Studies on two concurrent solvers for finite element analysis

This paper describes a study carried out on the development and implementation of two parallel equation solvers for static finite element analysis. The two direct solvers, one for banded storage and the other for skyline profile storage, are implemented on a tightly coupled shared memory system. Certain key issues like (algorithmic) portability across different parallel architectures, matrix sparsity and vectorisation have been kept in mind while designing the algorithms. Performance studies have been conducted by varying the number of processors and the size of the problem. The results indicate that higher efficiencies can be obtained with both the algorithms described in this paper. However, one has to obtained with both the algorithms described in this paper. However, one has to choose the appropriate solver based on the concurrent approach chosen for paralleling the finite element code. The pseudo-codes, the concurrent implementation of the two solvers, both for shared and message passing systems are presented.     

图像重建中 Total Variation 正则化项的有限元计算方法

为在迭代图像重建算法中获得更高质量的重建图像,推导出TV（Total Variation）正则化项关于重建图像的Fréchet导数,并给出该导数的有限元表示;利用两个数值实验,分别采用不同的网格尺寸和不同的形函数验证该有限元表示结果.数值实验结果表明：采用相同的k次单纯形元时,随着网格不断加密,计算结果的L1和L2误差均下降;采用相同的网格时,线性单纯形元函数计算结果明显优于分片常数有限元和二次单纯形元计算结果.     

Adaptive error control for multigrid finite element

We consider the problem of adaptive error control in the finite element method including the error resulting from, inexact solution of the discrete equations. We prove a posteriori error estimates for a prototype elliptic model problem discretized by the finite element with a canomical multigrid algorithm. The proofs are based on a combination of so-called strong stability and, the orthogonality inherent in both the finite element method can the multigrid algorithm.     

From Raster to Vectors: Extracting Visual Information from Line Drawings

Vectorisation of raster line images is a relatively mature subject in the document analysis and recognition field, but it is far from being perfect as yet. We survey the methods and algorithms developed to-date for the vectorisation of document images, and classify them into six categories: Hough transform-based, thinning-based, contour-based, run-graph-based, mesh-pattern-based, and sparse-pixel-based. The purpose of the survey is to provide researchers with a comprehensive overview of this technique, to enable a judicious decision while selecting a vectorisation algorithm for a system under development or a newly developed vectorisation algorithm. Received: 10 November 1998?Received in revised form: 7 January 1999?Accepted: 7 January 1999     

Comparing scalar and vector forms of the finite element method by example of an elliptic cylinder

An algorithm for constructing the stiffness matrix of a quadrangular curvilinear finite element in the form of a fragment of the middle surface of an elliptic cylinder with 18 degrees of freedom in the node is given. Implementation of the finite-difference procedure includes two variants of approximation of the sought variables, i.e., a scalar one and a vector one. Numerical examples are given and prove that the vector approximation has principal advantages over the scalar approximation for arbitrary shells with significant gradients of curvature of the lines of the middle surface or allowing for displacement as a rigid body.     

Adaptive multiple-levelh-refinement in automated finite element analyses

This paper discusses an automatic, adaptive finite element modeling system consisting of mesh generation, finite element analysis, and error estimation. The individual components interact with one another and efficiently reduce the finite element error to within an acceptable value and perform only a minimum number of finite element analyses.One of the necessary components in the automated system is a multiple-level local remeshing algorithm. Givenh-refinement information provided by an a posteriori error estimator, and adjacency information available in the mesh data structures, the local remeshing algorithm grades the refinement toward areas requesting refinement. It is shown that the optimal asymptotic convergence rate is achieved, demonstrating the effectiveness of the intelligent multiple-level localh-refinement.     

基于Jaumin的等参单元算法框架设计

针对等参有限元的计算特点和有限元软件多种单元的开发需求,基于高性能计算程序开发框架Jaumin,使用面向对象语言,采用抽象和多态技术以及工厂模式,为有限元软件PANDA设计等参单元算法框架.该框架具有良好的可复用性及可扩展性,开发过程清晰,有利于提高开发效率.给出等参单元算法框架中各个模块所对应的类以及类的接口.实例表明用PANDA中已实现的等参单元计算结果与ANSYS的计算结果一致.     

