bipolar fuzzy graphs in this paper we introduce the notion of bipolar fuzzy graphs describe various methods of their construction discuss the concept of isomorphisms of these graphs and investigate some of their important properties we then introduce the notion of strong bipolar fuzzy graphs and study some of their properties we also discuss some propositions of self complementary and self weak complementary strong bipolar fuzzy graphs

on the k tuple domination of generalized de brujin and kautz digraphs a vertex u in a digraph g v a is said to dominate itself and vertices v such that u v a for a positive integer k a k tuple dominating set of g is a subset d of vertices such that every vertex in g is dominated by at least k vertices in d the k tuple domination number of g is the minimum cardinality of a k tuple dominating set of g this paper deals with the k tuple domination problem on generalized de bruijn and kautz digraphs we establish bounds on the k tuple domination number for the generalized de bruijn and kautz digraphs and we obtain some conditions for the k tuple domination number attaining the bounds

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

variable node elements for non matching meshes by means of mls moving least square scheme a new class of finite elements is described for dealing with non matching meshes for which the existing finite elements are hardly efficient the approach is to employ the moving least square mls scheme to devise a class of elements with an arbitrary number of nodal points on the parental domain this approach generally leads to elements with the rational shape functions which significantly extends the function space of the conventional finite element method with a special choice of the nodal points and the base functions the method results in useful elements with the polynomial shape functions for which the c 1 continuity breaks down across the boundaries between the subdomains comprising one element the present scheme possesses an extremely high potential for applications which deal with various problems with discontinuities such as material inhomogeneity crack propagation phase transition and contact mechanics the effectiveness of the new elements for handling the discontinuities due to non matching interfaces is demonstrated using appropriate examples

introduction to fuzzy hypergraphs and hebbian structures abstract any finite collection of fuzzy subsets over a finite ground field determines a fuzzy hypergraph subtract the word fuzzy and the statement defines a crisp hypergraph from this inauspicious beginning hypergraph theory has become an interesting and useful discipline in this brief introduction where serious development must occur elsewhere a glimpse of what may be done within a fuzzy setting has been initiated of considerable importance is the question of applications the focal point in this regard is an extended outline which expresses an implementation of fuzzy hypergraphs into hebbian structures as introduced by hebb 1949 in his distinguished treatise the organization of behavior a neuropsychological theory

treatment of material discontinuities in finite element computations we consider finite element analysis of problems with discontinuous material coefficients for applications in which the material interface crosses an element we develop special elements with an embedded flux constraint at the interface this new procedure is compared with the standard finite element method with interface coincident with the element boundary and with an existing method proposed by steven 1 supporting numerical studies are conducted and rates of convergence for the solution and interface flux are examined some local superconvergence behaviour is observed

orbital hp clouds for solving schrodinger equation in quantum mechanics solving schrodinger equation in quantum mechanics presents a challenging task in numerical methods due to the high order behavior and high dimension characteristics in the wave functions in addition to the highly coupled nature between wave functions this work introduces orbital and polynomial enrichment functions to the partition of unity for solution of schrodinger equation under the framework of hp clouds an intrinsic enrichment of orbital function and extrinsic enrichment of monomial functions are proposed due to the employment of higher order basis functions a higher order stabilized conforming nodal integration is developed the proposed methods are implemented using the density functional theory for solution of schrodinger equation analysis of several single and multi electron nucleus structures demonstrates the effectiveness of the proposed method

subband image coding using watershed and watercourse lines of the wavelet transform reports progress in primitive based image coding using nonorthogonal dyadic wavelets a 3d isotropic wavelet is used to approximate the difference of gaussians d o g operator convolution of the image with dilated versions of the wavelet produces three band pass signals that approximate multiscale smoothed second derivatives an additional convolution of the image with a gaussian shaped low pass wavelet creates a fourth subband signal that preserves low frequency information not described by the three band pass signals the authors show that the original image can be recovered from the watershed and watercourse lines of the three band pass signals plus the lowpass subband signal by thresholding the watershed watercourse representation subsampling the low pass subband and using edge post emphasis the authors achieve data reduction with little loss of fidelity further compression of the watersheds and watercourses is achieved by chain coding their shapes and predictive coding their amplitudes prior to lossless arithmetic coding results are presented for grey level test images at data rates between 0 1 and 0 3 b pixel

the arithmetic of function fields 2 the cyclotomic theory contents i the ciassical rheoy qf cutx es orer a finite jeld 2 the cfclotomic construction for number jelds and function jields 2 1 number fields 2 2 function fields 3 complex arld p adic zeta functions 3 1 the complex theory 3 2 the p adic theory 4 classical iwasabila rheory 4 1 kummer s criterion 4 2 the theoq of the tower 5 two variable zera functions 5 1 the theory at infinity 5 2 special values 6 the theory for futzction fields 6 1 the basic set up 6 2 the kummer criterion 6 3 the theory of the tower 7 l nirs 7 i number fields 7 2 function fields references

