Performance of a Petrov–Galerkin algebraic multilevel preconditioner for finite element modeling of the semiconductor device drift‐diffusion equations

This study compares the performance of a relatively new Petrov–Galerkin smoothed aggregation (PGSA) multilevel preconditioner with a nonsmoothed aggregation (NSA) multilevel preconditioner to accelerate the convergence of Krylov solvers on systems arising from a drift‐diffusion model for semiconductor devices. PGSA is designed for nonsymmetric linear systems, Ax=b, and has two main differences with smoothed aggregation. Damping parameters for smoothing interpolation basis functions are now calculated locally and restriction is no longer the transpose of interpolation but instead corresponds to applying the interpolation algorithm to A^T and then transposing the result. The drift‐diffusion system consists of a Poisson equation for the electrostatic potential and two convection–diffusion‐reaction‐type equations for the electron and hole concentration. This system is discretized in space with a stabilized finite element method and the discrete solution is obtained by using a fully coupled preconditioned Newton–Krylov solver. The results demonstrate that the PGSA preconditioner scales significantly better than the NSA preconditioner, and can reduce the solution time by more than a factor of two for a problem with 110 million unknowns on 4000 processors. The solution of a 1B unknown problem on 24 000 processor cores of a Cray XT3/4 machine was obtained using the PGSA preconditioner. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

Damage assessment in structure from changes in static parameter using neural networks

Damage to structures may occur as a result of normal operations, accidents, deterioration or severe natural events such as earthquakes and storms. Most often the extent and location of damage may be determined through visual inspection. However, in some cases this may not be feasible. The basic strategy applied in this study is to train a neural network to recognize the behaviour of the undamaged structure as well as of the structure with various possible damaged states. When this trained network is subjected to the measured response, it should be able to detect any existing damage. This idea is applied on a simple cantilever beam. Strain and displacement are used as possible candidates for damage identification by a back-propagation neural network. The superiority of strain over displacement for identification of damage has been observed in this study     

Object‐oriented finite element analysis of thermo‐hydro‐mechanical (THM) problems in porous media

The design, implementation and application of a concept for object‐oriented in finite element analysis of multi‐field problems is presented in this paper. The basic idea of this concept is that the underlying governing equations of porous media mechanics can be classified into different types of partial differential equations (PDEs). In principle, similar types of PDEs for diverse physical problems differ only in material coefficients. Local element matrices and vectors arising from the finite element discretization of the PDEs are categorized into several types, regardless of which physical problem they belong to (i.e. fluid flow, mass and heat transport or deformation processes). Element (ELE) objects are introduced to carry out the local assembly of the algebraic equations. The object‐orientation includes a strict encapsulation of geometrical (GEO), topological (MSH), process‐related (FEM) data and methods of element objects. Geometric entities of an element such as nodes, edges, faces and neighbours are abstracted into corresponding geometric element objects (ELE–GEO). The relationships among these geometric entities form the topology of element meshes (ELE–MSH). Finite element objects (ELE–FEM) are presented for the local element calculations, in which each classification type of the matrices and vectors is computed by a unique function. These element functions are able to deal with different element types (lines, triangles, quadrilaterals, tetrahedra, prisms, hexahedra) by automatically choosing the related element interpolation functions. For each process of a multi‐field problem, only a single instance of the finite element object is required. The element objects provide a flexible coding environment for multi‐field problems with different element types. Here, the C++ implementations of the objects are given and described in detail. The efficiency of the new element objects is demonstrated by several test cases dealing with thermo‐hydro‐mechanical (THM) coupled problems for geotechnical applications. Copyright © 2006 John Wiley & Sons, Ltd.     

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。     

基于神经网络模型的舰面流场仿真算法

飞行甲板表面流场是影响直升机飞行安全的重要因素,在直升机实时飞行仿真中,流场速度分布特性直接影响直升机飞行动力学仿真的精确度。文章以纳维-斯托克斯方程为基础,利用BP神经网络算法,研究了实时确定流场速度分布的方法,该方法可用于甲板流场实时仿真,提高直升机飞行仿真的精度。