无穷扇形区域调和边值问题的重叠型区域分解法

51．引言边界元方法在力学和科学工程计算中有着广泛的应用问．它特别适合求解无界区域上的问题［‘’，‘’1．边界元和有限元耦合［‘，＼以及作适当的人工边界处理后再在有界区域上应用有限元技术＊＼都是处理无界区域问题时常用的方法．另一方面，近年发展起来的区域分解法不仅为并行计算提供了有效手段＊’］，也为边界元方法在无界区域问题上的应用提供了新的途径．其中，无界区域上基于自然边界归化的重叠型和不重叠型区域分解算法＊’，“－‘’］，同时具备了边界元法和区域分解法的优点．它将无界区域n分解为一个很小的有界区域01…     

无穷凹角区域椭圆边值问题的重叠型区域分解算法

§1.引言许多科学和工程计算问题都可归结为无界区域上的偏微分方程边值问题,数值求解无界     

基于FEM／SBFEM的无穷域势流问题重叠型区域分解计算

提出了一种将有限元和比例边界有限元相结合求解无穷域势流问题的算法．用两条封闭曲线将求解域划分为存在重叠的有限和无限两个区域,在有限域和无限域上分别用有限元和比例边界有限元方法求解原问题,通过重叠区域交换数据迭代计算,直至收敛．分析了重叠区域面积的大小对计算收敛速度的影响,发现随着重叠区域面积的增大迭代次数减少,收敛速度加快．数值算例显示了算法的正确性和收敛性．本算法为求解无穷域势流问题提供了一个方法．     

基于重叠网格法的高速列车明线交会分析

研究了高速列车在明线交会时产生的瞬态压力波以及气动作用力将会对列车的运行安全产生不利影响.采用三维、非定常、可压缩流体控制方程和双方程湍流模型的数值方法,基于重叠网格法对时速300km高速列车明线交会的压力波进行研究.研究结果表明：重叠网格法能够解决高速列车明线交会的压力波变化问题,主区域网格与从属区域的动网格数据传输准确;高速列车相距70m,0.42s时列车进入交会,此时出现车头鼻尖处交会压力波“头波”,车头鼻尖处所受压力达到最大;0.95s列车车头行驶到通过列车的车尾处,两车纵向重合,出现“尾波”.     

《多水平区域分解法在气象计算中的应用》通过验收

我所周振中研究员承担的“多水平区域分解法在气象计算中的应用”课题，通过与省气象科研所的合作研究，已取得初步的研究成果，该水平法在大气污染数值计算中的结果与实际观测较符合，计算速度较快，可有效地节省计算机时。1996年11月22日，由湖南省科委科技事业产业处主持，通过了课题验收。《多水平区域分解法在气象计算中的应用》通过验收$湖南省计算所     

Stokes方程的一种预处理方法

本文研究了Stokes方程基于混合有限元离散的预处理方法.基于三角形剖分上速度场的连续P_2元以及压力场的P_0元,我们采用局部子区域逆矩阵建立了预处理子.通过分析预处理矩阵的特征值分布,我们证明了该预处理子大大改善原问题系数矩阵的条件数.本文给出了相应的数值结果.     

Matlab多项式与插值运算编程

数值计算的研究领域包括数值逼近、数值微分和数值积分、数值代数、最优化方法、常微分方程数值解法、积分方程数值解法、偏微分方程数值解法、计算几何、计算概率统计等.随着计算机的广泛应用和发展,许多计算领域的问题,如计算物理、计算力学、计算化学、计算经济学等都可归结为数值计算问题.通过详实的编程实例,展现Matlab在数值计算方面的丰富接口.     