a jbig based approach to the encoding of contour maps previously a new technique for the lossless encoding of contour maps was introduced based on the concept of transition points in this paper we show that by using a simple representation for the transition points i e the map of transition points the problem of encoding arbitrary contour maps can be easily converted into a problem of lossless image coding experimental results show that the joint bilevel image experts group jbig image coding standard can be used successfully for encoding maps of transition points outperforming in most cases differential chain coding moreover if we take into account that jbig codecs are available as off the shelf components then the effort required to implement the proposed method is small

harmonic analysis and the flow of a drinfeld module abstract let c be the carlitz module associated to a fr u associated to c there are two types of flows a naive flow coming from the additive group and a twisted flow coming from the theory of v adic measures v e spec a the study of these flows leads us to the introduction of a new type of fourier transform for continuous characteristic p valued functions on zp this fourier transform is an invertible operator from continuous functions to continuous functions we establish analogs of classical results such as parseval s theorem and poisson summation the transforms in this paper should have applications in the study of the special functions i e characteristic p valued zeta and gamma functions that appear in the arithmetic of function fields indeed the techniques introduced here may eventually lead to the construction of such objects as theta series

an efficient augmented finite element method for arbitrary cracking and crack interaction in solids summary this paper presents an augmentation method that enables bilinear finite elements to efficiently and accurately account for arbitrary multiple intra elemental discontinuities in 2d solids the augmented finite element method a fem employs four internal nodes to account for the crack displacements due to an intra elemental weak or strong discontinuity and it permits repeated elemental augmentation to include multiple interactive cracks it thus enables a unified treatment of damage evolution from a weak discontinuity to a strong discontinuity and to multiple interactive cohesive cracks all within a single bilinear element that employs standard external nodal dofs only a novel elemental condensation procedure has been developed to solve the internal nodal dofs as functions of the external nodal dofs for any irreversible piece wise linear cohesive laws it leads to a fully condensed elemental equilibrium equation with mathematical exactness eliminating the need for nonlinear equilibrium iterations at elemental level the new a fem s high fidelity simulation capabilities to interactive cohesive crack formation and propagation in homogeneous and heterogeneous solids have been demonstrated through several challenging numerical examples it is shown that the proposed a fem empowered by the new elemental condensation procedure is numerically very efficient accurate and robust copyright 2014 john wiley sons ltd

blending isogeometric analysis and local maximum entropy meshfree approximants abstract we present a method to blend local maximum entropy lme meshfree approximants and isogeometric analysis the coupling strategy exploits the optimization program behind lme approximation treats isogeometric and lme basis functions on an equal footing in the reproducibility constraints but views the former as data in the constrained minimization the resulting scheme exploits the best features and overcomes the main drawbacks of each of these approximants indeed it preserves the high fidelity boundary representation exact cad geometry of isogeometric analysis out of reach for bare meshfree methods and easily handles volume discretization and unstructured grids with possibly local refinement while maintaining the smoothness and non negativity of the basis functions we implement the method with b splines in two dimensions but the procedure carries over to higher spatial dimensions or to other non negative approximants such as nurbs or subdivision schemes the performance of the method is illustrated with the heat equation and linear and nonlinear elasticity the ability of the proposed method to impose directly essential boundary conditions in non convex domains and to deal with unstructured grids and local refinement in domains of complex geometry and topology is highlighted by the numerical examples

fuzzy planar graphs fuzzy planar graph is a very important subclass of fuzzy graph in this paper two types of edges are mentioned for fuzzy graphs effective edges and considerable edges in addition a comparative study between kuratowski s graphs and fuzzy planar graph is made a new concept of a strong fuzzy planar graph is introduced some related results are established these results have certain applications in subway tunnels routes oil gas pipelines representation etc it is also shown that an image can be represented by a fuzzy planar graph and contraction of such an image can be made with the help of a fuzzy planar graph

free surface fluid dynamics on moving domains this paper presents a lagrangian approach for the simulation of two dimensional free surface flows along with a systematic validation fluid flow is traditionally modeled using an eulerian description in association with finite differences and more recently finite elements free surface flow introduces new difficulties in connection with the time dependence of the domain the proposed approach sets a framework for meshfree and finite element formulations it is extended to two phase media in preisig and zimmermann m preisig th zimmermann two phase free surface fluid dynamics on moving domains j comput phys 229 7 2010 2740 2758 in this paper triangular finite elements and a remeshing procedure to avoid excessive element distortion are chosen for their robustness convergence of the lagrangian description is analyzed and compared to results obtained with an eulerian description the equivalence of the two formulations for confined flows is demonstrated numerically illustrations include stratified flow flow over a backward facing step propagation of a solitary wave and dam break meshfree formulations will be addressed in separate papers c 2010 elsevier b v all rights reserved

