a three dimensional finite element method with arbitrary polyhedral elements the variable element topology finite element method vetfem is a finite element like galerkin approximation method in which the elements may take arbitrary polyhedral form a complete development of the vetfem is given here for both two and three dimensions a kinematic enhancement of the displacement based formulation is also given which effectively treats the case of near incompressibility convergence of the method is discussed and then illustrated by way of a 2d problem in elastostatics also the vetfem s performance is compared to that of the conventional fem with eight node hex elements in a 3d finite deformation elastic plastic problem the main attraction of the new method is its freedom from the strict rules of construction of conventional finite element meshes making automatic mesh generation on complex domains a significantly simpler matter copyright 2006 john wiley sons ltd

topology optimization using polytopes abstract meshing complex engineering domains is a challenging task arbitrary polyhedral meshes can provide the much needed flexibility in automated discretization of such domains the geometric property of polyhedral meshes such as its unstructured nature and the connectivity of faces between elements makes them specially attractive for topology optimization applications numerical anomalies in designs such as the single node connections and checkerboard pattern can be naturally circumvented with polyhedrons in the current work we solve the governing three dimensional elasticity state equation using the virtual element method vem approach the main characteristic difference between vem and standard finite element methods fem is that in vem the canonical basis functions are not constructed explicitly rather the stiffness matrix is computed directly utilizing a projection map which extracts the linear component of the deformation such a construction guarantees the satisfaction of the patch test used by engineers as an indicator of optimal convergence of numerical solutions under mesh refinement finally the computations reduce to the evaluation of matrices which contain purely geometric surface facet quantities the present work focuses on the first order vem in which the degrees of freedom are associated with the vertices the features of the current optimization approach are demonstrated using numerical examples for compliance minimization and compliant mechanism problems

the natural element method in solid mechanics the application of the natural element method nem 1 2 to boundary value problems in two dimensional small displacement elastostatics is presented the discrete model of the domain consists of a set of distinct nodes n and a polygonal description of the boundary in the natural element method the trial and test functions are constructed using natural neighbour interpolants these interpolants are based on the voronoi tessellation of the set of nodes n the interpolants are smooth c 1 everywhere except at the nodes where they are c 0 in one dimension nem is identical to linear nite elements the nem interpolant is strictly linear between adjacent nodes on the boundary of the convex hull which facilitates imposition of essential boundary conditions a methodology to model material discontinuities and non convex bodies cracks using nem is also described a standard displacement based galerkin procedure is used to obtain the discrete system of linear equations application of nem to various problems in solid mechanics which include the patch test gradient problems bimaterial interface and a static crack problem are presented excellent agreement with exact analytical solutions is obtained which exemplies the accuracy and robustness of nem and suggests its potential application in the context of other classes of problems crack growth plates and large deformations to name a few 1998 john wiley sons ltd

adaptive computations using material forces and residual based error estimators on quadtree meshes quadtree is a hierarchical data structure that is well suited for h adaptive mesh refinement due to the presence of hanging nodes classical shape functions are non conforming on quadtree meshes in this paper we use natural neighbor basis functions to construct conforming interpolants on quadtree meshes to this end the recently proposed construction of polygonal basis functions is adapted to quadtree elements a fast technique for calculating stiffness matrix on quadtree meshes is introduced residual based error estimators and material force technique are used to estimate the error on quadtree meshes the performance of the adaptive technique is demonstrated through the solution of linear and nonlinear boundary value problems

quadratic serendipity finite elements over convex polyhedra summary the conventional approach to construct quadratic elements for an n sided polygon will yield n n 1 2 shape functions which increases the computational effort it is well known that the serendipity elements based on isoparametric formulation suffers from mesh distortion floater and lai proposed a systematic way to construct higher order approximations over arbitrary polygons using the generalized barycentric coordinates and triangular coordinates this approach ensures 2n shape functions with nodes only on the boundary of the polygon in this paper we extend the polygonal splines approach to three dimensions and construct serendipity shape functions over hexahedra and convex polyhedra this is done by expressing the shape functions using the barycentric coordinates and the local tetrahedral coordinates the quadratic shape functions possess kronecker delta property and satisfy constant linear and quadratic precision the accuracy and the convergence properties of the quadratic serendipity shape elements are demonstrated with a series of standard patch tests the numerical results show that the quadratic serendipity elements pass the patch test yield optimal convergence rate and can tolerate extreme mesh distortion this article is protected by copyright all rights reserved

