a stabilized conforming nodal integration for galerkin mesh free methods domain integration by gauss quadrature in the galerkin mesh free methods adds considerable complexity to solution procedures direct nodal integration on the other hand leads to a numerical instability due to under integration and vanishing derivatives of shape functions at the nodes a strain smoothing stabilization for nodal integration is proposed to eliminate spatial instability in nodal integration for convergence an integration constraint ic is introduced as a necessary condition for a linear exactness in the mesh free galerkin approximation the gradient matrix of strain smoothing is shown to satisfy ic using a divergence theorem no numerical control parameter is involved in the proposed strain smoothing stabilization the numerical results show that the accuracy and convergent rates in the mesh free method with a direct nodal integration are improved considerably by the proposed stabilized conforming nodal integration method it is also demonstrated that the gauss integration method fails to meet ic in mesh free discretization for this reason the proposed method provides even better accuracy than gauss integration for galerkin mesh free method as presented in several numerical examples copyright 2001 john wiley sons ltd

a novel alpha finite element method αfem for exact solution to mechanics problems using triangular and tetrahedral elements abstract the paper presents an alpha finite element method fem for computing nearly exact solution in energy norm for mechanics problems using meshes that can be generated automatically for arbitrarily complicated domains three node triangular fem t3 and four node tetrahedral fem t4 elements with a scale factor are formulated for two dimensional 2d and three dimensional 3d problems respectively the essential idea of the method is the use of a scale factor 0 1 to obtain a combined model of the standard fully compatible model of the fem and a quasi equilibrium model of the node based smoothed fem n sfem this novel combination of the fem and n sfem makes the best use of the upper bound property of the n sfem and the lower bound property of the standard fem using meshes with the same aspect ratio a unified approach has been proposed to obtain a nearly exact solution in strain energy for linear problems the proposed elements are also applied to improve the accuracy of the solution of nonlinear problems of large deformation numerical results for 2d using fem t3 and 3d using fem t4 problems confirm that the present method gives the much more accurate solution comparing to both the standard fem and the n sfem with the same number of degrees of freedom and similar computational efforts for both linear and nonlinear problems

a graduated assignment algorithm for graph matching a graduated assignment algorithm for graph matching is presented which is fast and accurate even in the presence of high noise by combining graduated nonconvexity two way assignment constraints and sparsity large improvements in accuracy and speed are achieved its low order computational complexity o lm where l and m are the number of links in the two graphs and robustness in the presence of noise offer advantages over traditional combinatorial approaches the algorithm not restricted to any special class of graph is applied to subgraph isomorphism weighted graph matching and attributed relational graph matching to illustrate the performance of the algorithm attributed relational graphs derived from objects are matched then results from twenty five thousand experiments conducted on 100 mode random graphs of varying types graphs with only zero one links weighted graphs and graphs with node attributes and multiple link types are reported no comparable results have been reported by any other graph matching algorithm before in the research literature twenty five hundred control experiments are conducted using a relaxation labeling algorithm and large improvements in accuracy are demonstrated

scale and rotation invariant matching using linearly augmented trees we propose a novel linearly augmented tree method for efficient scale and rotation invariant object matching the proposed method enforces pairwise matching consistency defined on trees and high order constraints on all the sites of a template the pairwise constraints admit arbitrary metrics while the high order constraints use l1 norms and therefore can be linearized such a linearly augmented tree formulation introduces hyperedges and loops into the basic tree structure but different from a general loopy graph its special structure allows us to relax and decompose the optimization into a sequence of tree matching problems that are efficiently solvable by dynamic programming the proposed method also works on continuous scale and rotation parameters we can match with a scale up to any large value with the same efficiency our experiments on ground truth data and a variety of real images and videos show that the proposed method is efficient accurate and reliable

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

elementary solutions for a model boltzmann equation in one dimension and the connection to grossly determined solutions abstract the fourier transformed version of the time dependent slip flow model boltzmann equation associated with the linearized bgk model is solved in order to determine the solution s asymptotics the ultimate goal of this paper is to demonstrate that there exists a robust set of solutions to this model boltzmann equation that possess a special property that was conjectured by truesdell and muncaster that solutions decay to a subclass of the solution set uniquely determined by the initial mass density of the gas called the grossly determined solutions first we determine the spectrum and eigendistributions of the associated homogeneous equation then using case s method of elementary solutions we find analytic time dependent solutions to the model boltzmann equation for initial data with a specialized compact support condition under the fourier transform in doing so we show that the spectrum separates the solutions into two distinct parts one that behaves as a set of transient solutions and the other limiting to a stable subclass of solutions thus we demonstrate that for gas flows with this specialized initial density condition in time all gas flows for the one dimensional model boltzmann equation act as grossly determined solutions

quadratic maximum entropy serendipity shape functions for arbitrary planar polygons in this paper we present the development of quadratic serendipity shape functions on planar convex and nonconvex polygons drawing on the work of bompadre et al 2012 1 and hormann and sukumar 2008 2 we adopt a relative entropy measure for signed positive or negative shape functions with nodal prior weight functions that have the appropriate zero set on the boundary of the polygon we maximize the objective functional subject to the constraints for quadratic completeness proposed by rand et al 2013 3 along an edge of a polygon the approximation is identical to univariate bernstein polynomials the choice of the nodal prior weight function ensures that the shape functions satisfy a weak kronecker delta property on each edge the shape functions are well defined for arbitrary planar polygons without self intersections on using a modified numerical integration scheme we show that the quadratic patch test is passed on polygonal meshes with convex and nonconvex elements numerical tests for the poisson equation on self similar trapezoidal meshes and quasiuniform polygonal meshes are presented which reveal the sound accuracy of the method and optimal rates of convergence in the l2l2 norm and the h1h1 seminorm are established

