修正Taylor—Galerkin有限元法的构造及其在可压缩流场计算中…

本文从Ｔａｙｌｏｒ－Ｇａｌｅｒｋｉｎ有限元法出法，对它作了根本性的改进，构造了修正Ｔａｙｌｏｒ－Ｇａｌｅｒｋｉｎ算法，并用新、旧两种算法分别对亚、超音速的流场情况作了计算，计算结果表明，在达到同样计算精度的前提下，新方法较之老方法在收敛速度上有明显改进，结果是令人满意的。     

解微分方程组的改进尤拉方法的改进

对改进尤拉方法解微分方程组的方法作了改进,改进的算法与原来算法的计算量一样,但精度比较高.     

解微分方程组的Adams预测校正算法的改进方法

针对Adams预测校正算法求解微分方程组作了改进.算法的主要改进之处是在校正环节用已经计算出来的"新值"取代"旧值".最后,基于提出的改进方法和传统的Adams预测校正算法对同一微分方程组问题作了数值比较实验.数值实验结果表明改进的算法与传统的Adams预测校正算法的计算量一样,但精度大大提高.     

横肋管内流场的计算方法

利用Usawa-惩罚算法,本文计算了横肋管内的流场。其主要思想是将Usawa算法与惩罚算法相结合(参见[5]),以改进Usawa算法的收敛性。该方法在步长因子的选取上比Usawa算法有更大的余地。我们利用此方法得到的结果与文献[4]中给出结果符合很好。同时,本文讨论了Usawa-惩罚算法的收敛性条件,并讨论原问题的解的存在性和唯一性。一、引言横肋管在工业上广泛用于换热管,以强化传热,这种管内流场的计算,对了解传热强化的机理,改进设计方法有重要意义,因而引起研究者的重视[1]～[4],但还缺乏较好的计算方法。我们在本文中将[5]中的Usawa算法与惩罚算法相结合,以改进Usawa算法的收敛性。同时,我们对该算法的收敛性条件作了研究,从而在理论上证明了横肋管内     

用向量组共轭化方法改进Powell法

本文利用共轭化变换提高向量组共轭度的方法,对Powell法及修正Powell法作了改进。这一改进保持了原算法的二次终止性和关于连续可微严格凸函数的收敛性。文末用十六个公认的考机题检验了这一改进的效果。计算表明,改进后的Powell法及修正的Powell法比原算法收敛得快。     

ICCG与MICCG的一种改进算法

本文应用关于对角优势矩阵元素阶和阶矩阵等概念,分析了ICCG与MICCG的因子分解过程,在消去法计算中进行高阶截断,使ICCG与MICCG的因子分解计算量减少,从而实现了对这两种方法的改进。 一、ICCG算法与MICCG算法 对二维椭圆型方程边值问题作五点差,则差分系数阵A通常为五对角的对角优势阵。文献[1]提出了求解Au=b的ICCG(m)算法(即Incomplete Cholesky and     

基于固定序的Bellman-Ford算法的改进

固定序算法是Bellman-Ford算法的一种基本改进算法。为了改变固定序算法在稀疏图上的劣势,本文通过预先订制参与迭代的点的计算顺序,对该算法进行了改进。实验表明,在稀疏图上, 改进后的算法相对于原算法计算效率提高了近50%, 并能够与国际流行的先进先出算法相媲美。本文的工作表明,固定序算法不仅在大规模稠密图上具有明显的优势,而且在稀疏图上也具有很强的竞争力。     

负权最短路问题的新算法

Bellman-Ford算法自1958年以来一直是负权最短路问题的公认的最好算法之一．1970年,Yen对其进行了改进,理论上可以节省一半的计算量．本文得到了一种比Bellman-Ford算法更加优越的算法．尽管在理论上新算法无法保证完全超越于Yen的改进算法,但在许多情况下需要更少的计算量．     

一种改进的Fuzzy-HMMS算法及其收敛性

对D at T ran和M ichae lW agner等人提出的FCM-FE-HMM S算法作了进一步的补充和改进,提出了改进的FCM-FE-HMM S算法,并给出了算法收敛性分析,得出在给定初值的情况下该算法将收敛到一个局部最优解。     

带约束动力学辛算法的符号计算

首先对带约束动力学中的辛算法作了改进,利用吴消元法求解多项式类型Euler-Lagrange方程.在辛算法的基础上,根据线性方程组理论和相容条件提出了一个求解约束的新算法.新算法的推导过程比辛算法严格,而且计算也比辛算法简单,并且多项式类型的Euler-Lagrange仍可以用吴消元法求解.另外,对于某些非多项式类型的Euler-Lagrange方程,可以先化为多项式类型,再用吴消元法求解.利用符号计算软件,上述算法都可以在计算机上实现.     

Analysis of a continuum-based beam element in the framework of explicit-FEM

In this paper, a continuum-based (CB) beam element based on the original work of Belytschko [Nonlinear Finite Elements for Continua and Structures, Wiley, New York, 2001] has been modified and analysed in the framework of explicit finite element methods. Two main differences are introduced with respect to the original finite element technology proposed in Belytschko [Nonlinear Finite Elements for Continua and Structures, Wiley, New York, 2001]. Firstly, the velocity gradient tensor is computed in the slave nodes of the finite element rather than in the master nodes, enabling a more effective computational performance in terms of CPU-time as well as convergence. Secondly, the thickness of the element is assumed to be variable, which allows dilation and/or contraction when large deformation processes are involved. A series of numerical examples are presented in order to verify the robustness and capabilities of the algorithm.     