An energy conserving non-linear dynamic finite element formulation for flexible composite laminates

Finite element formulation for non-linear dynamic analysis of flexible composite laminates is presented. A first-order shear-deformation theory, capable of modelling finite deformations and finite rotations in geometrically exact manner, is developed. A model allows simulation of a general elastic material with varied mass density, degree of orthotropy and elastic material parameters and is suitable for non-linear elasto-dynamic analysis of relatively thin and flexible laminates composed of fibre-reinforced composites. Coupling of mid-surface and shell-director fields is exactly taken into account, so that the kinetic energy is not of simple quadratic form. An implicit, one-step, second-order accurate numerical time-integration scheme is applied. In particular, the energy and momentum conserving algorithm, which exactly preserves the fundamental constants of the shell-like body motion, is accomodated for composite laminates. Spatial finite element discretization is based on the four noded multilayered shell finite element with isoparametric interpolations. Fully discrete weak form of the initial boundary value problem is consistently linearized in order to achieve a quadratic rate of asymptotic convergence typical for the Newton–Raphson based solution procedures. Numerical examples are presented.     

The three-dimensional beam theory: Finite element formulation based on curvature

The article introduces a new finite element formulation of the three-dimensional ‘geometrically exact finite-strain beam theory’. The formulation employs the generalized virtual work principle with the pseudo-curvature vector as the only unknown function. The solution of the governing equations is obtained by using a combined Galerkin-collocation algorithm. The collocation ensures that the equilibrium and the constitutive internal force and moment vectors are equal at a set of chosen discrete points. In Newton’s iteration special update procedures for the pseudo-curvature and rotational vectors have to be employed because of the non-linearity of the configuration space. The accuracy and the efficiency of the derived numerical algorithm are demonstrated by several examples.     

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.     

Comparison of boundary element and finite element methods for dynamic analysis of elastoplastic plates

Boundary and finite element methodologies for the determination of the response of inelastic plates are compared and critically discussed. Flexural dynamic plate bending problems are considered and a hardening elastoplastic constitutive model is used to describe material behaviour. The domain/boundary element methodology using linear boundary and quadratic interior elements and the finite element method with quadratic Mindlin plate elements are used in this work. The discretized equations of motion in both methodologies are solved by an efficient step-by-step time integration algorithm. Numerical results obtained are presented and compared in order to access the accuracy and computational efficiency of the two methods. In order to make the comparison as meaningful as possible, boundary and finite element computer codes developed by the author are used in this paper. In general, boundary elements appear to be a better choice than finite elements with respect to computational efficiency for the same level of accuracy.     

Boundary element analysis of elastic contact problems using gap finite elements

Gap finite elements provide a practical approach for dealing with elastic contact problems, and it is not possible to derive something similar with boundary elements. This work introduces a simple technique for the analysis of elastic contact problems by coupling a gap finite element subregion with boundary element subregions. The developed algorithm proves to be accurate and reliable, combining the advantages within contact problems of both the gap finite element and the boundary element method.     

Large scale finite element analyses on a vector processor

Linear and nonlinear finite element software development considerations for vector processors are presented. Areas of discussion include performance measurement, data management, element level calculations and nonlinear problem solution. An example problem which demonstrates software performance is also presented.Incorporation of the methods presented in this paper can lead to finite element software which requires approximately one tenth the CPU time and as little as one-hundredth the I/O effort of conventional software.     

A hybrid ant colony optimization approach for finite element mesh decomposition

This paper examines the application of the ant colony optimization algorithm to the partitioning of unstructured adaptive meshes for parallel explicit time-stepping finite element analysis. The concept of the ant colony optimization technique for finding approximate solutions to combinatorial optimization problems is described.The application of ant colony optimization for partitioning finite element meshes based on triangular elements is described.A recursive greedy algorithm optimization method is also presented as a local optimization technique to improve the quality of the solutions given by the ant colony optimization algorithm. The partitioning is based on the recursive bisection approach.The mesh decomposition is carried out using normal and predictive modes for which the predictive mode uses a trained multilayered feed-forward neural network which estimates the number of triangular elements that will be generated after finite elements mesh generation is carried out.The performance of the proposed hybrid approach for the recursive bisection of finite element meshes is examined by decomposing two mesh examples.     

