further results for enhanced strain methods with isoparametric elements abstract in this contribution the enhanced strain finite element method is investigated further with particular attention given to the analysis of the method for isoparametric elements it is shown that the results established earlier b d reddy and j c simo stability and convergence of a class of enhanced strain methods siam j numer anal 32 1995 in press for affine equivalent meshes carry over to the case of isoparametric elements that is the method is stable and convergent provided that a set of three criteria is satisfied and for plane elements at least convergence is at the same rate as in the standard method a procedure for recovering the stress is shown to lead to an approximate stress which converges at the optimal rate to the actual stress with regard to computations a new basis for enhanced strains is introduced and numerical results are presented for this basis as well as for existing bases the results for enhanced strain methods are distinguished by the fact that the constant appearing in asymptotic error estimates is much smaller for these methods than for standard approaches

mdl denoising the so called denoising problem relative to normal models for noise is formalized such that noise is defined as the incompressible part in the data while the compressible part defines the meaningful information bearing signal such a decomposition is effected by minimization of the ideal code length called for by the minimum description length mdl principle and obtained by an application of the normalized maximum likelihood technique to the primary parameters their range and their number for any orthonormal regression matrix such as defined by wavelet transforms the minimization can be done with a threshold for the squared coefficients resulting from the expansion of the data sequence in the basis vectors defined by the matrix

well posedness and numerical performances of the strain gap method a mixed method of approximation is discussed starting from a suitably modified expression of the hu washizu variational principle in which the independent fields are displacements stresses and strain gaps defined as the difference between compatible strains and strain fields the well posedness of the discrete problem is discussed and necessary and sufficient conditions are provided the analysis of the mixed method reveals that the discrete problem can be split into a reduced problem and in a stress recovery accordingly the discrete stress solution is univocally determined once an interpolating stress subspace is chosen the enhanced assumed strain method by simo and rifai is based on an orthogonality condition between stresses and enhanced strains and coincides with the reduced problem it is shown that the mixed method is stable and converges computational issues in the context of the finite element method are discussed in detail and numerical performances and comparisons are carried out copyright 2001 john wiley sons ltd

on numerical cubatures of singular surface integrals in boundary element methods we present and analyze methods for the accurate and efficient evaluation of weakly cauchy and hypersingular integrals over piecewise analytic curved surfaces in 3 the class of admissible integrands includes all kernels arising in the numerical solution of elliptic boundary value problems in three dimensional domains by the boundary integral equation method the possibly not absolutely integrable kernels of boundary integral operators in local coordinates are pseudohomogeneous with analytic characteristics depending on the local geometry of the surface at the source point this rules out weighted quadrature approaches with a fixed singular weight for weakly singular integrals it is shown that duffy s triangular coordinates leadalways to a removal of the kernel singularity also asymptotic estimates of the integration error are provided as the size of the boundary element patch tends to zero these are based on the rabinowitz richter estimates in connection with an asymptotic estimate of domains of analyticity in 2 it is further shown that the modified extrapolation approach due to lyness is in the weakly singular case always applicable corresponding error and asymptotic work estimates are presented for the weakly singular as well as for cauchy and hypersingular integrals which e g arise in the study of crack problems we analyze a family of product integration rules in local polar coordinates these rules are hierarchically constructed from finite part integration formulas in radial and gaussian formulas in angular direction again we show how the rabinowitz richter estimates can be applied providing asymptotic error estimates in terms of orders of the boundary element size

stability and convergence of a class of enhanced strain methods a stability and convergence analysis is presented of a recently proposed variational formulation and finite element method for elasticity which incorporates an enhanced strain field the analysis is carried out for problems posed on polygonal domains in r n the finite element meshes of which are generated by affine maps from a master element the formulation incorporates as a special case the classical method of incompatible modes the problem initially has three variables viz displacement stress and enhanced strain but the stress is later eliminated by imposing a condition of orthogonality with respect to the enhanced strains two other conditions on the choice of finite element spaces ensure that the approximations are stable and convergent some features of nearly incompressible and incompressible problems are also investigated for these cases it is possible to argue that locking will not occur and that the only spurious pressures present are the so called checkerboard modes it is shown th

proof of a conjectured asymptotic expansion for the approximation of surface integrals georg introduced a new kind of trapezoidal rule and midpoint rule to approximate a surface integral over a curved triangular surface and conjectured the existence of an asymptotic expansion for this approximation as the subdivision of the surface gets finer the purpose of this paper is to prove the conjecture

simulation of the three dimensional ising model on the creutz cellular automaton abstract the three dimensional ising model is simulated on the creutz cellular automaton the values computed for the critical temperature and the static critical exponents within the framework of the finite size scaling theory are in agreement with their values obtained by different methods

