INFINITE ELEMENT METHOD FOR PROBLEMS ON UNBOUNDED AND MULTIPLY CONNECTED DOMAINS

The author studies the infinite element method for the boundary value problems of second order elliptic equations on unbounded and multiply connected domains. The author makes a partition of the domain into infinite number of elements. Without dividing the domain, as usual, into a bounded one and an exterior one, he derives an initial value problem of an ordinary differential equation for the combined stiffness matrix, then obtains the approximate solution with a small amount of computer work. Numerical examples are given.

On Univalent Functions in Multiply Connected Domains

The present article is an account of results on univalent functions in multiply connected domains obtained by the author. It contains two rery simple proofs of Villat's formula; Schwarz's formula, Poisson's formula and Poisson-Jensen formula in multiply connected domains; the differentiability theorem with respect to the parameter of analytic function family containing one parametric variable on multiply connected domains; variation theorem and parametric representation theorem of univalent functions in multiply connected domains; the solution of an extremal problem of differentiable functionals.

Equivalence of three kinds of well-posed-ness of discontinuous Riemann-Hilbert problem for elliptic complex equation in multiply connected domains

In this article, we first introduce the general linear elliptic complex equation of first order with certain conditions, and then propose discontinuous Riemann-Hilbert problem and some kinds of modified well-posed-ness for the complex equation. Then we verify the equivalence of three kinds of well-posed-ness. The discontinuous boundary value problem possesses many applications in mechanics and physics etc.

Approximate Method of Riemann-Hilbert Problem for Elliptic Complex Equations of First Order in Multiply Connected Unbounded Domains

In this article, we discuss the approximate method of solving the Riemann-Hilbert boundary value problem for nonlinear uniformly elliptic complex equation of first order (0.1) with the boundary conditions (0.2) in a multiply connected unbounded domain D, the above boundary value problem will be called Problem A. If the complex Equation (0.1) satisfies the conditions similar to Condition C of (1.1), and the boundary condition (0.2) satisfies the conditions similar to (1.5), then we can obtain approximate solutions of the boundary value problems (0.1) and (0.2). Moreover the error estimates of approximate solutions for the boundary value problem is also given. The boundary value problem possesses many applications in mechanics and physics etc., for instance from (5.114) and (5.115), Chapter VI, [1], we see that Problem A of (0.1) possesses the important application to the shell and elasticity.

General Boundary Value Problems for Nonlinear Uniformly Elliptic Equations in Multiply Connected Infinite Domains

This article discusses the general boundary value problem for the nonlinear uniformly elliptic equation of second order in D (0.1) and the boundary condition,(0.2) in a multiply connected infinite domain D with the boundary T. The above boundary value problem is called Problem G. Problem G extends the work [8] in which the equation (0.1) includes a nonlinear lower term and the boundary condition (0.2) is more general. If the complex equation (0.1) and the boundary condition (0.2) meet certain assumptions, some solvability results for Problem G can be obtained. By using reduction to absurdity, we first discuss a priori estimates of solutions and solvability for a modified problem. Then we present results on solvability of Problem G.

Distributed Lagrange Multiplier/Fictitious Domain Finite Element Method for a Transient Stokes Interface Problem with Jump Coefficients

The distributed Lagrange multiplier/fictitious domain(DLM/FD)-mixed finite element method is developed and analyzed in this paper for a transient Stokes interface problem with jump coefficients.The semi-and fully discrete DLM/FD-mixed finite element scheme are developed for the first time for this problem with a moving interface,where the arbitrary Lagrangian-Eulerian(ALE)technique is employed to deal with the moving and immersed subdomain.Stability and optimal convergence properties are obtained for both schemes.Numerical experiments are carried out for different scenarios of jump coefficients,and all theoretical results are validated.

Fully Coupled Fluid-Structure Interaction Model Based on Distributed Lagrange Multiplier/Fictitious Domain Method

This paper, with a finite element method, studies the interaction of a coupled incompressible fluid-rigid structure system with a free surface subjected to external wave excitations. With this fully coupled model, the rigid structure is taken as ＂fictitious＂ fluid with zero strain rate. Both fluid and structure are described by velocity and pressure. The whole domain, including fluid region and structure region, is modeled by the incompressible Navier-Stokes equations which are discretized with fixed Eulerian mesh. However, to keep the structure＇ s rigid body shape and behavior, a rigid body constraint is enforced on the ＂fictitious＂ fluid domain by use of the Distributed Lagrange Multipher/Fictitious Domain （DLM/ FD） method which is originally introduced to solve particulate flow problems by Glowinski et al. For the verification of the model presented herein, a 2D numerical wave tank is established to simulate small amplitude wave propagations, and then numerical results are compared with analytical solutions. Finally, a 2D example of fluid-structure interaction under wave dynamic forces provides convincing evidences for the method excellent solution quality and fidelity.

