General and efficient parallel approach of finite element-boundary integral-multilevel fast multipole algorithm

A general and efficient parallel approach is proposed for the first time to parallelize the hybrid finiteelement-boundary-integral-multi-level fast multipole algorithm （FE-BI-MLFMA）. Among many algorithms of FE-BI-MLFMA, the decomposition algorithm （DA） is chosen as a basis for the parallelization of FE-BI-MLFMA because of its distinct numerical characteristics suitable for parallelization. On the basis of the DA, the parallelization of FE-BI-MLFMA is carried out by employing the parallelized multi-frontal method for the matrix from the finiteelement method and the parallelized MLFMA for the matrix from the boundary integral method respectively. The programming and numerical experiments of the proposed parallel approach are carried out in the high perfor- mance computing platform CEMS-Liuhui. Numerical experiments demonstrate that FE-BI-MLFMA is efficiently parallelized and its computational capacity is greatly improved without losing accuracy, efficiency, and generality.

A New Iterative Method for Multi-Moving Boundary Problems Based Boundary Integral Method

The present paper deals with very important practical problems of wide range of applications. The main target of the present paper is to track all moving boundaries that appear throughout the whole process when dealing with multi-moving boundary problems continuously with time up to the end of the process with high accuracy and minimum number of iterations. A new numerical iterative scheme based the boundary integral equation method is developed to track the moving boundaries as well as compute all unknowns in the problem. Three practical applications, one for vaporization and two for ablation were solved and their results were compared with finite element, heat balance integral and the source and sink results and a good agreement were obtained.

Numerical Discrete-Domain Integral Formulations for Generalized Burger-Fisher Equation

In this study we use a boundary integral element-based numerical technique to solve the generalized Burger-Fisher equation. The essential feature of this method is the fundamental integral representation of the solution inside the problem domain by means of both the boundary and domain values. The occurrences of domain integrals within the problem arising from nonlinearity as well as the temporal derivative are not avoided or transferred to the boundary. However, unlike the classical boundary element approach, they are resolved within a finite-element-type discrete domain. The utility and correctness of this formulation are proved by comparing the results obtained herein with closed form solutions.

一种基于FE-BI的飞机进气道RCS的有效计算方法

针对飞机进气道RCS的计算,提出了一种基于有限元—边界积分(FE-BI)法的有效计算方法。该方法利用FE-BI法计算进气道散射时矩阵元素及激励向量的特点,基于广义高斯消去法,将进气道沿纵深方向划分为若干层,逐层推进计算。计算所需最大内存仅与进气道的横截面尺寸相关而与进气道的深度无关,计算时间与进气道的长度成正比。数值计算结果表明:在满足剖分及分层要求的前提下,该方法是一种精确的计算方法,且可以使计算效率明显提高。

FE-BI分析等离子体覆盖导体方柱的宽带RCS

文章将有限元-边界积分法(FE-BI)与渐进波形估计技术(AWE)相结合应用到宽带电磁散射特性分析中。首先应用该理论计算导体方柱的宽带雷达散射界面(RCS)并与FE-BI逐点计算进行了比较,接着计算了导体表面覆盖不同密度、不同碰撞频率的等离子体的宽带RCS。计算结果表明,FE-BI结合AWE技术比有限元逐点计算省时,且等离子体的使用能有效地减小雷达散射截面。

高阶FE-BI方法及一种新型的预条件技术

将基于六面体网格的高阶矢量基函数(higher order vector basisfunction)引入到矢量有限元-边界积分(FE-BI)混合方法中,用于建模带有深腔和狭长缝隙结构三维目标的电磁散射特性;提出了一种新型的预条件技术,用于加速FE-BI系统的迭代求解;给出了结合该预条件技术的GMRES方法求解腔体电磁散射的算例;数值结果证明了高阶FE-BI方法相对于低阶FE-BI方法的优势以及新型预条件技术的有效性。

基于多区多求解器的金属-介质复合目标电磁散射特性分析

在导弹类金属-介质复合目标电磁散射特性求解过程中,采用常规迭代求解方法存在难以收敛以及内迭代边界积分区域重复求解的问题。针对该问题,在传统有限元边界积分区域分解法(finite element boundary integral domain decomposition method,FE-BI-DDM)的基础上,采用了更为灵活的多区多求解器的方法(multi domain multi solver method,MDMSM)。该方法对导弹类金属-介质复合目标中难以收敛的金属区域,使用快速直接求逆的方法求解,由于可以使用独立的网格模型进行电磁建模,避免了内迭代部分的模型重复建立过程,从而大幅减少了整体模型求解时间。实验结果表明:所提方法可以在相同计算精度的条件下,以不过多增加内存空间为前提,大幅缩短了导弹类目标的金属-介质复合模型的电磁求解时间。该方法为开展导弹类目标特性分析提供了一条可行的技术途径。

