomain
problem is posed in both space and time; each iteration requires the parallel solution of these
spacetime subproblems, followed by an exchange of interface data defined over the whole
time window. An often cited advantage of WR methods is that they allow each subdomain to
use a different spatial and temporal grid that is adapted to the dynamics of the local
subproblem.
In this talk, I will first present some new results on the convergence of WR methods of the
NeumannNeumann type. Next, I will discuss two ways of introducing parallelism in time to
the basic WR method. The first approach uses a fixed timewindow size and yields an algorithm
that is mathematically equivalent to the original WR method. The second one, on the other
hand, chooses timewindow size dynamically based on how many free processors are available;
this leads to a method with improved convergence behaviour. We demonstrate the
effectiveness of both approaches by comparing their running times against those obtained
from classical timestepping methods, where the same number of processors is used to
parallelize in space only.

16:4517:30 
Hongyu Liu
Simultaneously recovering sources and mediums and its applications
In this talk, we shall consider a class of inverse problems of simultaneously
recovering an embedded source and it surrounding mediums. This type of inverse problems
arises from a variety of applications including thermoacoustic and photoacoustic tomography,
brain imaging and geomagnetic detection technology. I shall talk about the recent progress of
our study on those inverse problems.

18:0021:00 
Banquet 
 
Day 3: Sunday, 22 April 2018 
09:0011:00 
Free Discussion 
 