an eigenspace projection clustering method for inexact graph matching in this paper we show how inexact graph matching that is the correspondence between sets of vertices of pairs of graphs can be solved using the renormalization of projections of the vertices as defined in this case by their connectivities into the joint eigenspace of a pair of graphs and a form of relational clustering an important feature of this eigenspace renormalization projection clustering epc method is its ability to match graphs with different number of vertices shock graph based shape matching is used to illustrate the model and a more objective method for evaluating the approach using random graphs is explored with encouraging results

matching by linear programming and successive convexification we present a novel convex programming scheme to solve matching problems focusing on the challenging problem of matching in a large search range and with cluttered background matching is formulated as metric labeling with l1 regularization terms for which we propose a novel linear programming relaxation method and an efficient successive convexification implementation the unique feature of the proposed relaxation scheme is that a much smaller set of basis labels is used to represent the original label space this greatly reduces the size of the searching space a successive convexification scheme solves the labeling problem in a coarse to fine manner importantly the original cost function is reconvexified at each stage in the new focus region only and the focus region is updated so as to refine the searching result this makes the method well suited for large label set matching experiments demonstrate successful applications of the proposed matching scheme in object detection motion estimation and tracking

structural matching by discrete relaxation this paper describes a bayesian framework for performing relational graph matching by discrete relaxation our basic aim is to draw on this framework to provide a comparative evaluation of a number of contrasting approaches to relational matching broadly speaking there are two main aspects to this study firstly we focus on the issue of how relational inexactness may be quantified we illustrate that several popular relational distance measures can be recovered as specific limiting cases of the bayesian consistency measure the second aspect of our comparison concerns the way in which structural inexactness is controlled we investigate three different realizations of the matching process which draw on contrasting control models the main conclusion of our study is that the active process of graph editing outperforms the alternatives in terms of its ability to effectively control a large population of contaminating clutter

scale affine invariant interest point detectors in this paper we propose a novel approach for detecting interest points invariant to scale and affine transformations our scale and affine invariant detectors are based on the following recent results 1 interest points extracted with the harris detector can be adapted to affine transformations and give repeatable results geometrically stable 2 the characteristic scale of a local structure is indicated by a local extremum over scale of normalized derivatives the laplacian 3 the affine shape of a point neighborhood is estimated based on the second moment matrix our scale invariant detector computes a multi scale representation for the harris interest point detector and then selects points at which a local measure the laplacian is maximal over scales this provides a set of distinctive points which are invariant to scale rotation and translation as well as robust to illumination changes and limited changes of viewpoint the characteristic scale determines a scale invariant region for each point we extend the scale invariant detector to affine invariance by estimating the affine shape of a point neighborhood an iterative algorithm modifies location scale and neighborhood of each point and converges to affine invariant points this method can deal with significant affine transformations including large scale changes the characteristic scale and the affine shape of neighborhood determine an affine invariant region for each point we present a comparative evaluation of different detectors and show that our approach provides better results than existing methods the performance of our detector is also confirmed by excellent matching resultss the image is described by a set of scale affine invariant descriptors computed on the regions associated with our points

scaled boundary polygons for linear elastodynamics abstract a polygonal scaled boundary finite element method sbfem is proposed for linear elastodynamics in two dimensions the domain is divided into non overlapping polygonal elements and the scaled boundary finite element approach is employed over each polygon the advantages are that an arbitrary interpolation order can be used on each polygon and we can choose the optimal element order on each edge individually moreover the sbfem simplifies the numerical integration over the polygons when compared to conventional approaches the dynamic stiffness matrix is computed by employing the continued fraction expansion the influence of the shape of the polygon and the element order on the boundary of each polygon are studied the robustness and the accuracy of the approach are demonstrated with numerical examples

on the virtual element method for three dimensional linear elasticity problems on arbitrary polyhedral meshes abstract we explore the recently proposed virtual element method vem for the numerical solution of boundary value problems on arbitrary polyhedral meshes more specifically we focus on the linear elasticity equations in three dimensions and elaborate upon the key concepts underlying the first order vem while the point of departure is a conforming galerkin framework the distinguishing feature of vem is that it does not require an explicit computation of the trial and test spaces thereby circumventing a barrier to standard finite element discretizations on arbitrary grids at the heart of the method is a particular kinematic decomposition of element deformation states which in turn leads to a corresponding decomposition of strain energy by capturing the energy of linear deformations exactly one can guarantee satisfaction of the patch test and optimal convergence of numerical solutions the decomposition itself is enabled by local projection maps that appropriately extract the rigid body motion and constant strain components of the deformation as we show computing these projection maps and subsequently the local stiffness matrices in practice reduces to the computation of purely geometric quantities in addition to discussing aspects of implementation of the method we present several numerical studies in order to verify convergence of the vem and evaluate its performance for various types of meshes

graph matching with a dual step em algorithm this paper describes a new approach to matching geometric structure in 2d point sets the novel feature is to unify the tasks of estimating transformation geometry and identifying point correspondence matches unification is realized by constructing a mixture model over the bipartite graph representing the correspondence match and by affecting optimization using the em algorithm according to our em framework the probabilities of structural correspondence gate contributions to the expected likelihood function used to estimate maximum likelihood transformation parameters these gating probabilities measure the consistency of the matched neighborhoods in the graphs the recovery of transformational geometry and hard correspondence matches are interleaved and are realized by applying coupled update operations to the expected log likelihood function we evaluate the technique on two real world problems