a variational meshfree method for solving time discrete diffusion equations a meshfree method is developed for solving time discrete diffusion equations that arise in models in brain research important criteria for a suitable method are flexibility with respect to domain geometry and the ability to work with very small moving sources requiring easy refinement possibilities one part of the work concerns a meshfree discretization of the modified helmholtz equation based on the related minimization problem and a local least squares function approximation in a second part a node choosing algorithm is presented that moves around randomly distributed nodes for optimizing the node distribution and varying the node density as needed the method is illustrated by two numerical tests

vertex operator representation of some quantum tori lie algebras we are defining the trigonometric lie subalgebras in bar x infty bar a infty bar b infty bar c infty bar d infty which are the natural generalization of the well known sin lie algebra the embedding formulas into bar x infty are introduced these algebras can be considered as some lie algebras of quantum tori an irreducible representation ofa b series of trigonometric lie algebras is constructed special cases of the trigonometric lie factor algebras which can be considered as a quantum preserving lie algebra structure deformation of the kac moody algebras are considered

implicit boundary method for determination of effective properties of composite microstructures a method that uses a structured grid to perform micromechanical analysis for determining effective properties of a composite microstructure is presented this approach eliminates the need for constructing a mesh that has nodes along the interfaces between constituent materials of the composite implicit boundary method is used to ensure that interface conditions are satisfied at the material boundaries in this method solution structures for test and trial functions are constructed using approximate step functions such that the interface conditions are satisfied even if there are no nodes on the material interface boundary since a structured grid does not conform to the geometry of the analysis domain the geometry of the microstructure is defined independently using equations of the interface boundary curves surfaces structured grids that overlap the geometry are easy to generate and the elements in the grid are regular shaped and undistorted a numerical example is presented to demonstrate that the proposed solution structure accurately models the solution across material interface and convergence analysis is performed to show that the method converges as the grid density is increased fiber reinforced microstructures are analyzed to compute the effective elastic properties using both 2d and 3d models to show that the results match closely with the ones available in the literature

a study on the performance of natural neighbour based galerkin methods in this paper we address the problem of improving natural element simulations in terms of computational cost several problems are discussed that include an efficient natural neighbour search algorithm and a comparison of different natural neighbour based interpolation algorithms in particular we review the so called pseudo nem a moving least squares like approximation scheme that employs natural neighbours and compare it with traditional sibson and laplace interpolation schemes in terms of both accuracy and computational cost some examples in linear elasticity and visco plasticity are analysed in order to test the proposed schemes in engineering problems

a stabilized and coupled meshfree meshbased method for the incompressible navier stokes equations part i stabilization abstract a stabilized meshfree galerkin method is employed for the approximation of the incompressible navier stokes equations in eulerian or arbitrary lagrangian eulerian ale formulation equal order interpolations for velocities and pressure are used it is well known from the meshbased context i e from finite volume and finite element methods that in convection dominated flow problems in eulerian or ale formulation stabilization is a crucial requirement for reliable solutions also stabilization is needed in order to enable equal order interpolations of the incompressible navier stokes equations standard stabilization techniques developed in a meshbased context are extended to meshfree methods it is found that the same structure of the stabilization schemes may be used however the aspect of the stabilization parameter weighting the stabilization terms has to be reconsidered in part ii of this work the resulting stabilized meshfree galerkin method is coupled with a stabilized finite element method the resulting coupled method employs the comparatively costly meshfree galerkin method only where it is needed i e in areas of the domain where a mesh is difficult to maintain and the efficient meshbased finite element method is used in the rest of the domain the fluid solver resulting from this technique is able to solve complex flow problems involving large deformations of the physical domain and or moving and rotating obstacles