基于FE-BI的介质粗糙面上方涂覆目标电磁散射特性研究

采用有限元-边界积分(finite element boundary integral,FE-BI)方法研究了介质粗糙面上方涂覆目标的复合电磁散射特性,推导了一维介质粗糙面上方二维涂覆目标电磁散射的FE-BI公式.在仿真中,采用功能强大的有限元方法模拟涂覆目标内部场,对于涂覆目标与粗糙面之间的多重耦合作用则通过边界积分方程方法进行考虑.结合Monte-Carlo方法,数值计算了介质高斯粗糙面上方涂覆圆柱目标的电磁散射,分析了涂层材料介电常数、粗糙面粗糙度以及介质粗糙面介电常数变化对复合模型双站散射系数的影响.数值结果表明,相比于传统矩量法(method of moment,MoM),本文方法虽然在处理理想导体模型时效率略低,但可以处理MoM难以处理的复杂媒质电磁散射问题,且计算精度较高.

Analysis of multiple interfacial cracks in three-dimensional bimaterials using hypersingular integro-differential equation method

By using the concept of finite-part integral, a set of hypersingular integro-differential equations for multiple interracial cracks in a three-dimensional infinite bimaterial subjected to arbitrary loads is derived. In the numerical analysis, unknown displacement discontinuities are approximated with the products of the fundamental density functions and power series. The fundamental functions are chosen to express a two-dimensional interface crack rigorously. As illustrative examples, the stress intensity factors for two rectangular interface cracks are calculated for various spacing, crack shape and elastic constants. It is shown that the stress intensity factors decrease with the crack spacing.

基于sinh-sigmoidal组合式变换的薄型结构边界元分析方法

采用边界元法(BEM)分析薄型结构弹性静力学问题时,存在近奇异积分计算难题,为此,提出了一种非线性sinh-sigmoidal组合式变换方法,并将其集成到边界元程序,以消除积分在径向和角度方向的近奇异性。首先,针对积分单元运用了自适应分块技术,采用迭代sinh变换消除了积分核函数在径向上的近奇异性;然后,考虑sigmoidal变换核函数能向积分区间两端大量聚集高斯积分点的特点,其可用于消除角度方向上的近奇异性;最后,将sinh-sigmoidal组合变换方法集成到边界元程序,并以螺栓连接薄型垫片为分析对象,分别运用有限元法(FEM)与边界元法(BEM)对其弹性静力学问题进行了数值分析,验证了该方法的有效性。分析结果表明:在理想工况下,计算垫片各向面力的平均误差时,该方法具有良好的收敛性;在实际工况下,分析预紧力作用下薄型垫片的表面节点位移变化情况时,基于有限元法和边界元法的计算误差均小于1%,但边界元法的运算规模和计算效率优势明显。研究结果表明:sinh-sigmoidal组合变换法可有效消除积分在径向和角度方向的近奇异性;集成该方法的边界元程序在分析薄型垫片的弹性静力学问题时,具备相对较高的计算效率和计算精度。

Roll Flattening Analytical Model in Flat Rolling by Boundary Integral Equation Method

In order to improve rolled strip quality, precise plate shape control theory should be established. Roll flat- tening theory is an important part of the plate shape theory. To improve the accuracy of roll flattening calculation based on semi infinite body model, especially near the two roll barrel edges, a new and more accurate roll flattening model is proposed. Based on boundary integral equation method, an analytical model for solving a finite length semi infinite body is established. The lateral surface displacement field of the finite length semi-infinite body is simulated by finite element method （FEM） and lateral surface displacement decay functions are established. Based on the boundary integral equation method, the numerical solution of the finite length semi-infinite body under the distribu ted force is obtained and an accurate roll flattening model is established. Different from the traditional semi-infinite body model, the matrix form of the new roll flattening model is established through the mathematical derivation. The result from the new model is more consistent with that by FEM especially near the edges.

FINITE ELEMENT NONLINEAR GALERKIN COUPLINGMETHOD FOR THE EXTERIOR STEADY NAVIER-STOKESPROBLEM

In this paper we represent a new numerical method for solving the steady Navier-Stokes equations in three dimensional unbounded domain. The method consists in coupling the boundary integral and the finite element nonlinear Galerkin methods. An artificial smooth boundary is introduced seperating an interior inhomogeneous region from an exterior one. The Navier-Stokes equations in the exterior region are approximated by the Oseen equations and the approximate solution is represented by an integral equation over the artificial boundary. Moreover, a finite element nonlinear Galerkin method is used to approximate the resulting variational problem. Finally, the existence and error estimates are derived.

