down scaling for better transform compression the most popular lossy image compression method used on the internet is the jpeg standard jpeg s good compression performance and low computational and memory complexity make it an attractive method for natural image compression nevertheless as we go to low bit rates that imply lower quality jpeg introduces disturbing artifacts it is known that at low bit rates a down sampled image when jpeg compressed visually beats the high resolution image compressed via jpeg to be represented by the same number of bits motivated by this idea we show how down sampling an image to a low resolution then using jpeg at the lower resolution and subsequently interpolating the result to the original resolution can improve the overall psnr performance of the compression process we give an analytical model and a numerical analysis of the down sampling compression and up sampling process that makes explicit the possible quality compression trade offs we show that the image auto correlation can provide a good estimate for establishing the down sampling factor that achieves optimal performance given a specific budget of bits we determine the down sampling factor necessary to get the best possible recovered image in terms of psnr

shape optimization of three dimensional continuum structures via force approximation techniques the existing need to develop methods whereby the shape design efficiency can be improved through the use of high quality approximation methods is addressed an efficient approximation method for stress constraints in three dimensional shape design problems is proposed based on expanding the nodal forces in taylor series with respect to shape variations the significance of this new method is shown through elementary beam theory calculations and via numerical computations using three dimensional solid finite elements numerical examples including the classical cantilever beam structure and realistic automotive parts like the engine connecting rod are designed for optimum shape using the proposed method the numerical results obtained from these methods are compared with other published results to assess the efficiency and the convergence rate of the proposed method it is concluded that by taking advantage of this high quality approximation the total number of finite element analyses required for structural shape optimization can be reduced significantly resulting in the same level of efficiency achieved previously in sizing problems

the richardson extrapolation process with a harmonic sequence of collocation points let a y sim a sum infty k 1 alpha ky sigma k as y rightarrow 0 where y is a discrete or continuous variable assume that sigma k are known numbers that may be complex in general and that a y is known for y in 0 b for some b 0 the aim is to find or approximate a the limit or antilimit of a y as y rightarrow0 one very effective way of approximating a is by the richardson extrapolation process that is defined via the linear systems a y l a j n sum n k 1 overline alpha ky sigma k l j leq l leq j n here a j n are approximations to a and overline alpha k are additional unknowns the yl are picked such that y0 y1 y2 0 and lim l rightarrow infty y l 0 in this paper we give a detailed analysis of the convergence and stability of the column sequences a j n infty j 0 with n fixed when y l c l eta q for some positive c eta and q specifically we prove that convergence takes place as j to infty and give the precise rate at which it does we also prove that the process is unstable and quantify its instability asymptotically this instability may be dealt with numerically by using high precision floating point arithmetic

acceleration of convergence of general linear sequences by the shanks transformation the shanks transformation is a powerful nonlinear extrapolation method that is used to accelerate the convergence of slowly converging and even diverging sequences a n it generates a two dimensional array of approximations a j n to the limit or anti limit of a n defined as solutions of the linear systems a l a j n sum n k 1 bar beta k delta a l k 1 j leq l leq j n where bar beta k are additional unknowns in this work we study the convergence and stability properties of a j n as j with n fixed derived from general linear sequences a n where a n sim a sum m k 1 zeta k n sum infty i 0 beta ki n gamma k i as n where k 1 are distinct and 1 m and k 0 1 2 here a is the limit or the anti limit of a n such sequences arise for example as partial sums of fourier series of functions that have finite jump discontinuities and or algebraic branch singularities we show that definitive results are obtained with those values of n for which the integer programming problems begin array ll quad quad quad quad max limits s 1 ldots s m sum limits k 1 m left re gamma k s k s k s k 1 right rm subject to s 1 geq0 ldots s m geq0 quad rm and quad sum limits k 1 m s k n end array have unique integer solutions for s 1 s m a special case of our convergence result concerns the situation in which re gamma 1 cdots re gamma m alpha and n m with 1 2 for which the integer programming problems above have unique solutions and it reads a j n a o theta j j alpha 2 nu as j when compared with a j a o j j as j this result shows that the shanks transformation is a true convergence acceleration method for the sequences considered in addition we show that it is stable for the case being studied and we also quantify its stability properties the results of this work are the first ones pertaining to the shanks transformation on general linear sequences with m 1

