Parallel computing for finite element structural analysis using conjugategradient method based on domain decomposition

Parallel finite element method using domain decomposition technique is adapted to a distributed parallel environment of workstation cluster. The algorithm is presented for parallelization of the preconditioned conjugate gradient method based on domain decomposition. Using the developed code, a dam structural analysis problem is solved on workstation cluster and results are given. The parallel performance is analyzed.

Parallel finite element modeling of earthquake ground response and liquefaction

Parallel computing is a promising approach to alleviate the computational demand in conducting large-scale finite element analyses.This paper presents a numerical modeling approach for earthquake ground response and liquefaction using the parallel nonlinear finite element program,ParCYCLIC,designed for distributed-memory message-passing parallel computer systems.In ParCYCLIC,finite elements are employed within an incremental plasticity,coupled solid-fluid formulation,A constitutive model calibrated by physical tests represents the salient characteristics of sand liquefaction and associated accumulation of shear deformations.Key elements of the computational strategy employed in ParCYCLIC include the development of a parallel sparse direct solver,the deployment of an automatic domain decomposer,and the use of the Multilevel Nested Dissection algorithm for ordering of the finite element nodes.Simulation results of centrifuge test models using ParCYCLIC are presented.Performance results from grid models and geotechnical simulations show that ParCYCLIC is efficiently scalable to a large number of processors.

A parallel two-level finite element method for the Navier-Stokes equations

Based on domain decomposition, a parallel two-level finite element method for the stationary Navier-Stokes equations is proposed and analyzed. The basic idea of the method is first to solve the Navier-Stokes equations on a coarse grid, then to solve the resulted residual equations in parallel on a fine grid. This method has low communication complexity. It can be implemented easily. By local a priori error estimate for finite element discretizations, error bounds of the approximate solution are derived. Numerical results are also given to illustrate the high efficiency of the method.

Theory and Application of Characteristic Finite Element Domain Decomposition Procedures for Coupled System of Dynamics of Fluids in Porous Media

For a coupled system of multiplayer dynamics of fluids in porous media, the characteristic finite element domain decomposition procedures applicable to parallel arithmetic are put forward. Techniques such as calculus of variations, domain decomposition, characteristic method, negative norm estimate, energy method and the theory of prior estimates are adopted. Optimal order estimates in L^2 norm are derived for the error in the approximate solution.

THE DOMAIN DECOMPOSITION TECHNIQUES FOR THE FINITE ELEMENT PROBABILITY COMPUTATIONAL METHODS

In this paper, we shall study the domain decomposition techniques for the finite element probability computational methods. These techniques provide a theoretical basis for parallel probability computational methods.

Novel Finite Difference Discretization of Interface Boundary Conditions for Stablized Explicit-Implicit Domain Decomposition Methods

Stabilized explicit-implicit domain decomposition is a group of methods for solving time-dependent partial difference equations of the parabolic type on parallel computers. They are efficient, stable, and highly parallel, but suffer from a restriction that the interface boundaries must not intersect inside the domain. Various techniques have been proposed to handle this restriction. In this paper, we present finite difference schemes for discretizing the equation spatially, which is of high simplicity, easy to implement, attains second-order spatial accuracy, and allows interface boundaries to intersect inside the domain.

High performance parallel computing of large eddy simulation of the flow in a curved duct with square cross section

Large eddy simulation(LES) cooperated with a high performance parallel computing method is applied to simulate the flow in a curved duct with square cross section in the paper. The method consists of parallel domain decomposition of grids, creation of virtual diagonal bordered matrix, assembling of boundary matrix, parallel LDL^T decomposition, parallel solving of Poisson Equation, parallel estimation of convergence and so on. The parallel computing method can solve the problems that are difficult to solve using traditional serial computing. Furthermore, existing microcomputers can be fully used to resolve some large-scale problems of complex turbulent flow.

