numerical modelling of crack propagation automatic remeshing and comparison of different criteria modelling of a crack propagating through a finite element mesh under mixed mode conditions is of prime importance in fracture mechanics three different crack growth criteria and the respective crack paths prediction for several test cases are compared the maximal circumferential stress criterion the strain energy density fracture criterion and the criterion of the maximal strain energy release rate are implemented using advanced finite element techniques a fully automatic remesher enables to deal with multiple boundaries and multiple materials the propagation of the crack is calculated with both remeshing and nodal relaxation several examples are presented to check for the robustness of the numerical techniques and to study specific features of each criterion

an efficient 3 d infinite element for water wave diffraction problems an efficient and simple infinite element for modelling the far field potential of water wave diffraction problems is presented the shape functions in the radial direction comprise the first two terms of the asymptotic expansions of hankel functions the integrals with infinite limit for calculating the coefficient matrix have been worked out numerical tests on the diffraction by a surface piercing circular cylinder give surprisingly accurate resultant forces even if the infinite elements are placed very near to the cylinder other typical three dimensional examples also show that satisfactory results can be obtained by the use of this simple infinite element a computer program waload has been developed for computing the wave forces on fixed two and three dimensional bodies

investigation of nonplanar perfectly matched absorbers for finite element mesh truncation we present a detailed theoretical and numerical investigation of the perfectly matched layer pml concept as applied to the problem of mesh truncation in the finite element method fem we show that it is possible to extend the cartesian pml concepts involving half spaces to cylindrical and spherical geometries appropriate for closed boundaries in two and three dimensions by defining lossy anisotropic layers in the relevant coordinate systems by using the method of separation of variables it is possible to solve the boundary value problems in these geometries the analytical solutions demonstrate that under certain conditions outgoing waves are absorbed with negligible reflection and the transmitted wave is attenuated within the pml to reduce the white space in radiation or scattering problems conformal pmls are constructed via parametric mappings it is also verified that the pml concept which was originally introduced for problems governed by maxwell s equations can be extended to cases governed by the scalar helmholtz equation finally numerical results are presented to demonstrate the use of the pml in fem mesh truncation

analysing repeated measurements with possibly missing observations by modelling marginal distributions suppose that subjects are observed repeatedly over a common set of time points with possibly time dependent covariates and possibly missing observations at each time point we model the marginal distribution of the response variable and the effect of the covariates on that distribution using a class of quasi likelihood models studied in mccullagh and nelder no parametric model of dependence of the repeated observations of the subject is assumed for large samples the quasi likelihood estimates of the time specific regression coefficients over the set of predetermined time points are shown to be approximately jointly normal this coupled with various inference procedures provides a global picture about the effects of the covariates on the response variable over the entire study period a lack of fit test for testing the adequacy of the assumed quasi likelihood model is also provided all the methods considered here are illustrated with real life examples

a rigorous and unified mass lumping scheme for higher order elements abstract in dynamic analysis with explicit time integration schemes a lumped mass matrix lmm is preferable because lmm can avoid solving the large scale simultaneous algebraic equations mathematically rigorous mass lumping schemes such as the mass lumping by nodal quadrature and the row sum technique are applicable to only linear or bilinear elements for higher order elements such as 8 node serendipity elements the diagonal scaling procedure is the only lumping method that can be recommended to generate positive definite diagonal element mass matrices unfortunately there is no mathematical theory in support of this approach this study proposes a general mass lumping scheme applicable to higher order elements where the virtual work of initial force is integrated over the problem domain that is viewed as the manifold covered by the finite element patches by a series of numerical experiments both free and forced vibration problems it is suggested that even in the implicit time integration scheme the consistent mass matrix cmm can be superseded by the proposed lmm furthermore the proposed lmm has much stronger adaptability to distorted meshes

effects of time integration schemes on discontinuous deformation simulations using the numerical manifold method numerical stability by using certain time integration scheme is a critical issue for accurate simulation of discontinuous deformations of solids to investigate the effects of the time integration schemes on the numerical stability of the numerical manifold method the implicit time integration schemes ie the newmark the hht alpha and the wbz alpha methods and the explicit time integration algorithms ie the central difference the zhai s and chung lee methods are implemented their performance is examined by conducting transient response analysis of an elastic strip subjected to constant loading impact analysis of an elastic rod with an initial velocity and excavation analysis of jointed rock masses respectively parametric studies using different time steps are conducted for different time integration algorithms and the convergence efficiency of the open close iterations for the contact problems is also investigated it is proved that the hilber hughes taylor alpha hht alpha wood bossak zienkiewicz alpha wbz alpha zhai s and chung lee methods are more attractive in solving discontinuous deformation problems involving nonlinear contacts it is also found that the examined explicit algorithms showed higher computational efficiency compared to those implicit algorithms within acceptable computational accuracy

stochastic cascades and 3 dimensional navier stokes equations in this article we study the incompressible navier stokes equations in 3 the non linear integral equation satisfied by the fourier transform of the laplacian of the velocity field can be interpreted in terms of a branching process and a composition rule along the associated tree we derive from this representation new classes where global existence and uniqueness can be proven