a numerical integration scheme for finite element method based on symbolic manipulation this paper is concerned with the improvement of the efficiency and accuracy of the usual numerical integration procedures for the finite element method a modified numerical integration scheme based on both the symbolic manipulation system and the numerical integration formula is proposed its efficiency for the integration of complicated rational or irrational expressions is demonstrated through several numerical examples to verify its effectiveness in the calculation of the finite element stiffness matrix a simple numerical example is also presented

a formulation for the 4 node quadrilateral element a formulation for the plane 4 node quadrilateral finite element is developed based on the principle of virtual displacements for a deformable body incompatible modes are added to the standard displacement field then expressions for gradient operators are obtained from an expansion of the basis functions into a second order taylor series in the physical co ordinates the internal degrees of freedom of the incompatible modes are eliminated on the element level a modified change of variables is used to integrate the element matrices for a linear elastic material the element stiffness matrix can be separated into two parts these are equivalent to a stiffness matrix obtained from underintegration and a stabilization matrix the formulation includes the cases of plane stress and plane strain as well as the analysis of incompressible materials further the approach is suitable for non linear analysis there an application is given for the calculation of inelastic problems in physically non linear elasticity the element is efficient to implement and it is frame invariant locking effects and zero energy modes are avoided as well as singularities of the stiffness matrix due to geometric distortion a high accuracy is obtained for numerical solutions in displacements and stresses

geometrically non linear enhanced strain mixed methods and the method of incompatible modes a class of assumed strain mixed finite element methods for fully non linear problems in solid mechanics is presented which when restricted to geometrically linear problems encompasses the classical method of incompatible modes as a particular case the method relies crucially on a local multiplicative decomposition of the deformation gradient into a conforming and an enhanced part formulated in the context of a three field variational formulation the resulting class of mixed methods provides a possible extension to the non linear regime of well known incompatible mode formulations in addition this class of methods includes non linear generalizations of recently proposed enhanced strain interpolations for axisymmetric problems which cannot be interpreted as incompatible modes elements the good performance of the proposed methodology is illustrated in a number of simulations including 2 d 3 d and axisymmetric finite deformation problems in elasticity and elastoplasticity remarkably these methods appear to be specially well suited for problems involving localization of the deformation as illustrated in several numerical examples

the empirical distribution of rate constrained source codes let x x sub 1 be a stationary ergodic finite alphabet source x sup n denote its first n symbols and y sup n be the codeword assigned to x sup n by a lossy source code the empirical kth order joint distribution q spl circ sup k x sup n y sup n spl rceil x sup k y sup k is defined as the frequency of appearances of pairs of k strings x sup k y sup k along the pair x sup n y sup n our main interest is in the sample behavior of this random distribution letting i q sup k denote the mutual information i x sup k y sup k when x sup k y sup k spl sim q sup k we show that for any sequence of lossy source code s of rate spl les r lim sup sub n spl rarr spl infin 1 k i q spl circ sup k x sup n y sup n spl rfloor spl les r 1 k h x sub 1 sup k h x a s where h x denotes the entropy rate of x this is shown to imply for a large class of sources including all independent and identically distributed i i d sources and all sources satisfying the shannon lower bound with equality that for any sequence of codes which is good in the sense of asymptotically attaining a point on the rate distortion curve q spl circ sup k x sup n y sup n spl rfloor spl rarr sup d p x sup k y sup k a s whenever p sub x sup k sub y sup k is the unique distribution attaining the minimum in the definition of the kth order rate distortion function consequences of these results include a new proof of kieffer s sample converse to lossy source coding as well as performance bounds for compression based denoisers

enhanced assumed strain elements and locking in membrane problems abstract the assumptions which guarantee convergence of eas elements first introduced by simo and rifai can be reduced to two postulates specifically the stability condition refers to a relaxed stability of an associated hu washizu principle we investigate the problem of volume locking of membrane problems estimates of a certain type which for instance imply volume locking of the q1 element are fortunately not present with eas elements finally we verify an equivalence of the eas concept with a hellinger reissner method which was observed in numerical computations by andelfinger and ramm

computation of critical exponents for two dimensional ising model on a cellular automaton static critical exponents for the two dimensional ising model are computed on a cellular automaton the analysis of the data within the framework of the finite size scaling theory reproduces their well established values

