国家天元数学中部—东南中心联合报告会
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:2019-10-26 08:15 —— 2019-10-26 12:30
:厦门大学海韵园实验楼105
日程安排
日期 | 时间 | 事项 | 地点 |
10月26日 | 08:15-08:40 | 开幕式、合影 | |
主持人 | 吕锡亮 | ||
08:40-09:10 | 戴书洋(武汉大学):Modeling simulations of point defects in grain boundaries | 厦门大学海韵园实验楼105 | |
09:15-09:45 | 白正简(厦门大学):A Riemannian Newton-CG Method for Stochastic Inverse Singular Value Problems | ||
09:50-10:20 | 向华(武汉大学):Quantum Numerical Linear Algebra | ||
10:25-10:40 | 茶歇 | ||
主持人 | 杜魁 | ||
10:40-11:10 | 熊涛(厦门大学):High order semi-implicit IMEX WENO schemes for all-Mach Euler system | 厦门大学海韵园实验楼105 | |
11:15-11:45 | 翁上昆(武汉大学):Decay Rates of Second Order Derivatives of Axisymmetric D-Solutions to the Stationary Navier-Stokes Equations | ||
11:50-12:20 | 张剑文(厦门大学):Global Well-Posedness of Strong Solutions to the 3D Compressible Full Navier-Stokes Equations | ||
12:30 | 午餐 | 大丰苑 |
学术报告题目和摘要
Modeling simulations of point defects in grain boundaries
戴书洋(武汉大学)
We examine the common assumption that grain boundaries (GBs) are ideal sinks for point defects by comparing contrasting its implications with an explicit model of a low-angle tilt GB described by an array of edge dislocations. We solve the resultant diffusion equation in the absence presence of irradiation-induced point defects. We derive a reduced dimension description of GBs where the influence of GB structure is captured in a single parameter in a Robin boundary condition. For the case of a low-angle tilt GB, we explicitly relate this parameter to the GB structure. We discuss the generality of this approach for cases where the low-angle GB model applies parameterize the model so that it accurately reproduces the results of the two-dimensional dislocation model.
A Riemannian Newton-CG Method for Stochastic Inverse Singular Value Problems
白正简(厦门大学)
In this talk, we consider the stochastic inverse singular value problem of constructing a stochastic matrix from the prescribed realizable singular values. We propose several Riemannian inexact Newton-CG Methods for solving the stochastic inverse singular value problem. With different forcing terms, we show the proposed methods converges linearly or superlinearly under some assumptions. We also extend the proposed method to the case of prescribed entries. Finally, we report some numerical results to demonstrate the effectiveness of the proposed methods.
Quantum Numerical Linear Algebra
向华(武汉大学)
We will review the development of quantum algorithms, especially the HHL for solving linear algebraic systems, then switch to our quantum algorithms on the numerical linear algebra problems, including the circulant preconditioner, regularized least squares (LS), total least squares (TLS), tridiagonal eigensolvers. (1) We consider the quantum linear solver for Ax = b with the circulant preconditioner. The main technique is the modified singular value estimation (SVE). (2) The regularized LS can be used to solve an ill-conditioned problem. The determination of the proper regularization parameter is the key step. Combining the L-curve or the Hanke-Raus rule with the HHL quantum amplitude estimation, we propose quantum algorithms to compute the norms of regularized solution the corresponding residual, then locate the best regularization parameter by Grover's algorithm. This yields a quadratic speedup in the number of regularization parameters. (3) For the TLS problem, it is transformed to finding the ground state of a Hamiltonian matrix. We propose quantum algorithms for solving this problem based on quantum simulation of resonant transitions. Our algorithms can achieve at least polynomial speedup over the known classical algorithms.
High order semi-implicit IMEX WENO schemes for all-Mach Euler system
熊涛(厦门大学)
In this talk, we will propose a high order asymptotic preserving scheme for the Euler system with all-speed. Here material waves are treated explicitly, while acoustic waves are treated implicitly, thus avoiding severe CFL time step restrictions for low Mach flows. High order accuracy in space is obtained by finite difference WENO schemes, while high order in time is obtained by semi-implicit IMEX scheme with linearization treatment. The scheme is asymptotic preserving asymptotic accurate as the Mach number vanishes. Numerical tests will illustrate the effectiveness efficiency of our proposed approach.
Decay Rates of Second Order Derivatives of Axisymmetric D-Solutions to the Stationary Navier-Stokes Equations
翁上昆(武汉大学)
We study the asymptotic behavior of the axisymmetric solutions to the stationary Navier-Stokes equations in $\mathbb{R}^{3}$ with finite Dirichlet integral. We establish some new a priori decay rates for the second order derivatives of the velocity. The result is obtained by combining the weighted energy estimates, the Brezis-Galleout inequality the scaling argument.
Global Well-Posedness of Strong Solutions to the 3D Compressible Full Navier-Stokes Equations
张剑文(厦门大学)
This talk concerns the Cauchy problem of the full Navier-Stokes equations for three-dimensional compressible viscous heat-conducting fluids in the whole space $\R^3$. We obtain a kind of global strong solutions belonging to a new class of functions in which the uniqueness is shown to hold.