a particle method for history dependent materials abstract a broad class of engineering problems including penetration impact and large rotations of solid bodies causes severe numerical problems for these problems the constitutive equations are history dependent so material points must be followed this is difficult to implement in a eulerian scheme on the other hand purely lagrangian methods typically result in severe mesh distortion and the consequence is ill conditioning of the element stiffness matrix leading to mesh lockup or entanglement remeshing prevents the lockup and tangling but then interpolation must be performed for history dependent variables a process which can introduce errors proposed here is an extension of the particle in cell method in which particles are interpreted to be material points that are followed through the complete loading process a fixed eulerian grid provides the means for determining a spatial gradient because the grid can also be interpreted as an updated lagrangian frame the usual convection term in the acceleration associated with eulerian formulations does not appear with the use of maps between material points and the grid the advantages of both eulerian and lagrangian schemes are utilized so that mesh tangling is avoided while material variables are tracked through the complete deformation history example solutions in two dimensions are given to illustrate the robustness of the proposed convection algorithm and to show that typical elastic behavior can be reproduced also it is shown that impact with no slip is handled without any special algorithm for bodies governed by elasticity and strain hardening plasticity

surfaces generated by moving least squares methods an analysis of moving least squares m l s methods for smoothing and interpolating scattered data is presented in particular theorems are proved concerning the smoothness of interpolants and the description of m l s processes as projection methods some properties of compositions of the m l s projector with projectors associated with finiteelement schemes are also considered the analysis is accompanied by examples of univariate and bivariate problems

smooth interpolation of scattered data by local thin plate splines abstract an algorithm and the corresponding computer program for solution of the scattered data interpolation problem is described given points x k y k f k k 1 n a locally defined function f x y which has the property f x k y k f k k 1 n is constructed the algorithm is based on a weighted sum of locally defined thin plate splines and yields an interpolation function which is differentiable the program is available from the author

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

dot pattern processing using voronoi neighborhoods a sound notion of the neighborhood of a point is essential for analyzing dot patterns the past work in this direction has concentrated on identifying pairs of points that are neighbors examples of such methods include those based on a fixed radius k nearest neighbors minimal spanning tree relative neighborhood graph and the gabriel graph this correspondence considers the use of the region enclosed by a point s voronoi polygon as its neighborhood it is argued that the voronoi polygons possess intuitively appealing characteristics as would be expected from the neighborhood of a point geometrical characteristics of the voronoi neighborhood are used as features in dot pattern processing procedures for segmentation matching and perceptual border extraction using the voronoi neighborhood are outlined extensions of the voronoi definition to other domains are discussed

a natural neighbour based moving least squares approach for the element free galerkin method the element free galerkin method efg and the natural element method nem are two well known and widely used meshless methods whereas the efg method can represent moving boundaries like cracks only by modifying the weighting functions the nem requires an adaptation of the nodal set up but on the other hand the nem is computationally more efficient than efg in this paper a new concept for the automatic adjustment of nodal influence domains in the efg method is presented in order to obtain an efficiency similar to the nem this concept is based on the definition of natural neighbours for each meshless node which can be determined from a voronoi diagram of the nodal set up in this approach adapted nodal influence domains are obtained by interpolating the distances to the natural neighbours depending on the direction in the paper we show that this concept leads especially for problems with grading node density to a reduced number of influencing nodes at the interpolation points and consequently a significant reduction of the numerical effort copyright 2006 john wiley sons ltd

superconvergent gradient smoothing meshfree collocation method abstract a superconvergent meshfree collocation method with smoothed nodal gradients is presented in this method the first order smoothed gradients of meshfree shape function are constructed through a meshfree interpolation of the standard derivatives of meshfree shape function while the second order smoothed gradients are computed through directly differentiating the first order smoothed gradients it is noted that the second order smoothed gradients evaluated at meshfree nodes can be conveniently expressed as two successive first order gradient smoothing operations on the meshfree shape function which facilitates a trivial numerical implementation subsequently an employment of the second order smoothed gradients in the strong form of a given problem leads to the gradient smoothing meshfree collocation method purely using nodes as the collocation points based upon a local truncation error analysis it is systematically shown that the proposed meshfree collocation method yields superconvergent solutions for odd degree basis functions a key ingredient attributed to this superconvergence property is that the second order smoothed gradients meet the consistency conditions which go one order beyond the original basis degree of meshfree approximation another interesting fact is that the present formulation enables a convergent collocation scheme when the linear basis function is used in meshfree approximation which is non feasible in the conventional collocation formulation the effectiveness of the proposed methodology is validated by numerical examples for both potential and elasticity problems numerical results well demonstrate the superconvergence and higher efficiency of the present gradient smoothing meshfree collocation method