A FICTITIOUS DOMAIN METHOD FOR DIRICHLET PROBLEM AND ITS APPLICATIONS TO GENER ALIZED STOKES PROBLEM

This paper discusses a fictitious domain method for the linear Dirichlet problem and its applications to the generalized Stokes problem. This method treats Dirichlet boundary condit ion via a Lagrange multiplier technique and is well suited to the no-slip bound ary condition in viscous flow problems. In order to improve the accuracy of solu tions, meshes are refined according to the a posteriori error estimate. The mini -element discretization is applied to solve the generalized Stokes problem. Fin ally, some numerical results to validate this method are presented for partial d ifferential equations with Dirichlet boundary condition.

基于低中频采样的超宽带雷达波形产生器误差校正方法

针对超宽带(UWB)雷达波形合成中正交调制器、混频器、倍频器等模拟环节的误差因素特点,提出一种基于“低中频直接数字产生+倍频”途径的高质量UWB雷达LFM波形数字产生器方案。在频域建立该系统误差的数学模型,提出一种基于频谱对比途径的系统误差数字预失真校正方法,并进行实验验证和性能分析。该方法将系统失真的校正函数映射到系统数字输入端的波形库中,通过直接对存储的数字波形进行预失真融合处理实现系统误差的校正和补偿。结果表明该方法能够显著地提高产生UWB雷达LFM波形的质量和性能,证实提出的误差校正方法正确、有效和可行。

EBAPS闪烁噪声测试系统

电子轰击有源像素传感器(electron bombarded active pixel sensor,EBAPS)是新型的真空-固体混合型数字微光夜视器件。闪烁噪声是影响EBAPS分辨力和成像质量的关键因素,然而,目前EBAPS闪烁噪声的测试研究不足。为此,本文首先开展EBAPS闪烁噪声测试方法研究,使用连通域检测算法筛选高亮噪点区域,提出异常像素点自适应中值替代的离散系数测试方法,在此基础上研制了EBAPS闪烁噪声测试系统,采用离散系数和高亮噪点数量作为闪烁噪声的表征参数,驱动EBAPS将不同测试条件下采集到的图像数据传输至上位机进行噪声处理与分析,测试结果表明:合适的测试照度为1.27×10^(-3) lx,高亮噪点数量在-1000~-1300 V范围内数量较少,-1300~-1500 V时高亮噪点数量则明显提升。离散系数和连通域数量重复度均在3%以内,验证了测试系统的稳定性,为国产EBAPS闪烁噪声测试提供有效手段。

The Tricomi and Frankl Problems for Generalized Chaplygin Equations in Multiply Connected Domains

The present paper deals with Tricomi and Frankl problems for generalized Chaplygin equations in multiply connected domains. We first give the representation of solutions of the Tricomi problem for the equations, and then prove the uniqueness and existence of solutions for the problem by a new method, i.e. the complex functions in the elliptic domain and the hyperbolic complex functions in hyperbolic domain are used. Finally we discuss the Frankl problem for generalized Chaplygin equations in multiply connected domains.

Coefficient multipliers of H^p spaces over bounded symmetric domains in C

One way to give information about the Taylor coefficients of Hp functions is to describe the multipliers of Hp into various spaces. In the case of one complex variable, Duren and Shields described the multipliers of Hp into lq (0<p<1, p≤q≤∞). The Duren-Shields theorems to the case with the bounded symmetric domains in Cn are generalized. The results are sharp if q≥2. A sufficient condition of Hp into Hq is given for any p and q, 0<p<q<∞.

