c1 continuous stress recovery in finite element analysis abstract a penalized discrete least squares pdls variational principle is employed to recover c 1 continuous smooth stress fields from finite element stresses the error functional involves discrete least squares with a penalty constraint to enforce c 1 continuity of the recovered stresses the recovery procedure uses a smoothing element analysis sea with element based interpolation functions to minimize the error functional sea pdls recovers a superconvergent stress field of higher accuracy and continuity than the underlying consistent finite element stress field general and specialized formulations of the functional are given and an appropriate discretization strategy for the sea is discussed numerical results for both one and two dimensional stress fields are presented and compared with the corresponding solutions for the superconvergent patch recovery spr method of zienkiewicz and zhu the results demonstrate that in addition to achieving a higher degree of continuity sea pdls produces generally more accurate stresses than spr although an additional global analysis is required results indicate that two coarse mesh analyses finite element and smoothing produce solutions comparable to a single finite element analysis with a much greater degree of refinement and more computational effort the procedure is unique in that the recovered stress field is essentially c 1 continuous the results are shown to be insensitive to the value of the penalty parameter above a threshold and hence uncertainty in the choice of an appropriate penalty value is eliminated

the arithmetic of the digital computer a new approach a new approach to the arithmetic of the digital computer is surveyed the methodology for defining and implementing floating point arithmetic is described shortcomings of elementary floating point arithmetic are revealed through sample problems the development of automatic computation with emphasis on the user control of errors is reviewed the limitations of conventional rule of thumb procedures for error control in scientific computation are demonstrated by means of examples computer arithmetic is extended so that the arithmetic operations in the linear spaces and their interval correspondents which are most commonly used in computation can be performed with maximum accuracy on digital computers a new fundamental computer operation the scalar product is introduced to develop this advanced computer arithmetic a process of automatic error control called validation which delivers high accuracy with guarantees for scientific computations is described validation of computations for a large class of nu

a higher order compact adi method with monotone iterative procedure for systems of reaction diffusion equations this paper is concerned with an existing compact finite difference adi method published in the paper by liao et al 2002 3 for solving systems of two dimensional reaction diffusion equations with nonlinear reaction terms this method has an accuracy of fourth order in space and second order in time the existence and uniqueness of its solution are investigated by the method of upper and lower solutions without any monotone requirement on the nonlinear reaction terms the convergence of the finite difference solution to the continuous solution is proved an efficient monotone iterative algorithm is presented for solving the resulting discrete system and some techniques for the construction of upper and lower solutions are discussed an application using a model problem gives numerical results that demonstrate the high efficiency and advantages of the method

a simple vision algorithm for 3 d position determination using a single calibration object abstract we shall present a new method to determine the arbitrary 3 d location and orientation of a calibration object relative to the camera most of equations used to determine the 3 d position are simple and non trigonometric there is also no severe problem regarding the viewing angle we choose a cube to be our calibration object whose dimensions are known the basic theory behind our method for 3 d position determination is to express the 3 d line equations and the 3 d plane equations of the cube in terms of the 2 d coordinates of the vanishing points obtained from the perspective projection of the cube furthermore the given dimensions and edge perpendicularity property of the cube are used to determine the 3 d coordinates of the cube vertices more importantly in our method we iteratively modify the coordinates of the vanishing points on the image plane so that a the derived 3 d vertices comply with the given geometric constraints of the cube and b the cube image data given by the back projection is also in close agreement with what actually appears in the tv image thirty six real images are used in the experiments to illustrate the performance of the proposed method and a mitsubishi rm 101 robot arm is shown to be guided by the vision system to grasp the object too

on the convergence of the multidirectional search algorithm this paper presents the convergence analysis for the multidirectional search algorithm a direct search method for unconstrained minimization the analysis follows the classic lines of proofs of convergence for gradient related methods the novelty of the argument lies in the fact that explicit calculation of the gradient is unnecessary although it is assumed that the function is continuously differentiable over some subset of the domain the proof can be extended to treat most nonsmooth cases of interest the argument breaks down only at points where the derivative exists but is not continuous finally it is shown how a general convergence theory can be developed for an entire class of direct search methods which includes such methods as the factorial design algorithm and the pattern search algorithm that share a key feature of the multidirectional search algorithm