a smoothed finite element method for plate analysis a quadrilateral element with smoothed curvatures for mindlin reissner plates is proposed the curvature at each point is obtained by a non local approximation via a smoothing function the bending stiffness matrix is calculated by a boundary integral along the boundaries of the smoothing elements smoothing cells numerical results show that the proposed element is robust computational inexpensive and simultaneously very accurate and free of locking even for very thin plates the most promising feature of our elements is their insensitivity to mesh distortion

theoretical aspects of the smoothed finite element method sfem this paper examines the theoretical bases for the smoothed finite element method sfem which was formulated by incorporating cell wise strain smoothing operation into standard compatible finite element method fem the weak form of sfem can be derived from the hu washizu three field variational principle for elastic problems it is proved that 1d linear element and 2d linear triangle element in sfem are identical to their counterparts in fem while 2d bilinear quadrilateral elements in sfem are different from that of fem when the number of smoothing cells scs of the elements equals 1 the sfem solution is proved to be variationally consistent and has the same properties with those of fem using reduced integration when sc approaches infinity the sfem solution will approach the solution of the standard displacement compatible fem model when sc is a finite number larger than 1 the sfem solutions are not variationally consistent but energy consistent and will change monotonously from the solution of sfem sc 1 to that of sfem sc it is suggested that there exists an optimal number of sc such that the sfem solution is closest to the exact solution the properties of sfem are confirmed by numerical examples copyright 2006 john wiley sons ltd

improved robustness for nearly incompressible large deformation meshfree simulations on delaunay tessellations abstract a displacement based galerkin meshfree method for large deformation analysis of nearly incompressible elastic solids is presented nodal discretization of the domain is defined by a delaunay tessellation three node triangles and four node tetrahedra which is used to form the meshfree basis functions and to numerically integrate the weak form integrals in the proposed approach for nearly incompressible solids a volume averaged nodal projection operator is constructed to average the dilatational constraint at a node from the displacement field of surrounding nodes the nodal dilatational constraint is then projected onto the linear approximation space the displacement field is constructed on the linear space and enriched with bubble like meshfree basis functions for stability the new procedure leads to a displacement based formulation that is similar to f bar methodologies in finite elements and isogeometric analysis we adopt maximum entropy meshfree basis functions and the performance of the meshfree method is demonstrated on benchmark problems using structured and unstructured background meshes in two and three dimensions the nonlinear simulations reveal that the proposed methodology provides improved robustness for nearly incompressible large deformation analysis on delaunay meshes

a four point integration scheme with quadratic exactness for three dimensional element free galerkin method based on variationally consistent formulation abstract the formulation of three dimensional element free galerkin efg method based on the hu washizu three field variational principle is described the orthogonality condition between stress and strain difference is satisfied by correcting the derivatives of the nodal shape functions this leads to a variationally consistent formulation which has a similar form as the formulation of standard galerkin weak form based on this formulation an integration scheme which employs only four cubature points in each background tetrahedral element cell is rationally developed for three dimensional efg with quadratic approximation the consistency of the corrected nodal derivatives and the satisfaction of patch test conditions for the developed integration scheme are theoretically proved extension of the proposed method to small strain elastoplasticity is also presented the proposed method can exactly pass quadratic patch test that is quadratic exactness is achieved and thus it is named as quadratically consistent 4 point qc4 integration method in contrast efg with standard tetrahedral cubature and the existing linearly consistent 1 point lc1 integration fail to exactly pass quadratic patch test numerical results of elastic examples demonstrate the superiority of the proposed method in accuracy convergence efficiency and stability the capability of the proposed qc4 scheme in solving elastoplastic problems is also demonstrated by numerical examples

a new algorithm for error tolerant subgraph isomorphism detection we propose a new algorithm for error correcting subgraph isomorphism detection from a set of model graphs to an unknown input graph the algorithm is based on a compact representation of the model graphs this representation is derived from the set of model graphs in an off line preprocessing step the main advantage of the proposed representation is that common subgraphs of different model graphs are represented only once therefore at run time given an unknown input graph the computational effort of matching the common subgraphs for each model graph onto the input graph is done only once consequently the new algorithm is only sublinearly dependent on the number of model graphs furthermore the new algorithm can be combined with a future cost estimation method that greatly improves its run time performance

a face based smoothed finite element method fs fem for 3d linear and geometrically non linear solid mechanics problems using 4 node tetrahedral elements this paper presents a novel face based smoothed finite element method fs fem to improve the accuracy of the finite element method fem for three dimensional 3d problems the fs fem uses 4 node tetrahedral elements that can be generated automatically for complicated domains in the fs fem the system stiffness matrix is computed using strains smoothed over the smoothing domains associated with the faces of the tetrahedral elements the results demonstrated that the fs fem is significantly more accurate than the fem using tetrahedral elements for both linear and geometrically non linear solid mechanics problems in addition a novel domain based selective scheme is proposed leading to a combined fs ns fem model that is immune from volumetric locking and hence works well for nearly incompressible materials the implementation of the fs fem is straightforward and no penalty parameters or additional degrees of freedom are used the computational efficiency of the fs fem is found better than that of the fem copyright 2008 john wiley sons ltd