implicit boundary method for finite element analysis using non conforming mesh or grid in the finite element method fem a mesh is used for representing the geometry of the analysis and for representing the test and trial functions by piece wise interpolation recently analysis techniques that use structured grids have been developed to avoid the need for a conforming mesh the boundaries of the analysis domain are represented using implicit equations while a structured grid is used to interpolate functions such a method for analysis using structured grids is presented here in which the analysis domain is constructed by boolean combination of step functions implicit equations of the boundary are used in the construction of trial and test functions such that essential boundary conditions are guaranteed to be satisfied furthermore these functions are constructed such that internal elements through which no boundary passes have the same stiffness matrix this approach has been applied to solve linear elastostatic problems and the results are compared with analytical and finite element analysis solutions to show that the method gives solutions that are similar to the fem in quality but is less computationally expensive for dense mesh grid and avoids the need for a conforming mesh copyright 2007 john wiley sons ltd

weight vectors of the basic a1 1 module and the littlewood richardson rule the basic representation of a1 1 is studied the weight vectors are represented in terms of schur functions a suitable base of any weight space is given the littlewood richardson rule appears in the linear relations among weight vectors

the meshless finite element method a meshless method is presented which has the advantages of the good meshless methods concerning the ease of introduction of node connectivity in a bounded time of order n and the condition that the shape functions depend only on the node positions furthermore the method proposed also shares several of the advantages of the finite element method such as a the simplicity of the shape functions in a large part of the domain b c0 continuity between elements which allows the treatment of material discontinuities and c ease of introduction of the boundary conditions copyright 2003 john wiley sons ltd

structure of some categories of representations of infinite dimensional lie algebras the highest weight representations of a finite dimensional complex semisimple lie algebra 9 have been studied extensively and a number of interesting results have been obtained in the last few years an extensive bibliography is given in 7 in 2 3 a category cy of representations of g was introduced which turns out to be the proper setting for considering various questions regarding highest weight representations the aim of this paper is to extend the study of this notion to a kac moody algebra or more generally to a contragredient lie algebra g a corresponding to a square matrix a over c the study of such algebras was begun independently in 8 14 and subsequently a number of interesting results were proved these results show that many important properties from the finite dimensional setup i e from the context of 9 can be proved in the general setup involving g a in particular the notion of category was extended in 9 to the case of kac moody algebras and used in the proof of combinatorial identities

polytope finite elements in this paper finite elements based on arbitrary convex and non convex polytopes are introduced polytopes in combination with natural element coordinates necs permit a uniform element formulation of interpolation functions that are independent of the dimension of space localization and the number of vertices necs based on the natural neighbor interpolation are restricted to the polytope and can be understood as an extension of the barycentric coordinates on simplexes the differentiation and integration of these interpolation functions on the basis of necs is essential for finite element approximations the accuracy of the finite element interpolation or approximation can be controlled by either applying the h version or by utilizing the p version of the finite element method fem advantages in the handling of hanging nodes are discussed furthermore we present construction methods for lagrangian as well as for hierarchical interpolation functions based on necs numerical experiments on different convex and non convex decompositions will show the usability accuracy and convergence of the developed polytope fem copyright 2007 john wiley sons ltd

the natural neighbour petrov galerkin method for elasto statics in this paper an efficient and accurate meshless natural neighbour petrov galerkin method nnpg is proposed to solve elasto static problems in two dimensional space this method is derived from the generalized meshless local petrov galerkin method mlpg as a special case in the nnpg the local supported trial functions are constructed based on the non sibsonian interpolation and test functions are taken as the three node triangular fem shape functions the local weak forms of the equilibrium equation and the boundary conditions are satisfied in local polygonal sub domains these sub domains are constructed with delaunay tessellations and domain integrals are evaluated over included delaunay triangles by using gaussian quadrature scheme as this method combines the advantages of natural neighbour interpolation with petrov galerkin method together no stiffness matrix assembly is required and no special treatment is needed to impose the essential boundary conditions several numerical examples are presented and the results show the presented method is easy to implement and very accurate for these problems copyright 2005 john wiley sons ltd

