The Use of Curved Elements in the Finite Element Approximation of Thin Plates by High Order p and hp Methods

In this article we focus on the approximation of the Reissner–Mindlin (R–M) plate model by high-order p and hp versions of the Finite Element Method (FEM), in the case when the mesh includes curved elements; this is of particular interest when plates with smooth boundary are considered. Our main goal is to verify that an appropriately defined Mixed Interpolated Tensorial Components (MITC) FEM performs well, in the presence of curved elements, when the energy norm is used as an error measure, as well as when quantities of engineering interest are computed. Comments on the performance of the standard FEM formulation are also made     

Mixed Discontinuous Galerkin Finite Element Method for the Biharmonic Equation

In this paper, we first split the biharmonic equation Δ² u=f with nonhomogeneous essential boundary conditions into a system of two second order equations by introducing an auxiliary variable v=Δu and then apply an hp-mixed discontinuous Galerkin method to the resulting system. The unknown approximation v _h of v can easily be eliminated to reduce the discrete problem to a Schur complement system in u _h , which is an approximation of u. A direct approximation v _h of v can be obtained from the approximation u _h of u. Using piecewise polynomials of degree p≥3, a priori error estimates of u−u _h in the broken H ¹ norm as well as in L ² norm which are optimal in h and suboptimal in p are derived. Moreover, a priori error bound for v−v _h in L ² norm which is suboptimal in h and p is also discussed. When p=2, the preset method also converges, but with suboptimal convergence rate. Finally, numerical experiments are presented to illustrate the theoretical results. Supported by DST-DAAD (PPP-05) project.     

Selecting the Numerical Flux in Discontinuous Galerkin Methods for Diffusion Problems

In this paper we present numerical investigations of four different formulations of the discontinuous Galerkin method for diffusion problems. Our focus is to determine, through numerical experimentation, practical guidelines as to which numerical flux choice should be used when applying discontinuous Galerkin methods to such problems. We examine first an inconsistent and weakly unstable scheme analyzed in Zhang and Shu, Math. Models Meth. Appl. Sci. (M ³ AS) 13, 395–413 (2003), and then proceed to examine three consistent and stable schemes: the Bassi–Rebay scheme (J. Comput. Phys. 131, 267 (1997)), the local discontinuous Galerkin scheme (SIAM J. Numer. Anal. 35, 2440–2463 (1998)) and the Baumann–Oden scheme (Comput. Math. Appl. Mech. Eng. 175, 311–341 (1999)). For an one-dimensional model problem, we examine the stencil width, h-convergence properties, p-convergence properties, eigenspectra and system conditioning when different flux choices are applied. We also examine the ramifications of adding stabilization to these schemes. We conclude by providing the pros and cons of the different flux choices based upon our numerical experiments.This revised version was published online in July 2005 with corrected volume and issue numbers.     

Some schwarz methods for integral equations on surfaces-h and p versions

Abstact We present new results from 11, 7, 12 on various Schwarz methods for the h and p versions of the boundary element methods applied to prototype first kind integral equations on surfaces. When those integral equations (weakly/hypersingular) are solved numerically by the Galerkin boundary element method, the resulting matrices become ill-conditioned. Hence, for an efficient solution procedure appropriate preconditioners are necessary to reduce the numbers of CG-iterations. In the p version where accuracy of the Galerkin solution is achieved by increasing the polynomial degree the use of suitable Schwarz preconditioners (presented in the paper) leads to only polylogarithmically growing condition numbers. For the h version where accuracy is achieved by reducing the mesh size we present a multi-level additive Schwarz method which is competitive with the multigrid method. Communicated by: U. Langer Dedicated to George C. Hsiao on the occasion of his 70th birthday.     

An hp-Analysis of the Local Discontinuous Galerkin Method for Diffusion Problems

We present an hp-error analysis of the local discontinuous Galerkin method for diffusion problems, considering unstructured meshes with hanging nodes and two- and three-dimensional domains. Our estimates are optimal in the meshsize h and slightly suboptimal in the polynomial approximation order p. Optimality in p is achieved for matching grids and polynomial boundary conditions.     

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).     