空气动力学二維不定常問題的差分格式和带有脫体激波的繞流計算

引言本文描述一个二维不定常空气动力学问题的数值解法,该方法是在[1]内对一维计算所介绍的格式的直接发展。所提出的方法曾用于旋转体带有脱体激波定常绕流的计算。定常的压力、密度和速度分布的得出是把定常问题为作不定常问题来计算,     

PSO算法在含一阶导数变分问题中的应用

变分问题是一个研究泛函极值的经典数学问题,寻求变分问题的直接解法具有重要的理论和现实意义.鉴于PSO算法在极值问题中的广泛应用,利用分段Hermite插值.建立了求解含一阶导数的变分问题优化模型,构造出了适应度函数,从而使得PSO算法成功应用到变分问题的求解当中.数值实验结果表明了方法的可行性,同时也拓展了PSO算法的应用领域.     

基于CPU-MIC异构众核环境的行星流体动力学数值模拟

数值模拟是行星流体动力学研究的主要工具.本文介绍CPU-MIC异构众核平台的行星流体动力学数值模拟,计算并模拟地球外核的磁流体运动.本文在已有工作的基础上~([1-3]),添加了CPU-MIC异构众核环境的数值模拟支持.首先描述了CPU-MIC异构众核环境的上的数值模拟流程,然后给出了MIC上的分布式并行GMRES(m)众核解法器的实现算法.其次,实现了解法器的计算核心稀疏矩阵向量乘(SpMV)在MIC上的分布式并行算法,该SpMV实现了计算-通信重叠、数据传输-计算重叠.再次,为加速行星流体动力学方程收敛,给出了MIC上以SpMV为基本操作的分布式并行多项式预条件子.最后,提出了一些MIC众核平台的优化措施,如多线程、流存储和数据传输优化等.天河2号数值模拟表明相比CPU版的数值模拟,CPU-MIC异构众核环境下数值模拟在单MIC卡和64块MIC卡分别取得了6.93和6.0倍的加速比.     

二维Helmholtz方程外问题基于自然边界归化的重叠型区域分解算法

１．引 言 设是平面光滑闭曲线,是以为边界的外部区域,考虑二维Ｈｅｌｍｈｏｌｔｚ方程外Ｎｅｕｍａｎｎ问题并在无穷远处满足Ｓｏｍｍｅｒｆｅｌｄ辐射条件其中是区域的边界的外法线方向,即指向由包围的内部区域．κ在许多情况下（例如约化波动方程）是实数,在另一些情况下则是纯虚数．本文仅讨论κ为纯虚数的情况,且不失一般性,可设Ｉｍ（ｋ）＞０． 用某些数值方法求解线性抛物型方程或线性双曲型方程的初边值问题时,可能导致求解Ｈｅｌｍｈｏｌｔｚ方程的外问题．例如,用自然边界元法求解线性抛物型方程的初边值问题时就导致求…     

Stabilized continuous and discontinuous Galerkin techniques for Darcy flow

We design stabilized methods based on the variational multiscale decomposition of Darcy's problem. A model for the subscales is designed by using a heuristic Fourier analysis. This model involves a characteristic length scale, that can go from the element size to the diameter of the domain, leading to stabilized methods with different stability and convergence properties. These stabilized methods mimic different possible functional settings of the continuous problem. The optimal method depends on the velocity and pressure approximation order. They also involve a subgrid projector that can be either the identity (when applied to finite element residuals) or can have an image orthogonal to the finite element space. In particular, we have designed a new stabilized method that allows the use of piecewise constant pressures. We consider a general setting in which velocity and pressure can be approximated by either continuous or discontinuous approximations. All these methods have been analyzed, proving stability and convergence results. In some cases, duality arguments have been used to obtain error bounds in the L²-norm.     

弹性动力学问题的边界元区域分解算法

In this paper, the numerical implementation of boundary element methodswith overlapping domain decomposition method for solving the Navierequations of linear elastodynamics problems in Fourier transformed domain.The computer program is compiled with Fortran 77 and several numericalexamples are presented with the test on the relation of convergence ratewith the overlapping size     

WB法在多域声学分析中的应用

描述了振动声系统建模技术的基本概念.根据域分解的连续性条件,讨论了界面的压力和速度连续以及阻抗连续,应用加权余量法推导了两者的耦合模型.并用LMS/SYSNOISERev5.5进行了有限元数值模拟,计算结果与有限元结果符合得较好.通过比较两种连续性条件,发现前者更适合较小的计算模型而后者更适合较大的计算模型.最后对域分解提出了几个简单优化原则.     