bosonization in background of metric and gauge the paper extends the two dimensional bosonization formulas on a riemann surface to the case with abelian gauge field the result is used to bosonize the massless thirring model and as an alternative route to the chiral bosonization

extended finite element method on polygonal and quadtree meshes in this paper we present mesh independent modeling of discontinuous flelds on polygonal and quadtree flnite element meshes this approach falls within the class of extended and generalized flnite element methods where the partition of unity framework is used to introduce additional enrichment functions within the classical displacement based flnite element approximation for crack modeling a discontinuous function and the two dimensional asymptotic crack tip flelds are used as enrichment functions linearly complete partition of unity approximations are adopted on polygonal convex and nonconvex elements and quadtree meshes excellent agreement with reference solution results is obtained for mixed mode stress intensity factors on benchmark crack problems and crack growth simulations without remeshing are conducted on polygonal and quadtree meshes to reveal the potential of the proposed techniques in computational failure mechanics

treatment of material discontinuity in the element free galerkin method abstract a method is presented for application of the element free galerkin method efg to solid mechanics problems containing material discontinuities by using the efg method the trial and test functions for the weak form are constructed with moving least square interpolants in each material domain additional constraints are imposed at the variational level to ensure satisfaction of interface conditions as a result only nodal data no elemental connectivity is needed given c 1 continuity of the interpolant weighting function the dependent variable and its gradient are continuous in each material domain two linear elastic bi material examples are presented to illustrate the effectiveness of the method

new six node and seven node hexagonal finite elements abstract in this paper we introduce a six node and a seven node hexagonal elements both elements are based on the rotated trilinear interpolation in terms of the three directional coordinates optimal a priori error estimates are provided for the new elements by decomposing the consistency error into two parts that both can be estimated using the f e m test some numerical tests are carried out to verify the theoretical analysis comparisons to both the previously studied edge oriented hexagonal elements and the traditional linear triangular elements are also provided to show the efficiency and superiority of the new six node and seven node hexagonal elements

accurate fracture modelling using meshless methods the visibility criterion and level sets formulation and 2d modelling fracture modelling using numerical methods is well advanced in 2d using techniques such as the extended finite element method xfem the use of meshless methods for these problems lags somewhat behind but the potential benefits of no meshing particularly in 3d prompt continued research into their development in methods where the crack face is not explicitly modelled as the edge of an element for instance two procedures are instead used to associate the displacement jump with the crack surface the visibility criterion and the diffraction method the visibility criterion is simple to implement and efficient to compute especially with the help of level set coordinates however spurious discontinuities have been reported around crack tips using the visibility criterion whereas implementing the diffraction method in 3d is much more complicated than the visibility criterion in this paper a tying procedure is proposed to remove the difficulty with the visibility criterion so that crack tip closure can be ensured while the advantages of the visibility criterion can be preserved the formulation is based on the use of level set coordinates and the element free galerkin method and is generally applicable for single or multiple crack problems in 2d or 3d the paper explains the formulation and provides verification of the method against a number of 2d crack problems copyright 2011 john wiley sons ltd

a natural element updated lagrangian strategy for free surface fluid dynamics we present a novel algorithm to simulate free surface fluid dynamics phenomena at low reynolds numbers in an updated lagrangian framework it is based on the use of one of the most recent meshless methods the so called natural element method free surface tracking is performed by employing a particular instance of shape constructors called a shapes this means that at each time step the geometry of the domain is extracted by employing a particular member of the finite set of shapes described by the nodal cloud the lagrangian framework allows us to integrate the inertial terms of the navier stokes equations by employing the method of characteristics which are precisely the nodal pathlines a theoretical description of the method is included together with some examples showing its performance

