An algebraically partitioned FETI method for parallel structural analysis: performance evaluation

This paper presents the algorithmic performance of an algebraically partitioned Finite Element Tearing and Interconnection (FETI) method presented in a companion paper. A simple structural assembly topology is employed to illustrate the implementation steps in a Matlab software environment. Numerical results indicate that the method is scalable, provided the iterative solution preconditioner employs the reduced interface Dirichlet preconditioner. A limited comparison of the present method with the differentially partitioned FETI method with corner modes is also offered. Based on this comparison and a reasonable extrapolation, we conclude the present algebraically partitioned FETI method possesses a similar iteration convergence property of the differentially partitioned FETI method with corner modes. © 1997 John Wiley & Sons, Ltd.     

An algebraically partitioned FETI method for parallel structural analysis: algorithm description

An algebraically partitioned FETI method for the solution of structural engineering problems on parallel computers is presented. The present algorithm consists of three attributes: an explicit generation of the orthogonal null-space matrix associated with the interface nodal forces, the floating subdomain rigid-body modes computed from the subdomain static equilibrium equation of the classical force method and the identification of redundant interface force constraint operator that emanates when the interface force computations are localized. Comparisons of the present method with the previously developed differentially partitioned FETI method are offered in terms of the saddle-point formulations at the end of the paper. A companion paper reports implementation details and numerical performance of the proposed algorithm. © 1997 John Wiley & Sons, Ltd.     

板料成形数值模拟有限元求解算法

正确选用有限元求解算法是成形模拟成功的关键技术之一。阐述了板料成形数值模拟的4种有限元求解算法,即静力隐式算法、动力显式算法、静力显式算法和一步成形法,并对这4种算法进行了论述和比较,介绍了其在实际中的应用,探讨了在板料成形模拟中如何选择有限元算法进行可靠、高效的有限元分析。     

基于ALE的大型输水隧道地震动响应并行数值分析

提出基于ALE （Arbitrary Lagrangian-Eulerian）方法的输水隧道地震动响应并行数值分析方法,采用ALE方法模拟内水和隧道的相互作用,提出基于耦合负载均衡的并行计算方法加快求解速度,采用显式中心差分法完成方程求解。针对某大型输水隧道,建立内水-隧道-土体耦合的全三维数值模型,分析其在非一致地震激励下的动力响应。模型中考虑材料非线性、接触及流固耦合非线性等实际情况,并采用PML （Perfectly Matched Layer）建立人工边界模拟无限区域。在曙光5000A超级计算机上,利用所提方法,完成该大规模非线性问题的求解。通过与附加质量法对比,验证ALE方法模拟内水-隧道耦合的可行性;分析输水隧道地震激励下的应力及变形情况;讨论内水量及变形缝对隧道动力响应的影响;分析并行计算效率。结果表明：环向应力较大值出现在靠近工作井的截面,隧道结构满足强度要求;隧道截面变形量处于安全范围内;满水隧道较空隧道承受更大应力;变形缝可以降低隧道的动力响应;所提并行计算方法可以获得较好的并行效率。     

抛物方程的一类区域分解迎风差分算法

本文给出了一阶迎风差分、内边界二阶迎风差分和二阶迎风差分三种格式的算法和误差估计。为了减弱稳定性条件限制,先在内边界点上采用小时间步长和大的空间步长进行多层计算,再在内点用隐格式并行计算。这些算法结合了迎风和区域分解的优点,计算格式简单,易于编程实现。     

一般抛物方程的区域分裂差分方法

对稳定性有影响的一阶项采用中心差分格式,内边界点和各子区域分别对应显隐格式。在一定的稳定性条件下,由最大值原理得出最优收敛结果。最后用数值算例验证方法的实用性。     

An effective data parallel self-starting explicit methodology for computational structural dynamics on the connection machine CM-5