integration by table look up for p version finite elements on curved tetrahedra abstract we develop a method of evaluating element level matrices and vectors associated with p version finite element computations on tetrahedral meshes with curved boundaries the procedure uses optimal interpolation formula q chen i babuska approximate optimal points for polynomial interpolation of real functions in an interval and in a triangle comput methods appl mech engrg 128 1995 405 417 q chen i babuska approximate optimal polynomial interpolation points in the tetrahedron comput methods appl mech engrg 137 1997 89 94 for non polynomial portions of integrands followed by exact integration exact integrals of product combinations of polynomial interpolants and shape functions are stored so that different integrals may be efficiently evaluated by a table look up we present error analysis for our scheme applied to curvilinear tetrahedral meshes with exact geometric representation of the boundary of the domain as defined in a geometric modelling system numerical results are presented for problems involving the helmholtz equation

relations between enhanced strain methods and the hr method abstract the three field hu washizu functional is the starting point to develop a comparative analysis of approximate linear elastostatic problems in particular we will analyse the limitation phenomena concerning two mixed methods respectively denoted the strain gap method and the mixed enhanced strain method and the two field hellinger reissner hr finite element formulation accordingly two original limitation principles are contributed we provide the theoretical motivation of the numerical observations provided in computational literature on the coincidence of the displacement and stress solutions between the enhanced assumed strain method and the hr method if different choices of shape functions are made it is further shown that the hr method provides the exact stress solution and the exact nodal displacements with one element the related analytical motivation are thus given the theoretical analyses presented in the paper are supported by numerical examples on tipical benchmarks

conditions for equivalence between the hu washizu and related formulations and computational behavior in the incompressible limit the relationship of the hu washizu mixed formulation to other mixed and enhanced formulations is examined in detail in the context of linear elasticity with a view to presenting a unified framework for such formulations the hu washizu formulation is considered in both its classical form and in a modified form that is suited to establishing well posedness in the incompressible limit recently established theoretical results on uniform well posedness are studied computationally by considering a range of numerical examples which illustrate where appropriate the good behavior predicted by the theory as well as the locking behavior that is evident in those problems in which the conditions for stability and convergence are not satisfied 2005 elsevier b v all rights reserved

a stable affine approximate finite element method the notion of the affine figure closest to a given quadrilateral can be given a precise mathematical definition the resulting figure is referred to as the equivalent parallelogram associated with a quadrilateral equipped with such a concept it is then feasible to consider finite element approximations in which the original quadrilateral elements are replaced by their equivalent parallelograms the idea is appealing not least because of the resulting economy arising from computations performed on an element generated by an affine map furthermore numerical experiments reported recently indicate that highly efficient and accurate schemes result when such a concept is combined with the enhanced strain method or the method of incompatible modes the purpose of this work is to analyze finite element schemes resulting from approximation of quadrilaterals by their equivalent parallelograms the focus is on low order bilinear elements and the analysis is carried out in the context of linear elasticity for standard approximations as well as for those which use enhanced strains the affine approximation applies only to the element map and the primary unknown the displacement vector in the context of elasticity is approximated by conventional piecewise bilinear functions the analysis confirms convergence at the optimal rate provided that the deviations of the quadrilaterals from their equivalent parallelograms are at most o h

a meshfree enriched finite element method for compressible and near incompressible elasticity summary in this paper a two dimensional displacement based meshfree enriched fem me fem is presented for the linear analysis of compressible and near incompressible planar elasticity the me fem element is established by injecting a first order convex meshfree approximation into a low order finite element with an additional node the convex meshfree approximation is constructed using the generalized meshfree approximation method and it possesses the kronecker delta property on the element boundaries the gradient matrix of me fem element satisfies the integration constraint for nodal integration and the resultant me fem formulation is shown to pass the constant stress test for the compressible media the me fem interpolation is an element wise meshfree interpolation and is proven to be discrete divergence free in the incompressible limit to prevent possible pressure oscillation in the near incompressible problems an area weighted strain smoothing scheme incorporated with the divergence free me fem interpolation is introduced to provide the smoothing on strains and pressure with this smoothed strain field the discrete equations are derived based on a modified hu washizu variational principle several numerical examples are presented to demonstrate the effectiveness of the proposed method for the compressible and near incompressible problems copyright 2012 john wiley sons ltd

a comparison of transformation methods for evaluating two dimensional weakly singular integrals accurate numerical evaluation of integrals arising in the boundary element method is fundamental to achieving useful results via this solution technique in this paper a number of techniques are considered to evaluate the weakly singular integrals which arise in the solution of laplace s equation in three dimensions and poisson s equation in two dimensions both are two dimensional weakly singular integrals and are evaluated using in a product fashion methods which have recently been used for evaluating one dimensional weakly singular integrals arising in the boundary element method the methods used are based on various polynomial transformations of conventional gaussian quadrature points where the transformation polynomial has zero jacobian at the singular point methods which split the region of integration into sub regions are considered as well as non splitting methods in particular the newly introduced and highly accurate generalized composite subtraction of singularity and non linear transformation approach gssnt is applied to various two dimensional weakly singular integrals a study of the different methods reveals complex relationships between transformation orders position of the singular point integration kernel and basis function it is concluded that the gssnt method gives the best overall results for the two dimensional weakly singular integrals studied