voronoi cell finite difference method for accurate electronic structure calculation of polyatomic molecules on unstructured grids we introduce a new numerical grid based method on unstructured grids in the three dimensional real space to investigate the electronic structure of polyatomic molecules the voronoi cell finite difference vfd method realizes a discrete laplacian operator based on voronoi cells and their natural neighbors featuring high adaptivity and simplicity to resolve multicenter coulomb singularity in all electron calculations of polyatomic molecules this method utilizes highly adaptive molecular grids which consist of spherical atomic grids it provides accurate and efficient solutions for the schrodinger equation and the poisson equation with the all electron coulomb potentials regardless of the coordinate system and the molecular symmetry for numerical examples we assess accuracy of the vfd method for electronic structures of one electron polyatomic systems and apply the method to the density functional theory for many electron polyatomic molecules

polygonal finite elements for topology optimization a unifying paradigm in topology optimization literature the parameterization of design is commonly carried out on uniform grids consisting of lagrangian type finite elements e g linear quads these formulations however suffer from numerical anomalies such as checkerboard patterns and one node connections which has prompted extensive research on these topics a problem less often noted is that the constrained geometry of these discretizations can cause bias in the orientation of members leading to mesh dependent sub optimal designs thus to address the geometric features of the spatial discretization we examine the use of unstructured meshes in reducing the influence of mesh geometry on topology optimization solutions more specifically we consider polygonal meshes constructed from voronoi tessellations which in addition to possessing higher degree of geometric isotropy allow for greater flexibility in discretizing complex domains without suffering from numerical instabilities copyright 2009 john wiley sons ltd

conforming polygonal finite elements summary in this paper conforming finite elements on polygon meshes are developed polygonal finite elements provide greater flexibility in mesh generation and are better suited for applications in solid mechanics which involve a significant change in the topology of the material domain in this study recent advances in meshfree approximations computational geometry and computer graphics are used to construct different trial and test approximations on polygonal elements a particular and notable contribution is the use of meshfree natural neighbour nn basis functions on a canonical element combined with an affine map to construct conforming approximations on convex polygons this numerical formulation enables the construction of conforming approximation on n gons n 3 and hence extends the potential applications of finite elements to convex polygons of arbitrary order numerical experiments on second order elliptic boundary value problems are presented to demonstrate the accuracy and convergence of the proposed method copyright 2004 john wiley sons ltd

global local optimization for parameter structure identification in three dimensional groundwater modeling 1 this paper develops two global local optimization methods for three dimensional parameter structure identification in groundwater modeling parameter structure identification is formulated in terms of solving a generalized inverse problem which allows for a determination of an appropriate level of parameter structure complexity and the identification of its pattern and the associated parameter values the structure complexity is determined by calculating the parameter structure error measured in the prediction space or management space while the structure pattern and the associated parameter values are identified simultaneously by minimizing the fitting residual measured in the observation space the former requires solving a continuous maximum minimum max min optimization problem and the latter requires solving a combinatorial optimization problem in this paper voronoi zonation is used to parameterize the unknown distributed parameter for each given level of structure complexity a sequential global local optimization method which consists of a genetic algorithm a quasi newton method and local search is developed to solve the combinatorial problem in addition the continuous max min problem is transformed to a hierarchical optimization problem and solved by a hybrid global local method sensitivities of state variables to the unknown parameters are calculated by the sensitivity equations the validity and applicability of the proposed methodology are demonstrated by numerical experiments we have shown that the choice of an objective function in model application impacts the determination of the parameter structure complexity

modelling three dimensional piece wise homogeneous domains using the α shape based natural element method in this paper the application of the natural element method nem to the numerical analysis of two and three dimensional piece wise homogeneous domains is presented the nem differs from other meshless methods in its capability to accurately reproduce essential boundary conditions along convex boundaries the shape based extension of this method nem generalizes this behaviour to non convex domains enables us to construct models entirely in terms of the initial cloud of points and allows us to simulate material discontinuities in a straightforward manner in the following sections simple and effective algorithms are presented for the construction of shapes in domains composed of various materials examples are presented in two and three dimensional cases in the context of linear elastostatics showing good performance even with the simple numerical quadrature used copyright 2002 john wiley sons ltd