linear smoothed polygonal and polyhedral finite elements the strain smoothing technique over higher order elements and arbitrary polytopes yields less accurate solutions than other techniques such as the conventional polygonal finite element method in this work we propose a linear strain smoothing scheme that improves the accuracy of linear and quadratic approximations over convex polytopes the main idea is to subdivide the polytope into simplicial subcells and use a linear smoothing function in each subcell to compute the strain this new strain is then used in the computation of the stiffness matrix the convergence properties and accuracy of the proposed scheme are discussed by solving a few benchmark problems numerical results show that the proposed linear strain smoothing scheme makes the approximation based on polytopes able to deliver the same optimal convergence rate as traditional quadrilateral and hexahedral approximations the accuracy is also improved and all the methods tested pass the patch test to machine precision

an edge based smoothed finite element method es fem for static free and forced vibration analyses of solids abstract this paper presents an edge based smoothed finite element method es fem to significantly improve the accuracy of the finite element method fem without much changing to the standard fem settings the es fem can use different shape of elements but prefers triangular elements that can be much easily generated automatically for complicated domains in the es fem the system stiffness matrix is computed using strains smoothed over the smoothing domains associated with the edges of the triangles intensive numerical results demonstrated that the es fem possesses the following excellent properties 1 the es fem model possesses a close to exact stiffness it is much softer than the overly stiff fem and much stiffer than the overly soft ns fem model 2 the results are often found superconvergence and ultra accurate much more accurate than the linear triangular elements of fem and even more accurate than those of the fem using quadrilateral elements with the same sets of nodes 3 there are no spurious non zeros energy modes found and hence the method is also temporally stable and works well for vibration analysis and 4 the implementation of the method is straightforward and no penalty parameter is used and the computational efficiency is better than the fem using the same sets of nodes in addition a novel domain based selective scheme is proposed leading to a combined es ns fem model that is immune from volumetric locking and hence works very well for nearly incompressible materials these properties of the es fem are confirmed using examples of static free and forced vibration analyses of solids

a displacement based finite element formulation for general polyhedra using harmonic shape functions summary a displacement based continuous galerkin finite element formulation for general polyhedra is presented for applications in nonlinear solid mechanics the polyhedra can have an arbitrary number of vertices or faces the faces of the polyhedra can have an arbitrary number of edges and can be nonplanar the polyhedra can be nonconvex with only the mild restriction of star convexity with respect to the vertex averaged centroid conforming shape functions are constructed using harmonic functions defined on the undeformed configuration thus requiring the use of a total lagrangian finite element formulation in large deformation applications for nonlinear applications with computationally intensive constitutive models it is important to minimize the number of element quadrature points for this reason an integration scheme is adopted in which the number of quadrature points is equal to the number of vertices as a first step toward verifying the element behavior in the general nonlinear setting several linear verification examples are presented using both random voronoi meshes and distorted hexahedral meshes for the hexahedral meshes results for the polyhedral formulation are compared to those of the standard trilinear hexahedral formulation the element behavior in the nearly incompressible regime is also examined copyright 2013 john wiley sons ltd

quadratic serendipity finite elements on polygons using generalized barycentric coordinates we introduce a nite element construction for use on the class of convex planar polygons and show it obtains a quadratic error convergence estimate on a convex n gon satisfying simple geometric criteria our construction produces 2n basis functions associated in a lagrange like fashion to each vertex and each edge midpoint by transforming and combining a set of n n 1 2 basis functions known to obtain quadratic convergence the technique broadens the scope of the so called serendipity elements previously studied only for quadrilateral and regular hexahedral meshes by employing the theory of generalized barycentric coordinates uniform a priori error estimates are established over the class of convex quadrilaterals with bounded aspect ratio as well as over the class of generic convex planar polygons satisfying additional shape regularity conditions to exclude large interior angles and short edges numerical evidence is provided on a trapezoidal quadrilateral mesh previously not amenable to serendipity constructions and applications to adaptive meshing are discussed

extended finite element method with edge based strain smoothing esm xfem for linear elastic crack growth abstract this paper presents a strain smoothing procedure for the extended finite element method xfem the resulting edge based smoothed extended finite element method esm xfem is tailored to linear elastic fracture mechanics and in this context to outperform the standard xfem in the xfem the displacement based approximation is enriched by the heaviside and asymptotic crack tip functions using the framework of partition of unity this eliminates the need for the mesh alignment with the crack and re meshing as the crack evolves edge based smoothing es relies on a generalized smoothing operation over smoothing domains associated with edges of simplex meshes and produces a softening effect leading to a close to exact stiffness super convergence and ultra accurate solutions the present method takes advantage of both the es fem and the xfem thanks to the use of strain smoothing the subdivision of elements intersected by discontinuities and of integrating the singular derivatives of the approximation functions is suppressed via transforming interior integration into boundary integration numerical examples show that the proposed method improves significantly the accuracy of stress intensity factors and achieves a near optimal convergence rate in the energy norm even without geometrical enrichment or blending correction

feature matching with affine function transformation models feature matching is an important problem and has extensive uses in computer vision however existing feature matching methods support either a specific or a small set of transformation models in this paper we propose a unified feature matching framework which supports a large family of transformation models we call the family of transformation models the affine function family in which all transformations can be expressed by affine functions with convex constraints in this framework the goal is to recover transformation parameters for every feature point in a template point set to calculate their optimal matching positions in an input image given pairwise feature dissimilarity values between all points in the template set and the input image we create a convex dissimilarity function for each template point composition of such convex functions with any transformation model in the affine function family is shown to have an equivalent convex optimization form that can be optimized efficiently four example transformation models in the affine function family are introduced to show the flexibility of our proposed framework our framework achieves 0 0 percent matching errors for both cmu house and hotel sequences following the experimental setup in 6