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

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

high degree efficient symmetrical gaussian quadrature rules for the triangle gaussian quadrature is required for the computation of matrices based on the isoparametric formulztion of the finite element method a brief review of existing quadrature rules for the triangle is given and the method for the determination of high degree efficient symmetrical rules for the triangle is discussed new quadrature rules of degree 12 20 are presented and a short fortran program is included

convergence and accuracy of the path integral approach for elastostatics abstract this paper addresses convergence rate and accuracy of a numerical technique for linear elastostatics based on a path integral formulation int j numer math eng 47 2000 1463 the computational implementation combines a simple polynomial approximation of the displacement field with an approximate statement of the exact evolution equations which is designated as functional integral method a convergence analysis is performed for some simple nodal arrays this is followed by two different estimations of the optimum parameter one is based on statistical arguments and the other on inspection of third order residuals when the eight closest neighbors to a node are used for polynomial approximation the optimum parameter is found to depend on poisson s ratio and lie in the range 0 5 0 while bilinear finite elements corresponds exactly to the choice 0 5 the use of the optimum parameter provides better precision than the other two methods with similar computational cost other nodal arrays are also studied both in two and three dimensions and the performance of the fim compared with the corresponding finite element and collocation schemes finally the implementation of fim on unstructured meshes is discussed and a numerical example solving laplace equation is analyzed it is shown that fim compares favorably with fem and offers a number of advantages

a new fully coupled two scales modelling for mechanical problems involving microstructure the 95 5 technique in this work we propose a new fully coupled two scales modelling for mechanical problems involving microstructure which makes use of a meshless constrained natural element approximation for accounting the large and very localized variations in the nodal density this approach is an appealing choice for treating problems involving a microstructure requiring fine local descriptions whose evolution can be accurately described in the macroscopic scale using coarse approximations this approach leads to a model where more than 95 of the nodes are in less than 5 of the considered domain volume the technique proposed in this paper allows considering simultaneously both scales the one related to the microstructure description and the one related to its evolution the macroscopic one moreover in contrast to the vast majority of homogenization techniques the presented approach allows an accurate description of the boundary conditions because the microscopic domains can be located on the domain boundary

moving particle finite element method with superconvergence nodal integration formulation and applications abstract a new approach of moving particle finite element method has been developed which is capable to gain a global superconvergence through solving particle kernel function to satisfy high order consistencies the nodal based moving particle finite element method inconjunction with the proposed superconvergence approach provides an optimized combination in numerical accuracy and computation efficiency the three dimensional engineering scale simulations demonstrate that this scheme is robust and capable to handle high speed penetration and dynamic crack propagation with intersonic and supersonic speeds

intuitionistic fuzzy hypergraphs with applications hypergraphs are considered a useful tool for modeling system architectures and data structures and to represent a partition covering and clustering in the area of circuit design in this paper we apply the concept of intuitionistic fuzzy set theory to generalize results concerning hypergraphs for each intuitionistic fuzzy structure defined we use cut level sets to define an associated sequence of crisp structures we determine what properties of the sequence of crisp structures characterize a given property of the intuitionistic fuzzy structure we also present applications of intuitionistic fuzzy hypergraphs

fluid structure interaction using the particle finite element method abstract in the present work a new approach to solve fluid structure interaction problems is described both the equations of motion for fluids and for solids have been approximated using a material lagrangian formulation to approximate the partial differential equations representing the fluid motion the shape functions introduced by the meshless finite element method mfem have been used thus the continuum is discretized into particles that move under body forces gravity and surface forces due to the interaction with neighboring particles all the physical properties such as density viscosity conductivity etc as well as the variables that define the temporal state such as velocity and position and also other variables like temperature are assigned to the particles and are transported with the particle motion the so called particle finite element method pfem provides a very advantageous and efficient way for solving contact and free surface problems highly simplifying the treatment of fluid structure interactions

bipolar fuzzy graph representation of concept lattice formal concept analysis fca is a mathematical framework for knowledge processing tasks fca has been successfully incorporated into fuzzy setting and its extension interval valued fuzzy set for handling vagueness and impreciseness in data however the analysis in such settings is restricted to unipolar space recently some applications of bipolar information are shown in bipolar fuzzy graph lattice theory as well as in fca the adequate analysis of bipolar information using fca requires incorporation of bipolar fuzzy set and an appropriate lattice structure for this purpose we propose an algorithm for generating the bipolar fuzzy formal concepts a method for cut of bipolar fuzzy formal context and its implications with illustrative examples

embedded interfaces by polytope fem in this paper the polytope finite element method is employed to model an embedded interface through the body independent of the background fem mesh the elements that are crossed by the embedded interface are decomposed into new polytope elements which have some nodes on the interface line the interface introduces discontinuity into the primary variable strong or into its derivatives weak both strong and weak discontinuities are studied by the proposed method through different numerical examples including fracture problems with traction free and cohesive cracks and heat conduction problems with dirichlet and dirichlet neumann types of boundary conditions on the embedded interface for traction free cracks which have tip singularity the nodes near the crack tip are enriched with the singular functions through the extended finite element method the concept of natural element coordinates necs is invoked to drive shape functions for the produced polytopes a simple treatment is proposed for concave polytopes produced by a kinked interface and also for locating crack tip inside an element prior to using the singularity enrichment the proposed method pursues some implementational details of extended generalized finite element methods for interfaces but here the additional dofs are constructed on the interface lines in contrast to x g fem which attach enriched dofs to the previously existed nodes copyright 2011 john wiley sons ltd