meshless method for shallow water equations with free surface flow solving problems with free surface often encounters numerical difficulties related to excessive mesh distortion as is the case of dambreak or breaking waves in this paper the natural element method nem is used to simulate a 2d shallow water flows in the presence of theses strong gradients this particle based method used a fully lagrangian formulation based on the notion of natural neighbors in the present study we consider the full non linear set of shallow water equations with a transient flow under the coriolis effect for the numerical treatment of the nonlinear terms we used a lagrangian technique based on the method of characteristics this will allow avoiding divergence of newton raphson scheme when dealing with the convective terms we also define a thin area close to the boundaries and a computational domain dedicated for nodal enrichment at each time step two numerical test cases were performed to verify the well founded hopes for the future of this method in real applications

affine demazure modules and t fixed point subschemes in the affine grassmannian let g be a simple algebraic group defined over c and t be a maximal torus of g for a dominant coweight of g the t fixed point subscheme formula of the schubert variety formula in the affine grassmannian grg is a finite scheme we prove that for all such if g is of type a or d and for many of them if g is of type e there is a natural isomorphism between the dual of the level one affine demazure module corresponding to and the ring of functions twisted by certain line bundle on grg of formula we use this fact to give a geometrical proof of the frenkel kac segal isomorphism between basic representations of affine algebras of a d e type and lattice vertex algebras

the brauer group of burnside rings abstract the brauer group of a commutative ring is an important invariant of a commutative ring a common journeyman to the group of units and the picard group burnside rings of finite groups play an important role in representation theory and their groups of units and picard groups have been studied extensively in this short note we completely determine the brauer groups of burnside rings they vanish

higher order natural element methods towards an isogeometric meshless method the problem of generalizing the natural element method nem in terms of higher order consistency and continuity is addressed here it is done by means of the de boor algorithm the same employed to obtain b splines by linear combinations of linear interpolants in one dimension by noting that any form of natural neighbour interpolation can be considered as a suitable generalization of linear interpolation to two and higher dimensions the de boor algorithm is extended to two or higher dimensions thus obtaining a new form of interpolation that can be used in a galerkin framework to develop a new class of meshless methods this new class of meshless methods closely resembles the isogeometric analysis developed by hughes et al comput methods appl mech eng 2005 194 4135 4195 however unlike b splines the new class of interpolants does not rely on an underlying tensor product quadrilateral mesh it is based on the delaunay triangulation of the cloud of knots and does not require any regularity on the connectivity in addition the new method conserves many of the attractive features of the nem such as strict interpolation on the boundary and thus directs imposition of essential boundary conditions after a theoretical description of the proposed method some numerical examples are shown to test its performance in the context of linear elastostatics copyright 2007 john wiley sons ltd

voronoi cell finite difference method for the diffusion operator on arbitrary unstructured grids voronoi cells and the notion of natural neighbours are used to develop a finite difference method for the diffusion operator on arbitrary unstructured grids natural neighbours are based on the voronoi diagram which partitions space into closest point regions the sibson and the laplace non sibsonian interpolants which are based on natural neighbours have shown promise within a galerkin framework for the solution of partial differential equations in this paper we focus on the laplace interpolant with a two fold objective first to unify the previous developments related to the laplace interpolant and to indicate its ties to some well known numerical methods and secondly to propose a voronoi cell finite difference scheme for the diffusion operator on arbitrary unstructured grids a conservation law in integral form is discretized on voronoi cells to derive a finite difference scheme for the diffusion operator on irregular grids the proposed scheme can also be viewed as a point collocation technique a detailed study on consistency is conducted and the satisfaction of the discrete maximum principle stability is established owing to symmetry of the laplace weight a symmetric positive definite stiffness matrix is realized which permits the use of efficient linear solvers on a regular rectangular or hexagonal grid the difference scheme reduces to the classical finite difference method numerical examples for the poisson equation with dirichlet boundary conditions are presented to demonstrate the accuracy and convergence of the finite difference scheme copyright 2003 john wiley sons ltd

