Indirect methods of collocation: Trefftz‐Herrera collocation

A nonstandard collocation method (TH‐collocation) is presented, where collocation is used to construct specialized weighting functions instead of the solution itself, as it is usual, so that in this sense it is an indirect method. TH‐collocation is shown to be as accurate as standard collocation, but computationally far more efficient. The present article is the first of a series devoted to explore thoroughly collocation methods. The following classification of collocation methods is introduced: direct‐nonoverlapping; indirect‐nonoverlapping; direct‐overlapping; and indirect‐overlapping. Most of the effort reported in the literature has gone to direct‐nonoverlapping methods. The procedure presented in this article falls into the indirect‐nonoverlapping category and it is based on Trefftz‐Herrera formulation. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 709–738, 1999     

频域光学相干层析术系统中高准确度高灵敏度补偿色散法

将色散测量方法和快速扫描延迟线技术相结合,在谱域光学相干层析系统中实现了对群延迟色散的精确补偿.在该方法中,先在样品臂中放入平面反射镜,等间隔移动参考臂中快速扫描延迟线系统中光栅的位置,同时测量系统参考臂和样品臂之间的群延迟色散差值.当该值为零时,则表明系统色散匹配.将该方法与基于点扩散函数半高宽的方法进行比较,发现基于半高宽方法的测量误差为4.43%,而该方法的测量误差为0.76%;在色散补偿过程中,随着色散匹配点的靠近,半高宽方法的灵敏度由92.105 3fs2减小到1.344 7×103 fs2,而新方法的灵敏度则保持165.789 5fs2,表明本文提出的色散补偿法具有较高的色散补偿准确度和灵敏度.实验表明,色散补偿后的系统分辨率接近理论值;在补偿系统色散的同时,还可以根据测量所得色散值的符号来判定光栅的移动方向,从而更容易地完成补偿工作.     

Indices of Toeplitz tuples on pseudoregular domains

This paper proves an index theorem of Toeplitz tuples on pseudoregular domains in Cn. Geometrically, the index of Toeplitz tuple TΦn is (-1)n time wrapping number of Φn around the origin. As one of the applications of the index theorem, we completely characterize the automorphism groups of Toeplitz algebras on Poincaré domain. As another application, it is shown that C*(Ω)C*(Bn) for every Poincare domain Ω in Cn(n≠2). It is also noticed that C*(Ω)C*(B2) if and only if the Poincaré conjecture is true for Ω.     

An approximation for the boundary optimal control problem of a heat equation defined in a variable domain

In this paper, we consider a numerical approximation for the boundary optimal control problem with the control constraint governed by a heat equation defined in a variable domain. For this variable domain problem, the boundary of the domain is moving and the shape of theboundary is defined by a known time-dependent function. By making use of the Galerkin finite element method, we first project the original optimal control problem into a semi-discrete optimal control problem governed by a system of ordinary differential equations. Then, based on the aforementioned semi-discrete problem, we apply the control parameterization method to obtain an optimal parameter selection problem governed by a lumped parameter system, which can be solved as a nonlinear optimization problem by a Sequential Quadratic Programming （SQP） algorithm. The numerical simulation is given to illustrate the effectiveness of our numerical approximation for the variable domain problem with the finite element method and the control parameterization method.     

利用自然边界归化求解平面弹性方程外边值问题的SCHWARZ算法

1引言平面弹性方程在水利土建等工程技术领域有着广泛应用．其中,孔边应力集中等问题,都是无界区域问题．我们可以通过各种实验手段研究上述问题．而随着计算机和有限元技术的迅猛发展,数值解法提供了一种研究上述问题的有效途径．对于有界区域上的平面弹性方程,我们可以直接利用有限元方法求解,对于其中的大规模问题可以利用区域分解和并行技术求解．但这些方法难以处理无界区域问题．虽然对于某些典型区域上的外问题（例如,圆孔外区域和＿些规则形状裂纹）可以针对具体情况利用复变函数论方法予以解决,但对于一般的无界区域问题广…     

原位Raman光谱技术应用于铁电陶瓷畴变与电疲劳研究

基于铁电陶瓷材料90°畴变导致Raman光谱变化的原理,自行设计并搭建了铁电材料原位测试分析和数据采集系统,通过与Raman光谱仪的联用,利用特制的样品旋转装置,从实验上证实在外加电场作用下铁电材料中的90°畴变使平均电畴的择优取向发生改变,从而导致Raman光谱强度的变化,利用铁电材料原位测试分析和数据采集系统,实现...     