large displacement optical flow descriptor matching in variational motion estimation optical flow estimation is classically marked by the requirement of dense sampling in time while coarse to fine warping schemes have somehow relaxed this constraint there is an inherent dependency between the scale of structures and the velocity that can be estimated this particularly renders the estimation of detailed human motion problematic as small body parts can move very fast in this paper we present a way to approach this problem by integrating rich descriptors into the variational optical flow setting this way we can estimate a dense optical flow field with almost the same high accuracy as known from variational optical flow while reaching out to new domains of motion analysis where the requirement of dense sampling in time is no longer satisfied

the carleman type singular integral equations we present a consolidated account of carleman type singular integral equations we have started from the most basic equation of this type and have at first attempted to integrate from the existing literature the progress which has been made so far in this field many different techniques are presented to solve these types of integral equations both in the real and the complex domains in the complex domain both closed and open contours for integrals are considered in the process of this study we find that many known methods need to be polished and extended we attempt to accomplish this and then interrelate different concepts and solutions thereby we obtain solutions of more general singular integral equations of the carleman type many interesting examples are presented to illustrate the general theory

the half hartley and the half hilbert transform inversion formulas are obtained for the restrictions of the hartley and hilbert transforms to r regularity results are derived and an illustrative example presented

consistent element free galerkin method an element free galerkin efg method with linear quadratic and cubic approximations which can exactly in a numerical sense pass the corresponding patch tests is proposed and is named as consistent efg cefg method the development of this method is based on the hu washizu three field variational principle numerical integration schemes with corrected nodal derivatives at quadrature points are proposed according to the satisfaction of the orthogonality condition between stress and strain difference thus the method is variationally consistent the consistency of the corrected nodal derivatives and the satisfaction of patch test conditions are theoretically proved and also numerically validated numerical results show that the proposed cefg method greatly improves the numerical performance of the efg method in terms of accuracy convergence efficiency and stability especially the proposed cubic cefg method which shows exceptional accuracy and convergence copyright 2014 john wiley sons ltd

volume averaged nodal projection method for nearly incompressible elasticity using meshfree and bubble basis functions we present a displacement based galerkin meshfree method for the analysis of nearly incompressible linear elastic solids where low order simplicial tessellations i e 3 node triangular or 4 node tetrahedral meshes are used as a background structure for numerical integration of the weak form integrals and to get the nodal information for the computation of the meshfree basis functions in this approach a volume averaged nodal projection operator is constructed to project the dilatational strain into an approximation space of equal or lower order than the approximation space for the displacement field resulting in a locking free method the stability of the method is provided via bubble like basis functions because the notion of an element or cell is not present in the computation of the meshfree basis functions such low order tessellations can be used regardless of the order of the approximation spaces desired first and second order meshfree basis functions are chosen as a particular case in the proposed method numerical examples are provided in two and three dimensions to demonstrate the robustness of the method its ability to avoid volumetric locking in the nearly incompressible regime and its improved performance when compared to the mini finite element scheme on the simplicial mesh

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

on the approximation in the smoothed finite element method sfem this letter aims at resolving the issues raised in the recent short communication int j numer meth engng 2008 76 8 1285 1295 doi 10 1002 nme 2460 and answered by int j numer meth engng 2009 doi 10 1002 nme 2587 by proposing a systematic approximation scheme based on non mapped shape functions which both allows to fully exploit the unique advantages of the smoothed finite element method sfem comput mech 2007 39 6 859 877 doi 10 1007 s00466 006 0075 4 commun numer meth engng 2009 25 1 19 34 doi 10 1002 cnm 1098 int j numer meth engng 2007 71 8 902 930 comput meth appl mech engng 2008 198 2 165 177 doi 10 1016 j cma 2008 05 029 comput meth appl mech engng 2007 submitted int j numer meth engng 2008 74 2 175 208 doi 10 1002 nme 2146 comput meth appl mech engng 2008 197 13 16 1184 1203 doi 10 1016 j cma 2007 10 008 and resolve the existence linearity and positivity deficiencies pointed out in int j numer meth engng 2008 76 8 1285 1295 we show that wachspress interpolants a rational basis for function approximation academic press inc new york 1975 computed in the physical coordinate system are very well suited to the sfem especially when elements are heavily distorted obtuse interior angles the proposed approximation leads to results that are almost identical to those of the sfem initially proposed in comput mech 2007 39 6 859 877 doi 10 1007 s00466 006 0075 4 these results suggest that the proposed approximation scheme forms a strong and rigorous basis for the construction of sfems copyright 2009 john wiley sons ltd

steady currents in composite conductors eigenfunction expansions and exactly solvable linear integral equations a novel connection is uncovered between the simple physics of steady current flow in a composite conductor and the theory of integral equations with a judicious choice of eigenfunction expansions exploitation of the physical continuity of current flow across a chosen interface in a composite conductor is shown to yield an infinite class of integral equations with exact closed form solutions the mathematical derivation of this class is based on the elementary but also new notion of formally equating two different eigenfunction expansions of a given arbitrary function the new class contains as special cases the celebrated abel integral equation of classical mechanics and the kramers kronig relations of electromagnetic scattering but it also contains new integral equations with exact solutions some with the cauchy singularity 1 x y in their kernels and a new summation equation these new equations are in themselves intriguing and their exact solutions do not appear to be derivable by the known m

