Parallel Finite Element Software Development and Performance Analysis in an Object-Oriented Programming Framework     

Brian J. Henz  Dale R. Shires 《Journal of Mathematical Modelling and Algorithms》2005,4(1):17-34

The use of object-oriented programming techniques in the development of parallel, finite element analysis software enhances code reuse and increases efficiency during application development. In this paper, an object-oriented programming framework developed by the authors is utilized in the implementation of parallel finite element software for modeling of the resin transfer molding manufacturing process. The motivation for choosing the resin transfer molding finite element application and implementing it with the object-oriented framework is that it was originally developed and parallelized in a functional programming paradigm thus offering the possibility of direct comparisons. Discussion of the software development effort and performance results are presented and analyzed.Mathematics Subject Classifications (2000) 65M60, 65Y05.  相似文献   

Computing the face lattice of a polytope from its vertex-facet incidences     

Volker Kaibel  Marc E. Pfetsch 《Computational Geometry》2002,23(3):281-290

We give an algorithm that constructs the Hasse diagram of the face lattice of a convex polytope P from its vertex-facet incidences in time O(min{n,m}··), where n is the number of vertices, m is the number of facets, is the number of vertex-facet incidences, and  is the total number of faces of P. This improves results of Fukuda and Rosta [Computational Geometry 4 (4) (1994) 191–198], who described an algorithm for enumerating all faces of a d-polytope in O(min{n,m}·d·²) steps. For simple or simplicial d-polytopes our algorithm can be specialized to run in time O(d··). Furthermore, applications of the algorithm to other atomic lattices are discussed, e.g., to face lattices of oriented matroids.  相似文献   

On Acyclic Orientations and Sequential Dynamical Systems     

C. M. Reidys 《Advances in Applied Mathematics》2001,27(4):790

We study a class of discrete dynamical systems that consists of the following data: (a) a finite (labeled) graph Y with vertex set {1, …, n}, where each vertex has a binary state, (b) a vertex labeled multi-set of functions (F_i, Y: ₂ⁿ →  ₂ⁿ)_i, and (c) a permutation π  S_n. The function F_i, Y updates the binary state of vertex i as a function of the states of vertex i and its Y-neighbors and leaves the states of all other vertices fixed. The permutation π represents a Y-vertex ordering according to which the functions F_i, Y are applied. By composing the functions F_i, Y in the order given by π we obtain the sequential dynamical system (SDS):In this paper we first establish a sharp, combinatorial upper bound on the number of non-equivalent SDSs for fixed graph Y and multi-set of functions (F_i, Y). Second, we analyze the structure of a certain class of fixed-point-free SDSs.  相似文献   

λ_5-geometry中的Steiner树问题(Ⅰ)     

陈光亭  姚恩瑜 《高校应用数学学报(A辑)》2001,(3)

本文首先提出了 λ5-geometry中的 Steiner最小树问题 .讨论了 λ5-ge-ometry中的 Steiner最小树的若干性质 ,并给出了给定点数为 3或 4时 Steiner最小树的基本结构 .  相似文献   

Nonlinear constitutive behavior of orthotropic materials     

J. Lellep  J. Majak 《Mechanics of Composite Materials》2000,36(4):261-266

The problem of optimal material orientation is studied in the case of nonlinear elastic materials. Optimal orientations corresponding to extreme (maximal or minimal) energy density are obtained for orthotropic materials. The material behavior (the stress-strain relation) is simulated in a general form, which includes, as particular cases, different versions of the power law stress-strain relations. The optimality conditions are derived for the general cases. Local and global extremums are determined for particular cases.Presented at the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000).Tartu University, Estonia. Published in Mekhanika Kompozitnykh Materialov, Vol. 36, No. 4, pp. 445–454, March–April, 2000.  相似文献   