the equivalent parallelogram and parallelepiped and their application to stabilized finite elements in two and three dimensions a new class of quadrilateral and hexahedral elements four and eight noded in two and three dimensions respectively is presented these elements are obtained by combining the concept of the equivalent parallelogram for plane problems and the equivalent parallelepiped for three dimensional problems with the notion of incompatible modes a key feature of the new elements is that integration of the element stiffness matrices is carried out using one point integration the use of affine equivalent elements parallelograms and parallelepipeds permits a closed form eigenvalue analysis which includes the incompatible modes and a stabilization procedure based on the eigenvalue analysis ensures the full rank of the stiffness matrix numerical results for problems in elasticity and plasticity indicate equivalent or superior performance of the new elements when compared with various elements based on enhanced strains or incompatible modes

approximating rate distortion graphs of individual data experiments in lossy compression and denoising classical rate distortion theory requires specifying a source distribution instead we analyze rate distortion properties of individual objects using the recently developed algorithmic rate distortion theory the latter is based on the noncomputable notion of kolmogorov complexity to apply the theory we approximate the kolmogorov complexity by standard data compression techniques and perform a number of experiments with lossy compression and denoising of objects from different domains we also introduce a natural generalization to lossy compression with side information to maintain full generality we need to address a difficult searching problem while our solutions are therefore not time efficient we do observe good denoising and compression performance

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

a reduced integration solid shell finite element based on the eas and the ans concept geometrically linear problems in this paper a new reduced integration eight node solid shell finite element is presented the enhanced assumed strain eas concept based on the hu washizu variational principle requires only one eas degree of freedom to cure volumetric and poisson thickness locking one key point of the derivation is the taylor expansion of the inverse jacobian with respect to the element center which closely approximates the element shape and allows us to implement the assumed natural strain ans concept to eliminate the curvature thickness and the transverse shear locking the second crucial point is a combined taylor expansion of the compatible strain with respect to the center of the element and the normal through the element center leading to an efficient and locking free hourglass stabilization without rank deficiency hence the element requires only a single integration point in the shell plane and at least two integration points in thickness direction the formulation fulfills both the membrane and the bending patch test exactly which has to the authors knowledge not yet been achieved for reduced integration eight node solid shell elements in the literature owing to the three dimensional modeling of the structure fully three dimensional matenal models can be implemented without additional assumptions

a variational multiscale approach to strain localization formulation for multidimensional problems abstract the multiscale approach to strain localization problems developed earlier is generalized to higher dimensions the key idea is the identification of the fine scale field with a component of the displacement that has a large gradient the difference between the total displacement and the fine scale is the coarse scale field the formulation is variationally based with the weak form as the point of departure with suitable assumptions on the space of fine scale fields the weak form is separable into coarse and fine scale parts the weak form of the fine scale problem is used to eliminate the fine scales from the formulation this is achieved by way of a projection onto the fine scale space and allows a reformulation of the full problem in terms of coarse scale components alone in this framework fine scale interpolations are identified that ensure sharp resolution of localized displacement irrespective of the underlying finite element mesh it is demonstrated that by correctly accounting for the microstructural fine scale behavior the formulation results in solutions devoid of pathological mesh sensitivity for problems wherein the detailed structure of the localized displacement is of interest recovery of the fine scale components can be performed to reconstruct the entire displacement field several numerical examples are presented that demonstrate the robustness of the formulation

feedback does not increase the capacity of discrete channels with additive noise we consider discrete time finite alphabet channels with additive random noise we show that output feedback does not increase the capacity of such channels this result holds in the most general case i e for arbitrary additive noise processes

quadrature rules for rational functions summary it is shown how recent ideas on rational gauss type quadrature rules can be extended to gauss kronrod gauss turan and cauchy principal value quadrature rules numerical examples illustrate the advantages in accuracy thus achievable

