automatic mesh generation and adaptation by using contours a general and efficient remeshing algorithm is presented for the discretization of arbitrary planar domains into triangular elements in consistency with the given node spacing funstion the contour lines of the node spacing function at suitable calculated levels provide the natural lines of division of the problem domain into subregions where finite elements meshes of different element sizes zre generated using the available general purpose mesh generators

automatic mesh generation over intersecting surfaces a fully automatic general scheme is proposed to determine and analyse the intersections between two groups of surfaces composed of triangular facets by carefully maintaining the spatial position of the lines of intersection in regenerating mesh locally around surface intersections pieces of surfaces can be arbitrarily combined and merged a great variety of objects can be easily created by selectively putting together different surface parts derived from surface intersections the new algorithm is best applied in conjunction with an existing surface mesh generator to enhance its general capability in dealing with objects built from intersecting surfaces in fact it is a powerful surface mesh manipulator and through the repeated use of the process complex structures can be rapidly and accurately constructed

bayesian inference for small sample capture recapture data we consider data on the survival of a population of cephalorhynchus hectori hector s dolphins in a marine area of new zealand to estimate survival probabilities of animal populations a multiple capture recapture sampling scheme can be used in this paper we propose a practical methodology to derive approximations to posterior distributions based on laplace methods we show how to calculate bayes estimates and credible intervals in this setting

on the geometry of wave solutions of a delayed reaction diffusion equation abstract the aim of this paper is to study the existence and the geometry of positive bounded wave solutions to a non local delayed reaction diffusion equation of the monostable type

a new mesh generation scheme for arbitrary planar domains this paper describes a new algorithm to generate interior nodes within any arbitrary multi connected regions the boundary nodes and the interior nodes are then linked up to form the best possible triangular elements by a completely revised technique in an efficient and stable manner owing to the generality of the central generation program the global domain is allowed to be divided into as many irregular subdomains as desired in order to model closely the actual physical situation moreover the boundaries of the sub domains are updated from time to time when necessary to include the possibilities of progressive refinement around a sharp corner generating radiating mesh from a prescribed node generating mesh between two circular arcs etc despite its flexibility and capabilities data for triangulation have been kept to a minimum by a logical input module no connectivity information between subregions is needed and common boundaries are defined once only all these features have contributed to a powerful method to generate 3 node or 6 node triangular element meshes of great variety within the most irregular heterogeneous regions

plotting of contours in a natural way a simple and straightforward scheme for plotting contours is introduced for any function the appropriate contours are traced on the paths of constant function values disclosing the information contained in the shape functions the exactness of the contours matches that of the finite element analysis extreme value considerations must be carried out to decide whether contours appear in an element at all three co ordinate systems are dealt with the local the global and the screen co ordinate system and the necessary mutual transformations a short section deals with the treatment of contour discontinuities across element borders which frequently occur with stresses and heat fluxes finally some examples are shown

existence of global solutions to nonlinear mixed type functional differential equations abstract the paper considers systems of nonlinear mixed type functional differential equations it aims to find conditions for the existence of global solutions with graphs staying in a prescribed domain a relevant result is proved by schauder tychonoff fixed point technique with illustrative examples shown a linear variant of the derived result is formulated comparisons with known results are discussed and some open problems are formulated

analytical and numerical investigation of mixed type functional differential equations this paper is concerned with the approximate solution of a linear non autonomous functional differential equation with both advanced and delayed arguments we search for a solution x t defined for t 1 k k n that satisfies this equation almost everywhere on 0 k 1 and assumes specified values on the intervals 1 0 and k 1 k we provide a discussion of existence and uniqueness theory for the problems under consideration and describe numerical algorithms for their solution giving an analysis of their convergence

numerical treatment of oscillatory functional differential equations in this paper we are concerned with oscillatory functional differential equations that is those equations where all the solutions oscillate under a numerical approximation our interest is in the preservation of qualitative properties of solutions under a numerical discretisation we give conditions under which an equation is oscillatory and consider whether the discrete schemes derived using linear q methods will also be oscillatory we conclude with some general theory

the advancing front mesh generation method revisited this paper presents a mesh generation method of the advancing front type which is designed in such a way that the well known difficulties of the classical advancing front method are not present the retained solution consists of using the first steps of a voronoi delaunay method to construct a background mesh which is then used to govern the algorithm the two dimensional case is considered in detail and possible extensions to adaption problems and three dimensions are indicated

