附件：报告题目及摘要
Retirement Spending and Biological Age
黄华雄
Retirement sustability is a problem faced by many countries. In this talk, we proposed a Brownian bridge model for retirement spending under age uncertainty in the sense that chronological age may not be a good indicator of the "true" biological age. This is joint work with Moshe Milevsky and Tom Salisbury.
Numerical Methods and Analysis for Landau–Lifshitz equation
孙伟伟
The Landau–Lifshitz equation has been widely used to describe the dynamics of mag-netization in a ferromagnetic material, which is highly nonlinear with the nonconvex constraint |m| = 1. In this talk, I will present an overview of recent development on numerical methods and analysis for the Landau–Lifshitz type equation. A crucial issue in designing eﬃcient numerical schemes for this equation is to preserve this constraint in the discrete level. A simple and frequently-used one is the projection method which projects the numerical solution onto a unit sphere at each time step. Due to the simplic-ity of the sphere-projection approach, the method has been extensively used in various applications, including for energy-conserving or symplectic system and the evolution on a manifold. However, no rigorous error estimate is available up to now. Classical energy approach fails to be applied directly in the analysis of the projection method since both projected and unprojected solutions are involved in the discrete system. We shall present our recent works on optimal error analysis of linearized ﬁnite diﬀerence and ﬁnite element methods for the Landau–Lifshitz equation. The analysis is based on a more precise estimate of the diﬀerence between the errors of projected and unprojected solutions. Some numerical experiments are provided to conﬁrm our theoretical results.
Optimal investment strategy and consumption strategy under fixed and proportional transaction Costs
张强
In modern finance, the goal of portfolio management is to reduce the risks and to enhance the performance of the portfolio. For this reason, various investment strategies and the consumption strategies have been developed. For most of these strategies, the execution requires constantly adjusting the risky assets holding. This is not feasible in practice since in reality the transaction costs are unavoidable. Therefore transection costs must be included in the strategy selection process. Transaction costs can occur in the form of proportional cost and fixed cost. This leads to the questions: when not to make an adjustment to avoid excessive transaction costs; when to buy some more risky asset; how many shares to buy; when to sell some risky asset; and how many shares to sell. Mathematically, answers to these questions requires solving a nonlinear partial differential equation with four free boundaries. In this talk we present the solution to this problem. We obtained the analytical expressions for the optimal asset allocation strategy and optimal consumption strategy under both fixed and proportional transaction costs. Our approach is based on expected utility maximization, dynamic programing and singular perturbation expansion.
Theoretical analysis for rising bubble in Hele-Shaw cell
邸亚娜
In this talk, we calculate the shape and the velocity of a bubble rising in an infinitely large and closed Hele-Shaw cell using Park and Homsy's boundary condition which accounts for the change of the three dimensional structure in the perimeter zone.
High-order gas-kinetic scheme for Euler and Navier-Stokes equations
潘亮
The high-order gas-kinetic scheme (HGKS) has achieved success in simulating compressible flows. Recently, based on the time-dependent flux function, a two-stage fourth-order method was developed for Lax-Wendroff type flow solvers, particularly applied for the hyperbolic conservation laws. Under the multi-stage multi-derivative framework, a reliable two-stage fourth-order GKS has been developed, and even higher-order of accuracy can be achieved. The current fourth-order method not only improves the accuracy of the scheme, but also reduces the complexity of the gas-kinetic flux solver greatly. More importantly, this scheme is as robust as the second-order scheme and works perfectly from subsonic to hypersonic flows. With the two-stage framework, the HGKS with moving-meshes and HGKS in the curvilinear coordinates are developed as well. Numerical results validate the outstanding reliability and applicability of the scheme for three-dimensional flows, such as the direct numerical simulation for supersonic isotropic turbulence. Recently, HGKS is implemented for the direct numerical simulation (DNS) and implicit large eddy simulation (iLES) for compressible turbulent flows, including the compressible turbulent channel flow and compressible turbulent flow over periodic hills. The HGKS results are in good agreement with the refereed spectral method and high-order finite difference method. The performance of HGKS demonstrates its capability as a powerful tool for the numerical simulation of turbulent flows.
On a model of surface imaging with double negative metamaterial
王玉亮
We consider the problem of imaging a periodic surface by acoustic or electromagnetic waves. A slab of double negative metamaterial is placed above the surface and the scattered field is measured on the top boundary of the slab. The imaged surface is assumed to be a small perturbation of the flat surface so that we can make a transformed field expansion to linearize the problem and obtain a simple reconstruction formula. We show by analysis of the formula and numerical experiments that the resolution of the reconstruction can be greatly enhanced due to the double negative slab.
生物育种驱动的高效能数值代数在统计推断与关联分析中的应用
朱圣鑫
学习和挖掘海量数据中表征与本征间的潜在关联，做出合理推断/推荐是数据科学研究的重要内容之一。随着生物育种、医药试验、生态进化、多源感知、搜索引擎、社交网络、征信风控和广告推荐等应用中异构数据的激增，一些经典的统计模型在分析和计算海量异构数据时面临空前的算法挑战。本报告将介绍海量育种数据驱动的一个经典推断模型中的核心数值计算问题和挑战。并介绍巧妙的矩阵分析，信息分裂和高效能数值代数技术在提高经典模型可扩展性，支撑高通量生物育种软件开发中的关键作用。 最后我们讨论该技术潜在的应用。
New superconvergent structures developed from the finite volume element method
王翔
Abstract: New superconvergence structures are introduced by the finite volume element method (FVEM), which gives us the freedom to choose the superconvergent points of the derivative and the function value for k>=3. The general orthogonal condition and the modified M-decomposition (MMD) technique are established to prove the superconvergence properties of the new structures. In addition, the relationships between the orthogonal condition and the convergence properties for the FVE schemes are carried out in this talk.
A class of efficient spectral methods and error analysis for nonlinear Hamiltonian systems
曹外香
We investigate efficient numerical methods for nonlinear Hamiltonian systems.
Three polynomial spectral methods (including spectral Galerkin, Petrov-Galerkin, and collocation methods) coupled with domain decomposition are presented and analyzed. Our main results include the energy and symplectic structure-preserving properties and error estimates. We prove that the spectral Petrov-Galerkin method preserves the energy exactly while both the spectral Gauss collocation and spectral Galerkin methods are energy conserving up to spectral accuracy.
While it is well known that collocation at Gauss points preserves symplectic structure, we prove that the Petrov-Galerkin method preserves the symplectic structure up to a Gauss numerical quadrature error and the spectral Galerkin method preserves the symplectic structure up to spectral accuracy error.
Finally, we show that all three methods converge exponentially, which makes it possible to simulate the long time behavior of the system. Numerical experiments indicate that our algorithms are efficient.
Polymeric Bilayer Interfaces and Their Elastic Properties: Application of Self-Consistent Field Theory
蔡永强
Bilayer membranes self-assembled from amphiphilic molecules are ubiquitous in biological and soft matter systems. The mechanical response and shape of self-assembled bilayer membranes depend crucially on their elastic properties characterised by a set of elastic moduli. This talk will provide methods to calculate the elastic moduli of self-assembled bilayers within the framework of the self-consistent field theory.