on an equivalence between a discontinuous galerkin method and reduced integration with hourglass stabilization for finite elasticity abstract discontinuous galerkin methods and methods of reduced integration with hourglass stabilization have different points of origin whereas the discontinuous galerkin idea was developed to investigate a wide range of applications among them problems of electrodynamics fluid and solid mechanics the reduced integration technology started out from the observation of the so called locking problem in linear elasticity today the two methodologies are still considered separately from each other although it has already been recognized that discontinuous galerkin methods can be also used to circumvent locking phenomena in elasticity the idea of the present contribution is to find a direct equivalence between a discontinuous galerkin method and a finite element technology based on reduced integration with hourglass stabilization the transfer between the two methods is carried out in the context of finite elasticity thus the derivation is valid for arbitrarily large deformations the main advantage of this analysis is that the choice of the free parameter in nitsche s method often also called stabilization parameter is no longer unclear but prescribed by the connection to the hourglass stabilization further important in this context is the replacement of the scalar parameter by a symmetric 2 2 matrix if two dimensional problems are considered which is here the case the result of the derivation is a discontinuous galerkin formulation which shows very good convergence behaviour not only in the limit of incompressibility but also for bending of thin structures

critical behavior of the two dimensional ising model with next nearest neighbor antiferromagnetic interaction on the creutz cellular automaton the two dimensional ising model with nearest and next nearest neighbor antiferromagnetic interactions of ratio r is simulated on the creutz cellular automaton the values of the critical temperature and the critical exponents for o r are estimated within the framework of the finite size scaling theory the dependence of tc on r agrees with the crossover scaling theory for 1 75 the results for 0 r are compatible with ising critical behavior

analysis of some quadrilateral nonconforming elements for incompressible elasticity in this work some nonconforming elements on arbitrary quadrilateral meshes in solving incompressible elastic equations are analyzed a uniform optimal convergence rate is established at the incompressible limit nu 0 5 for both displacement and stresses or pressure in the case of incompressible flow

a local projection operator for quadrilateral finite elements this note studies the approximation error of a local projection operator on polynomials of total degree k defined on quadrilaterals among other applications this projection operator permits to derive easily error estimates for quadrature formulas

denoising via mcmc based lossy compression it has been established in the literature in various theoretical and asymptotic senses that universal lossy compression followed by some simple postprocessing results in universal denoising for the setting of a stationary ergodic source corrupted by additive white noise however this interesting theoretical result has not yet been tested in practice in denoising simulated or real data in this paper we employ a recently developed mcmc based universal lossy compressor to build a universal compression based denoising algorithm we show that applying this iterative lossy compression algorithm with appropriately chosen distortion measure and distortion level followed by a simple derandomization operation results in a family of denoisers that compares favorably both theoretically and in practice with other mcmc based schemes and with the discrete universal denoiser dude

some geometrical results and estimates for quadrilateral finite elements abstract the concept of the equivalent parallelogram associated with a quadrilateral is introduced the quadrilateral may be regarded as a perturbation of this parallelogram which is most conveniently described by making use of properties of the isoparametric map which defines the quadrilateral the equivalent parallelogram generates a natural means of defining a regular family of quadrilaterals this definition is used together with other properties to obtain in a relatively simple manner estimates in appropriate seminorms or norms of the isoparametric map and its jacobian for use in the determination of finite element interpolation error estimates

integration of rational functions of bivariate polynomial numerators with linear denominators over a 1 1 square in a local parametric two dimensional space abstract this paper is concerned with explicit formulas and algorithms for computing integral of rational function of bivariate polynomial numerators with linear denominators over a 1 1 square in the local parametric space these integrals arise in finite element formulations of second order partial differential equations explicit evaluation of these integrals produce analytical finite element relations provided that the original element geometry is restricted to a linear convex quadrilateral we have also presented two algorithms either of these can be used to compute n n 1 2 integrals of 0th to nth order bivariate polynomial numerator whenever n 1 such integrals of order 0 zero to n in one of the variates are known by explicit integration formulas the analytical quadrature formulas from cubic to quintic monomial numerator in one of the vari tes due to different element geometry are for clarity and reference summarized in tabular forms all the explicit formulas are constructed with three simple functions of element nodal values they can be easily coded and save much computation time besides their inherent merit on numerical accuracy associated with analytical integration we have also derived some integration formulas for the product of global derivatives which has applications to second order linear partial differential equations in a variety of disciplines finally an application example to compute the torsional constant k for an equilateral triangular cross section is also considered for which we have explained the detailed computational scheme

numerical integration with taylor truncations for the quadrilateral and hexahedral finite elements for general quadrilateral or hexahedral meshes the finite element methods require evaluation of integrals of rational functions instead of traditional polynomials it remains as a challenge in mathematics to show the traditional gauss quadratures would ensure the correct order of approximation for the numerical integration in general however in the case of nested refinement the refined quadrilaterals and hexahedra converge to parallelograms and parallelepipeds respectively based on this observation the rational functions of inverse jacobians can be approximated by the taylor expansion with truncation then the gauss quadrature of exact order can be adopted for the resulting integrals of polynomials retaining the optimal order approximation of the finite element methods a theoretic justification and some numerical verification are provided in the paper