shape matching and object recognition using shape contexts we present a novel approach to measuring similarity between shapes and exploit it for object recognition in our framework the measurement of similarity is preceded by 1 solving for correspondences between points on the two shapes 2 using the correspondences to estimate an aligning transform in order to solve the correspondence problem we attach a descriptor the shape context to each point the shape context at a reference point captures the distribution of the remaining points relative to it thus offering a globally discriminative characterization corresponding points on two similar shapes will have similar shape contexts enabling us to solve for correspondences as an optimal assignment problem given the point correspondences we estimate the transformation that best aligns the two shapes regularized thin plate splines provide a flexible class of transformation maps for this purpose the dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points together with a term measuring the magnitude of the aligning transform we treat recognition in a nearest neighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image results are presented for silhouettes trademarks handwritten digits and the coil data set

on the stationary distribution of the block counting process for population models with mutation and selection abstract we consider two population models subject to the evolutionary forces of selection and mutation the moran model and the wright fisher model in such models the block counting process traces back the number of potential ancestors of a sample of the population at present under some conditions the block counting process is positive recurrent and its stationary distribution is described via a linear system of equations in this work we first characterise the measures leading to a geometric stationary distribution the bolthausen sznitman model being the most prominent example having this feature next we solve the linear system of equations corresponding to the moran model for the wright fisher model we show that the probability generating function associated to the stationary distribution of the block counting process satisfies an integro differential equation we solve the latter for the kingman model and the star shaped model

second order accurate derivatives and integration schemes for meshfree methods summary the consistency condition for the nodal derivatives in traditional meshfree galerkin methods is only the differentiation of the approximation consistency dac one missing part is the consistency between a nodal shape function and its derivatives in terms of the divergence theorem in numerical forms in this paper a consistency framework for the meshfree nodal derivatives including the dac and the discrete divergence consistency ddc is proposed the summation of the linear ddc over the whole computational domain leads to the so called integration constraint in the literature a three point integration scheme using background triangle elements is developed in which the corrected derivatives are computed by the satisfaction of the quadratic ddc we prove that such smoothed derivatives also meet the quadratic dac and therefore the proposed scheme possesses the quadratic consistency that leads to its name qc3 numerical results show that qc3 is the only method that can pass both the linear and the quadratic patch tests and achieves the best performances for all the four examples in terms of stability convergence accuracy and efficiency among all the tested methods particularly it shows a huge improvement for the existing linearly consistent one point integration method in some examples copyright 2012 john wiley sons ltd

linear smoothed extended finite element method the extended finite element method was introduced in 1999 to treat problems involving discontinuities with no or minimal remeshing through appropriate enrichment functions this enables elements to be split by a discontinuity strong or weak and hence requires the integration of discontinuous functions or functions with discontinuous derivatives over elementary volumes a variety of approaches have been proposed to facilitate these special types of numerical integration which have been shown to have a large impact on the accuracy and the convergence of the numerical solution the smoothed extended finite element method xfem for example makes numerical integration elegant and simple by transforming volume integrals into surface integrals however it was reported in the literature that the strain smoothing is inaccurate when non polynomial functions are in the basis in this paper we investigate the benefits of a recently developed linear smoothing procedure which provides better approximation to higher order polynomial fields in the basis some benchmark problems in the context of linear elastic fracture mechanics are solved and the results are compared with existing approaches we observe that the stress intensity factors computed through the proposed linear smoothed xfem is more accurate than that obtained through smoothed xfem

on the performance of strain smoothing for quadratic and enriched finite element approximations xfem gfem pufem by using the strain smoothing technique proposed by chen et al comput mech 2000 25 137 156 for meshless methods in the context of the finite element method fem liu et al comput mech 2007 39 6 859 877 developed the smoothed fem sfem although the sfem is not yet well understood mathematically numerical experiments point to potentially useful features of this particularly simple modification of the fem to date the sfem has only been investigated for bilinear and wachspress approximations and is limited to linear reproducing conditions the goal of this paper is to extend the strain smoothing to higher order elements and to investigate numerically in which condition strain smoothing is beneficial to accuracy and convergence of enriched finite element approximations we focus on three widely used enrichment schemes namely a weak discontinuities b strong discontinuities c near tip linear elastic fracture mechanics functions the main conclusion is that strain smoothing in enriched approximation is only beneficial when the enrichment functions are polynomial cases a and b but that non polynomial enrichment of type c lead to inferior methods compared to the standard enriched fem e g xfem copyright c 2011 john wiley sons ltd

gaussian field consensus a robust nonparametric matching method for outlier rejection abstract in this paper we propose a robust method called gaussian field consensus gfc for outlier rejection from given putative point set matching correspondences finding correct correspondences inliers is a key component in many computer vision and pattern recognition tasks and the goal of outlier mismatch rejection is to fit the transformation function that maps one feature point set to another our gfc starts by inputting a putative correspondence set which is contaminated by many outliers and the main task of our gfc is to identify the underlying true correspondences from outliers then we formulate this challenging problem by gaussian field nonparametric matching model which bases on the exponential distance loss and kernel method in a reproducing kernel hilbert space next we introduce a local linear constraint based on the regularization theory to preserve the topological structure of the feature points moreover the sparse approximation is used to reduce the search space in this way we can handle a large number of points easily finally we test the gfc method on several real image datasets in the presence of outliers where the experimental results show that our proposed method outperforms current state of the art methods in most test scenarios