sparse representation based down sampling image compression in this paper we give an analytical model of the compression error of down sampled compression based on wavelet transform which explains why down sampling before compression can improve coding performance and we approximate the missing details due to down sampling and compression by using the linear combination of a set of basis vectors with l 1 norm then we propose a down sampled and high frequency information approximated coding scheme and apply it to natural images and achieve gains of both subjective quality and objective quality compared with jpeg2000

recent results relevant to the evaluation of infinite series abstract a review is made of recent results concerning the convergence properties of the punctual pade approximant method the technique involves the use of shanks non linear transformations of the sequence of partial sums of the series under consideration which is actually equivalent to using ordinary pade approximants at a particular point previous theorems are extended and stated more generally so that they may be of use in other areas besides that of potential scattering theory for which they were originally intended the results show the value of the approach as a convergence acceleration method when dealing with convergent series and as a regularization procedure otherwise

review of options for structural design sensitivity analysis part 1 linear systems the paper reviews options for structural design sensitivity analysis including global finite differences continuum derivatives discrete derivatives and computational or automated differentiation the objective is to put these different approaches to design sensitivity analysis in the context of accuracy and consistency computational cost and implementation options and effort linear static analysis and transient dynamic analysis are reviewed in a separate appendix special attention is paid to the semi analytical method a future paper will address design sensitivity analysis in nonlinear structural problems

a simple approach to asymptotic expansions for fourier integrals of singular functions abstract in this work we are concerned with the derivation of full asymptotic expansions for fourier integrals a b f x e i sx dx as s where s is real positive a b is a finite interval and the functions f x may have different types of algebraic and logarithmic singularities at x a and x b this problem has been treated in the literature by techniques involving neutralizers and mellin transforms here we derive the relevant asymptotic expansions by a method that employs simpler and less sophisticated tools

shape optimal design using b splines abstract shape optimal design of an elastic structure is formulated using a design element technique it is shown that bezier and b spline curves typical of the cad philosophy are well suited to the definition of design elements complex geometries can be described in a very compact way by a small set of design variables and a few design elements because of the b splines flexibility it is no longer necessary to piece design elements together in order to agree with the shape complexity nor to restrict the shape variations moreover the additional optimization constraints that are most often needed to avoid unrealistic designs when the shape variables are the nodal coordinates of a finite element mesh are automatically taken into account in the new formulation an analytical derivation of the sensitivity analysis will be established giving rise to numerical efficiency it will be seen that the resulting optimization problem does not involve highly nonlinear functions with respect to the shape variables so that simple mathematical programming algorithms can be applied to solve it some numerical examples are offered to demonstrate the power and generality of the new approach presented in this paper

asymptotic expansions of legendre series coefficients for functions with interior and endpoint singularities abstract let n 0 en f pn x be the legendre expansion of a function f x on 1 1 in an earlier work a sidi asymptot anal 65 2009 pp 175 190 we derived asymptotic expansions as n for en f assuming that f c 1 1 but may have arbitrary algebraic logarithmic singularities at one or both endpoints x 1 in the present work we extend this study to functions f x that are infinitely differentiable on 0 1 except at finitely many points x1 xm in 1 1 and possibly at one or both of the endpoints x0 1 and xm 1 1 where they may have arbitrary algebraic singularities including finite jump discontinuities specifically we assume that for each r f x has asymptotic expansions of the form

a freeform shape optimization of complex structures represented by arbitrary polygonal or polyhedral meshes in this paper we propose a new scheme for freeform shape optimization on arbitrary polygonal or polyhedral meshes the approach consists of three main steps 1 surface partitioning of polygonal meshes into different patches 2 a new freeform perturbation scheme of using the cox de boor basis function over arbitrary polygonal meshes which supports multi resolution shape optimization and does not require cad information 3 freeform shape optimization of arbitrary polygonal or polyhedral meshes numerical experiments indicate the effectiveness of the proposed approach copyright 2004 john wiley sons ltd

constructive solid geometry approach to three dimensional structuralshape optimization this paper presents a constructive solid geometry approach to generic three dimensional shape optimization the problem definition and shape control are based on constructive solid geometry whereas the assets of boundary representation are exploited to specify the physics of the problem and for meshing the object this approach is strongly coupled to an automatic mesh generator and uses to its advantage the explicit association of the finite element data with the model geometry for performing shape sensitivity analysis hybrid approximation methods are used to minimize the number of finite element analyses a classical example of a cantilevered plate with a hole and a realistic aircraft turbine disk problem are solved for optimum shape using this new approach

