Mass‐lumping or not mass‐lumping for eigenvalue problems

In this article we analyze the effect of mass‐lumping in the linear triangular finite element approximation of second‐order elliptic eigenvalue problems. We prove that the eigenvalue obtained by using mass‐lumping is always below the one obtained with exact integration. For singular eigenfunctions, as those arising in non convex polygons, we prove that the eigenvalue obtained with mass‐lumping is above the exact eigenvalue when the mesh size is small enough. So, we conclude that the use of mass‐lumping is convenient in the singular case. When the eigenfunction is smooth several numerical experiments suggest that the eigenvalue computed with mass‐lumping is below the exact one if the mesh is not too coarse. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 653–664, 2003     

Shape Optimization and Fictitious Domain Approach for Solving Free Boundary Problems of Bernoulli Type

This contribution deals with an efficient method for the numerical realization of the exterior and interior Bernoulli free boundary problems. It is based on a shape optimization approach. The state problems are solved by a fictitious domain solver using boundary Lagrange multipliers.     

Iterative regularization methods for atmospheric remote sensing

In this paper we present different inversion algorithms for nonlinear ill-posed problems arising in atmosphere remote sensing. The proposed methods are Landweber's method (LwM), the iteratively regularized Gauss-Newton method, and the conventional and regularizing Levenberg-Marquardt method. In addition, some accelerated LwMs and a technique for smoothing the Levenberg-Marquardt solution are proposed. The numerical performance of the methods is studied by means of simulations. Results are presented for an inverse problem in atmospheric remote sensing, i.e., temperature sounding with an airborne uplooking high-resolution far-infrared spectrometer.     

Rational Functions with Prescribed Global and Local Minimizers

A family of multivariate rational functions is constructed. It has strong local minimizers with prescribed function values at prescribed positions. While there might be additional local minima, such minima cannot be global. A second family of multivariate rational functions is given, having prescribed global minimizers and prescribed interpolating data.     

非线性不适定问题一种双循环的牛顿型迭代格式

本文研究非线性算子方程F(x)=y的解,结合最速下降法,Newton-Landweber迭代格式及正则化思想,在F满足适当的条件下,构造出新的双循环迭代格式。本文对格式的收敛性进行了严格论证,并估计出迭代格式的收敛精度。     

溃坝问题的间断有限元方法

本文研究90年代初提出的Runge-Kutta间断Galerkin有限元方法，给出该方法的精度分析，通过经典算例验证该方法处理间断问题、捕捉锐利波形的能力，并将其推广到求解浅水问题．针对坝底无摩擦，无坡度的理想情形进行讨论，给出方溃坝和圆溃坝问题的数值模拟结果．     

对于工学硕士的《数理统计》教学的研究

工学硕士的《数理统计》教学 ,要根据工学硕士的培养目标和数理统计课程的特点编写教材、确定讲授内容和授课方式 .力求使学员掌握处理随机数据的思考方法 ,培养解决问题、分析问题和善于应用知识的能力 .改革《数理统计》教学 ,实现和普及多媒体教学是时代发展的趋势 .     

高师英语职业技能教育改革

高师院校肩负着培养基础教育师资的重任。衡量师资素质的重要标准之一，是教师职业素质与技能掌握、运用的程度。因而职业技能教育是高师教育中一个重要组成部分。本文通过对高师院校英语职业技能教育的反思，以及对基础教育发展需求分析，提出从可持续发展、教育的内在价值与创新教育的三个层面探讨高师英语职业技能教育改革。     

水切割机中超高压预应力复合缸体研究

针对水切割机中高压缸经常爆裂的现象,本文研究了预应力缸体、高压缸的失效原因及预应力缸体的基本特点,最后进行了缸体疲劳实验。     

Innovation on Petroleum Engineering Technology of China Beach and Shallow Water Areas

1Chinaoffshoreoil&gasresourcesandtheircharacteristicfeatures　Chinaoffshoreoil&gasexplorationstartedduringthe1 95 0s .Until 1 971 ,thecommercialHai 4fieldwasfoundinBohai.Subsequentlytwoproductionplatformswereconstruc ted ,thefirstChinaoffshoreoilfieldwasformed .Fromthenon ,Chinaoffshoreoil&gasexplorationandexploitationspeedbecameprogressivelyfaster.Afteralargeamountofexplorationwork ,theoilandgasresourcesinChinacoastalareasweremadeclearpreliminarily .AccordingtoState sSecondaryResourceEva…