degrees of acyclicity for hypergraphs and relational database schemes database schemes winch intuitively are collecuons of table skeletons can be wewed as hypergraphs a hypergraph is a generalization of an ordinary undirected graph such that an edge need not contain exactly two nodes but can instead contain an arbitrary nonzero number of nodes a class of acychc database schemes was recently introduced a number of basic desirable propemes of database schemes have been shown to be equivalent to acyclicity this shows the naturalness of the concept however unlike the situation for ordinary undirected graphs there are several natural noneqmvalent notions of acyclicity for hypergraphs and hence for database schemes various desirable properties of database schemes are constdered and it is shown that they fall into several equivalence classes each completely characterized by the degree of acycliclty of the scheme the results are also of interest from a purely graph theoretic viewpomt the original notion of aeyclicity has the countermtmtive property that a subhypergraph of an acychc hypergraph can be cyclic this strange behavior does not occur for the new degrees of acyelicity that are considered

interval valued fuzzy graphs we define the cartesian product composition union and join on interval valued fuzzy graphs and investigate some of their properties we also introduce the notion of interval valued fuzzy complete graphs and present some properties of self complementary and self weak complementary interval valued fuzzy complete graphs

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

computational geometry an introduction from the reviews this book offers a coherent treatment at the graduate textbook level of the field that has come to be known in the last decade or so as computational geometry the book is well organized and lucidly written a timely contribution by two founders of the field it clearly demonstrates that computational geometry in the plane is now a fairly well understood branch of computer science and mathematics it also points the way to the solution of the more challenging problems in dimensions higher than two

a new fourth order cubic spline method for second order nonlinear two point boundary value problems abstract bickley 5 had suggested the use of cubic splines for the solution of general linear two point boundary value problems it is well known since then that this method gives only order h 2 uniformly convergent approximations but cubic spline interpolation itself is a fourth order process we present a new fourth order cubic spline method for second order nonlinear two point boundary value problems y f x y y a x b 0 y a 0 y a a 0 y b 1 y b b we generate the solution at the nodal points by a fourth order method and then use conditions of continuity to obtain smoothed approximations for the second derivatives of the solution needed for the construction of the cubic spline solution we show that our method provides order h 4 uniformly convergent approximations over a b the fourth order of the presented method is demonstrated computationally by two examples

a collocation meshless method based on local optimal point interpolation this paper deals with the use of the local optimal point interpolating lopi formula in solving partial differential equations pdes with a collocation method lopi is an interpolating formula constructed by localization of optimal point interpolation formulas that reproduces polynomials and verifies the delta kronecker property this scheme results in a truly meshless method that produces high quality output and accurate solutions

on the optimum support size in meshfree methods a variational adaptivity approach with maximum entropy approximants we present a method for the automatic adaption of the support size of meshfree basis functions in the context of the numerical approximation of boundary value problems stemming from a minimum principle the method is based on a variational approach and the central idea is that the variational principle selects both the discretized physical fields and the discretization parameters here those defining the support size of each basis function we consider local maximum entropy approximation schemes which exhibit smooth basis functions with respect to both space and the discretization parameters the node location and the locality parameters we illustrate by the poisson linear and non linear elasticity problems the effectivity of the method which produces very accurate solutions with very coarse discretizations and finds unexpected patterns of the support size of the shape functions copyright 2009 john wiley sons ltd

generalized delaunay triangulations of non convex domains akrraet the delaunay triangulation associated with a finite set s of points in the plane is a triangulation of the convex hull of s delaunay triangulations have been used in a number of computational methods for example in lagrangian fluid dynamics in this paper we discuss two natural generalizations of the notion of delaunay triangulation to non convex domains we show that the two generalizations are equivalent and describe a method for the construction of generalized delaunay triangulations

an enriched meshless method for non linear fracture mechanics this paper presents an enriched meshless method for fracture analysis of cracks in homogeneous isotropic non linear elastic two dimensional solids subject to mode i loading conditions the method involves an element free galerkin formulation and two new enriched basis functions types i and ii to capture the hutchinson rice rosengren singularity field in non linear fracture mechanics the type i enriched basis function can be viewed as a generalized enriched basis function which degenerates to the linear elastic basis function when the material hardening exponent is unity the type ii enriched basis function entails further improvements of the type i basis function by adding trigonometric functions four numerical examples are presented to illustrate the proposed method the boundary layer analysis indicates that the crack tip field predicted by using the proposed basis functions matches with the theoretical solution very well in the whole region considered whether for the near tip asymptotic field or for the far tip elastic field numerical analyses of standard fracture specimens by the proposed meshless method also yield accurate estimates of the j integral for the applied load intensities and material properties considered also the crack mouth opening displacement evaluated by the proposed meshless method is in good agreement with finite element results furthermore the meshless results show excellent agreement with the experimental measurements indicating that the new basis functions are also capable of capturing elastic plastic deformations at a stress concentration effectively copyright 2003 john wiley sons ltd