two new classes of nonlinear transformations for accelerating the convergence of infinite integrals and series two new classes of nonlinear transformations the d transformation to accelerate the convergence of infinite integrals and the d transformation to accelerate the convergence of infinite series are presented in the course of the development of these transformations two interesting asymptotic expansions one for infinite integrals and the other for infinite series are derived the transformations d and d can easily be applied to infinite integrals 0f t dt whose integrands f t satisfy linear differential equations of the form f t s m k 1p k t f k t and to infinite series s r 1f r w terms f r satisfy a linear difference equation of the form f r s m k 1p k r d kf r such that in both cases the p k have asymptotic expansions in inverse powers of their arguments in order to be able to apply these transformations successfully one need not know explicitly the differential equation that the integrand satisfies or the difference equation that the terms of the series satisfy mere knowledge of the existence of such a differential or difference equation and its order m is enough this broadens the areas to which these methods can be applied the connection between the d and d transformations with some known transformations in shown the use and the remarkable efficiency of the d and d transformations are demonstrated through several numerical examples the computational aspects of these transformations are described in detail

min max boundary domain decomposition domain decomposition is one of the most effective and popular parallel computing techniques for solving large scale numerical systems in the special case when the amount of computation in a subdomain is proportional to the volume of the subdomain domain decomposition amounts to minimizing the surface area of each subdomain while dividing the volume evenly motivated by this fact we study the following min max boundary multi way partitioning problem given a graph g and an integer k 1 we would like to divide g into k subgraphs g1 gk by removing edges such that i gi g k for all i 1 k and ii the maximum boundary size of any subgraph the set of edges connecting it with other subgraphs is minimized we provide an algorithm that given g a well shaped mesh in d dimensions finds a partition of g into k subgraphs g1 gk such that for all i gi has g k vertices and the number of edges connecting gi with the other subgraphs is o g k 1 1 d our algorithm can find such a partition in o g logk time finally we extend our results to vertex weighted and vertex based graph decomposition our results can be used to simultaneously balance the computational and memory loads on a distributed memory parallel computer without incurring large communication overhead

three dimensional shape optimization using fully automatic mesh generation introduction t he technique for associating design variables with mesh data is the most crucial factor in three dimensional shape optimization previously work in three dimensional shape optimization involved specifying design variables by associating parameters directly with grid points on an existing mesh for realistic problems this can be a very tedious and errorprone process in the past shape optimization capabilities have been developed based on a variety of design analysis capabilities ranging from associating parameters with a mesh created manually to associating parameters with control points of a mapped mesh generator special techniques have also been developed to properly move internal grid points during sensitivity calculations more recently a capability based on constructive solid geometry csg has been developed but csg representations are not particularly suitable for design optimization a new optimization approach is demonstrated in this note that uses a new fully automatic mesh generation capability the design model is developed based on design oriented geometric primitives that represent recognizable features of a part and can be assembled into complete solid models that are defined in terms of a small set of design parameters

lower bounds for quartic anharmonic and double well potentials rigorous and remarkably accurate lower bounds to the lower eigenvalue spectrum of the schrodinger equation with quartic anharmonic and symmetric double well potentials of the form v a b ax2 2 bx4 b 0 are presented this procedure exploits some exactly soluble model potentials and appears to be of quite general utility

convex decomposition of polyhedra and robustness this paper presents a simple algorithm to compute a convex decomposition of a nonconvex polyhedron of arbitrary genus handles and shells internal voids for such a polyhedron s with n edges and rnotches features causing nonconvexity in polyhedra the algorithm produces a worst case optimal o r 2 number of convex polyhedra s i with u i 1 k s i s in o nr 2 r 7 2 time and o nr r 5 2 space recently chazelle and palios have given a fast o n r 2 log r time and o n r 2 space algorithm to tetrahedralize a nonconvex polyhedron their algorithm however works for a simple polyhedron of genus zero and with no shells internal voids the algorithm presented here is based on the simple cut and split paradigm of chazelle with the help of zone theorems on arrangements it is shown that this cut and split method is quite efficient the algorithm is extended to work for a certain class of nonmanifold polyhedra also presented is an algorithm for the same problem