土壤表面与部分埋藏多目标复合散射的时域有限差分方法

采用Dobson半经验模型和电介质复介电常数表示土壤介电常数的实部和虚部,用指数型分布粗糙面和Monte Carlo方法模拟土壤表面,运用时域有限差分方法研究土壤表面与部分埋藏多个矩形截面混凝土柱复合模型的电磁散射.结果表明：复合散射系数随散射角振荡变化;土壤表面高度起伏均方根、土壤含水率、目标介电常数、入射角对复合散射系数影响较大;土壤表面相关长度、目标截面宽度、高度、间距、倾角对复合散射系数影响较小;目标埋藏深度对复合散射系数几乎没有影响.与其他数值计算方法比较,采用时域有限差分方法既可获得较高的准确性,又可减少计算时间和内存占用量.可以用来计算地、海粗糙面与附近任意多目标的复合散射.     

Simulation of Incompressible Viscous Flows by Local DFD-Immersed Boundary Method

A local domain-free discretization-immersed boundary method (DFD-IBM) is presented in this paper to solve incompressible Navier-Stokes equations in the primitive variable form. Like the conventional immersed boundary method (IBM), the local DFD-IBM solves the governing equations in the whole domain including exterior and interior of the immersed object. The effect of immersed boundary to the surrounding fluids is through the evaluation of velocity at interior and exterior dependent points. To be specific, the velocity at interior dependent points is computed by approximate forms of solution and the velocity at exterior dependent points is set to the wall velocity. As compared to the conventional IBM, the present approach accurately implements the non-slip boundary condition. As a result, there is no flow penetration, which is often appeared in the conventional IBM results. The present approach is validated by its application to simulate incompressible viscous flows around a circular cylinder. The obtained numerical results agree very well with the data in the literature.     

Composite finite element approximation for nonlinear parabolic problems in nonconvex polygonal domains

We study a new class of finite elements so‐called composite finite elements (CFEs), introduced earlier by Hackbusch and Sauter, Numer. Math., 1997; 75:447‐472, for the approximation of nonlinear parabolic equation in a nonconvex polygonal domain. A two‐scale CFE discretization is used for the space discretizations, where the coarse‐scale grid discretized the domain at an appropriate distance from the boundary and the fine‐scale grid is used to resolve the boundary. A continuous, piecewise linear CFE space is employed for the spatially semidiscrete finite element approximation and the temporal discretizations is based on modified linearized backward Euler scheme. We derive almost optimal‐order convergence in space and optimal order in time for the CFE method in the L^∞(L²) norm. Numerical experiment is carried out for an L‐shaped domain to illustrate our theoretical findings.     

芳香族氨基酸的太赫兹光谱研究

利用太赫兹时域光谱研究了三种芳香族氨基酸，即酪氨酸、色氨酸和苯丙氨酸，在02—1 6THz波段的光学特性，得到了对应的吸收谱.对比各自的吸收谱发现，酪氨酸和色氨酸分 别在0976THz和1465THz有明显的吸收峰，而苯丙氨酸则没有明显的吸收峰.利用密度泛 函(DFT)理论初步计算表明，氨基酸在THz波段的吸收是由分子转动或扭动造成的，氨基酸的 不同结构造成了它们在THz波段不同的吸收峰位.另外，还得到了三种氨基酸在该波段的折射 率谱并首次定量给出了三种氨基酸在02—16THz波段的平均折射率.酪氨酸、色氨酸和苯 丙氨酸的平均折射率分别为1507，1526和1686.这项研究不仅为研究生物分子结构和 动力学提供了新的理论和实验方法，而且对进一步利用THz时域光谱研究其他生物大分子具 有借鉴意义. 关键词： 太赫兹(THz)时域光谱 芳香族氨基酸 吸收谱 分子动力学