multidimensional edge detection by hypersurface fitting one way to define operators for detecting edges in digital images is to fit a surface plane quadric to a neighborhood of each image point and take the magnitude of the gradient of the surface as an estimate of the rate of change of gray level in the image at that point this approach is extended to define edge detectors applicable to multidimensional arrays of data e g three dimensional arrays obtained by reconstruction from projections by locally fitting hypersurfaces to the data the resulting operators for hypersurfaces of degree 1 or 2 are closely analogous to those in the two dimensional case examples comparing some of these three dimensional operators with their twodimensional counterparts are given

reduced integration post processing techniques for darcy s velocity recovery in bilinear quadrilaterals in this work we propose the use of a reduced integration technique for bilinear quadrilateral elements in the determination of the darcy s velocity via global and local post processing techniques this approach increases accuracy in distorted meshes and leads to a reduction in the computational effort for matrix coefficients and residuals evaluations numerical examples are shown to validate our approach accessing its efficiency and accuracy copyright 2007 john wiley sons ltd

analysis of material interface discontinuities and superconvergent fluxes in finite difference theory abstract an analysis of material interface discontinuities is developed and applied in finite difference theory to determine mathematically rigorous averaging techniques for material properties this result is compared with other averaging techniques particularly harmonic averaging which is often applied in practice we also develop a class of formulas of high accuracy for post processing the difference formula to compute derivatives fluxes stresses and conduct supporting numerical studies

the accuracy of floating point summation the usual recursive summation technique is just one of several ways of computing the sum of n floating point numbers five summation methods and their variations are analyzed here the accuracy of the methods is compared using rounding error analysis and numerical experiments four of the methods are shown to be special cases of a general class of methods and an error analysis is given for this class no one method is uniformly more accurate than the others but some guidelines are given on the choice of method in particular cases

minimizing roundoff errors of prefix sums via dynamic construction of huffman trees the prefix sum operation which returns all prefix sums on a sequence of numbers plays an important role in many applications we study how to efficiently evaluate prefix sums on positive floating point numbers such that the worst case roundoff error of each sum is minimized a direct approach to this problem builds a huffman tree for each prefix subsequence from scratch requiring exactly quadratic time for every input x we can do better by taking advantage of the current huffman tree to build the next huffman tree using dynamic insertions and deletions on huffman trees consequently subquadratic time suffices for various input patterns we also provide experimental comparisons of all the algorithms studied in this paper on inputs that are randomly and uniformly generated

stabilized methods and post processing techniques for miscible displacements abstract stabilized finite element formulations and post processing techniques are presented for darcy flow and miscible displacement problems in these techniques all primary unknowns are approximated in space by standard equal order interpolations we presented a review of the main mathematical results including convergence estimates for global post processing to solve the pressure velocity problem and for the stabilized solution of the complete set of coupled partial differential equations in both space time and semi discrete frameworks demonstration problems are solved to show that we obtained numerically high rates of convergence than those predicted achieving good accuracy in the solution of monophasic flow problems in adverse conditions

high order linear and non linear residual distribution schemes for turbulent compressible flows a high order residual distribution scheme for the solution of the compressible rans equations is developed the one equation spalart allmaras turbulence model is solved in a fully coupled approach the mean flow equations as well as the turbulence equation are solved with high order of accuracy a continuous approximation of the solution is adopted and standard lagrangian basis functions are used to construct the discrete space since viscous terms involve the gradient of the numerical solution which has a discontinuous normal component across the faces of the elements a continuous approximation of the gradient of the numerical solution is recovered at each degree of freedom of the grid and then interpolated with the same basis functions used for the solution the non linear system of equations resulting from the numerical discretization is solved with the non linear lu sgs method several numerical experiments are performed to verify the accuracy of the numerical method these are based on both subsonic and transonic flows in two and three spatial dimensions