analysis of mismatched estimation errors using gradients of partition functions we consider the problem of signal estimation denoising from a statistical mechanical perspective in continuation to a recent work on the analysis of mean square error mse estimation using a direct relationship between optimum estimation and certain partition functions this paper consists of essentially two parts in the first part using the aforementioned relationship we derive single letter expressions of the asymptotic mismatched mse of a codeword from a randomly selected code corrupted by a gaussian vector channel in the second part we provide several examples to demonstrate phase transitions in the behavior of the mse these examples enable us to understand more deeply and to gather intuition regarding the roles of the real and the mismatched probability measures in creating these phase transitions

analytical integral formulae related to convex quadrilateral finite elements abstract analytical quadrature formulae for rational functions integrated over finite elements with quadrilateral geometry are presented definitively for second order differential equations these formulae produce algebraic finite element relations associated with the isoparametrical or subparametrical rectangular interpolations

a uniform strain hexahedron and quadrilateral with orthogonal hourglass control the treatment of zero energy modes which arise due to one point integration of first order isoparametric finite elements is addressed a method for precisely isolating these modes for arbitrary geometry is developed two hourglass control schemes viscous and elastic are presented and examined in addition a convenient one point integration scheme which analytically integrates the element volume and uniform strain modes is presented

fixed slope universal lossy data compression corresponding to any lossless codeword length function l three universal lossy data compression schemes are presented one is with a fixed rate another is with a fixed distortion and a third is with a fixed slope the former two universal lossy data compression schemes are the generalization of yang kieffer s see ibid vol 42 no 1 p 239 45 1995 results to the general case of any lossless codeword length function l whereas the third is new in the case of fixed slope spl lambda 0 our universal lossy data compression scheme works as follows for any source sequence x sup n of length n the encoder first searches for a reproduction sequence y sup n of length n which minimizes a cost function n sup 1 l y sup n spl lambda spl rho sub n x sup n y sup n over all reproduction sequences of length n and then encodes x sup n into the binary codeword of length l y sup n associated with y sup n via the lossless codeword length function l where spl rho sub n x sup n y sup n is the distortion per sample between x sup n and y sup n under some mild assumptions on the lossless codeword length function l it is shown that when this fixed slope data compression scheme is applied to encode a stationary ergodic source the resulting encoding rate per sample and the distortion per sample converge with probability one to r sub spl lambda and d sub spl lambda respectively where d sub spl lambda r sub spl lambda is the point on the rate distortion curve at which the slope of the rate distortion function is spl lambda this result holds particularly for the arithmetic codeword length function and lempel ziv codeword length function the main advantage of this fixed slope universal lossy data compression scheme over the fixed rate fixed distortion universal lossy data compression scheme lies in the fact that it converts the encoding problem to a search problem through a trellis and then permits one to use some sequential search algorithms to implement it simulation results show that this fixed slope universal lossy data compression scheme combined with a suitable search algorithm is promising

a fast method of numerical quadrature for p version finite element matrices a new technique of numerical quadrature especially suited for quadrilateral and hexahedron p version finite element matrices is presented this new technique separates the integrand into two parts and numerically operates on each part separately the objective of this scheme is to minimize the computational cost of integrating the entire element matrix as opposed to minimizing the cost of integrating a single function the efficiency of the new technique is compared with gaussian quadrature and found to take a small fraction of the computational effort

best wavelet packet bases in a rate distortion sense a fast rate distortion r d optimal scheme for coding adaptive trees whose individual nodes spawn descendents forming a disjoint and complete basis cover for the space spanned by their parent nodes is presented the scheme guarantees operation on the convex hull of the operational r d curve and uses a fast dynamic programing pruning algorithm to markedly reduce computational complexity applications for this coding technique include r coefman et al s yale univ 1990 generalized multiresolution wavelet packet decomposition iterative subband coders and quadtree structures applications to image processing involving wavelet packets as well as discrete cosine transform dct quadtrees are presented

numerical integrations over an arbitrary quadrilateral region in this paper double integrals over an arbitrary quadrilateral are evaluated exploiting finite element method the physical region is transformed into a standard quadrilateral finite element using the basis functions in local space then the standard quadrilateral is subdivided into two triangles and each triangle is further discretized into 4xn 2 right isosceles triangles with area 12n 2 and thus composite numerical integration is employed in addition the affine transformation over each discretized triangle and the use of linearity property of integrals are applied finally each isosceles triangle is transformed into a 2 square finite element to compute new n 2 extended symmetric gauss points and corresponding weight coefficients where n is the lower order conventional gauss legendre quadratures these new gauss points and weights are used to compute the double integral examples are considered over an arbitrary domain and rational and irrational integrals which can not be evaluated analytically