3D finite element meshing from imaging data

This paper describes an algorithm to extract adaptive and quality 3D meshes directly from volumetric imaging data. The extracted tetrahedral and hexahedral meshes are extensively used in the finite element method (FEM). A top-down octree subdivision coupled with a dual contouring method is used to rapidly extract adaptive 3D finite element meshes with correct topology from volumetric imaging data. The edge contraction and smoothing methods are used to improve mesh quality. The main contribution is extending the dual contouring method to crack-free interval volume 3D meshing with boundary feature sensitive adaptation. Compared to other tetrahedral extraction methods from imaging data, our method generates adaptive and quality 3D meshes without introducing any hanging nodes. The algorithm has been successfully applied to constructing quality meshes for finite element calculations.     

An assembled surface normal algorithm for interior node removal in three-dimensional finite element meshes

An algorithm is developed for identifying interior nodes and edges in finite element meshes of three-dimensional solids. The algorithm is extremely simple and quite fast. The interior nodes are identified by assembling the normals to all surfaces of the model according to the usual finite element assembly procedure. Comparison with a sort-search algorithm shows a tenfold reduction in running time; running time is a linear function of the number of nodes or elements.     

Panpenalty finite element programming for plastic limit analysis

A unified panpenalty finite element programming method for limit analysis is established based on the theory of convex analysis, and a penalty-duality finite element model is constructed, which provides an efficient algorithm for the exact solution of the safety factor. In order to reduce the number of degrees-of-freedom in nonlinear programming, a generalized matrix inverse technique is suggested, resulting in a decrease in computer time. Several numerical results for structural analysis are presented.     

Complementary error bounds for foolproof finite element mesh generation

The use of complementary variational principles in finite element analysis is examined. It is shown that complementary finite element solutions provide an element by element measure of the accuracy of the solution. By solving a problem repeatedly, beginning with a coarse mesh and refining those elements having the largest errors, an automatic, foolproof finite element mesh generation procedure is developed. Finite element solutions obtained by the new procedure have the property that the finest elements are concentrated in regions of greatest need while large elements are found in less important regions. A computer program which implements the new algorithm is described and examples of finite element solutions generated by the program are presented.     

A Dorodnitsyn finite element formulation for turbulent boundary layers

The Dorodnitsyn boundary layer formulation is combined with a modified Galerkin finite element formulation and an implicit, non-iterative marching scheme to generate a computational algorithm that is both accurate and very economical. For four representative pressure gradient cases taken from the 1968 Stanford Turbulent Boundary Layer Conference the Dorodnitsyn finite element formulation is compared with a Dorodnitsyn spectral formulation and a representative finite difference package. All methods produce solutions of high accuracy but the Dorodnitsyn finite element formulation is about ten times more economical than the other methods.     

Non-linear analysis of structures by the finite element method as a supplement to a linear analysis

The discrete elements of finite dimensions which replace the structural continuum in the finite element method can always be chosen sufficiently small that the linear relations between element deformations and element stresses remain valid to the same degree of approximation as is considered acceptable in the linear theory of elasticity. This observation formed the basis for the treatment of geometrical nonlinearities by Argyris and his co-workers in their natural mode technique [1]and [2].Here we give an alternative development of the theory. The element deformations, linearly related to nodal displacements and rotations in a local coordinate system, are expressed as analytic functions of the nodal coordinates in the global system. Then, for structures with an initially linear behaviour, the stability and postbuckling analysis is developed on the basis of the general theory founded by Koiter [3].The theory is illustrated by the example of frame-structures. The location of the nodal points is defined in terms of the displacement vector, while the orientation of an orthogonal triad attached to each nodal point is described by means of modified angular coordinates of Euler. The accuracy of the analysis is demonstrated for a problem solved analytically by Koiter [5]and verified experimentally by Roorda [4].