moving particle finite element method with global smoothness we describe a new version of the moving particle finite element method mpfem that provides solutions within a c 0 finite element framework the finite elements determine the weighting for the moving partition of unity a concept of general shape function is proposed which extends regular finite element shape functions to a larger domain these are combined with shepard functions to obtain a smooth approximation the moving particle finite element method combines desirable features of finite element and meshfree methods the proposed approach in fact can be interpreted as a moving partition of unity finite element method or moving kernel finite element method this method possesses the robustness and efficiency of the c 0 finite element method while providing at least c 1 continuity

monomial cubature rules since stroud a compilation a bibliography of references to cubature rules which have appeared since the publication of stroud s book 1971 is presented the standard regions that are treated in this paper are the n cube the n simplex the n sphere and the entire space

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

on solving large strain hyperelastic problems with the natural element method in this paper an extension of the natural element method nem is presented to solve finite deformation problems since nem is a meshless method its implementation does not require an explicit connectivity definition consequently it is quite adequate to simulate large strain problems with important mesh distortions reducing the need for remeshing and projection of results extremely important in three dimensional problems nem has important advantages over other meshless methods such as the interpolant character of its shape functions and the ability of exactly reproducing essential boundary conditions along convex boundaries the nem extension generalizes this behaviour to non convex boundaries a total lagrangian formulation has been employed to solve different problems with large strains considering hyperelastic behaviour several examples are presented in two and three dimensions comparing the results with the ones of the finite element method nem performs better showing its important capabilities in this kind of applications copyright 2004 john wiley sons ltd

image approximation by variable knot bicubic splines this paper presents a degree of freedom or information content analysis of images in the context of digital image processing as such it represents an attempt to quantify the number of truly independent samples one gathers with imaging devices the degrees of freedom of a sampled image itself are developed as an approximation problem here bicubic splines with variable knots are employed in an attempt to answer the question as to what extent images are finitely representable in the context of digital sensors and computers relatively simple algorithms for good knot placement are given and result in spline approximations that achieve significant parameter reductions at acceptable error levels the knots themselves are shown to be useful as an indicator of image activity and have potential as an image segmentation device as well as easy implementation in ccd signal processing and focal plane smart sensor arrays both mathematical and experimental results are presented

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

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

node connectivity and arc connectivity of a fuzzy graph the fuzzy graph approach is more powerful in cluster analysis than the usual graph theoretic approach due to its ability to handle the strengths of arcs effectively the concept of node strength sequence is introduced and is studied in a complete fuzzy graph two new connectivity parameters in fuzzy graphs namely fuzzy node connectivity k and fuzzy arc connectivity k are introduced and obtained the fuzzy analogue of whitney s theorem fuzzy node cut fuzzy arc cut and fuzzy bond are defined fuzzy bond is a special type of a fuzzy bridge it is proved that at least one of the end nodes of a fuzzy bond is a fuzzy cutnode it is shown that k k for a fuzzy tree and it is the minimum of the strengths of its strong arcs the relationships of the new parameters with already existing vertex and edge connectivity parameters are studied and is shown that the value of all these parameters are equal in a compete fuzzy graph also a new clustering technique based on fuzzy arc connectivity is introduced

mls moving least square based finite elements for three dimensional nonmatching meshes and adaptive mesh refinement abstract with the aid of moving least square mls approximation a new class of three dimensional finite elements are proposed for treating nonmatching meshes and adaptive mesh refinement for which the existing finite elements are hardly efficient with a special choice of the weight function supports and the base functions the method results in useful elements with the polynomial shape function for which the c 1 continuity breaks down on the boundaries between the neighboring subdomains comprising one element the effectiveness of the new elements in handling the discontinuities due to nonmatching interfaces and automatic mesh refinement is demonstrated via three dimensional examples

a partition of unity based fe meshfree quad4 element for geometric non linear analysis the recently published fe meshfree quad4 element is extended to geometrical non linear analysis the shape functions for this element are obtained by combining meshfree and finite element shape functions the concept of partition of unity pu is employed for the purpose the new shape functions inherit their higher order completeness properties from the meshfree shape functions and the mesh distortion tolerant compatibility properties from the finite element fe shape functions updated lagrangian formulation is adopted for the non linear solution several numerical example problems are solved and the performance of the element is compared with that of the well known q4 qm6 and q8 elements the results show that for regular meshes the performance of the element is comparable to that of qm6 and q8 elements and superior to that of q4 element for distorted meshes the present element has better mesh distortion tolerance than q4 qm6 and q8 elements copyright 2009 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

