A priori estimates for two multiscale finite element methods using multiple global fields to wave equations

We consider a scalar wave equation with nonseparable spatial scales. If the solution of the wave equation smoothly depends on some global fields, then we can utilize the global fields to construct multiscale finite element basis functions. We present two finite element approaches using the global fields: partition of unity method and mixed multiscale finite element method. We derive a priori error estimates for the two approaches and theoretically investigate the relation between the smoothness of the global fields and convergence rates of the approximations for the wave equation. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2011     

Numerical evaluation of the two-dimensional partition of unity boundary integrals for Helmholtz problems

There has been considerable attention given in recent years to the problem of extending finite and boundary element-based analysis of Helmholtz problems to higher frequencies. One approach is the Partition of Unity Method, which has been applied successfully to boundary integral solutions of Helmholtz problems, providing significant accuracy benefits while simultaneously reducing the required number of degrees of freedom for a given accuracy. These benefits accrue at the cost of the requirement to perform some numerically intensive calculations in order to evaluate boundary integrals of highly oscillatory functions. In this paper we adapt the numerical steepest descent method to evaluate these integrals for two-dimensional problems. The approach is successful in reducing the computational effort for most integrals encountered. The paper includes some numerical features that are important for successful practical implementation of the algorithm.     

UBI-QEP法研究氧化钴上的催化还原脱硫反应

应用UBI QEP能学方法,研究了氧化钴表面上的催化还原脱硫反应. 发现在CO还原SO2的过程中,低温条件下,反应遵循氧化还原（Redox）机理,即CO先与晶格氧反应在表面产生氧缺位,然后SO2在氧阴离子空穴上被还原;在高温条件下,COS中间态确实存在,反应为Redox机理和COS中间态机理共同作用.中间产物SO是极不稳定的,即能很快被CO继续还原,又可以为表面氧物种所氧化.COS可抑制表面氧物种,因此能起到间接控制该反应的作用.     

Bourgain's analytic projection revisited

For a positive function on the unit circle with , the following two statements are equivalent: (a) ; (b) there is an operator projecting onto for all at once and having weak type (1,1) with respect to .

     

面向卓越工科的“模拟电子技术”教学探索

立足卓越工科支柱课程的定位,分析新时代背景下“模拟电子技术”课程中存在的挑战,通过思政元素与科创潜力两翼的引领,开展了一系列的探索：融入思政元素的授课内容、理实合一的专题式教学、多层次的实践教学、基于智慧教学的多元化考评。这些教改实践提升了模电课程的整体教学效果与学生平均成绩,有助于培养大量具备国际竞争力的卓越工科人才。     

Implementation of zero current switch turn-ON based buck-boost-buck type rectifier for low power applications

A single-stage single-switch AC–DC integrated converter is proposed in this paper, as a tight DC voltage regulator with unity input power factor for the fundamental component of the input current. Proposed converter is formed by the integration of buck-boost configuration with a buck converter operated by a single switch. The buck-boost section of the proposed configuration is operated in current discontinuous conduction mode (DCM) to get unity input power factor at the supply terminals and the buck section is operated up to boundary current conduction mode (BCM). The features acquired by the converter operating in complete discontinuous conduction mode (DCM) are unity input power factor, zero-current turn-ON for the Switch, fast and good DC output voltage regulation with extensive conversion range and low voltage stress on the switch. Additionally, the intermediate capacitor voltage stress is independent of converter load variations and so the switch also is subjected to constant peak voltage stress. A comprehensive study is carried out to obtain the necessary design equations. A design model is implemented using simulation and hardware. The results confirm the performance of the proposed configuration.     

Green polynomials at roots of unity and Springer modules for the symmetric groups

We consider the Green polynomials at roots of unity. We obtain a recursive formula for the Green polynomials at roots of unity whose orders do not exceed some positive integer. The formula is described in a combinatorial manner. The coefficients of the recursive formula are realized by the cardinality of a set of permutations. The formula gives an interpretation of a combinatorial property on a family of graded modules for the symmetric group in terms of representation theory.     

Two-grid partition of unity method for second order elliptic problems

A two-grid partition of unity method for second order elliptic problems is proposed and analyzed. The standard two-grid method is a local and parallel method usually leading to a discontinuous solution in the entire computational domain. Partition of unity method is employed to glue all the local solutions together to get the global continuous one, which is optimal in HI-norm. Furthermore, it is shown that the L^2 error can be improved by using the coarse grid correction. Numerical experiments are reported to support the theoretical results.     

重叠型非匹配网格抛物型方程的有限元法及收敛性分析

基于单位分解技术,本文介绍了重叠型非匹配网格抛物型方程初边值问题的有限元方法,分别给出了半离散有限元、全离散有限元格式和收敛性分析的结果,并给出了数值例子.