a modular approach for three dimensional shape optimization of structures an approach for shape optimization of three dimensional solid structures is described a major consideration in the development of this capability was the desire to use a commercially available finite element program such as nastran for analysis since nastran cannot be called a subroutine a system architecture of independently executable modules was developed in which sequential execution is controlled by job control language also sensitivities are not commonly available in commercial programs a material derivative approach was developed to obtain shape sensitivities by postprocessing finite element boundary stresses stored on files a parameterized surface description and mesh generation are provided using isoparametric mapping patches the feasible directions algorithm conmin is used for optimization several automotive related examples are used to evaluate the program s effectiveness

downsampling of bounded bandlimited signals and the bandlimited interpolation analytic properties and computability downsampling and the computation of the bandlimited interpolation of discrete time signals are two important concepts in signal processing in this paper we analyze the downsampling operation regarding its impact on the existence and computability of the bounded bandlimited interpolation we assume that the discrete time signal is obtained by downsampling the samples of a bounded bandlimited signal that vanishes at infinity and we study two problems first we investigate the existence of the bounded bandlimited interpolation for such discrete time signals from a signal theoretic perspective and show that there exist signals for which the bounded bandlimited interpolation does not exist second we analyze the algorithmic generation of the bounded bandlimited interpolation using the concept of turing computability turing computability models what is theoretically implementable on a digital computer interestingly it turns out that even if the bounded bandlimited interpolation exists analytically it is not always computable which implies that there exists no algorithm on a digital computer that can always compute it computability is important in order that the approximation error be controlled if a signal is not computable we cannot ascertain whether the computed signal is sufficiently close to the true signal i e we cannot verify every approximation accuracy

comparison between the variational and implicit differentiation approaches to shape design sensitivities the most commonly used approach to the shape design sensitivity problem results from the implicit differentiation of the discretized equilibrium equations the most general implementation of this technique requires that finite differences be used to differentiate the element stiffness matrices proper choice of the step size is necessary to obtain high levels of accuracy and to avoid round off errors furthermore since it is necessary to operate on the element matrices this method is difficult to implement into a general purpose finite element program a more recent shape design sensitivity formulation based upon variational calculus avoids having to differentiate the discretized equations and results in an analytical expression for the derivative the approach is based upon the total derivative of the variational state equation and uses an adjoint variable technique for design sensitivity analysis only structural response data on the boundary of the structure is necessary thereby making implementation into a general purpose program less difficult this paper attempts to compare the two different techniques and point out the similarities two test problems are shown to demonstrate the accuracy of the variational approach

three dimensional shape optimization using the boundary element method a practical design sensitivity calculation technique of displacements and stresses for three dimensional bodies based on the direct differentiation method of discrete boundary integral equations is formulated in detail then the sensitivity calculation technique is applied to determine optimum shapes of minimum weight subjected to stress constraints where an approximated subproblem is constructed repeatedly and solved sequentially by the mathematical programming method the shape optimization technique suggested here is applied to determine optimum shapes of a cavity in a cube and a connecting rod

displacement minimization of thermoelastic structures by evolutionary thickness design structural optimization aims at finding an appropriate material distribution to achieve the best structural performance in this paper the evolutionary structural optimization method is further developed to deal with thermoelastic optimization where structural material is progressively redistributed so as to minimize the displacement under thermal and mechanical loading to evaluate the effects of material removal or addition on the displacement of thermoelastic structures a sensitivity number is proposed on the basis of the thickness variation of an element the method proves to be very simple in its mathematical operations and suitable for computer implementation the numerical examples are compared against those by the homogenization method to verify and validate this method of solving thermoelastic optimizations in addition the effect of various temperature distributions on the final optimum structures is investigated in detail

