Distributed finite element computations using object-oriented techniques

An object-oriented parallel finite element framework has been developed to facilitate rapid prototyping of a wide variety of parallel finite element computations. Parallel computing and object-oriented technologies are integrated to achieve efficiency in both computation and software development. The paper presents various reusable and extensible components that constitute the parallel finite element architecture.     

A parallel preconditioned conjugate gradient solution method for finite element problems with coarse–fine mesh formulation

The object of this paper is a parallel preconditioned conjugate gradient iterative solver for finite element problems with coarse-mesh/fine-mesh formulation. An efficient preconditioner is easily derived from the multigrid stiffness matrix. The method has been implemented, for the sake of comparison, both on a IBM-RISC590 and on a Quadrics-QH1, a massive parallel SIMD machine with 128 processors. Examples of solutions of simple linear elastic problems on rectangular grids are presented and convergence and parallel performance are discussed.     

Tuning the Schur complement computations for finite element partitions

The domain decomposition method (DDM) is an efficient algorithmic tool for the parallelization of finite element computer codes. A variant of the DDM with direct solution algorithm is based on computation of Schur complement matrices for finite element partitions. This paper describes a simple technique that considerably improves execution rate of computationally intensive routines of the Schur complement computations. The technique uses ‘block of columns’ matrix operations and loop unrolling to reduce load instructions from cache memory and to increase instruction-level parallelism. For superscalar RISC processors, experimental results show that it is possible to improve performance of the DDM solution procedure by several times.     

A parallel finite element procedure for contact-impact problems

An efficient parallel finite element procedure for contact-impact problems is presented within the framework of explicit finite element analysis with thepenalty method. The procedure concerned includes a parallel Belytschko-Lin-Tsay shell element generation algorithm and a parallel contact-impact algorithm based on the master-slave slideline algorithm. An element-wise domain decomposition strategy and a communication minimization strategy are featured to achieve almost perfect load balancing among processors and to show scalability of the parallel performance. Throughout this work, a prototype code, named GT-PARADYN, is developed on the IBM SP2 to implement the procedure presented, under message-passing paradigm. Some examples are provided to demonstrate the timing results of the algorithms, discussing the accuracy and efficiency of the code.     

三维结构分析并行自适应有限元软件PHG-Solid

介绍了所研制的一个开源三维结构分析并行自适应有限元软件PHG-Solid。它是以并行自适应有限元软件平台PHG为基础开发的,支持在纯三维结构上进行并行自适应有限元分析。与现有的商业和开源结构分析有限元软件相比,PHG-Solid的特点和优势在于:1)支持完全自动化且高度并行的自适应有限元计算;2)能稳健高效地求解大规模问题,具有很好的计算规模可扩展性;3)易于扩展,用户可根据需要添加相应的计算模块。通过几个大型数值算例来展示该软件的计算能力和并行可扩展性,其中的最大计算规模超过了5亿自由度,最大并行规模达到了1024个MPI进程。     

Object oriented implementation of distributed finite element analysis in .NET

The paper describes a detailed study into the object-oriented implementation of distributed finite element analysis on desktop computers using the .NET framework. The software design aspects are described in some detail for both direct and iterative solution algorithms. The use of interfaces played an important role in the software design. This, together with the .NET framework, enabled remote objects to be implemented in a relatively seamless fashion. The solution routines were “blind” to whether the objects were local or remote. Numerical tests were carried out and reasonable speed-up was achieved, particularly for direct solution methods. It is concluded that .NET provides a viable framework for implementing distributed computing on networks of personal computers.     

Parallel processing, neural networks and genetic algorithms

In an earlier paper[1] some recent developments in computational technology to structural engineering were described. The developments included: parallel and distributed computing; neural networks; and genetic algorithms. In this paper, the authors concentrate on parallel implementations of neural networks and genetic algorithms. In the final section of the paper the authors show how a parallel finite element analysis may be undertaken in an efficient manner by preprocessing of the finite element model using a genetic algorithm utilizing a neural network predictor. This preprocessing is the partitioning of the finite element mesh into sub-domains to ensure load balancing and minimum interprocessor communication during the parallel finite element analysis on a MIMD distributed memory computer. © 1998 Published by Elsevier Science Limited. All rights reserved.     