The Enumeration of Coxeter Elements     

Jian-yi Shi 《Journal of Algebraic Combinatorics》1997,6(2):161-171

Let (W,S, ) be a Coxeter system: a Coxeter group W with S its distinguished generator set and its Coxeter graph. In the present paper, we always assume that the cardinality l=|S| ofS is finite. A Coxeter element of W is by definition a product of all generators s S in any fixed order. We use the notation C(W) to denote the set of all the Coxeter elements in W. These elements play an important role in the theory of Coxeter groups, e.g., the determination of polynomial invariants, the Poincaré polynomial, the Coxeter number and the group order of W (see [1–5] for example). They are also important in representation theory (see [6]). In the present paper, we show that the set C(W) is in one-to-one correspondence with the setC() of all acyclic orientations of . Then we use some graph-theoretic tricks to compute the cardinality c(W) of the setC(W) for any Coxeter group W. We deduce a recurrence formula for this number. Furthermore, we obtain some direct formulae of c(W) for a large family of Coxeter groups, which include all the finite, affine and hyperbolic Coxeter groups.The content of the paper is organized as below. In Section 1, we discuss some properties of Coxeter elements for simplifying the computation of the value c(W). In particular, we establish a bijection between the sets C(W) andC() . Then among the other results, we give a recurrence formula of c(W) in Section 2. Subsequently we deduce some closed formulae of c(W) for certain families of Coxeter groups in Section 3.  相似文献   

Spectra of some interesting combinatorial matrices related to oriented spanning trees on a directed graph     

Christos A. Athanasiadis 《Journal of Algebraic Combinatorics》1996,5(1):5-11

The Laplacian of a directed graph G is the matrix L(G) = O(G) –, A(G) where A(G) is the adjaceney matrix of G and O(G) the diagonal matrix of vertex outdegrees. The eigenvalues of G are the eigenvalues of A(G). Given a directed graph G we construct a derived directed graph D(G) whose vertices are the oriented spanning trees of G. Using a counting argument, we describe the eigenvalues of D(G) and their multiplicities in terms of the eigenvalues of the induced subgraphs and the Laplacian matrix of G. Finally we compute the eigenvalues of D(G) for some specific directed graphs G. A recent conjecture of Propp for D(H _n ) follows, where H _n stands for the complete directed graph on n vertices without loops.  相似文献   

Object oriented modeling of social networks     

Evelien P. H. Zeggelink  Reinier Van Oosten  Frans N. Stokman 《Computational & Mathematical Organization Theory》1996,2(2):115-138

The aim of this paper is to explain principles of object oriented modeling in the scope of modeling dynamic social networks. As such, the approach of object oriented modeling is advocated within the field of organizational research that focuses on networks.We provide a brief introduction into the field of social networks and present an overview of existing network models and methods. Subsequently we introduce an elementary problem field in the social sciences in general, and in studies of organizational change and design in particular: the micro-macro link. We argue that the most appropriate way to hadle this problem is the principle of methodological individualism. For social network analysis, to contribute to this theoretical perspective, it should include an individual choice mechanism and become more dynamically oriented. Subsequently, object oriented modeling is advocated as a tool to meet these requirements for social network analysis. We show that characteristics of social systems that are emphasized in the methodological individualistic approach have their direct equivalences in object oriented models. The link between the micro level where actors act, and the macro level where phenomena occur as a consequence and cause of these actions, can be modelled in a straightforward way.  相似文献   

On the Decomposition of Graphs into Complete Bipartite Graphs     

Jinquan Dong  Yanpei Liu 《Graphs and Combinatorics》2007,23(3):255-262

In a complete bipartite decomposition π of a graph, we consider the number ϑ(v;π) of complete bipartite subgraphs incident with a vertex v. Let ϑ(G)= ϑ(v;π). In this paper the exact values of ϑ(G) for complete graphs and hypercubes and a sharp upper bound on ϑ(G) for planar graphs are provided, respectively. An open problem proposed by P.C. Fishburn and P.L. Hammer is solved as well.  相似文献   

A visual programming system for defining behavior in simulation models of manufacturing systems     

Timothy Thomasma  Youyi Mao  Onur M. Ülgen 《Annals of Operations Research》1994,53(1):357-389

A visual programming system is described that allows the modeler full flexibility in defining the behavior of a manufacturing system simulation model. Decision-making behavior of objects in the simulation can be viewed by watching an animation of the system layout, viewing function block diagrams of rules that govern behavior, or noting the progress of an object in carrying out sequences of activities that are pictured as operation networks. Rules, elemental operations and operation networks are structured and associated with particular objects, groups of objects, and locations on the manufacturing system layout. The objective of this system is to reduce the time and expense required to construct and modify models, given that manufacturing system data have been collected.  相似文献