a fast geometrical approach to camera extrinsic parameters abstract a fast geometrical approach is proposed to determine the camera extrinsic parameters using a trihedral normal angle tna no intrinsic camera parameters are known in advance so alignment error can be avoided the formula derived by this approach can be computed analytically the line and point features required in deriving the extrinsic parameters can be extracted by simple well developed image processing techniques thus the method is more accurate and faster than other methods in which complicated procedures are essential in finding curve or surface features from the experimental results the time for calculating the camera parameters is 0 8 sec and the measurement error is less than 3 on average

accuracy of mixed and control volume finite element approximations to darcy velocity and related quantities the accuracy of the darcy velocity flux and stream function computed from lowest order triangle based control volume and mixed finite element approximations to the two dimensional pressure equation is considered the control volume finite element method similar to integrated finite difference methods and analogous to the interpolation of galerkin finite element results over control volumes is shown to yield a conservative velocity field and smooth streamlines the streamlines and fluxes through the system computed with the control volume finite element approach are compared to those computed from the mixed finite element method which approximates the pressure and velocity variables separately it is shown that for systems with only moderate degrees of heterogeneity the control volume finite element method is the more computationally efficient alternative i e it provides more accurate flow results for a given number of unknowns for more variable or discontinuous permeability fields by contrast such as sand shale systems the mixed finite element method is shown to approximate flow variables more accurately and more realistically than the control volume method with the same number of unknowns

approximate boundary flux calculations abstract a technique for determining derivatives fluxes or stresses from finite element solutions is developed the approach is a generalization to higher dimensions of a procedure known to give highly accurate results in one dimension numerical experiments demonstrate that certain difficulties are associated with corners in the higher dimensional extensions and two variants of the method are examined we consider both triangular and quadrilateral elements and observe some interesting differences in the numerical rates of convergence finally this post processing scheme is tested for nonlinear problems

the superconvergent patch recovery spr and adaptive finite element refinement abstract the error estimation processes which have been developed by the authors depend on the accuracy with which stresses gradients can be recovered the recovery methods available currently such as the l 2 projection and averaging are inaccurate and an improved process is needed this paper presents a very much improved recovery process yielding superconvergent values throughout the domain details of this method named the superconvergent patch recovery are presented with test results showing its efficiency examples of adaptive h based refinement are given showing high local and overall efficiency indices for error estimation

the superconvergent patch recovery and a posteriori error estimates part 1 the recovery technique this is the first of two papers concerning superconvergent recovery techniques and a posteriori error estimation in this paper a general recovery technique is developed for determining the derivatives stresses of the finite element solutions at nodes the implementation of the recovery technique is simple and cost effective the technique has been tested for a group of widely used linear quadratic and cubic elements for both one and two dimensional problems numerical experiments demonstrate that the recovered nodal values of the derivatives with linear and cubic elements are superconvergent one order higher accuracy is achieved by the procedure with linear and cubic elements but two order higher accuracy is achieved for the derivatives with quadratic elements in particular an o h4 convergence of the nodal values of the derivatives for a quadratic triangular element is reported for the first time the performance of the proposed technique is compared with the widely used smoothing procedure of global l2 projection and other methods it is found that the derivatives recovered at interelement nodes by using l2 projection are also superconvergent for linear elements but not for quadratic elements numerical experiments on the convergence of the recovered solutions in the energy norm are also presented higher rates of convergence are again observed the results presented in this part of the paper indicate clearly that a new powerful and economical process is now available which should supersede the currently used post processing procedures applied in most codes

analysis of the superconvergent patch recovery technique and a posteriori error estimator in the finite element method ii abstract this is the first in a series of two papers in which the patch recovery technique proposed by zienkiewicz and zhu is analyzed in this work it is proved that the recovered derivative by the least squares fitting is superconvergent for the two point boundary value problems further the a posteriori error estimator based on the recovery technique is shown to be asymptotically exact this confirms the computational results obtained in 1 2