asymptotic analysis of a generalized richardson extrapolation process on linear sequences in this work we give a detailed convergence and stability analysis for the author s generalized richardson extrapolation process grep m as this is being applied to linearly convergent or divergent infinite sequences a n where a n a m k 1 n k i 0 ki n k i as n k 1 being distinct the quantity we would like to compute is a whether it is the limit or antilimit of a n such sequences arise for example as partial sums of power series and of fourier series of functions that have algebraic and or logarithmic branch singularities specifically we define the grep m approximation a n m j to a with n n 1 n m and 0 via the linear systems a l a n m j m k 1 l k n i 0 1 ki l k 1 j l j m k 1 n k where ki are additional unknowns we study the convergence and stability properties of a n m j as j we show in particular that a n m j a m k 1 o j k j k 2nk as j when compared with a j a m k 1 o j k j k as j this result shows that grep m is a true convergence acceleration method for the sequences considered in addition we show that grep m is stable for the case being studied and we also quantify its stability properties the results of this work are the first ones pertaining to grep m with m 1

shape optimization of 2d structures using simulated annealing the goal of this study is to obtain globally optimum shapes for two dimensional structures subject to quasi static loads and restraints for this purpose a technique is proposed using which the volume or weight of a structure can be minimized the emphasis is on how one can define the shape precisely and find a shape that accurately reflects the globally optimum shape as design constraints stresses developed in the structure should not exceed the maximum allowable stress and connectivity of the structure should not be lost during shape changes optimization is achieved by a stochastic search algorithm called direct simulated annealing dsa which seeks the global minimum through randomly generated configurations in order to obtain random configurations a boundary variation technique is used in this technique a set of key points is chosen and connected by cubic splines to describe the boundary of the structure whenever the positions of the key points are changed in random directions a new shape is obtained thus coordinates of the key points serve as design variables in order to apply the optimization procedure a general computer code was developed using ansys parametric design language a number of cases were examined to test its effectiveness the results show that this technique can be applied to two dimensional shape optimization problems with high reliability even for cases where the entire free boundary is allowed to vary 2007 elsevier b v all rights reserved

on a generalization of the richardson extrapolation process a convergence result for a generalized richardson extrapolation process is improved upon considerably and additional results of interest are proved an application of practical importance is also given finally some known results concerning the convergence of levin s t transformation are reconsidered in light of the results of the present work

acceleration of convergence of vector sequences a general approach to the construction of convergence acceleration methods for vector sequences is proposed using this approach one can generate some known methods such as the minimal polynomial extrapolation the reduced rank extrapolation and the topological epsilon algorithm and also some new ones some of the new methods are easier to implement than the known methods and are observed to have similar numerical properties the convergence analysis of these new methods is carried out and it is shown that they are especially suitable for accelerating the convergence of vector sequences that are obtained when one solves linear systems of equations iteratively a stability analysis is also given and numerical examples are provided the convergence and stability properties of the topological epsilon algorithm are likewise given

convex partitions of polyhedra a lower bound and worst case optimal algorithm the problem of partitioning a polyhedron into a minimum number of convex pieces is known to be np hard we establish here a quadratic lower bound on the complexity of this problem and we describe an algorithm that produces a number of convex parts within a constant factor of optimal in the worst case the algorithm is linear in the size of the polyhedron and cubic in the number of reflex angles since in most applications areas the former quantity greatly exceeds the latter the algorithm is viable in practice

accurate correction of surface noises of polygonal meshes summary in this paper we propose a new algorithm for accurate correction of surface noises of polygonal meshes it consists of three basic components a feature preserving pre smoothing b partitioning of feature and non feature regions c second order predictor for non feature regions and median filter for feature regions the unique contributions of our approach include a an idea of partitioning an input surface into feature and non feature regions so that different smoothing algorithms which are best suited for either feature or non feature regions can be respectively applied b a secondorder predictor that provides higher smoothing accuracy and better convergence on smoothly curved surfaces in comparison with several existing algorithms our algorithm is evaluated quantitatively in terms of surface normal and vertex distance error metrics numerical experiments indicate the effectiveness of our approach in the aspects of convergence and accuracy copyright 2005 john wiley sons ltd

interpolation dependent image downsampling traditional methods for image downsampling commit to remove the aliasing artifacts however the influences on the quality of the image interpolated from the downsampled one are usually neglected to tackle this problem in this paper we propose an interpolation dependent image downsampling idid where interpolation is hinged to downsampling given an interpolation method the goal of idid is to obtain a downsampled image that minimizes the sum of square errors between the input image and the one interpolated from the corresponding downsampled image utilizing a least squares algorithm the solution of idid is derived as the inverse operator of upsampling we also devise a content dependent idid for the interpolation methods with varying interpolation coefficients numerous experimental results demonstrate the viability and efficiency of the proposed idid