Strategies of domain decomposition for the design of parallel algorithms

This is a framework of the domain decomposition method (DDM) for solving PDEs on parallel computers. Three types of DDM: DDM with overlapping, DDM without overlapping and DDM with fictitious components are discussed in a uniform framework.     

Pseudospectral matrix element methods for flow in complex geometry

A pseudospectral matrix element (PSME) method, which extended the global pseudospectral method to a multi-element scheme, has been applied to the solution of the incompressible, primitive variable, Navier-Stokes equations for complex geometries with rectilinear or curvilinear boundaries. For a simple complex geometry, a direct solution for pressure Poisson equation is feasible, while in a much more complex geometry the pressure solution is accomplished by a new implementation of domain decomposition approach. According to this approach, the computational domain can be divided into a number of overlapping subdomains where the grid points inside the overlapping area may or may not be located at the same place. Each subdomain can be mapped onto a square domain by an algebraic (or isoparametric) mapping, of simpler geometry with patched elements, in which the pressure solution is more easily obtained by an eigenfunction expansion technique for cartesian-type geometries or a direct solver for noncartesian-type geometries with rectilinear (or curvilinear) boundaries. With an iterative Schwarz alternating procedure (SAP) between subdomains, the complete solution is found. The novel feature of this approach are (i) the continuity equation is satisfied everywhere, in the interior (including the inter-element points) and on the boundary; (ii) reducing the global storage size to local (subdomain) storage locations for which parallel computation is easily implemented; (iii) producing the desired grid points without solving any grid-generating equations is easy; and (iv) consistent mass conservation holds at geometrical singular points despite their discontinuous slope (i.e., singular vorticity). Numerical examples of flow over a triangular and parabolic bump as well as flow in a bifurcation with a daughter branch entering the main channel at angles 45° and 90° are presented in this paper.     

基于双树复小波的色谱重叠峰分解方法研究

针对色谱分析中重叠峰的分解问题,提出一种基于双树复小波变换的色谱重叠峰分解方法。首先深入研究了双树复小波变换相较于离散小波变换的优越性;然后利用双树复小波变换分解与重构模拟色谱信号,计算分离度、峰位和峰面积,与离散小波变换的结果对比,并对噪声信号进行测试;最后利用双树复小波变换分解与重构实验所测得的色谱信号。实验结果表明,双树复小波分解色谱重叠峰比一般的实数小波准确,能够有效地分离重叠峰,分解后峰形平滑对称未发生畸变,峰位相对误差与峰面积相对误差较小,适合定性定量分析。     

An application of domain decomposition methods with non-conforming spectral element/Fourier expansions for the incompressible Navier–Stokes equations

An application of domain decomposition methods is presented for the incompressible Navier–Stokes equations. Non-conforming spectral element/Fourier expansions in the separate domains are employed, and a simple iterative algorithm is used, based on the Dirichlet/Neumann method at the domain interface. Thus, a new element in the present approach is that patching of mixed algebraic/trigonometric polynomial spaces is applied at the domain interface, whereas usually in domain decomposition methods finite-order polynomial spaces have been employed in the separate domains. By applying a coupled scheme for the velocity and pressure fields in each domain, a stable algorithm is obtained. New numerical results are presented on a 3-D model problem of flow in a channel, where both bounding surfaces have corrugations, but of different orientation. Smooth solutions across the domain interface are obtained. Steady flow and the onset of flow instability is simulated and discussed. The results demonstrate that spectral element/Fourier expansions, which have been previously used to study flows in geometries with one homogeneous dimension, may be employed to tackle flow problems in relatively more complex geometries. Furthermore, the results suggest that decomposition into domains with 3-D elements and domains with 2-D elements/Fourier expansions, or domains handled by spectral methods, may be an attractive possibility. The advantage is due to the orthogonality and decoupling of the Fourier modes, which leads to a computational load increasing only linearly with resolution. A related attractive feature is that a natural way for parallel implementation is offered.