Eddy Current Analyses by Domain Decomposition Method Using Double-Double Precision

A matrix equation solved in an eddy current analysis,??-??method based on a domain decomposition method becomes a complex symmetric system.In general,iterative method is used as the solver.Convergence of iterative method in an interface problem is improved by increasing an accuracy of a solution of an iterative method of a subdomain problem.However,it is difficult to improve the convergence by using a small convergence criterion in the subdomain problem.Therefore,authors propose a method to introduce double-double precision into the interface problem and the subdomain problem.This proposed method improves the convergence of the interface problem.In this paper,first,we describe proposed method.Second,we confirm validity of the method by using Team Workshop Problem 7,standard model for eddy current analysis.Finally,we show effectiveness of the method from two numerical results.

A PARALLEL ITERATIVE DOMAIN DECOMPOSITION ALGORITHM FOR ELLIPTIC PROBLEMS

An iterative nonoverlapping domain decomposition procedure is proposed and analyzed for linear elliptic problems. At the interface of two subdomains, one subdomain problem requires that Dirichlet data be passed to it from the previous iteration level, while the other subdomain problem requires that Neumann data be passed to it. This procedure is suitable for parallel processing. A convergence analysis is established. Standard and mixed finite element methods are employed to give discrete versions of this domain decomposition algorithm. Numerical experiments arc conducted to show the effectiveness of the method.

Simulation and computational heat transfer in the human eye with Dirichlet–Neumann domain decomposition approximation

In this paper,a bioheat model of temperature distribution in the human eye is studied,the mathematical formulation of this model is described using adequate mathematical tools.The existence and the uniqueness of the solution of this problem is proven and four algorithms based on finite element method approximation and domain decomposition methods are presented in details.The validation of all algorithm is done using a numerical application for an example where the analytical solution is known.The properties and parameters reported in the open literature for the human eye are used to approximate numerically the temperature for bioheat model by finite element approximation and nonoverlapping domain decomposition method.The obtained results that are verified using the experimental results recorded in the literature revealed a better accuracy by the use of algorithm proposed.

A Parallel Finite Element Algorithm for the Unsteady Oseen Equations

Based on fully overlapping domain decomposition,a parallel finite element algorithm for the unsteady Oseen equations is proposed and analyzed.In this algorithm,each processor independently computes a finite element approximate solution in its own subdomain by using a locally refined multiscale mesh at each time step,where conforming finite element pairs are used for the spatial discretizations and backward Euler scheme is used for the temporal discretizations,respectively.Each subproblem is defined in the entire domain with vast majority of the degrees of freedom associated with the particular subdomain that it is responsible for and hence can be solved in parallel with other subproblems using an existing sequential solver without extensive recoding.The algorithm is easy to implement and has low communication cost.Error bounds of the parallel finite element approximate solutions are estimated.Numerical experiments are also given to demonstrate the effectiveness of the algorithm.

A New Hybrid Hierarchical Parallel Algorithm to Enhance the Performance of Large-Scale Structural Analysis Based on Heterogeneous Multicore Clusters

Heterogeneous multicore clusters are becoming more popular for high-performance computing due to their great computing power and cost-to-performance effectiveness nowadays.Nevertheless,parallel efficiency degradation is still a problem in large-scale structural analysis based on heterogeneousmulticore clusters.To solve it,a hybrid hierarchical parallel algorithm(HHPA)is proposed on the basis of the conventional domain decomposition algorithm(CDDA)and the parallel sparse solver.In this new algorithm,a three-layer parallelization of the computational procedure is introduced to enable the separation of the communication of inter-nodes,heterogeneous-core-groups(HCGs)and inside-heterogeneous-core-groups through mapping computing tasks to various hardware layers.This approach can not only achieve load balancing at different layers efficiently but can also improve the communication rate significantly through hierarchical communication.Additionally,the proposed hybrid parallel approach in this article can reduce the interface equation size and further reduce the solution time,which can make up for the shortcoming of growing communication overheads with the increase of interface equation size when employing CDDA.Moreover,the distributed sparse storage of a large amount of data is introduced to improve memory access.By solving benchmark instances on the Shenwei-Taihuzhiguang supercomputer,the results show that the proposed method can obtain higher speedup and parallel efficiency compared with CDDA and more superior extensibility of parallel partition compared with the two-level parallel computing algorithm(TPCA).