bayesian recognition of local 3 d shape by approximating image intensity functions with quadric polynomials the recognition in image data of viewed patches of spheres cylinders and planes in the 3 d world is discussed as a first step to complex object recognition or complex object location and orientation estimation accordingly an image is partitioned into small square windows each of which is a view of a piece of a sphere or of a cylinder or of a plane windows are processed in parallel for recognition of content new concepts and techniques include approximations of the image within a window by 2 d quadric polynomials where each approximation is constrained by one of the hypotheses that the 3 d surface shape seen is either planar cylindrical or spherical a recognizer based upon these approximations to determine whether the object patch viewed is a piece of a sphere or a piece of a cylinder or a piece of a plane lowpass filtering of the image by the approximation the shape recognition is computationally simple and for large windows is approximately bayesian minimum probability of error recognition these classifications are useful for many purposes one such purpose is to enable a following processor to use an appropriate estimator to estimate shape and orientation and location parameters for the 3 d surface seen within a window

from multiple stereo views to multiple 3 d surfaces we present a framework for 3 dimensional surface reconstruction that can be used to model fully 3 d scenes from an arbitrary number of stereo views taken from vastly different viewpoints this is a key step toward producing 3 d world descriptions of complex scenes using stereo and is a very challenging problem real world scenes tend to contain many 3 d objects they do not usually conform to the 2 1 2 d assumption made by traditional algorithms and one cannot take it for granted that the computed 3 d points can easily be clustered into separate groups furthermore stereo data is often incomplete and sometimes erroneous which makes the problem even more difficult by combining a particle based representation robust fitting and optimization of an image based objective function we have been able to reconstruct surfaces without any a priori knowledge of their topology and in spite of the noisiness of the stereo data our current implementation goes through three steps initializing a set of particles from the input 3 d data optimizing their location and finally grouping them into global surfaces using several complex scenes containing multiple objects we demonstrate the competence of this method and its ability to merge information and thus to go beyond what can be done with conventional stereo alone

derivative calculation from finite element solutions abstract a technique is considered whereby very accurate derivatives of a finite element solution can be calculated efficiently it is demonstrated here that most of the necessary quantities for this subsidiary computation are available as computed by products in the preceding finite element solution procedure the calculation is shown in this note to be a particular form of a procedure for which superconvergent theoretical error estimates have been proven elsewhere numerical experiments confirm the superior accuracy in the computed derivative stress or flux

a variational method for finite element stress recovery and error estimation abstract a variational method for obtaining smoothed stresses from a finite element derived non smooth stress field is presented the method is based on minimizing a functional involving discrete least squares error plus a penalty constraint that ensures smoothness of the stress field an equivalent accuracy criterion is developed for the smoothing analysis which results in a c1 continuous smoothed stress field possessing the same order of accuracy as that found at the superconvergent optimal stress points of the original finite element analysis application of the smoothing analysis to residual error estimation is also demonstrated

high order compact scheme for the steady stream function vorticity equations a higher order compact scheme that is o h4 on the nine point 2 d stencil is formulated for the steady stream function vorticity form of the navier stokes equations the resulting stencil expressions are presented and hence this new scheme can be easily incorporated into existing industrial software we also show that special treatment of the wall boundary conditions is required the method is tested on representative model problems and compares very favourably with other schemes in the literature

mesh refinement strategies without mapping of nonlinear solutions for the generalized and standard fem analysis of 3 d cohesive fractures summary a robust and efficient strategy is proposed to simulate mechanical problems involving cohesive fractures this class of problems is characterized by a global structural behavior that is strongly affected by localized nonlinearities at relatively small sized critical regions the proposed approach is based on the division of a simulation into a suitable number of sub simulations where adaptive mesh refinement is performed only once based on refinement window s around crack front process zone s the initialization of newton raphson nonlinear iterations at the start of each sub simulation is accomplished by solving a linear problem based on a secant stiffness rather than a volume mapping of nonlinear solutions between meshes the secant stiffness is evaluated using material state information stored read on crack surface facets which are employed to explicitly represent the geometry of the discontinuity surface independently of the volume mesh within the generalized finite element method framework moreover a simplified version of the algorithm is proposed for its straightforward implementation into existing commercial software data transfer between sub simulations is not required in the simplified strategy the computational efficiency accuracy and robustness of the proposed strategies are demonstrated by an application to cohesive fracture simulations in 3 d copyright 2016 john wiley sons ltd