improved versions of assumed enhanced strain tri linear elements for 3d finite deformation problems abstract improved three dimensional tri linear elements for finite deformation problems are developed based on an assumed enhanced strain methodology which in the linear regime incorporates the classical method of incompatible modes as a particular case three crucial modifications of a recently proposed element which reduces to wilson s brick in the linear regime are introduced to prevent locking response in distorted configurations and to maintain proper rank while preserving excellent performance in bending dominated and localization problems i a modified quadrature rule ii an additional enhancement of the divergence term and iii a modification of the isoparametric shape function derivatives for the three dimensional problem moreover these modified shape function derivatives are shown to improve the performance of the standard tri linear brick in distorted configurations in addition a strategy is described to circumvent the memory storage requirements in the static condensation procedure of the enhanced strain parameters the excellent performance of the improved methodology is illustrated in representative numerical simulations

object oriented finite elements iii theory and application of automatic programming in a first paper 1 the authors have developed the key features of an object oriented environment for the symbolic derivation of linear initial boundary value problems the approach was illustrated on a simple example of an elastic bar in dynamics in a companion paper 2 the structure of the proposed environment was described at length in this article the key features of the automatic generation of finite elements in a symbolic object oriented environment are given a few examples of derivation and automatic programming are developed and numerically tested first a classical galerkin formulation of stokes flow is compared to a galerkin least squares stabilization formulation then various stabilized formulations are tested on a simple scalar diffusion model equation

analytical integration formulae for linear isoparametric finite elements exact and approximate analytical expressions can be derived for integrals arising in finite element methods employing isoparametric linear quadrilaterals in two space dimensions with bilinear basis functions the formulae associated with rectangular elements arbitrarily oriented in space can be shown to be a special case the proposed method provides considerable savings in computational effort in comparison with a numerical method that employs gaussian quadrature procedures in addition the method when applied to a quadrilateral inscribable in a circle can be shown to produce better accuracy than the associated 2 2 gaussian quadrature formulae

critical exponents of the three dimensional blume capel model on a cellular automaton abstract the static critical exponents of the three dimensional blume capel model which has a tricritical point at d j 2 82 value are estimated for the standard and the cooling algorithms which improved from creutz cellular automaton the analyses of the data using the finite size scaling and power law relations reproduce their well established values in the d j 3 and d j 2 8 parameter region at standard and cooling algorithms respectively for the cooling algorithm at d j 2 8 value of single ion anisotropy parameter the static critical exponents are estimated as 0 31 1 6 0 32 and 0 87 these values are different from 0 31 1 25 0 12 and 0 64 universal values this case indicated that the bc model exhibits an ununiversal critical behavior at the d j 2 8 parameter value near the tricritical point d j 2 82 the simulations were carried out on a simple cubic lattice with periodic boundary conditions

the effect of the increase of linear dimensions on exponents obtained by finite size scaling relations for the six dimensional ising model on the creutz cellular automaton the six dimensional ising model is simulated on the creutz cellular automaton using the finite size lattices with the linear dimension 4

an analysis of quadrature errors in second kind boundary integral methods this paper considers the effect of quadrature errors on galerkin methods for approximating the solution of second kind fredholm integral equations with weakly singular kernels defined on a smooth closed surface in three dimensions a quadrature strategy for galerkin methods that use piecewise poly nomials both continuous and discontinuous on a quadrilateral based mesh is proposed the error resulting from this further discretization is proved to be no larger than the original discretization error and moreover the amount of work needed to compute the resulting matrix for the corresponding linear system is shown to be proportional to the number of matrix entries

quadrature over curved surfaces by extrapolation in this paper the authors describe and justify a method for integrating over curved surfaces this method does not require that the jacobian be known explicitly this is a natural extension of extrapolation or romberg integration for planar squares or triangles 9 refs

the estimation of a ktc p j p phase diagram for a two dimensional site diluted ising model using a microcanonical algorithm abstract the site diluted ising model has been investigated using an improved microcanonical algorithm from creutz cellular automaton for a microcanonical algorithm the basic problem is to estimate the correct temperatures using average values of the kinetic energy in the simulations of site diluted ising model in this study the average kinetic energy has been re described with an expression dependent on dilution x 1 p the values of the temperature have been calculated using the new expression and the critical temperatures have been estimated from the peaks of specific heat for each value of dilution x the obtained phase transition line k t c p j p is in good agreement with functional prediction for the site diluted ising model the simulations were carried out on a square lattice with periodic boundary conditions