PARALLEL COMPUTATION AND DOMAIN DECOMPOSITION FOR A CLASS OF HYPERBOLIC PROBLEMS

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高功率微波作用下三维结构中多物理场耦合过程仿真方法研究综述

电子系统暴露在高功率微波中,产生的多物理耦合效应会引发其性能降低甚至损毁。为指导其电磁防护设计,需要研究大规模电(磁)-热-应力耦合并行仿真方法。通过集成高性能并行计算框架和区域分解方法(domain decomposition method,DDM),可以实现超大规模复杂结构的高效数值模拟。在无源结构的电-热-应力耦合数值模拟中,每个时间步都需要反复求解电流连续性方程、热传导方程和热应力方程,场间通过焦耳热和温变材料参数实现耦合,当达到稳态后,进入下一个时间步;在射频无源结构的电磁-热-应力耦合过程数值模拟中,每个时间步内分别求解电磁场和热场,并通过耗散功率和温变材料参数实现场间耦合,当达到稳态后,根据温升计算热应力,然后进入下一个时间步。本文回顾了电(磁)-热-应力大规模并行仿真的实现方法,并列举了国内外科研团队在键合线阵列、系统级封装、微波滤波器等多种复杂结构的多物理场模拟方面的标志性成果。

面向SW26010间断有限元算法的多级并行计算

间断有限元算法(Discontinuous Galerkin Finite Element Method,DGM)是一种高精度的数值求解算法,针对电磁工程应用中DGM并行计算效率低、计算量较大的问题,提出了基于SW26010平台的并行DGM算法。通过区域分解、数据结构重构、热点函数从核并行计算、计算与通信重叠及从核缓冲优化技术完成了DGM算法的并行优化。实现结果表明,与基于MPI进程级的DGM并行算法相比,可以获得46.8的平均加速比。

汽车碰撞有限元仿真的并行计算及其性能研究

并行计算是提高汽车碰撞有限元仿真的计算速度和求解能力的有效途径。文章简要介绍了汽车碰撞有限元仿真并行计算的区域分解方法,给出了处理接触时的并行计算流程,分析了并行求解过程以及主要时间开销。在此基础上,研究了两种硬件体系结构和不同处理器数目对计算效率的影响。最后研究了不同的区域分解策略对整车碰撞计算效率的影响。研究结果对最终用户选择合适的硬件平台和计算软件具有指导意义。

弹性波传播数值模拟的区域分裂法

本文针对弹性波波场传播的数学模型 ,提出了一种基于有限元和有限差分耦合的区域分裂方法 .它有灵活的网格剖分 ,克服了单纯用差分方法对区域的依赖性 ,可以适用于曲边地表 ;达到同样精度所需的计算量比有限元方法小 ;并易于实现并行计算 .

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-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。

并行有限元计算中的接触算法

针对动态接触问题的有限元并行计算,提出了一种新的接触算法．新算法引入局部拉氏乘子技术来计算接触力．由于同时考虑了无穿透的接触约束条件和相邻接触对的相互影响,较之广泛使用的罚参数法,新算法使接触约束条件和系统平衡方程得到更充分的满足．虽然为提高接触计算精度而在局部采用了迭代技术,但算法仍然具有较高的效率,且与显式时间积分方案完全相容．此外,通过构造专门的区域分解方案,实现了将现有为串行程序开发的搜索算法平滑移植到并行环境的目标．数值算例表明,所提出的接触算法具有很好的并行性,在保证了接触问题并行计算精度的同时,取得了满意的并行效率．

并行求解含有电位悬浮导体的静电场数值问题

并行计算是电磁场数值模拟的主要工具,但是对于含有悬浮电位导体的静电场问题的并行模拟却很少提及。该文提供了一种针对这类问题的区域分解方法,并利用强加齐次边界条件法对有限元矩阵进行处理,进而利用并行机群系统求解含有多个电位悬浮导体的计算模型。通过对含有3个悬浮电位导体的平行板电容器模型和330 kV架空输电线路的玻璃绝缘子串场计算模型的并行模拟,验证了该方法在二维和三维静电场问题中的有效性。该文提出的方法能够很好的解决因悬浮导体存在而带来的并行处理中的模型分区困难,并且可以很好的并行求解多导体问题,对该类问题的并行计算提供了可能。