delaunay triangulation of non convex planar domains this paper investigates the possibility of integrating the two currently most popular mesh generation techniques namely the method of advancing front and the delaunay triangulation algorithm the merits of the resulting scheme are its simplicity efficiency and versatility with the introduction of non delaunay line segments the concept of using delaunay triangulation as a means of mesh generation is clarified an efficient algorithm is proposed for the construction of delaunay triangulations over non convex planar domains interior nodes are first generated within the planar domain these interior nodes and the boundary nodes are then linked up together to produce a valid triangulation in the mesh generation process the delaunay property of each triangle is ensured by selecting a node having the smallest associated circumcircle in contrast to convex domains intersection between the proposed triangle and the domain boundary has to be checked this can be simply done by considering only the non delaunay segments on the generation front through the study of numerous examples of various characteristics it is found that high quality triangular element meshes are obtained by the proposed algorithm and the mesh generation time bears a linear relationship with the number of elements nodes of the triangulation

automatic mesh generation with tetrahedron elements to reduce the manual work involved in the application of the fem in practice preprocessors can be applied for the construction of network structures which are complicated in generation strategy and do not form any optimum discrete structure the time necessary for generation can be minimized even more by the application of only one element type within the whole network structure a technique for the automatic generation of 3d network structures with tetrahedron elements is presented in this paper in this proposed technique the nodal points of the network structure must be defined manually before the generation procedure since a random positioning of points is usually undesirable for fem calculation the nodal points are connected by a program to a network structure consisting of tetrahedron elements which have optimum form for the numerical computation of the element matrices after the generation the element sides forming any part of the boundary surface of the network structure can be automatically identified if necessary the network structure can be automatically refined

3d delaunay mesh generation coupled with an advancing front approach abstract this paper describes a fully automatic mesh generation method suitable for domains of any shape in r 3 initially a so called boundary mesh is generated wherein internal points are created using advancing front point placement and inserted using a delaunay method the algorithm combines the advantages of efficiency and nice mathematical properties of a delaunay approach with advancing front high quality point placement strategy several three dimensional examples are presented to demonstrate the overall efficiency and the relevance of the combined procedure the present method can be extended to isotropic or anisotropic adaptive mesh generation

an automatic adaptive refinement finite element procedure for 2d elastostatic analysis an automatic adaptive refinement procedure for finite element analysis is presented the procedure is applied to two dimensional elastostatic problems to obtain solutions of prescribed accuracy through the combined use of new mesh generator using contour developed by lo1 and the concept of strain energy concentration high quality graded finite element meshes are generated the whole process is fully automatic and no user intervention is required during the successive cycles of the mesh refinements the zienkiewicz and zhu2 error estimator is found to be effective and has been adopted for the present implementation in the numerical examples tested the error estimator gives an accurate error norm estimation and the effectivity index of the estimator converges to a value close to unity

a new concept in two dimensional auto adaptative mesh generation the new method presented here is capable of building finite element meshes and managing their adaptation simultaneously to the object load case and geometry before any calculations i e an a priori mesh adaptation is conducted the principle relies on an analogy between a finite element mesh and the equilibrium position of a network of branches each branch is adequately sized by setting force length ratios called force densities starting from these data the nodal co ordinates are obtained through the solution of a linear system which describes the equilibrium state of the net this method seems very attractive since the only given data are a connectivity table the number of boundary and interior nodes and a geometrical description of the boundaries

mesh rezoning of 2d isoparametric elements by inversion the method uses techniques from elimination theory to solve the parametric inversion problem for each node on the new undistorted mesh these parameter values are then used in the elemental shape functions to transfer the nodal state variables from the distorted mesh to each node in the new mesh by interpolation the method has been implemented for bilinear and biquadratic elements the method is based on fundamental finite element approximations since the interpolation functions which define the element are also used to perform rezoning

parametric surface meshing using a combined advancing front generalized delaunay approach an indirect method for meshing parametric surfaces conforming to a user specifiable size map is presented first from this size specification a riemannian metric is defined so that the desired mesh is one with unit length edges with respect to the related riemannian space the so called unit mesh then based on the intrinsic properties of the surface the riemannian structure is induced into the parametric space finally a unit mesh is generated completely inside the parametric space such that it conforms to the metric of the induced riemannian structure this mesh is constructed using a combined advancing front delaunay approach applied within a riemannian context the proposed method can be applied to mesh composite parametric surfaces several examples illustrate the efficiency of our approach copyright 2000 john wiley sons ltd