an algorithm for a generalization of the richardson extrapolation process in this paper we present a recursive method designated the w m algorithm for implementing a generalization of the richardson extrapolation process that has been ntroduced in 8 compared to the direct solution of the linear systems of equations defining the extrapolation procedure this method requires a small number of arithmetic operations and very little storage the technique is also applied to solve recursively the coefficient problem associated with the rational approximations obtained by applying the d transformation of 6 13 to power series in the course of development a new recursive algorithm for implementing a very general extrapolation procedure is introduced which is similar to that given in 2 4 for solving the same problem a fortran program for the w m algorithm is also appended

numerical comparisons of nonlinear convergence accelerators as part of a continuing program of numerical tests of convergence accelerators we have compared the iterated aitken s a2 method wynn s algorithm brezinski s 0 algorithm and levin s u transform on a broad range of test problems linearly convergence alternating monotone and irregular sign series logarithmically convergent series power method and bernoulli method sequences alternating and monotone asymptotic series and some perturba tion series arising in applications in each category either the algorithm or the u transform gives the best results of the four methods tested in some cases differences among methods are slight and in others they are quite striking 1 introduction we reported in 19 on a numerical test program that compared eleven different scalar convergence accelerators on a broad range of infinite series problems in an attempt to find an across the board accelerator that would handle both linear and logarithmic convergence and both alternating and monotone series or sequences the best candidates to emerge from that study were levin s u transform 14 and brezinski s 0 algorithm 6 we also provided some theoretical support for that conclusion in terms of the wide range of series summed exactly by these methods and by proving that 02 and the levin transforms all accelerate linear convergence the other levin transforms t and v produced essentially equivalent numerical results to u except that t fails on logarithmic convergence we have continued the test program started with 19 to include monotone linearly convergent series series with irregular sign patterns specifically fourier series and sequences whose terms do not depend explicitly on the previous term and or the index e g bernoulli s method since convergence accelerators are often known to transform divergent series to convergent ones we have also included in our test program divergent power series asymptotic series and a few perturbation series the methods considered in this paper are the u and 0 algorithms noted above and

design sensitivity analysis for shape optimization based on the lie derivative abstract the paper presents a theoretical framework for the shape sensitivity analysis of systems governed by partial differential equations the proposed approach based on geometrical concepts borrowed from differential geometry shows that sensitivity of a performance function i e any function of the solution of the problem with respect to a given design variable can be represented mathematically as a lie derivative i e the derivative of that performance function along a flow representing the continuous shape modification of the geometrical model induced by the variation of the considered design variable theoretical formulae to express sensitivity analytically are demonstrated in detail in the paper and applied to a nonlinear magnetostatic and a linear elastic problem following both the direct and the adjoint approaches following the analytical approach one linear system of which only the right hand side needs be evaluated the system matrix being known already has to be solved for each of the design variables in the direct approach or for each performance functions in the adjoint approach a substantial gain in computation time is obtained this way compared to a finite difference evaluation of sensitivity which requires solving a second nonlinear system for each design variable this is the main motivation of the analytical approach there is some freedom in the definition of the auxiliary flow that represents the shape modification we present a method that makes benefit of this freedom to express sensitivity locally as a volume integral over a single layer of finite elements connected to both sides of the surfaces undergoing shape modification all sensitivity calculations are checked with a finite difference in order to validate the analytic approach convergence is analyzed in 2d and 3d with first and second order finite elements

a physics based parameterization method for shape optimization a physical approach is presented to provide shape modification of nurbs curve the movement of the control polygon of nurbs is simulated by a physical frame structure and the curve deformation is then carried out through changes of the mode coordinates which are derived from the eigenvectors of the finite element equations of the physical frame system the shape of the design boundaries is described by a linear combination of the mode shape vectors based on the presented design variable representation and p version finite element analysis an integrated approach to structural shape optimization is discussed a method is developed that enables the description of the shape to be adaptively refined during the shape optimization process numerical examples are used to demonstrate the applicability of this approach to structural shape optimization