基于乘子法的地震波波速和介质密度的多参数稳健反演

地震波速和介质密度的多参数全波形反演能够充分利用地震数据的运动学和动力学信息,精确重构地下介质模型参数,在地下介质描述与岩性解释中扮演着重要角色。针对地震波多参数全波形反演对初始模型依赖程度高、不同参数之间存在串扰噪声及反演精度不高的缺陷,提出一种基于多尺度策略的多参数乘子法反演框架。将时间域多尺度策略与乘子法相结合,首先进行低频带反演,获取模型空间大尺度信息;随后采用乘子法更新迭代,并将低频带反演结果作为高频带初始模型进行逐频带反演,在每一个尺度下均采用乘子法更新迭代。简单透射模型及1994BP标准地质模型的实验表明:基于多尺度策略的乘子法反演算法具有较好的稳健性与适用性,即使初始模型较差时,仍能获得较好的反演结果,且在不降低地震波速反演精度的同时,提高密度的反演精度。

On the Multipliers of H^p Spaces on Bounded Symmetric Domains

Let Ω be a bounded symmetric domain in Cn which contains the origin, b its Silov boundary and Γ its holomorphic automorphism group. Let Γ0 be a subgroup of F with fixed point origin. There exists a unique Γ0-invariant measure σ on b such that σ（b）=1. We denote the unit ball in Cn by B and the unit disc in C by U.

H^p Multipliers on Bounded Symmetric Domains

The following results are obtained in this paper: (i) if and then is a multiplier of into then thereis a sequence with which is not a multiplier of Hp(B) intothen there is a sequence with which is not a muitiplier of HP(B) into Hq(B).

Convex hull theorem for multiply connected domains in the plane with an estimate of the quasiconformal constant

For any multiply connected domain Ω in ?2, let S be the boundary of the convex hull in H 3 of ?2Ω which faces Ω. Suppose in addition that there exists a lower bound l > 0 of the hyperbolic lengths of closed geodesics in Ω. Then there is always a K-quasiconformal mapping from S to Ω, which extends continuously to the identity on ?S = ?Ω, where K depends only on l. We also give a numerical estimate of K by using the parameter l.

不同大小粒子之间相互作用的直接数值模拟

应用改进的拉格朗日乘子/虚拟区域算法对不同大小的两个圆形粒子在二维方槽中的沉降过程和相互作用进行了直接数值模拟,并进行了实验验证· 结果表明不同大小的两个粒子在沉降过程中的相互作用可以描述为追尾、接触、旋转和分离4个过程,只有当两个粒子尺度差异很小时,才会重复进行DKT过程· 在两个粒子相互作用的过程中,小粒子的运动受到大粒子的影响更剧烈一些。

有限元/边界元法求解多连通域声辐射问题

本文用混合有限元 /边界元法求解浸没在无限流域中任意形状结构物的声辐射问题。求解多连通域声辐射问题时 ,采用有限元构建内流域和结构域 ,边界元构建外流域 ,应用流体结构域交界面法向速度连续性条件耦合声流域和结构间的相互作用。对球形结构的数值计算同其理论结果的比较表明其有效性。对环肋双层柱形结构分别对考虑和不考虑腔间进水做了计算 。

电磁散射的拉格朗日乘子区域分解算法

针对电磁散射问题,提出了一种基于广义变分原理的区域分解算法.将原求解区域划分为若干个不重叠的子区域,引入拉格朗日乘子法以满足相邻子区域之间场的连续性要求,并建立其修正泛函,使原问题转化为求解拉格朗日乘子.研究了子区域系数矩阵的可逆性.为了进一步提高效率,采用了重启的广义最小残量法为求解器.数值算例验证了本文方法的准确性和有效性.

混凝土中氯离子扩散分析的两相边界元模型

提出了一个两相混凝土的多连域边界元模型,用来研究混凝土中的氯离子扩散与分布规律。将混凝土看作由砂浆和粗骨料组成的两相非均匀材料,并假定氯离子扩散只发生在砂浆浆体中。建立了混凝土中氯离子扩散的多连域边界元模型,分析了粗骨料粒径、含量和排列方式对混凝土中氯离子扩散和分布规律的影响。通过与有限元模型的对比证明了提出的两相多连域边界元模型的合理性和优势,说明本研究模型可以用于混凝土中氯离子扩散的分析。研究结果表明,粗骨料的存在会形成阻滞作用,引发氯离子浓度场的局部梯度变化;粗骨料的含量对混凝土中氯离子扩散的阻滞作用影响明显。