the numerical solution of forward backward differential equations decomposition and related issues this paper focuses on the decomposition by numerical methods of solutions to mixed type functional differential equations mfdes into sums of forward solutions and backward solutions we consider equations of the form x t ax t bx t 1 cx t 1 and develop a numerical approach using a central difference approximation which leads to the desired decomposition and propagation of the solution we include illustrative examples to demonstrate the success of our method along with an indication of its current limitations

an automatic procedure with a control of accuracy for finite element analysis in 2d elasticity abstract this paper gives a procedure for an automation of the entire finite element analysis for 2d or axisymmetric elastic structures with a control of accuracy the user describes the problem and the level of desired accuracy the procedure then provides an approximate solution for a minimal computation cost this procedure uses an error measure based on the constitutive relation 1 5 and an efficient adaptive technique 6 which automatically take account of the regions of stress concentration examples are presented for discretizations using 3 or 6 node triangular elements

nonoscillation for functional differential equations of mixed type abstract an example is given to show that the linear autonomous functional differential equation of mixed type t 1 1 d s x t s 0 may have a nonoscillatory solution in spite of the nonexistence of real roots of its characteristic equation under a regularity condition on at 1 exponential boundedness and asymptotic expansions are obtained for the nonoscillatory solutions

an analysis of metal forming processes using large deformation elastic plastic formulations a concise survey of the literature related to the large deformation elasto plasticity problems including unilateral contact and friction is presented together with an extension of the friction law for large deformation analysis starting from the principle of virtual work the so called total lagrangian and updated lagrangian formulations are derived based on some fundamental assumptions in linearizing the nonlinear equations by introducing the zaremba jaumann co rotational increment to the cauchy stress tensor the classical prandtl reuss equations are generalized for describing the elastic plastic material behavior to allow a proper consideration of the contact conditions in the incremental analysis a general friction law with an associated isotropic coulomb sliding rule is obtained by the similarity between dry friction and plasticity finite element discretizations and approximations are applied to the resulting formulation of the updated lagrangian approach four example problems are solved to test the formulations developed in this paper the emphasis is made toward the numerical accuracy of the finite element solutions

mixed type functional differential equations a numerical approach the equations considered in this paper are mixed type functional equations sometimes known as forward backward differential equations that take the form u t au t bu t 1 cu t 1 t i r we consider basic existence and uniqueness properties when i t 1 t 2 and we seek solutions u c t 1 1 t 2 1 that satisfy u t w 1 t t t 1 1 t 1 u t w 2 t t t 2 t 2 1 for prescribed functions w 1 w 2 absolutely continuous respectively on t 1 1 t 1 t 2 t 2 1 with arbitrary boundary conditions specified in this way the problem turns out to be ill posed and so existence and uniqueness questions have an important role to play in developing numerical schemes we consider with t 1 t 2 n numerical approximations of a solution when it exists the numerical methods that we consider are linear q methods and we investigate computationally their effectiveness through some illustrative examples

effective and practical h p version adaptive analysis procedures for the finite element method two practical and effective h p type finite element adaptive procedures are presented the procedures allow not only the final global energy norm error to be well estimated using hierarchic p refinement but in addition give a nearly optimal mesh the design of this is guided by the local information computed on the previous mesh the desired accuracy can always be obtained within one or at most two h p refinements the rate of convergence of the adaptive h p version analysis procedures has been tested for some examples and found to be very strong the presented procedures can easily be incorporated into existing p or h type code structures

robust boundary triangulation and delaunay triangulation of arbitrary planar domains a simple and robust boundary triangulation algorithm is proposed and based on it completely automatic delaunay mesh generation procedures are developed the algorithm is equally applicable to convex non convex and multiply connected planar domains in this approach given the nodes the number of triangles formed is precisely known and any desired control over mesh generation is possible

a class of data structures for 2 d and 3 d adaptive mesh refinement a family of tree data structures for adaptive mesh refinement is described and details concerning the associated logic are provided the data structures encompass triangular elements and quadrilateral elements in two dimensions and quadrilateral bricks in three dimensions furthermore both linear bilinear and quadratic biquadratic element types respectively are developed representative refinement results are given for the bilinear trilinear and biquadratic types and associated performance studies made for the refinement procedure