国家自然科学基金(10571053)

作品数：14被引量：78H指数：6
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A COUPLED CONTINUOUS-DISCONTINUOUS FEM APPROACH FOR CONVECTION DIFFUSION EQUATIONS被引量：7
《Acta Mathematica Scientia》2011年第2期601-612,共12页祝鹏 谢资清 周叔子 
Supported by National Natural Science Foundation of China (10571046, 10571053, and 10871066);Program for New Century Excellent Talents in University (NCET-06-0712);Key Laboratory of Computational and Stochastic Mathematics and Its Applications, Universities of Hunan Province, Hunan Normal University;the Project of Scientific Research Fund of Hunan Provincial Education Department (09K025);the Key Scientific Research Topic of Jiaxing University (70110X05BL)
In this article, we introduce a coupled approach of local discontinuous Calerkin and standard finite element method for solving convection diffusion problems. The whole domain is divided into two disjoint subdomains. ...
关键词：Convection diffusion problems local discontinuous Galerkin method finiteelement method SUPERCONVERGENCE 
SUPER-GEOMETRIC CONVERGENCE OF A SPECTRAL ELEMENT METHOD FOR EIGENVALUE PROBLEMS WITH JUMP COEFFICIENTS被引量：1
《Journal of Computational Mathematics》2010年第3期418-428,共11页Lin Wang Ziqing Xie Zhimin Zhang 
supported in part by the Programme for New Century Excellent Talents in University (NCET-06-0712);the National Natural Science Foundation of China (NSFC 10871066, 10571053);Key Laboratory of High Performance Computing and Stochastic Information Processing, Ministry of Education of China, Hunan Normal University;supported in part by the US National Science Foundation grant DMS-0612908
We propose and analyze a C^0 spectral element method for a model eigenvalue problem with discontinuous coefficients in the one dimensional setting. A super-geometric rate of convergence is proved for the piecewise con...
关键词：EIGENVALUE Spectral method COLLOCATION Galerkin finite element method. 
THE ACCELERATED SEARCH-EXTENSION METHOD FOR COMPUTING MULTIPLE SOLUTIONS OF SEMILINEAR PDEs被引量：2
《Acta Mathematica Scientia》2009年第4期803-816,共14页刘跃武 谢资清 陈传淼 
supported by the National Natural Science Foundation of China (10571053, 10871066, 10811120282);Programme for New Century Excellent Talents in University(NCET-06-0712)
In this paper, we propose an accelerated search-extension method （ASEM） based on the interpolated coefficient finite element method, the search-extension method （SEM） and the two-grid method to obtain the multiple...
关键词：semilinear PDEs multiple solutions accelerated search-extension method （ASEM） two-grid method 
A NUMERICAL STUDY OF UNIFORM SUPERCONVERGENCE OF LDG METHOD FOR SOLVING SINGULARLY PERTURBED PROBLEMS被引量：11
《Journal of Computational Mathematics》2009年第2期280-298,共19页Ziqing Xie Zuozheng Zhang Zhimin Zhang 
Supported by the National Natural Science Foundation of China (10571053,10871066);the Programme for New Century Excellent Talents in University (NCET-06-0712).
In this paper, we consider the local discontinuous Galerkin method （LDG） for solving singularly perturbed convection-diffusion problems in one- and two-dimensional settings. The existence and uniqueness of the LDG s...
关键词：Singularly perturbed problems Local discontinuous Galerkin method Numerical fluxes Uniform superconvergence 
A Robust Discontinuous Galerkin Method for Solving Convection-diffusion Problems被引量：4
《Acta Mathematicae Applicatae Sinica》2008年第3期483-496,共14页Zuo-zheng Zhang Zi-qing Xie Xia Tao 
the National Natural Science Foundation of China(No.10571053);Programme for New Century Excellent Talents in University(NCET-06-0712);the Excellent Youth Project of the Education Department of Hunan Province of China(0513039)
In this paper, a new DG method was designed to solve the model problem of the one-dimensional singularly-perturbed convection-diffusion equation. With some special chosen numerical traces, the existence and uniqueness...
关键词：Discontinuous Galerkin method singularly perturbed CONVECTION-DIFFUSION numerical traces 
Analysis of extrapolation cascadic multigrid method(EXCMG)被引量：23
《Science China Mathematics》2008年第8期1349-1360,共12页CHEN ChuanMiao HU HongLing XIE ZiQing LI ChenLiang 
the National Natural Science Foundation of China(Grant Nos.10771063,10571053);Doctoral Programme of National Education Ministry of China(Grant No.20050542006);Programme for New Century Excellent Talents in University(Grant No.NCET-060712)
Based on an asymptotic expansion of finite element,a new extrapolation formula and extrapolation cascadic multigrid method(EXCMG)are proposed,in which the new extrapolation and quadratic interpolation are used to prov...
关键词：cascadic multigrid finite element new extrapolation error analysis 65N30 
基于搜索延拓的多启动参数微分法求解非线性微分方程多解问题
《湖南师范大学自然科学学报》2008年第1期14-18,共5页李璨 刘跃武 谢资清 
国家自然科学基金资助项目(10571053);湖南省教育厅优秀青年资助项目(05B039)
基于搜索延拓法,结合参数微分法,计算出了立方非线性问题Δu+u3=0在Ω内,u=0在Ω上的多个解,减少了计算量,缩短了计算时间,并通过数值例子证实了该方法的有效性.
关键词：参数微分法 搜索延拓法 非线性微分方程 多解 
Analysis of search-extension method for finding multiple solutions of nonlinear problem被引量：4
《Science China Mathematics》2008年第1期42-54,共13页CHEN ChuanMiao XIE ZiQing 
This work was supported by the National Major Basic Research Projects (Grant No. G1999032804);the National Natural Science Foundation of China (Grant No.10471038, 10571053);the Research Fonds for Doctor Programme (Grant No. 20050542006);Programme for New Century Excellent Talent in University (GrantNo. NCET-06-0717)
For numerical computations of multiple solutions of the nonlinear elliptic problem Δu + f(u = 0 in Ω, u = 0 on Γ, a search-extension method (SEM) was proposed and systematically studied by the authors. This paper s...
关键词：nonlinear isolated solution REGULARITY search-extension finite elements error analysis 65N30 
Wilson元特征值下逼近准确特征值被引量：10
《计算数学》2007年第3期319-321,共3页张智民 杨一都 陈震 
国家自然科学基金(No.10571053);贵州省优秀科技教育人才省长专项资金(黔科教办[2005]155号)资助项目.
该文讨论矩形域上Laplace算子特征值问题有限元近似.证明了Wilson非协调有限元特征值下逼近准确特征值,从而解决了有限元法中长期存在的一个猜想.
关键词：特征值 WILSON元 
基于多重网格法的实时流体模拟被引量：9
《计算机辅助设计与图形学学报》2007年第7期935-940,共6页周世哲 满家巨 
国家自然科学基金(10571053);湖南省教育厅青年基金(04B037)
在GPU上实现了多重网格法,并用该方法改进了二维的实时流体模拟,更充分地利用GPU的并行计算能力.使用4层网格,依靠渲染到纹理的计算方式、帧缓存扩展的纹理管理方法,提高了图形硬件的利用率.实验对比表明,在同样的帧数下该方法能提高GP...
关键词：GPU 实时流体模拟 多重网格法 帧缓存扩展 
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