Parallel solution for finite element linear systems of equations on workstation cluster

With the advances in the high speed computers network technologies, a workstation cluster is becoming the main environment for parallel processing. Finite element linear systems of equations are common throughout structural analysis in Civil Engineering. The preconditioned conjugate gradient method （PCGM） is an iterative method used to solve the finite element systems of equations with symmetric positive definite system matrices. In this paper, the algorithm of PCGM is parallelized and implemented on DELL workstation cluster. Optimization techniques for the sparse matrix vector multiplication are adopted in programming. The storage scheme is analyzed in detail. The experiment result shows that the designed parallel algorithm has high speedup and good efficiency on the high performance workstation cluster. This illustrates the power of parallel computing in solving large problems much faster than on a single processor.     

A parallel block LU decomposition method for distributed finite element matrices

In this work we present a new parallel direct linear solver for matrices resulting from finite element problems. The algorithm follows the nested dissection approach, where the resulting Schur complements are also distributed in parallel. The sparsity structure of the finite element matrices is used to pre-compute an efficient block structure for the LU factors. We demonstrate the performance and the parallel scaling behavior by several test examples.     

基于工作站机群并行求解有限元线性方程组

随着计算机高速网络技术的发展,工作站机群正在成为并行计算的主要平台.有限元线性方程组在土木工程结构分析中是最常见的问题.预处理共轭梯度法(PCGM)是求解线性方程组的迭代方法.对预处理共轭梯度法进行并行化并在两个不同的机群上实现,对存储方式进行详细分析,编程中采用了稀疏矩阵向量相乘的优化技术.数值结果表明,设计的并行算法具有良好的加速比和并行效率,说明并行计算能更快地求解大规模问题.     

An algorithm for automatic 2D finite element mesh generation with line constraints

In this study, an algorithm is designed specifically for automatic finite element (FE) mesh generation on the transverse structure of hulls reinforced by stiffeners. Stiffeners attached to the transverse structure are considered as line constraints in the geometry boundary. For the FE mesh generation used in this study, the line constraints are treated as boundaries and by that means the geometry domain attached to the line constraints is decomposed into sub-domains, constrained only by the closed boundaries. Then, the mesh can be generated directly on those sub-domains by the traditional approach. The performance of the proposed algorithm is evaluated and the quality of the generated mesh meets expectations.     

Normalized explicit finite element approximate inverse preconditioning

Normalized explicit approximate inverse matrix techniques for computing explicitly various families of normalized approximate inverses based on normalized approximate factorization procedures for solving sparse linear systems, which are derived from the finite difference and finite element discretization of partial differential equations are presented. Normalized explicit preconditioned conjugate gradient-type schemes in conjunction with normalized approximate inverse matrix techniques are presented for the efficient solution of linear and non-linear systems. Theoretical estimates on the rate of convergence and computational complexity of the normalized explicit preconditioned conjugate gradient method are also presented. Applications of the proposed methods on characteristic linear and non-linear problems are discussed and numerical results are given.     

Parallel performance of a lattice-Boltzmann/finite element cellular blood flow solver on the IBM Blue Gene/P architecture

We discuss the parallel implementation and scaling results of a hybrid lattice-Boltzmann/finite element code for suspension flow simulations. This code allows the direct numerical simulation of cellular blood flow, fully resolving the two-phase nature of blood and the deformation of the suspended phase. A brief introduction to the numerical methods employed is given followed by an outline of the code structure. Scaling results obtained on Argonne National Laboratories IBM Blue Gene/P (BG/P) are presented. Details include performance characteristics on 512 to 65,536 processor cores.     

Parallel Implementation of a Least-Squares Spectral Element Solver for Incompressible Flow Problems

Least-squares spectral element methods (LSQSEM) are based on two important and successful numerical methods: spectral/hp element methods and least-squares finite element methods. Least-squares methods lead to symmetric and positive definite algebraic systems which circumvent the Ladyzhenskaya–Babuka–Brezzi (LBB) stability condition and consequently allow the use of equal order interpolation polynomials for all variables. In this paper, we present results obtained with a parallel implementation of the least-squares spectral element solver on a distributed memory machine (Cray T3E) and on a virtual shared memory machine (SGI Origin 3800).     

Distributed parameter system identification using finite element differential neural networks