person re identification by saliency learning human eyes can recognize person identities based on small salient regions i e person saliency is distinctive and reliable in pedestrian matching across disjoint camera views however such valuable information is often hidden when computing similarities of pedestrian images with existing approaches inspired by our user study result of human perception on person saliency we propose a novel perspective for person re identification based on learning person saliency and matching saliency distribution the proposed saliency learning and matching framework consists of four steps 1 to handle misalignment caused by drastic viewpoint change and pose variations we apply adjacency constrained patch matching to build dense correspondence between image pairs 2 we propose two alternative methods i e k nearest neighbors and one class svm to estimate a saliency score for each image patch through which distinctive features stand out without using identity labels in the training procedure 3 saliency matching is proposed based on patch matching matching patches with inconsistent saliency brings penalty and images of the same identity are recognized by minimizing the saliency matching cost 4 furthermore saliency matching is tightly integrated with patch matching in a unified structural ranksvm learning framework the effectiveness of our approach is validated on the four public datasets our approach outperforms the state of the art person re identification methods on all these datasets

exact solution of a boundary value problem in semiconductor kinetic theory an explicit solution of the stationary one dimensional half space boundary value problem for the linear boltzmann equation is presented in the presence of an arbitrarily high constant external field the collision kernel is assumed to be separable which is also known as relaxation time approximation the relaxation time may depend on the electron velocity our method consists in a transformation of the half space problem into a non normal singular integral equation which has an explicit solution

structural matching in computer vision using probabilistic relaxation in this paper we develop the theory of probabilistic relaxation for matching features extracted from 2d images derive as limiting cases the various heuristic formulae used by researchers in matching problems and state the conditions under which they apply we successfully apply our theory to the problem of matching and recognizing aerial road network images based on road network models and to the problem of edge matching in a stereo pair for this purpose each line network is represented by an attributed relational graph where each node is a straight line segment characterized by certain attributes and related with every other node via a set of binary relations

local grayvalue invariants for image retrieval this paper addresses the problem of retrieving images from large image databases the method is based on local grayvalue invariants which are computed at automatically detected interest points a voting algorithm and semilocal constraints make retrieval possible indexing allows for efficient retrieval from a database of more than 1 000 images experimental results show correct retrieval in the case of partial visibility similarity transformations extraneous features and small perspective deformations

a fully smoothed xfem for analysis of axisymmetric problems with weak discontinuities in this paper we propose a fully smoothed extended finite element method for axisymmetric problems with weak discontinuities the salient feature of the proposed approach is that all the terms in the stiffness and mass matrices can be computed by smoothing technique this is accomplished by combining the gaussian divergence theorem with the evaluation of indefinite integral based on smoothing technique which is used to transform the domain integral into boundary integral the proposed technique completely eliminates the need for isoparametric mapping and the computing of jacobian matrix even for the mass matrix when employed over the enriched elements the proposed technique does not require sub triangulation for the purpose of numerical integration the accuracy and convergence properties of the proposed technique are demonstrated with a few problems in elastostatics and elastodynamics with weak discontinuities it can be seen that the proposed technique yields stable and accurate solutions and is less sensitive to mesh distortion

a rkhs interpolator based graph matching algorithm we present an algorithm for performing attributed graph matching this algorithm is derived from a generalized framework for describing functionally expanded interpolators which is based on the theory of reproducing kernel hilbert spaces rkhs the algorithm incorporates a general approach to a wide class of graph matching problems based on attributed graphs allowing the structure of the graphs to be based on multiple sets of attributes no assumption is made about the adjacency structure of the graphs to be matched

a polytree based adaptive polygonal finite element method for multi material topology optimization abstract this study presents a polytree based adaptive methodology for multi material topology optimization mmtop polytree data structure is introduced as a general recursive multi level mesh that is automatically refined in processing based on error analysis in order to resolve hanging nodes in element edges the wachspress coordinate is employed on a reference element before using a mapping scheme to obtain shape functions and their derivatives for any polygons a new definition of filter radius is also proposed to improve the efficiency of filters and optimized results the combination of polytree meshes and adaptive filters not only clarifies the interfaces between material phases including void phase but also decreases the computing time of the overall process in comparison to using the regular fine meshes several benchmark and practical problems are considered to show distinct features of the proposed method

an efficient and rapid numerical quadrature to generate element matrices for quadrilateral and hexahedral elements in functionally graded materials fgms abstract this research paper introduces a robust efficient and stabilized midpoint quadrature to generate element stiffness matrices for quadrilateral and hexahedral elements in finite element method fem this new quadrature is established based on passive richardson extrapolation which has the inherent ability to stabilize and improve the accuracy of the extrapolated results the new quadrature includes a simple artificial stabilizing function with gauss one point quadrature 1gp as an anti hourglass effect for the first approximation the 1gp sampling point to be considered at origin 0 0 is done to evaluate element matrices thermal conductivity matrices capacitance matrices etc in the 4 square element 2 2 x 2 2 in the plane as a stabilizing function sampling points are considered to be either at the center of the four element edges or center of the four quadrants in the reference square element with appropriate constant weighting functions for hexahedral elements also the element stiffness coefficients are calculated only in the center of the element and center of all the octants of the reference cubic element 2 2 x 2 2 x 2 2 the proposed method deals mostly with integer variables and sampling at 0 0 0 whereas gauss quadrature uses lengthy float variables corresponding to irrational numbers in terms of decimals in the stiffness matrix calculations thus consuming time a number of standard example problems are demonstrated to assess the efficiency of the proposed method the results of all the numerical examples are found to be in good agreement with the exact results and conventional gauss quadrature results