natural neighbour galerkin methods summary natural neighbour co ordinates sibson co ordinates is a well known interpolation scheme for multivariate data tting and smoothing the numerical implementation of natural neighbour co ordinates in a galerkin method is known as the natural element method nem in the natural element method natural neighbour co ordinates are used to construct the trial and test functions recent studies on nem have shown that natural neighbour co ordinates which are based on the voronoi tessellation of a set of nodes are an appealing choice to construct meshless interpolants for the solution of partial dierential equations in belikov et al computational mathematics and mathematical physics 1997 37 1 9 15 a new interpolation scheme non sibsonian interpolation based on natural neighbours was proposed in the present paper the nonsibsonian interpolation scheme is reviewed and its performance in a galerkin method for the solution of elliptic partial dierential equations that arise in linear elasticity is studied a methodology to couple nite elements to nem is also described two signicant advantages of the non sibson interpolant over the sibson interpolant are revealed and numerically veried the computational eciency of the non sibson algorithm in 2 dimensions which is expected to carry over to 3 dimensions and the ability to exactly impose essential boundary conditions on the boundaries of convex and non convex domains copyright 2001 john wiley sons ltd

the meshless galerkin boundary node method for stokes problems in three dimensions the galerkin boundary node method gbnm is a boundary only meshless method that combines an equivalent variational formulation of boundary integral equations for governing equations and the moving least squares mls approximations for generating the trial and test functions in this approach boundary conditions can be implemented directly and easily despite of the fact that the mls shape functions lack the delta function property besides the resulting formulation inherits the symmetry and positive definiteness of the variational problems the gbnm is developed in this paper for solving three dimensional stationary incompressible stokes flows in primitive variables the numerical scheme is based on variational formulations for the first kind integral equations which are valid for both interior and exterior problems simultaneously a rigorous error analysis and convergence study of the method for both the velocity and the pressure is presented in sobolev spaces the capability of the method is also illustrated and assessed through some selected numerical examples copyright 2011 john wiley sons ltd

stabilized conforming nodal integration in the natural element method a stabilized conforming nodal integration scheme is implemented in the natural neighbour method in conjunction with non sibsonian interpolation in this approach both the shape functions and the integration scheme are defined through use of first order voronoi diagrams the method illustrates improved performance and significant advantages over previous natural neighbour formulations the method also shows substantial promise for problems with large deformations and for the computation of higher order gradients copyright 2004 john wiley sons ltd

analysis of 3d solids using the natural neighbour radial point interpolation method abstract in this work an improved meshless method is proposed based on the combination of the natural neighbour finite element method with the radial point interpolation method the natural neighbour radial point interpolation method nnrpim the nodal connectivity and the node dependent integration background mesh are constructed resorting to the voronoi tessellation and to the delaunay triangulation within nnrpim the obtained shape functions pass through all nodes inside the influence cell providing shape functions with the delta kronecker property optimization tests and examples of well known 2d and 3d problems are solved in order to prove the high accuracy and convergence rate of the proposed method

meshless methods with application to metal forming in recent years a new family of computational methods has emerged the so called meshless or mesh free methods have been investigated and used by many researchers for treating a large variety of engineering problems involving usually large displacements as encountered for example in forming process simulations the main advantage of meshless methods is the fact that the interpolation accuracy is not significantly affected by the nodal distribution nevertheless a troublesome task in these techniques is the imposition of essential boundary conditions as in general the kronecker delta property is not satisfied despite of several techniques have been proposed to overcome this problem an appealing alternative technique which allows to circumvent this difficulty lies in the use of the natural neighbor interpolation nem this paper focuses on the description and analysis of the natural element method and its application for simulating some forming processes involving large displacements as well as fixed or moving discontinuities