Most of the previous work on identification involves systems described by ordinary differential equations (ODEs). Many industrial processes and physical phenomena, however, should be modeled using partial differential equations (PDEs) which offer both spatial and temporal distributions that are simply not available with ODE models. Systems described by a PDE belong to a class of system called distributed parameter system (DPS). This article presents a method for solving the problem of identification of uncertain DPSs using a differential neural network (DNN). The DPS, assumed to be described by a PDE, is approximated using the finite element method (FEM). The FEM discretizes the domain into a set of distributed and connected nodes, thereby, allowing a representation of the DPS in a finite number of ODEs. The proposed DNN follows the same interconnection structure of the FEM, thus allowing the DNN to identify the FEM approximation of the DPS in both 2D and 3D domains. Lyapunov's second method was used to derive adaptive learning laws for the proposed DNN structure. The identification algorithm, here developed in Nvidia's CUDA/C to reduce the execution time, runs mostly on the graphics processing unit (GPU). A physical experiment served to validate the 2D case. In the experiment, the DNN followed the trajectory of 57 markers that were placed on an undulating square piece of silk. The proposed DNN is compared against a method based on principal component analysis and an artificial neural network trained with group search optimization. In addition to the 2D case, a simulation validated the 3D case, where input data for the DNN was generated by solving a PDE with appropriate initial and boundary conditions over an unitary domain. Results show that the proposed FEM-based DNN approximates the dynamic behavior of both a real 2D and a simulated 3D system.     

Skeleton-based computational method for the generation of a 3D finite element mesh sizing function

This paper focuses on the generation of a three-dimensional (3D) mesh sizing function for geometry-adaptive finite element (FE) meshing. The mesh size at a point in the domain of a solid depends on the geometric complexity of the solid. This paper proposes a set of tools that are sufficient to measure the geometric complexity of a solid. Discrete skeletons of the input solid and its surfaces are generated, which are used as tools to measure the proximity between geometric entities and feature size. The discrete skeleton and other tools, which are used to measure the geometric complexity, generate source points that determine the size and local sizing function at certain points in the domain of the solid. An octree lattice is used to store the sizing function as it reduces the meshing time. The size at every lattice-node is calculated by interpolating the size of the source points. The algorithm has been tested on many industrial models, and it can be extended to consider other non-geometric factors that influence the mesh size, such as physics, boundary conditions, etc.Sandia National Laboratory is a multiprogram laboratory operated by the Sandia Corporation, a Lockheed Martin Company, for the US Department of Energy under contract DE-AC04-94AL85000.     

ppohDEM: Computational performance for open source code of the discrete element method

We investigate performance improvements for the discrete element method (DEM) used in ppohDEM. First, we use OpenMP and MPI to parallelize DEM for efficient operation on many types of memory, including shared memory, and at any scale, from small PC clusters to supercomputers. We also describe a new algorithm for the descending storage method (DSM) based on a sort technique that makes creation of contact candidate pair lists more efficient. Finally, we measure the performance of ppohDEM using the proposed improvements, and confirm that computational time is significantly reduced. We also show that the parallel performance of ppohDEM can be improved by reducing the number of OpenMP threads per MPI process.Program summaryProgram title: ppohDEMCatalogue identifier: AESI_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AESI_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 39007No. of bytes in distributed program, including test data, etc.: 2482843Distribution format: tar.gzProgramming language: Fortran.Computer: CPU based workstations and parallel computers.Operating system: Linux, Windows.Has the code been vectorized or parallelized?: Yes, using MPI. Tested with up to 8 processors.RAM: Dependent upon the numbers of particles and contact particle pairs (1 GB for the example program supplied with the package)Classification: 6.5, 13.External routines: MPI-2, OpenMPNature of problem:Collision dynamics of viscoelastic particles with friction in powder engineering and soil mechanics.Solution method:Parallelized DEM running on shared and/or distributed systems is the solution method based particle model in which geometrical size and shape attributes are provided for each element. In the DEM, the Voigt model and Coulomb friction model are considered at each contact point between particles.Running time:10 min for the example program supplied with the package using 2 CPU (each with 10 cores) of Intel Xeon E7-4870.     

Processing of fiber architecture data for finite element modeling of 3D woven composites

An efficient procedure to process the textile simulation data and generate realistic finite element meshes of woven composites is proposed. The textile topology data in point cloud format is used to identify individual yarns, interpolate their cross-sectional contours, and generate smooth yarn surfaces. A robust algorithm to repair possible interpenetrations between yarn surfaces is developed and implemented in MATLAB. A 3D finite element mesh of the unit cell of composite material is generated based on the obtained yarn surfaces. The anisotropic material properties of the constituents are assigned with proper orientations.The procedure is successfully applied to generate four finite element models with 1–10 million degrees of freedom. The models are used to predict effective elastic properties of an orthogonal 3D woven composite. The sensitivity of results to the level of finite element discretization is investigated.     

大型隧道工程三维数值分析的并行计算方法

建立了黄浦江某大型越江隧道的三维精细非线性有限元模型,采用接触均衡的并行计算技术,解决了大型隧道工程数值模拟时规模庞大的问题。数值模拟了越江隧道的静应力场,比较了两种不同分区方案对并行加速比的影响。数值模拟结果能够为大型隧道工程设计提供参考依据。