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福建省数学建模与高性能科学计算重点实验室2016年年会

发布时间:2016年12月16日 浏览次数:发布者:mathky

福建省数学建模与高性能科学计算

重点实验室2016年年会

日程安排表

12月17日(星期六),海韵实验楼105报告厅

9:15

接送

金沙湾宾馆酒店大堂集合,统一乘车前往会场

9:30-9:40

开幕式

致辞,合影

9:40-10:10

刘兴军

低维材料组织演化的相场模拟

10:15-10:45

刘颜回

阵列天线布局及方向图综合中的数学优化问题

10:50-11:20

杜  魁

Any admissible harmonic Ritz value set is possible for GMRES

11:25-11:55

陈黄鑫

Reduced models for flow in fractured porous media: adaptation and two-scale model

Title and Abstract

 

低维材料组织演化的相场模拟

刘兴军

阵列天线布局及方向图综合中的数学优化问题

刘颜回

摘要列天线在无线通信及雷达域具有广泛而重要的用。告介绍归纳列天线布局及方向图综问题的主要型,并着重介了随机算法、数学算法、自适应阵列理等方法在问题中的用。合方法可以适于任意的构、并可以考虑阵列中元方向各不相同的情况(元指向不同、元互耦、平台效)。出了若干合的例子,包括副瓣压缩、主瓣形、元耦合影响、唯相位合、宽带宽描稀疏DBF列、共形列等用例子。最后,从数学化方法的角度讨论了目前列天线综域存在的主要问题 

 

Any admissible harmonic Ritz value set is possible for GMRES

杜魁

Abstract: The convergence behavior of Krylov subspace methods has been linked to the convergence of Ritz values, in particular for the CG method. For the GMRES method, some results suggest that the convergence of Ritz values often goes hand in hand with an acceleration of residual norm convergence and may in fact be the cause of superlinear convergence. However, mathematically, any residual norm history is possible with any set of Ritz values in the individual iterations of the GMRES process. This result can be regarded as a generalization of the fact that any residual norm history is possible with any set of final Ritz values, i.e., of eigenvalues. However surprising this may seem, the Ritz values are not the roots of GMRES polynomials and this makes it more credible that GMRES residual norms can be completely independent from Ritz values. The roots of the GMRES polynomials are the harmonic Ritz values. In our talk we show that not even harmonic Ritz values need have any influence on the residual norm history of GMRES (provided the stagnation case is treated correctly). In other words, any residual norm history is possible with any set of harmonic Ritz values in the individual iterations of the GMRES process.

 

Reduced models for flow in fractured porous media: adaptation and two-scale model 

陈黄鑫

Abstract: In this talk we will introduce an a posteriori error estimator for the Raviart-Thomas mixed finite element method for single-phase Darcy flow in a two-dimensional fractured porous media. The discrete fracture model (DFM) is applied to model the fractures by one-dimensional fractures in a two-dimensional domain. We derive a robust residual-based a posteriori error estimator for the problem with non-intersecting fractures. The reliability and efficiency of the a posteriori error estimator are established for the error measured in an energy norm. We will also introduce a two-scale reduced model for simulating the Darcy flow in two-dimensional porous media with conductive fractures. We apply the approach motivated by the embedded fracture model (EFM) to simulate the flow on the coarse scale, and the effect of fractures on each coarse scale grid cell intersecting with fractures is represented by the DFM on the fine scale. Several numerical results will be shown to demonstrate the efficiency of the adaptive algorithm and the proposed two-scale model.