Exact Non-Reflecting Boundary Conditions on Perturbed Domains and <Emphasis Type="Italic">hp</Emphasis>-Finite Elements

For exterior scattering problems one of the chief difficulties arises from the unbounded nature of the problem domain. Inhomogeneous obstacles may require a volumetric discretization, such as the Finite Element Method (FEM), and for this approach to be feasible the exterior domain must be truncated and an appropriate condition enforced at the far, artificial, boundary. An exact, non-reflecting boundary condition can be stated using the classical DtN-FE method if the Artificial Boundary’s shape is quite specific: circular or elliptical. Recently, this approach has been generalized to permit quite general Artificial Boundaries which are shaped as perturbations of a circle resulting in the “Enhanced DtN-FE” method. In this paper we extend this method to a two-dimensional FEM featuring high-order polynomials in order to realize a high rate of convergence. This is more involved than simply specifying high-order test and trial functions as now the scatterer shape and Artificial Boundary must be faithfully represented. This entails boundary elements which conform (to high order) to the true boundary shapes. As we show, this can be accomplished and we realize an arbitrary order FEM without spurious reflections.     

A Fully Syntactic AC-RPO

We present the first fully syntactic (i.e., non-interpretation-based) AC-compatible recursive path ordering (RPO). It is simple, and hence easy to implement, and its behaviour is intuitive as in the standard RPO. The ordering is AC-total and defined uniformly for both ground and nonground terms, as well as for partial precedences. More important, it is the first one that can deal incrementally with partial precedences, an aspect that is essential, together with its intuitive behaviour, for interactive applications such as Knuth–Bendix completion.     

L2(H1 Norm A PosterioriError Estimation for Discontinuous Galerkin Approximations of Reactive Transport Problems

Explicita posteriori residual type error estimators in L²(H¹) norm are derived for discontinuous Galerkin (DG) methods applied to transport in porous media with general kinetic reactions. They are flexible and apply to all the four primal DG schemes, namely, Oden–Babuška–Baumann DG (OBB-DG), non-symmetric interior penalty Galerkin (NIPG), symmetric interior penalty Galerkin (SIPG) and incomplete interior penalty Galerkin (IIPG). The error estimators use directly all the available information from the numerical solution and can be computed efficiently. Numerical examples are presented to demonstrate the efficiency and the effectivity of these theoretical estimators.The authors would like to thank the anonymous referees for their incisive suggestions which contributed toward improving the paper. AMS subject classifications:65M15;65M60;65M50.This revised version was published online in July 2005 with corrected volume and issue numbers.     

hp-Discontinuous Galerkin Finite Element Methods with Least-Squares Stabilization

We consider a family of hp-version discontinuous Galerkin finite element methods with least-squares stabilization for symmetric systems of first-order partial differential equations. The family includes the classical discontinuous Galerkin finite element method, with and without streamline-diffusion stabilization, as well as the discontinuous version of the Galerkin least-squares finite element method. An hp-optimal error bound is derived in the associated DG-norm. If the solution of the problem is elementwise analytic, an exponential rate of convergence under p-refinement is proved. We perform numerical experiments both to illustrate the theoretical results and to compare the various methods within the family.     

An extension theorem for polynomials on triangles

We present an extension theorem for polynomial functions that proves a quasi-optimal bound for a lifting from L ² on edges onto a fractional-order Sobolev space on triangles. The extension is such that it can be further extended continuously by zero within the trace space of H ¹. Such an extension result is critical for the analysis of non-overlapping domain decomposition techniques applied to the p-and hp-versions of the finite and boundary element methods for elliptic problems of second order in three dimensions. Supported by the FONDAP Programme in Applied Mathematics, Chile.     

Discontinuous Galerkin Spectral/hp Element Modelling of Dispersive Shallow Water Systems

Two-dimensional shallow water systems are frequently used in engineering practice to model environmental flows. The benefit of these systems are that, by integration over the water depth, a two-dimensional system is obtained which approximates the full three-dimensional problem. Nevertheless, for most applications the need to propagate waves over many wavelengths means that the numerical solution of these equations remains particularly challenging. The requirement for an accurate discretization in geometrically complex domains makes the use of spectral/hp elements attractive. However, to allow for the possibility of discontinuous solutions the most natural formulation of the system is within a discontinuous Galerkin (DG) framework. In this paper we consider the unstructured spectral/hp DG formulation of (i) weakly nonlinear dispersive Boussinesq equations and (ii) nonlinear shallow water equations (a subset of the Boussinesq equations). Discretization of the Boussinesq equations involves resolving third order mixed derivatives. To efficiently handle these high order terms a new scalar formulation based on the divergence of the momentum equations is presented. Numerical computations illustrate the exponential convergence with regard to expansion order and finally, we simulate solitary wave solutions.This revised version was published online in July 2005 with corrected volume and issue numbers.     