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

image surface approximation with irregular samples a method to approximate image surfaces using irregular samples is proposed experimental results show that a high compression ratio can be achieved for simple or complicated images a method accounting for the three dimensional effects is proposed as a way of selecting the irregular samples from the image approximation spline knots are chosen along the contours and the knot replacement is sensitive to the curvature along contours and the density of contours in the near neighborhood in general the proposed method was shown to reduce the reconstruction error both qualitatively and quantitatively and can be used to model the image surface for the purpose of data compression and representation this approach retains key features in images and throws away redundant data

the meshless standard and hypersingular boundary node methods applications to error estimation and adaptivity in three dimensional problems the standard singular boundary node method bnm and the novel hypersingular boundary node method hbnm are employed for the usual and adaptive solutions of three dimensional potential and elasticity problems these methods couple boundary integral equations with moving least squares interpolants while retaining the dimensionality advantage of the former and the meshless attribute of the latter the hypersingular residuals developed for error estimation in the mesh based collocation boundary element method bem and symmetric galerkin bem by paulino et al are extended to the meshless bnm setting a simple a posteriori error estimation and an effective adaptive refinement procedure are presented the implementation of all the techniques involved in this work are discussed which includes aspects regarding parallel implementation of the bnm and hbnm codes several numerical examples are given and discussed in detail conclusions are inferred and relevant extensions of the methodology introduced in this work are provided copyright 2001 john wiley sons ltd

dominating sets in directed graphs we consider the problem of incrementally computing a minimal dominating set of a directed graph after the insertion or deletion of a set of arcs earlier results have either focused on the study of the properties that minimum not minimal dominating sets preserved or lacked to investigate which update affects a minimal dominating set and in what ways in this paper we first show how to incrementally compute a minimal dominating set on arc insertions we then reduce the case of computing a minimal dominating set on arc deletions to the case of insertions some properties on minimal dominating sets are provided to support the incremental strategy lastly we give a new bound on the size of minimum dominating sets based on those results

operations on fuzzy graphs abstract we define the operations of cartesian product composition union and join on fuzzy subgraphs of graphs g1 and g2 if the graph g is formed from g1 and g2 by one of these operations we determine necessary and sufficient conditions for an arbitrary fuzzy subgraph of g also to be formed by the same operation from fuzzy subgraphs of g1 and g2

a new finite element approach for solving three dimensional problems using trimmed hexahedral elements summary in this paper a novel finite element approach is presented to solve three dimensional problems using trimmed hexahedral elements generated by cutting a simple block consisting of regular hexahedral elements with a computer aided design cad surface trimmed hexahedral elements which are polyhedral elements with curved faces are placed at the boundaries of finite element models and regular hexahedral elements remain in the interior regions shape functions for trimmed hexahedral elements are developed by using moving least square approximation with harmonic weight functions based on an extension of wachspress coordinates to curved faces a subdivision of polyhedral domains into tetrahedral sub domains is performed to construct shape functions for trimmed hexahedral elements and numerical integration of the weak form can be carried out consistently over the tetrahedral sub domains trimmed hexahedral elements have similar properties to conventional finite elements regarding the continuity the completeness the node element connectivity and the inter element compatibility numerical examples for three dimensional linear elastic problems with complex geometries show the efficiency and effectiveness of the present method copyright 2015 john wiley sons ltd

meshless method with ridge basis functions abstract meshless collocation methods for the numerical solutions of pdes are increasingly adopted due to their advantages including efficiency and flexibility and radial basis functions are popularly employed to represent the solutions of pdes motivated by the advantages of ridge basis function representation of a given function such as the connection to neural network fast convergence as the number of terms is increased better approximation effects and various applications in engineering problems a meshless method is developed based on the collocation method and ridge basis function interpolation this method is a truly meshless technique without mesh discretization it neither needs the computation of integrals nor requires a partition of the region and its boundary moreover the method is applied to elliptic equations to examine its appropriateness numerical results are compared to that obtained from other meshless methods and influence factors of accuracy for numerical solutions are analyzed

second order convex maximum entropy approximants with applications to high order pde we present a new approach for second order maximum entropy max ent meshfree approximants that produces positive and smooth basis functions of uniform aspect ratio even for non uniform node sets and prescribes robustly feasible constraints for the entropy maximization program defining the approximants we examine the performance of the proposed approximation scheme in the numerical solution by a direct galerkin method of a number of partial differential equations pdes including structural vibrations elliptic second order pdes and fourth order pdes for kirchhoff love thin shells and for a phase field model describing the mechanics of biomembranes the examples highlight the ability of the method to deal with non uniform node distributions and the high accuracy of the solutions surprisingly the first order meshfree max ent approximants with large supports are competitive when compared to the proposed second order approach in all the tested examples even in the higher order pdes

polygon wise constant curvature natural element approximation of kirchhoff plate model abstract a polygon wise constant curvature natural element approximation is presented in this paper for the numerical implementation of the abstract kirchhoff plate model the strict c 1 continuity requirement in the displacement field is relaxed by converting the area integral of the curvatures into the boundary integral along the voronoi boundary curvatures and bending moments are assumed to be constant within each voronoi polygon and the voronoi polygon wise constant curvatures are derived in a selective manner for the sake of the imposition of essential boundary conditions the numerical results illustrating the proposed method are also given