Enriching the Finite Element Method with meshfree techniques in structural mechanics

The automatic generation of meshes for the Finite Element method can be an expensive computational burden, especially in structural problems with localized stress peaks. The use of meshless methods can address such an issue, as these techniques do not require the existence of an underlying connection among the nodes selected in a general domain. However, a thoroughly meshfree technique can be computationally quite expensive. Usually, the most expensive tasks rely on identifying the nodal contacts and computing the Galerkin integrals. In this thesis we advance a novel hybrid technique that blends Finite Elements with the Meshless Local Petrov-Galerkin method with the aim at exploiting the most attractive properties of each procedure. The idea relies on the use of the Finite Element Method to compute a background solution that is locally improved by enriching the approximating space with the basis functions associated to a few meshless nodes, thus taking advantage of the flexibility ensured by the use of particles disconnected from an underlying grid. Adding the meshless particles only where needed avoids the cost of mesh refining, or even of re-meshing, without the prohibitive burden of a thoroughly meshfree approach. In particular, two enriching methods are introduced and discussed, with applications in structural mechanics. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A term by term stabilization algorithm for finite element solution of incompressible flow problems

This paper introduces a stabilization technique for Finite Element numerical solution of 2D and 3D incompressible flow problems. It may be applied to stabilize the discretization of the pressure gradient, and also of any individual operator term such as the convection, curl or divergence operators, with specific levels of numerical diffusion for each one of them. Its computational complexity is reduced with respect to usual (residual-based) stabilization techniques. We consider piecewise affine Finite Elements, for which we obtain optimal error bounds for steady Navier-Stokes and also for generalized Stokes equations (including convection). We include some numerical experiment in well known 2D test cases, that show its good performances. Received March 15, 1996 / Revised version received January 17, 1997     

Convergence analysis of non-conforming Trigonometric Finite Wave Elements

Trigonometric Finite Wave Elements (TFWE) are finite elements for solving problems in computational optics. The solution of those problems consist of highly oscillatory waves. TFWE are designed for obtaining optimal approximation properties for such kinds of waves with a changing wave number k. In this article, we study the convergence properties of 2-dimensional non-conforming TFWE by applying Strang’s Lemma.     

Convergence of finite elements enriched with mesh-less methods

Summary A combined hierarchical approximation based on finite elements and mesh-less methods is proposed and studied. Finite Elements are enriched adding hierarchical shape functions based on a particle distribution. Convergence results are presented and proved. Mathematics Subject Classification (2000):65N15, 65N30, 65N99Grant sponsor: Ministerio de Ciencia y Tecnologí a. Grant number: REN2001-0925-C03-01     

Testing of screw joint hybrid composite materials

Laminate composite materials have excellent coefficient of stiffness to weight and because of this laminates are very widely applied often replacing raditional materials. A very interesting group of such a type materials are the hybrid ones. A main disadvantage of hybrid composite materials is the weak impact strength. The paper presents results of testing handmade screw joint hybrid composite materials. Results of testing are compared with numerical analysis based on the Finite Elements Method. Investigations were made on designed for this purpose the statical stresses laboratory stand. The testing specimens were made by a contact method (handmade laminating) and laminar mats or woven fabrics spreading (resin supersaturated). (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analysis of Calving Events in Antarctic Ice Shelves Using Configurational Forces

Previous studies on the sensitivity of cracks in ice shelves with different boundary conditions, stress states and density profiles revealed the need for further analyses. As the transfer of boundary conditions from dynamic ice flow simulations to the linear elastic fracture analyses proved to be a critical point in previous studies, a new approach to relate viscous and elastic material behaviour is proposed. The numerical simulations are conducted using Finite Elements utilizing the concept of configurational forces. To show the applicability of the approach, a 2-dimensional plane stress geometry with volume loads due to the ice shelf flow is analyzed. The resulting crack path is compared to available crack paths from satellite images. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling of growth inhomogeneities in timber structures for realistic computations

This contribution discusses the numerical analysis of timber structures by means of the Finite Elements Method. As a naturally grown and fibrous material, wood shows distinctive material directions, which are captured by a cylindrically anisotropic model. Due to the growth conditions of a tree, the fiber course in wooden structural parts can differ. Especially branches, leading to knots, affect the mechanical properties. Therefore, an approach for the modelling of these growth inhomogeneities is presented. For the three-dimensional determination of the fiber course in the area of the inhomogeneities, an optimization procedure, using the idea of minimization of shear stresses in tree growth, has been developed. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Identification of the Velocity Field of 2D and 3D Tunnel Models with Frequency Domain Full Waveform Inversion

Full Waveform Inversion (FWI see [1]) has capability to identify the velocity field of a domain with a good precision. Its power comes from the fact that this approach does not only try to fit travel times of waves, but it tries to fit the whole seismogram. This work is about the application of acoustic full waveform inversion to 2D and 3D tunnel models. The necessary boundary conditions are applied to the models and the acoustic equation is solved by higher-order Finite Elements Method. The Conjugate Gradient (CG) method is utilized to minimize the misfit function. The results were verified with synthetic models. The synthetic tunnel models contain few bodies with different shapes and locations. Starting from a homogeneous velocity field, the synthetic model is sought over iterations. To avoid the ill-posedness, the locations and numbers of the source and receiver points have to be successfully chosen. Apart from this, the frequency set has also to be carefully constructed. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)