An A Priori Error Analysis of the hp-Version of the Continuous Galerkin FEM for Nonlinear Initial Value Problems

A continuous Galerkin finite element time-stepping method for the approximation of nonlinear initial value problems is analyzed within an hp-context. We derive a priori error bounds in the L²- and H¹-norm that are explicit with respect to the time steps and the approximation orders. In particular, it is shown that, for analytic solutions (with certain possible start-up singularities) exponential convergence rates can be achieved. Moreover, we prove that the scheme superconverges at the nodal points of the time partition. Numerical experiments illustrate the performance of the method.     

Automatic parallelization ofwhile-loops using speculative execution

Automatic parallelization of imperative sequential programs has focused on nests offor-loops. The most recent of them consist in finding an affine mapping with respect to the loop indices to simultaneously capture the temporal and spatial properties of the parallelized program. Such a mapping is usually called a “space-time transformation.” This work describes an extension of these techniques towhile-loops using speculative execution. We show that space-time transformations are a good framework for summing up previous restructuration techniques ofwhile-loop, such as pipelining. Moreover, we show that these transformations can be derived and applied automatically. Partly supported by the French CNRS Coordinated Research Program on Concurrency, Communication and Cooperation C³, PRC/MRE contract ParaDigme and DRET contract 91/1180     

A Generalization of Local Fuzzy Structures

The class of bounded residuated lattice ordered monoids Rl-monoids) contains as proper subclasses the class of pseudo BL-algebras (and consequently those of pseudo MV-algebras, BL-algebras and MV-algebras) and of Heyting algebras. In the paper we introduce and investigate local bounded Rl-monoids which generalize local algebras from the above mentioned classes of fuzzy structures. Moreover, we study and characterize perfect bounded Rl-monoids.     

Development of a mixed control volume – Finite element method for the advection–diffusion equation with spectral convergence

In this paper we attack the problem of devising a finite volume method for computational fluid dynamics and related phenomena which can deal with complex geometries while attaining high-orders of accuracy and spectral convergence at a reasonable computational cost. As a first step towards this end, we propose a control volume finite element method for the solution of the advection–diffusion equation. The numerical method and its implementation are carefully tested in the paper where h- and p-convergence are checked by comparing numerical results against analytical solutions in several relevant test-cases. The numerical efficiency of a selected set of operations implemented is estimated by operation counts, ill-conditioning of coefficient matrices is avoided by using an appropriate distribution of interpolation points and control-volume edges.     

旅客列车全自动报站多媒体系统

介绍了一种由下位单片机、上层PC机、通过串行通信组成的列车全自动报站多媒体系统的原理及组成和软、硬件设计。谊系统能自动识别列车所到达站点．并以多媒体形式介绍相关的交通和旅游信息，方便了旅客，改善了乘车环境，是列车报站的发展方向。     

A batch arrival queue with a vacation time under single vacation policy

We consider an M^x/G/1 queueing system with a vacation time under single vacation policy, where the server takes exactly one vacation between two successive busy periods. We derive the steady state queue size distribution at different points in times, as well as the steady state distributions of busy period and unfinished work (backlog) of this model.Scope and purposeThis paper addresses issues of model building of manufacturing systems of job-shop type, where the server takes exactly one vacation after the end of each busy period. This vacation can be utilized as a post processing time after clearing the jobs in the system. To be more realistic, we further assume that the arrivals occur in batches of random size instead of single units and it covers many practical situations. For example in manufacturing systems of job-shop type, each job requires to manufacture more than one unit; in digital communication systems, messages which are transmitted could consist of a random number of packets. These manufacturing systems can be modeled by M^x/G/1 queue with a single vacation policy and this extends the results of Levy and Yechiali, Manage Sci 22 (1975) 202, and Doshi, Queueing Syst 1 (1986) 29.     

多模态过程的全自动离线模态识别方法

多模态是复杂工业生产过程的普遍特性.不同模态具有不同的过程特性,需要建立不同的模型,因此离线建模数据的模态划分与识别是整个多模态过程建模的关键问题之一.目前,常用的聚类算法需要对其结果进行人工分析和后续处理,无法真正实现多模态过程的全自动模态识别.因此,本文提出一种全自动的多模态过程离线模态识别方法.首先通过宽度为H的大切割窗口对数据进行切割,利用改进的K-means聚类算法对窗口单元进行聚类;根据聚类结果,对稳定模态淹没现象进行处理,得到模态的初步划分结果;最终,利用小滑动窗口L,对稳定模态及过渡模态交接区域进行细划分,准确定位稳定模态与过渡模态的分割点.算法实现了多模态过程的全自动离线识别,并给出合理有效的识别结果.仿真分析表明此方法能够实现模态的自动识别,且识别结果准确.