computational method for optimization of structural shapes in the direct method of shape optimum design mesh regridding is a necessary step in avoiding the distortion of finite element grids the effect of internal nodal movements on the shape design sensitivity associated with the regridding process has been carefully examined in this paper it shows that to maintain computational accuracy the effects of internal nodal movement should be considered in shape design sensitivity analysis to take the internal nodal movement into account the numerical accuracy of the speed method is investigated a new approach which constructs the velocity field over the element domain is presented although it takes more computational time the new approach does improve the accuracy of shape design sensitivity

a new scheme for efficient and direct shape optimization of complex structures represented by polygonal meshes in this paper a new shape optimization approach is proposed to provide an efficient optimization solution of complex structures represented by polygonal meshes our approach consists of three main steps 1 surface partitioning of polygonal meshes 2 generation of shape design variables on the basis of partitioned surface patches and 3 gradient based shape optimization of the structures by reducing a weighted compliance among all load cases the main contributions of this paper include i that our approach can be directly applied on polygonal meshes with the reduction of design variables or decision variables by 10 to 1000 times compared to the conventional design variable scheme of using each mesh node ii our perturbation scheme is mathematically proven with respect to maintaining the smoothness of each surface patch except on its boundary and iii overall our approach can be used to automate time consuming shape optimization of polygonal meshes to a greater extent numerical experiments have been conducted and the results indicate the effectiveness of the approach copyright 2003 john wiley sons ltd

reduction of the gibbs phenomenon for smooth functions with jumps by the e algorithm recently brezinski has proposed to use wynn s e algorithm in order to reduce the gibbs phenomenon for partial fourier sums of smooth functions with jumps by displaying very convincing numerical experiments in the present paper we derive analytic estimates for the error corresponding to a particular class of hypergeometric functions and obtain the rate of column convergence for such functions possibly perturbed by another sufficiently differentiable function we also analyze the connection to pade fourier and pade chebyshev approximants including those recently studied by kaber and maday

optimization of geometrically nonlinear thin shells subject to displacement and stability constraints a methodology is developed for shape optimization of thin plate and shell structures undergoing large deflections subject to displacement and system stability constraints the optimization method considers shape parameters and overall thickness of the structure as the design variables and aims to minimize the total mass of the structure subject to stability or displacement constraint two optimality criteria based on karush kuhn tucker conditions are developed for mass minimization problems optimality criteria are combined with nonlinear corotational analysis to optimize structures with geometric nonlinearity the method is applied to plate and shallow shell structures the efficiency of the developed design optimization methodology is compared with that of the gradient based method of optimization sequential quadratic programming

down sampling design in dct domain with arbitrary ratio for image video transcoding this paper proposes a designing framework for down sampling compressed images video with arbitrary ratio in the discrete cosine transform dct domain in this framework we first derive a set of dct domain down sampling methods which can be represented by a linear transform with double sided matrix multiplication ltds in the dct domain and show that the set contains a wide range of methods with various complexity and visual quality then for a preselected spatial domain down sampling method we formulate an optimization problem for finding an ltds to approximate the given spatial domain down sampling method for a trade off between the visual quality and the complexity by modeling ltds as a multiple layer network a so called structural learning with forgetting algorithm is then applied to solve the optimization problem the proposed framework has been applied to discover optimal ltdss corresponding to a spatial down sampling method with butterworth low pass filtering and bicubic interpolation experimental results show that the resulting ltds achieves a significant reduction on the complexity when compared with other methods in the literature with similar visual quality

adaptive downsampling to improve image compression at low bit rates at low bit rates better coding quality can be achieved by downsampling the image prior to compression and estimating the missing portion after decompression this paper presents a new algorithm in such a paradigm based on the adaptive decision of appropriate downsampling directions ratios and quantization steps in order to achieve higher coding quality with low bit rates with the consideration of local visual significance the full resolution image can be restored from the dct coefficients of the downsampled pixels so that the spatial interpolation required otherwise is avoided the proposed algorithm significantly raises the critical bit rate to approximately 1 2 bpp from 0 15 0 41 bpp in the existing downsample prior to jpeg schemes and therefore outperforms the standard jpeg method in a much wider bit rate scope the experiments have demonstrated better psnr improvement over the existing techniques before the critical bit rate in addition the adaptive mode decision not only makes the critical bit rate less image independent but also automates the switching coders in variable bit rate applications since the algorithm turns to the standard jpeg method whenever it is necessary at higher bit rates