a new class of cn interpolations and its application to the finite element method a new class of cn continuous interpolations is presented these interpolations consist of two or more lagrangian interpolations blended by pseudo hermitian interpolation using this class of interpolations a new cn family of displacement type elements is developed the properties of this new family of elements such as their precision and their superconvergent points are discussed some solutions to the corner elements problem and implication of different boundary conditions are proposed using this new kind of element several examples of deflection of elastic beams and plates are treated the results of which are encouraging copyright 2001 john wiley sons ltd

superconvergent derivatives a taylor series analysis an analysis based on the use of taylor series expansions is developed to determine accuracy estimates for derivatives in one and two dimensions computed by differentiation of a finite element interpolant or approximation the analysis clarifies some issues concerning special points at which the derivatives are believed to be exceptionally accurate with higher convergence rates superconvergence moreover it leads directly to a class of post processing strategies for the derivatives and offers a more direct constructive approach to the subject

3 d space location and orientation parameter estimation of lambertian spheres and cylinders from a single 2 d image by fitting lines and ellipses to thresholded data an approach to object location and orientation estimation is discussed in which objects in 3 d space are approximated by chunks of spheres cylinders and planes the surface shape parameters of these chunks of primitive subobjects are estimated in real time from a single 2 d image assuming a lambertian reflection model this processing is realized by partitioning an image into small square windows and processing the windows in parallel it is assumed that a small window views a portion of one of the spherical cylindrical or planar chunks the paper applies standard statistical estimators in new ways to the estimation of the 3 d shape parameters for spherical and cylindrical surfaces linear regression and scatter matrix eigenvalue analysis techniques are used here the algorithms are computationally simple yet are robust and can handle noisy highly variable data

recovery procedures in error estimation and adaptivity part i adaptivity in linear problems abstract the procedures of error estimation using stress or gradient recovery were introduced by zienkiewicz and zhu in 1987 3 and with the improvement of recovery procedures introduction of superconvergent patch recovery spr since that date the authors have succeeded in making these error estimators the most robust of those currently available very recently introduced methods of recovery such as rep recovery by equilibrium in patches allow general application in this paper the general idea of using recovery based error estimation in adaptive procedure of linear problems is explained through which the latest developments in recovery techniques is described the fundamental basis of a patch test introduced by babuska et al 11 14 is explained and applied to the recovery based error estimators using both spr and rep

describing complicated objects by implicit polynomials this paper introduces and focuses on two problems first is the representation power of closed implicit polynomials of modest degree for curves in 2 d images and surfaces in 3 d range data super quadrics are a small subset of object boundaries that are well fitted by these polynomials the second problem is the stable computationally efficient fitting of noisy data by closed implicit polynomial curves and surfaces the attractive features of these polynomials for vision is discussed

linear time approximation algorithms for computing numerical summation with provably small errors given a multiset x x1 xn of real numbers the floating point set summation problem asks for sn x1 xn let e n denote the minimum worst case error over all possible orderings of evaluating sn we prove that if x has both positive and negative numbers it is np hard to compute sn with the worst case error equal to e n we then give the first known polynomial time approximation algorithm that has a provably small error for arbitrary x our algorithm incurs a worst case error at most 2 lceil log n 1 rceil 1 e n all logarithms log in this paper are base 2 after x is sorted it runs in o n time for the case where x is either all positive or all negative we give another approximation algorithm with a worst case error at most lceil log log n rceil e n even for unsorted x this algorithm runs in o n time previously the best linear time approximation algorithm had a worst case error at most lceil log n rceil e n while e n was known to be attainable in o n log n time using huffman coding

superconvergence phenomena in the finite element method abstract we give a brief survey of superconvergence phenomena in finding a numerical solution of differential equations by finite elements several new results and open problems are introduced