the test of the finite size scaling relations for the six dimensional ising model on the creutz cellular automaton the six dimensional ising model is simulated on the creutz cellular automaton using the finite size lattices with the linear dimension 4 l 10 the exponents in the finite size scaling relations for the magnetic susceptibility and the order parameter at the infinite lattice critical temperature are computed to be 3 00 12 and 1 47 10 using 6 l 10 respectively which are in very good agreement with the theoretical predictions of and the critical temperature for the infinite lattice is found to be 10 835 5 using 4 l 10 which is also in very good agreement with the precise results the finite size scaling relation for the magnetic susceptibility at the infinite lattice critical temperature is also valid for the maxima of the magnetic susceptibilities of the finite size lattices the finite size scaling plots of the magnetic susceptibility and the order parameter verify the finite size scaling relations about the infinite lattice critical temperature

on the nested refinement of quadrilateral and hexahedral finite elements and the affine approximation it is shown in this paper that the optimal approximation property of bilinear or trilinear finite elements would be retained when the affine mapping is used to replace the q1 mapping on each element if the grids are refined nestedly the new method truncates the quadratic and cubic terms in reference mappings and produces constant jacobians and jacobian matrices this would avoid a shortcoming of the quadrilateral and hexahedral elements where the integrals of rational functions have to be computed or approximated numerical tests verify the analysis

control of spurious modes in the nine node quadrilateral element the nine node quadrilateral is much more accurate than its eight node relative if elements are non rectangular however the nine node element may display spurious low energy modes under 2 2 gauss quadrature these modes can be controlled by using the 3 3 quadrature rule but at added cost this paper investigates two inexpensive control devices that can be used with 2 2 gauss quadrature

computation of correlation functions of the two dimensional ising model abstract the spin spin and energy energy correlation functions of the two dimensional ising model are computer on the creutz cellular automaton from the data for the spin spin correlation functions the values of the critical exponents and are obtained they are in agreement with their theoretical values

rational approach for assumed stress finite elements a new method for the formulation of hybrid elements by the hellinger reissner principle is established by expanding the essential terms of the assumed stresses as complete polynomials in the natural coordinates of the element the equilibrium conditions are imposed in a variational sense through the internal displacements which are also expanded in the natural co ordinates the resulting element possesses all the ideal qualities i e it is invariant it is less sensitive to geometric distortion it contains a minimum number of stress parameters and it provides accurate stress calculations for the formulation of a 4 node plane stress element a small perturbation method is used to determine the equilibrium constraint equations the element has been proved to be always rank sufficient

a class of mixed assumed strain methods and the method of incompatible modes a three field mixed formulation in terms of displacements stresses and an enhanced strain field is presented which encompasses as a particular case the classical method of incompatible modes within this frame work incompatible elements arise as particular compatible mixed approximations of the enhanced strain field the conditions that the stress interpolation contain piece wise constant functions and be l2 ortho gonal to the enhanced strain interpolation ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation the preceding conditions are formulated in a form particularly convenient for element design as an illustration of the methodology three new elements are developed and shown to exhibit good performance a plane 3d elastic plastic quad an axisymmetric element and a thick plate bending quad the formulation described herein is suitable for non linear analysis

meshfree enriched simplex elements with strain smoothing for the finite element analysis of compressible and nearly incompressible solids abstract this paper presents a meshfree enriched finite element formulation for triangular and tetrahedral elements in the analysis of two and three dimensional compressible and nearly incompressible solids the new formulation is first established in two dimensional case by introducing a meshfree approximation into a linear triangular finite element with an enriched node the interpolation functions of the four noded triangular element are constructed by the meshfree convex approximations and are completed to a polynomial of degree one the reference mapping using the constructed interpolation functions is shown to be invertible everywhere in the element and the global element area is proven to be conserved under a standard three point integration rule the triangular element formulation is extendable to the tetrahedral element in three dimensional case to provide a locking free analysis for the nearly incompressible materials an area weighted strain smoothing is developed in conjunction with the enriched interpolation functions to yield a discrete divergence free property at the integration point the resultant element formulation with strain smoothing is shown to pass the patch test to introduce the smoothed strain into galerkin formulation a modified hu washizu variational principle is adopted to formulate the discrete equations since the kronecker delta property in element interpolation is held along the element boundary using meshfree convex approximation boundary conditions can be treated in a standard way several numerical benchmarks are provided to demonstrate the effectiveness and accuracy of the proposed method

occam filters for stochastic sources with application to digital images an occam filter employs lossy data compression to separate signal from noise previously it was shown that occam filters can filter random noise from deterministic signals here we show that occam filters can also separate two stochastic sources depending on their relative compressibility we also compare the performance of occam filters and wavelet based denoising on digital images