a local search algorithm for natural neighbours in the natural element method a local basis algorithm for searching natural neighbours in natural element method nem is presented for solving the elasticity problems in this paper comparison with the global sweep algorithm used in natural element method or natural neighbour method nnm for searching natural neighbours the proposed algorithm is more expedient and convenient in the constructions and computation of natural neighbour interpolations in the proposed nem based on local search the laplace non sibson interpolations are constructed with respect to the natural neighbour nodes of the given point which have been locally defined the shape functions from the laplace approximations have the delta function property and the laplace interpolants are strictly linear between adjacent nodes which facilitate imposition of essential boundary conditions and treatment of material discontinuity with ease as it is in the conventional finite element method the laplace interpolants derived from the local algorithm and the global algorithm in nem are identical because of the uniqueness of the voronoi diagram numerical results and convergence studies also show that the present nem based on local search algorithm possesses the same accuracy and rate of convergence as they are in previous nem

implicit boundary method for analysis using uniform b spline basis and structured grid several analysis techniques such as extended finite element method x fem have been developed recently which use structured grid for the analysis implicit boundary method uses implicit equations of the boundary to apply boundary conditions in x fem framework using structured grids solution structures for test and trial functions are constructed using implicit equations such that the boundary conditions are satisfied even if there are no nodes on the boundary in this paper this method is applied for analysis using uniform b spline basis defined over a structured grid solution structures that are c1 or c2 continuous throughout the analysis domain can be constructed using b spline basis functions as a structured grid does not conform to the geometry of the analysis domain the boundaries of the analysis domain are defined independently using equations of the boundary curves surfaces compared with conforming mesh it is easier to generate structured grids that overlap the geometry and the elements in the grid are regular shaped and undistorted numerical examples are presented to demonstrate the performance of these b spline elements the results are compared with analytical solutions as well as with traditional finite element solutions convergence studies for several examples show that b spline elements provide accurate solutions with fewer elements and nodes compared with traditional fem they also provide continuous stress and strain in the analysis domain thus eliminating the need for smoothing stress strain results copyright 2008 john wiley sons ltd

a stabilized and coupled meshfree meshbased method for the incompressible navier stokes equations part ii coupling in part i of this work meshfree galerkin methods have been used for the approximation of the incompressible navier stokes equations in eulerian or arbitrary lagrangian eulerian formulation the problem of stabilization of meshfree methods is addressed there analogously in the meshbased context the finite element method is frequently used in similar stabilized formulations for the simulation of flow problems in order to combine the advantages of both methods different coupling techniques are examined in this part of the work standard coupling approaches are modified in order to fulfill the requirements for a reliable stabilization found in part i of this work the resulting stabilized and coupled meshfree meshbased flow solver employs the comparatively costly meshfree galerkin method only where it is needed i e in areas of the domain where a mesh is difficult to maintain and the efficient meshbased finite element method in the rest of the domain this enables the solution of complex flow problems as thus involving large deformations of the physical domain and or moving and rotating obstacles

polyhedrization of an arbitrary 3d point set abstract given a 3d point set the problem of defining the volume associated dividing it into a set of regions elements and defining a boundary surface is tackled several physical problems need to define volume domains boundary surfaces and approximating functions from a given point distribution this is for instance the case of particle methods in which all the information is the particle positions and there are not boundary surfaces definition until recently all the fem mesh generators were limited to the generation of simple elements as tetrahedral or hexahedral elements or triangular and quadrangular in 2d problems the reason of this limitation was the lack of any acceptable shape function to be used in other kind of geometrical elements nowadays there are several acceptable shape functions for a very large class of polyhedra these new shape functions together with a generalization of the delaunay tessellation presented in this paper gives an optimal marriage and a powerful tool to solve a large variety of physical problems by numerical methods the domain partition into polyhedra presented here is not a standard mesh generation the problem here is for a given node distribution to find a suitable boundary surface and a suitable mesh to be used in the solution of a physical problem by a numerical method to include new nodes or change their positions is not allowed