on the discrete variant of the traction method in parameter free shape optimization abstract one of the major challenges in the parameter free approach to computational shape optimization is the avoidance of oscillating i e non smooth boundaries in the optimal design trials in order to achieve this we investigate a method for regularization that corresponds to the discrete variant of the so called traction method in this approach the design updates are generated in terms of a displacement field which is obtained as the solution to an auxiliary boundary value problem that is defined on the actual design domain the main idea herein is to apply fictitious nodal forces corresponding to the discrete sensitivity of the objective function we propose an algorithm in which constraint functions will be taken into account by using an augmented lagrangian formulation and a step length control ensures a sufficient decrease condition in terms of the objective function within each iteration we examine the benefits of the proposed regularization method on the basis of some numerical examples in comparison to an unregularized steepest descent algorithm

shape optimal design using fictitious loads implementation aspects of the natural velocity field approach for shape optimal design are discussed the problem of concern is to find the optimum shape of an elastic body that requires minimizing an objective function subject to stress displacement frequency and manufacturing constraints in this paper fictitious loads are applied at certain control nodes on an auxiliary structure and the deformation produced by these loads is used to update the shape the use of beam stiffeners in the auxiliary structure leads to smoother shapes furthermore softer material properties in the auxiliary structure result in faster convergence when iterating through the feasibile region the method is applied in conjunction with both discrete and continuum methods of design sensitivity analysis

compressive sampling based image coding for resource deficient visual communication in this paper a new compressive sampling based image coding scheme is developed to achieve competitive coding efficiency at lower encoder computational complexity while supporting error resilience this technique is particularly suitable for visual communication with resource deficient devices at the encoder compact image representation is produced which is a polyphase down sampled version of the input image but the conventional low pass filter prior to down sampling is replaced by a local random binary convolution kernel the pixels of the resulting down sampled pre filtered image are local random measurements and placed in the original spatial configuration the advantages of the local random measurements are two folds 1 preserve high frequency image features that are otherwise discarded by low pass filtering and 2 remain a conventional image and can therefore be coded by any standardized codec to remove the statistical redundancy of larger scales moreover measurements generated by different kernels can be considered as the multiple descriptions of the original image and therefore the proposed scheme has the advantage of multiple description coding at the decoder a unified sparsity based soft decoding technique is developed to recover the original image from received measurements in a framework of compressive sensing experimental results demonstrate that the proposed scheme is competitive compared with existing methods with a unique strength of recovering fine details and sharp edges at low bit rates

quantitative and constructive aspects of the generalized koenig s and de montessus s theorems for pade approximants abstract the generalized koenig s theorem and de montessus s theorem are two classical results concerning the convergence of the rows of the pade table for meromorphic functions employing a technique that was recently developed for the analysis of vector extrapolation methods refined versions of these theorems are proved in the present work specifically complete expansions for the numerators and denominators of pade approximants are derived these expansions are then used to obtain 1 precise asymptotic rates of convergence of the poles of the pade approximants to the corresponding poles simple or multiple of the meromorphic function in question and 2 the precise asymptotic behavior of the error in the relevant pade approximants one important feature of the asymptotic results derived in this work is that these are expressed in terms of a very small number of parameters approximations of optimal accuracy to multiple poles and the principal parts of the corresponding laurent expansions are also constructed in addition the convergence problem for the case in which the only singularities on the circle of meromorphy are poles is solved completely through the solution of a nonlinear integer programming problem

a perceptually motivated three component image model part i description of the model some psychovisual properties of the human visual system are discussed and interpreted in a mathematical framework the formation of perception is described by appropriate minimization problems and the edge information is found to be of primary importance in visual perception having introduced the concept of edge strength it is demonstrated that strong edges are of higher perceptual importance than weaker edges textures we have also found that smooth areas of an image influence our perception together with the edge information and that this influence can be mathematically described via a minimization problem based on this study we have proposed to decompose the image into three components i primary ii smooth and iii texture which contain respectively the strong edges the background and the textures an algorithm is developed to generate the three component image model and an example is provided in which the resulting three components demonstrate the specific properties as expected finally it is shown that the primary component provides a superior representation of the strong edge information as compared with the popular laplacian gaussian operator edge extraction scheme