三维热权函数法和多虚拟裂纹扩展技术

热权函数法直接利用温度场与热权函数的乘积的积分来求应力强度因子(SIF)的过渡过程,它可以免除对每一时刻进行热弹性力学有限元或边界元应力分析,计算效率大大提高。本文给出了三维热权函数法的基本方程,并提出了求解三维热权函数法基本方程的多虚拟裂纹扩展法(MVCE法)。在MVCE法中,可以引入无穷多个虚拟裂纹扩展模式;虚拟裂纹扩展模式与应力强度因子的插值直接相联系,所得到的方程组的系数矩阵是一个三对角矩阵,具有良好的计算性能。它对于裂纹前缘SIF分布急剧变化的情况,有良好的数值模拟能力。实例计算表明,MVCE法具有极高的计算效率,并具有很高的计算精度。

基于边界积分方程法的六辊轧机辊系变形分析

精确的板形控制理论对提高带钢质量具有重要意义,而辊间压扁理论是板形控制理论的重要组成部分。针对半无限体模型在计算辊间压扁时的误差问题,给出一种计算辊间压扁的新模型。应用有限元法模拟有限长度半无限体两侧面的位移场,建立侧面的位移衰减函数。基于边界积分方程法,得到有限长度半无限体在表面分布力作用下的数值解,从而建立求解有限长度半无限体的解析模型,并用有限元法验证该模型的准确性。基于该压扁模型建立新型六辊轧机辊系变形模型,所得结果与有限元法,半无限体模型和费普尔公式进行对比,发现新模型所得结果与有限元法更加接近。考虑板宽和窜辊量的影响,利用新模型与半无限体模型、费普尔公式进行对比计算,发现新模型所得辊间压力和压扁优于其他两模型,特别是在轧辊边部区域比其他两模型更符合实际。

航空磁探中潜艇磁场建模方法分析

为提高航空磁探中潜艇磁场模型精度,分析现有潜艇磁场建模方法,对边界积分法、有限元法、积分方程法、磁体模拟法等主要潜艇磁场建模方法的基本原理和推导过程进行分析。通过数值分析比较各方法的建模精度,最后归纳潜艇低空磁场建模方法的基本要点。

电大尺寸开口腔体电磁散射特性的DDM/FEM-BIE混合法分析

该文将超松弛重叠及非重叠区域分裂法(DDM)与矢量有限元方法(EB-FEM)、边界积分方程(BIE)法相结合对三维电大尺寸开口腔体的电磁(EM)散射特性进行分析。通过DDM将原腔体分解成若干子腔体,在各子腔体内应用EB-FEM进行分析。腔体间应用矢量传输条件进行耦合,最终腔体内电场分布通过迭代获得。在原腔体口面,运用积分方程进行描述.在分析过程中,将传输条件和BIE统一成第三类边界条件形式。最后给出的数值结果验证了DDM/FEM-BIE混合方法分析腔体的电磁散射特性的精确性及高效性。

加筋板结构声传输研究

采用有限元法和Rayleigh积分建立了空气中嵌在无限大刚性障板上加筋板结构在简谐平面声波斜入射情况下的声传输计算模型 ,并研究分析了加筋板结构的板厚、肋骨惯性矩和间距、边界条件、板材和平面声波入射角度等对结构传声损失的影响以及平面声波入射角度与隔声低谷的关系 ,得到了一些有意义的结论 ,从而为揭示加筋板结构声传输特性 ,改善结构的隔声性能提供了一定的依据。

有限元法和边界元法的多重校正

本文对两点边值问题和具有光滑核积分方程的有限元解给出了多重校正公式.从理论上讲,这些问题可以作任意次的校正。

有限元-边界法在光电目标散射计算中的应用

为了解决三维目标电磁散射计算中准确性与有效性的矛盾,建立了有限元-边界法的计算模型,对三维腔体目标的电磁散射计算方法进行了研究。首先,分析了针对三维电磁腔体目标的电磁散射计算边界积分方法,引入了矢量格林函数,利用麦克斯韦方程得到电磁场形式与三维腔体形式的关系,建立了三维开口腔体边界模型;然后,结合光电目标曲面建模方法及高阶基函数的方法,建立了三维光电目标的有限元泛函,完成了有限元-边界法在三维腔体目标电磁散射计算中的应用;最后,进行了实例验证。分析显示,当三维腔体内部为空或为各向异性物质时,角度吻合非常理想,与传统模式匹配法所得结果的吻合度达90%以上。结果表明,采用本方法对三维腔体目标进行电磁散射计算,准确度、效率均有所提高。

大型火电厂主厂房带边框柱剪力墙有限元分析

通过对某大型火电厂主厂房纵向框架-剪力墙模型结构进行的伪静力试验,研究了此类工业厂房中纵向带边框柱剪力墙结构的抗震性能问题,并采用宏观有限元方法将这种剪力墙模型结构简化为一个多垂直杆模型,通过将竖向弹簧杆元放置在Gauss积分点处,不仅可以模拟出剪力墙结构的滞回曲线、骨架曲线以及延性等性能,还明显提高了计算效率。另外,比较计算结果与试验数据可以看出:两者在滞回曲线、延性等方面基本吻合,验证了该方法的准确性与有效性,可为推广使用提供参考。