This paper discusses the implementation aspects and our experiences towards a data parallel explicit self-starting finite element transient methodology with emphasis on the Connection Machine (CM-5) for linear and non-linear computational structural dynamic applications involving structured and unstructured grids. The parallel implementation criteria that influence the efficiency of an algorithm include the amount of communication, communication routing, and load balancing. To provide simplicity, high level of accuracy, and to retain the generality of the finite element implementation for both linear and non-linear transient explicit problems on a data parallel computer which permit optimum amount of communications, we implemented the present self-starting dynamic formulations (in comparison to the traditional approaches) based on nodal displacements, nodal velocities, and elemental stresses on the CM-5. Data parallel language CMFortran is employed with virtual processor constructs and with:SERIAL and:PARALLEL layout directives for arrays. The communications via the present approach involve only one gather operation (extraction of element nodal displacements or velocities from global displacement vector) and one scatter operation (dispersion of element forces onto global force vector) for each time step. These gather and scatter operations are implemented using the Connection Machine Scientific Software Library communication primitives for both structured and unstructured finite element meshes. The implementation aspects of the present self-starting formulations for linear and elastoplastic applications on serial and data parallel machines are discussed. Numerical test models for linear and non-linear one-dimensional applications and a two-dimensional unstructured finite element mesh are then illustrated and their performance studies are discussed.     

有限元并行计算中网格自动区域划分的研究

本文针对集群系统下大规模并行有限元分析,设计了简单实用的网格自动区域划分算法,以使并行计算时减少由于负载不均衡所引起的效率下降,并应用于“汽车碰撞模拟”项目中的车架模型的分割。重点讨论并改进了贪婪算法和ANP算法,并比较了两种算法各自的特点及其适用性。通过数值算例证明,对于不同类型的有限元网格都得到了满意的结果,本文的算法具有广泛的适用性。且对该算法稍加改进,则可应用于各类动态并行计算问题所提出的动态负载均衡要求。     

冲击-接触问题有限元仿真的并行计算

冲击．接触问题广泛存在于汽车碰撞等的模拟计算中。简单介绍了求解该类问题的显式有限元方法，对显式有限元方法的并行性进行了讨论。根据显式有限元和冲击一接触问题的计算特点，设计并实现了接触均衡的分区算法。算例计算结果表明：该并行算法具有较好的加速比和并行效率。     

Comparative efficiencies of three parallel algorithms for nonlinear implicit transient dynamic analysis

The work reported in this paper is motivated by the need to develop portable parallel processing algorithms and codes which can run on a variety of hardware platforms without any modifications. The prime aim of the research work reported here is to test the portability of the parallel algorithms and also to study and understand the comparative efficiencies of three parallel algorithms developed for implicit time integration technique. The standard message passing interface (MPI) is used to develop parallel algorithms for computing nonlinear dynamic response of large structures employing implicit time-marching scheme. The parallel algorithms presented in this paper are developed under the broad framework of non-overlapped domain decomposition technique. Numerical studies indicate that the parallel algorithm devised employing the conventional form of Newmark time integration algorithm is faster than the predictor-corrector form. It is also accurate and highly adaptive to fine grain computations. The group implicit algorithm is found to be extremely superior in performance when compared to the other two parallel algorithms. This algorithm is better suited for large size problems on coarse grain environment as the resulting submeshes will obviously be large and thus permit larger time steps without losing accuracy.     

近场数值波动分析中地震波输入的一种简化方法

在显式有限元方法结合黏弹性人工边界的时域波动方法的基础上,建立了地震波垂直输入时的一种简化输入方法。将近场有限元模型沿高度方向进行分层,将地震动的入射运动转化为作用于人工边界底面及分层后每层侧面上的均布力,以实现地震动的输入。与以等效节点力的方式实现的地震动输入相比,施加均布力的方式简化了地震波输入的前处理工作,且又能保证与等效节点力方式相同的精度。自由场数值算例表明：当本文方法中的分层高度与波动有限元网格离散要求的最大尺寸相等时,本文方法与等效节点力方法具有相同的精度;当局部区域按网格离散要求的最大尺寸进行分层而在其它区域放大分层高度时,局部区域上的近场波动响应仍可保证具有相当高的精度。另外,某隧道结构地震响应算例的计算结果同样说明了本文方法的有效性。