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学术预告:白中治研究员谈“数值代数”系列学术报告

作者:理学院   点击:0  发布时间:2017-12-05 09:42:32

报告人:白中治研究员

单位:中科院数学与系统科学研究院

Title 1:Optimization of extrapolated Cayley transform with non-Hermitian positive definite matrix

Abstract

For the extrapolated Cayley transform, we give necessary and sufficient conditions for guaranteeing its convergence and contraction (in the Euclidean norm). We derive upper bounds for the convergence and the contraction factors, and compute the optimal parameters minimizing these upper bounds and the corresponding optimal values of these upper bounds. Numerical computations show that these upper bounds are reasonably sharp compared with the exact convergence and the exact contraction factors of the extrapolated Cayley transform, respectively.

报告时间:10月16日下午1:30

Title 2:On approximated ILU and UGS preconditioning methods for linearized discretized steady incompressible Navier-Stokes equations

Abstract

When the artificial compressibility method in conjunction with high-order upwind compact finite difference schemes is employed to discretize the steady-state incompressible Navier-Stokes equations, in each pseudo-time step we need to solve a structured system of linear equations approximately by, for example, a Krylov subspace method such as the preconditioned GMRES. In this paper, based on the special structure and concrete property of the linear system we construct a structured preconditioner for its coefficient matrix and estimate eigenvalue bounds of the correspondingly preconditioned matrix. Numerical examples are given to illustrate the effectiveness of the proposed preconditioning methods.

报告时间:10月16日下午18:00

Title 3:On order-reducible sinc discretizations and block-diagonal preconditioning methods for linear third-order ordinary differential equations

Abstract

By introducing a variable substitution, we transform the two-point boundary value problem of a third-order ordinary differential equation into a system of two second-order ordinary differential equations (ODEs). We discretize this order-reduced system of ODEs by both sinc-collocation and sinc-Galerkin methods, and average these two discretized linear systems to obtain the target system of linear equations. We prove that the discrete solution resulting from the linear system converges exponentially to the true solution of the order-reduced system of ODEs.

报告时间:10月17日上午10:00

报告地点:教学楼D楼204会议室

专家简介:

白中治研究员,中国科学院数学与系统科学研究院研究员、科学与工程计算国家重点实验室副主任,曾获国家杰出青年科学基金、冯康科学计算奖、国家教委科学技术进步奖三等奖、中国科学院青年科学家奖二等奖,国家级“新世纪百千万人才工程计划”以及国务院政府特殊津贴。主要研究领域有数值线性代数、数值优化、并行计算及微分方程数值解。他在线性与非线性代数方程组和互补问题的高效数值方法,同步与异步并行迭代算法及其收敛性理论,矩阵方程的快速求解算法等领域均有重要贡献。在《SIAM Journal on Scientific Computing》等著名国际学术刊物上发表科研论文300余篇,其中2003由白中治和美国科学院院士、斯坦福大学教授G.H. Golub等提出的HSS迭代算法被认为具有重要的里程碑意义,是线性系统迭代算法研究领域近20年来最重要的进展之一。此外,白中治研究员己连续多年入选Elsevier中国高被引学者榜(数学前5名)。