asymptotic analysis of the high field semiconductor boltzmann equation abstract we present an asymptotic analysis for long times and large distances of the linear semiconductor boltzmann equation for a given strong electric field slowly varying in real space by means of singular perturbation techniques using the multiple scale formalism we show that the initial value and the boundary value problem lead to different asymptotic evolution equations for the initial value problem we derive thornber s augmented drift diffusion equation in case of the boundary value problem thornber s equation describes only the hot part of the asymptotic distribution function the cold part staying in thermal equilibrium with the lattice at the boundary is described asymptotically by means of a new evolution equation in this way we solve the well known inconsistency problem occuring if thornber s equation is applied to an equilibrium situation in the presence of large built in fields

object matching using a locally affine invariant and linear programming techniques in this paper we introduce a new matching method based on a novel locally affine invariant geometric constraint and linear programming techniques to model and solve the matching problem in a linear programming formulation all geometric constraints should be able to be exactly or approximately reformulated into a linear form this is a major difficulty for this kind of matching algorithm we propose a novel locally affine invariant constraint which can be exactly linearized and requires a lot fewer auxiliary variables than other linear programming based methods do the key idea behind it is that each point in the template point set can be exactly represented by an affine combination of its neighboring points whose weights can be solved easily by least squares errors of reconstructing each matched point using such weights are used to penalize the disagreement of geometric relationships between the template points and the matched points the resulting overall objective function can be solved efficiently by linear programming techniques our experimental results on both rigid and nonrigid object matching show the effectiveness of the proposed algorithm

smooth finite element methods convergence accuracy and properties a stabilized conforming nodal integration finite element method based on strain smoothing stabilization is presented the integration of the stiffness matrix is performed on the boundaries of the finite elements a rigorous variational framework based on the hu washizu assumed strain variational form is developed we prove that solutions yielded by the proposed method are in a space bounded by the standard finite element solution infinite number of subcells and a quasi equilibrium finite element solution a single subcell we show elsewhere the equivalence of the one subcell element with a quasi equilibrium finite element leading to a global a posteriori error estimate we apply the method to compressible and incompressible linear elasticity problems the method can always achieve higher accuracy and convergence rates than the standard finite element method especially in the presence of incompressibility singularities or distorted meshes for a slightly smaller computational cost it is shown numerically that the one cell smoothed four noded quadrilateral finite element has a convergence rate of 2 0 in the energy norm for problems with smooth solutions which is remarkable for problems with rough solutions this element always converges faster than the standard finite element and is free of volumetric locking without any modification of integration scheme copyright 2007 john wiley sons ltd

virtual and smoothed finite elements a connection and its application to polygonal polyhedral finite element methods summary we show both theoretically and numerically a connection between the smoothed finite element method sfem and the virtual element method and use this approach to derive stable cheap and optimally convergent polyhedral fem we show that the stiffness matrix computed with one subcell sfem is identical to the consistency term of the virtual element method irrespective of the topology of the element as long as the shape functions vary linearly on the boundary using this connection we propose a new stable approach to strain smoothing for polygonal polyhedral elements where instead of using sub triangulations we are able to use one single polygonal polyhedral subcell for each element while maintaining stability for a similar number of degrees of freedom the proposed approach is more accurate than the conventional sfem with triangular subcells the time to compute the stiffness matrix scales with the o dofs 1 1 in case of the conventional polygonal fem while it scales as o dofs 0 7 in the proposed approach the accuracy and the convergence properties of the sfem are studied with a few benchmark problems in 2d and 3d linear elasticity copyright 2015 john wiley sons ltd

virtual elements for linear elasticity problems we discuss the application of virtual elements to linear elasticity problems for both the compressible and the nearly incompressible case virtual elements are very close to mimetic finite differences see for linear elasticity l beirao da veiga m2an math model numer anal 44 2010 pp 231 250 and in particular to higher order mimetic finite differences as such they share the good features of being able to represent in an exact way certain physical properties conservation incompressibility etc and of being applicable in very general geometries the advantage of virtual elements is the ductility that easily allows high order accuracy and high order continuity

linear local models for monocular reconstruction of deformable surfaces recovering the 3d shape of a nonrigid surface from a single viewpoint is known to be both ambiguous and challenging resolving the ambiguities typically requires prior knowledge about the most likely deformations that the surface may undergo it often takes the form of a global deformation model that can be learned from training data while effective this approach suffers from the fact that a new model must be learned for each new surface which means acquiring new training data and may be impractical in this paper we replace the global models by linear local models for surface patches which can be assembled to represent arbitrary surface shapes as long as they are made of the same material not only do they eliminate the need to retrain the model for different surface shapes they also let us formulate 3d shape reconstruction from correspondences as either an algebraic problem that can be solved in closed form or a convex optimization problem whose solution can be found using standard numerical packages we present quantitative results on synthetic data as well as qualitative results on real images

spectral correspondence for point pattern matching this paper investigates the correspondence matching of point sets using spectral graph analysis in particular we are interested in the problem of how the modal analysis of point sets can be rendered robust to contamination and drop out we make three contributions first we show how the modal structure of point sets can be embedded within the framework of the em algorithm second we present several methods for computing the probabilities of point correspondences from the modes of the point proximity matrix third we consider alternatives to the gaussian proximity matrix we evaluate the new method on both synthetic and real world data here we show that the method can be used to compute useful correspondences even when the level of point contamination is as large as 50 we also provide some examples on deformed point set tracking