a hermite reproducing kernel approximation for thin plate analysis with sub domain stabilized conforming integration a hermite reproducing kernel rk approximation and a sub domain stabilized conforming integration ssci are proposed for solving thin plate problems in which second order differentiation is involved in the weak form although the standard rk approximation can be constructed with an arbitrary order of continuity the proposed approximation based on both deflection and rotation variables is shown to be more effective in solving plate problems by imposing the kirchhoff mode reproducing conditions on deflectional and rotational degrees of freedom simultaneously it is demonstrated that the minimum normalized support size coverage of kernel functions can be significantly reduced with this proposed approximation the galerkin meshfree framework for thin plates is then formulated and the integration constraint for bending exactness is also derived subsequently an ssci method is developed to achieve the exact pure bending solution as well as to maintain spatial stability numerical examples demonstrate that the proposed formulation offers superior convergence rates accuracy and efficiency compared with those based on higher order gauss quadrature rule copyright 2007 john wiley sons ltd

polygonal finite element methods for contact impact problems on non conformal meshes in this paper a polygonal finite element method is presented for large deformation frictionless dynamic contact impact problems with non conformal meshes the geometry and interfaces of the problem are modeled independent of the background mesh based on the level set method to produce polygonal elements at the intersection of the interface with the regular fe mesh various polygonal shape functions are employed to investigate the capability of polygonal fem technique in modeling frictionless contact impact problems the contact constraints are imposed between polygonal elements produced along the contact surface through the node to surface contact algorithm several contact impact problems are modeled using various polygonal interpolation functions including the wachspress interpolation functions the metric coordinate shape functions the natural neighbor based functions and the mean value coordinate functions to demonstrate the efficiency of proposed technique in modeling contact impact problems

a stabilized finite point method for analysis of fluid mechanics problems in this paper a meshless procedure termed the finite point method for solving convection diffusion and fluid flow type problems is presented the method is based on the use of a weighted least square interpolation procedure together with point collocation for evaluating the approximation integrals special emphasis is given to the stabilization of the convective terms and the neumann boundary condition which has been found to be essential to obtain accurate results some examples of application to diffusive and convective transport and compressible flow problems using quadratic fp interpolations are presented

on the c1 continuous discretization of non linear gradient elasticity a comparison of nem and fem based on bernstein bezier patches in gradient elasticity the appearance of strain gradients in the free energy density leads to the need of c 1 continuous discretization m ethods in the present work the performances of c 1 finite elements and the c 1 natural element method nem are compared the triangular argyris and hsieh clough tocher finite elements are reparametrized in terms of the bernstein polynomials the quadrilateral bogner fox schmidt element is used in an isoparametric framework for which a preprocessing algorithm is presented additionally the c 1 nem is applied to non linear gradient elasticity several numerical examples are analyzed to compare the convergence behavior of the different methods it will be illustrated that the isoparametric elements and the nem show a significantly better performance than the triangular elements

to mesh or not to mesh that is the question in the last decade a family of methods called meshless methods has been developed both for structural and fluid mechanics problems after these ideas a possible classification for numerical formulations may be to separate the methods that make use of a standard finite element mesh such as those made of tetrahedra or hexahedra from those that do not need a standard mesh namely the meshless methods for solving a partial different equation by a numerical method a possible alternative may be either to use a mesh method or a meshless method this paper discusses this issue to show that this choice is not in the large majorities of the cases the right question

image coding with ridge and valley primitives a high compression image coding scheme is presented based on thread like ridge and valley primitives the use of these primitives is motivated by their success in economically representing image structure the original image is sampled along the primitives using a fractal yardstick method to determine sample spacing the primitives themselves are compressed using vector coding and chain coding reconstruction at the receiver is a scattered data interpolation problem solved here using c sup 0 natural neighbor interpolation results are presented showing data rates between 0 1 and 0 4 b pixel the degradations are discussed and prospects for improvement outlined

meshless local petrov galerkin mlpg approximation to the two dimensional sine gordon equation during the past few years the idea of using meshless methods for numerical solution of partial differential equations pdes has received much attention throughout the scientific community and remarkable progress has been achieved on meshless methods the meshless local petrov galerkin mlpg method is one of the truly meshless methods since it does not require any background integration cells the integrations are carried out locally over small sub domains of regular shapes such as circles or squares in two dimensions and spheres or cubes in three dimensions in this paper the mlpg method for numerically solving the non linear two dimensional sine gordon sg equation is developed a time stepping method is employed to deal with the time derivative and a simple predictor corrector scheme is performed to eliminate the non linearity a brief discussion is outlined for numerical integrations in the proposed algorithm some examples involving line and ring solitons are demonstrated and the conservation of energy in undamped sg equation is investigated the final numerical results confirm the ability of proposed method to deal with the unsteady non linear problems in large domains