the stability of infinite element schemes for transient wave problems the transformation of conjugated infinite elements from the frequency domain to the time domain is described this procedure yields discrete numerical models for transient acoustics which are local in space and time these can be integrated in time to solve unsteady problems of radiation or scattering in infinite domains provided that the discrete equations themselves are stable with time the conditions under which this is true are investigated in this article a numerical study is presented which shows that the stability of the numerical scheme depends critically upon the form of the inner surface of the infinite element domain solutions for test problems are presented to demonstrate that such criteria also apply when the equations are discretised in time and that stable solutions can be obtained using implicit time integration schemes when simple criteria are correctly applied axisymmetric spherical and spheroidal formulations are considered

ergodicity of the 2d navier stokes equations with random forcing we consider the navier stokes equation on a two dimensional torus with a random force acting at discrete times and analytic in space for arbitrarily small viscosity coefficient we prove the existence and uniqueness of the invariant measure for this system as well as exponential mixing in time

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

s r decomposition based numerical manifold method the numerical manifold method nmm surmounting the mesh dependence has successfully solved very complicated problems involving small deformation and large movement but had few applications to large deformation and large rotation problems because the false volume expansion and other issues exist in this study it is shown that the false volume expansion in nmm can be excellently resolved by using the s r strain rotation decomposition theorem which can precisely reflect complex physical behaviors occurring in the process of large rotation and large deformation the numerical methods based on the s r decomposition theorem have been limited to the static analysis of large deformations to remove this limitation a new formulation taking into account dynamical features is proposed based on the weak form of momentum conservation law under the framework of nmm the generalized a method is employed to discretize the temporal variables the updates of variables are described using the updated co moving coordinate system thus a new method named s r d based nmm is established the new formulation can be implemented in any other partition of unity based methods as well so as to improve the performances of such methods in the analysis of dynamic large deformations c 2016 elsevier b v all rights reserved

stochastic dissipative pde s and gibbs measures we study a class of dissipative nonlinear pde s forced by a random force omega t x with the space variable x varying in a bounded domain the class contains the 2d navier stokes equations under periodic or dirichlet boundary conditions and the forces we consider are those common in statistical hydrodynamics they are random fields smooth in t and stationary short correlated in time t in this paper we confine ourselves to kick forces of the form where the k s are smooth bounded identically distributed random fields the equation in question defines a markov chain in an appropriately chosen phase space a subset of a function space that contains the zero function and is invariant for the random flow of the equation concerning this markov chain we prove the following main result see theorem 2 2 the markov chain has a unique invariant measure to prove this theorem we present a construction assigning to any invariant measure a gibbs measure for a 1d system with compact phase space and apply a version of ruelle perron frobenius uniqueness theorem to the corresponding gibbs system we also discuss ergodic properties of the invariant measure and corresponding properties of the original randomly forced pde

combining dependent tests with incomplete repeated measurements summary in comparing the effectiveness of two treatments repeated measurements of the same characteristic are often taken under two or more distinct conditions for each experimental subject a locally best linear combination of individual test statistics obtained under different conditions is proposed to test the equality of the two treatments the test procedure allows different patterns of missing observations for the two groups to be compared special cases such as combining wilcoxon tests t tests and 2 x 2 tables are discussed in detail with real examples

semi parametric and non parametric methods for the analysis of repeated measurements with applications to clinical trials techniques applicable for the analysis of longitudinal data when the response variable is non normal are not nearly as comprehensive as for normally distributed outcomes however there have been several recent developments semi parametric and non parametric methodology for the analysis of repeated measurements is reviewed the commonly encountered design in which for each subject one assesses a univariate response variable at multiple fixed time points is considered the types of outcomes considered include binary ordered categorical and continuous but extremely non normal response variables all of the methods considered allow for incomplete data due to the occurrence of missing observations in addition discrete and or continuous covariates which may be time dependent are accommodated by some of the approaches the methods are demonstrated using data from three clinical trials

linear regression analysis for highly stratified failure time data abstract in this article we consider cases where data consist of many small and independent groups of correlated failure time observations for each failure time which may be censored some important covariates are also recorded our goal is to examine the covariate effects on the individual failure time observations we assume that the logarithm of each failure time is linearly related to its covariates we then take a population averaged model approach to obtain inference procedures for the regression parameters without specifying the joint distribution of the observations within the group the new proposals do not need complicated and unstable nonparametric estimates for the hazard function of the error term their properties are extensively examined for practical sample sizes comparisons among various procedures are also performed all the methods studied in this article are illustrated with examples

regression analysis of multivariate incomplete failure time data by modeling marginal distributions abstract many survival studies record the times to two or more distinct failures on each subject the failures may be events of different natures or may be repetitions of the same kind of event in this article we consider the regression analysis of such multivariate failure time observations each marginal distribution of the failure times is formulated by a cox proportional hazards model no specific structure of dependence among the distinct failure times on each subject is imposed the regression parameters in the cox models are estimated by maximizing the failure specific partial likelihoods the resulting estimators are shown to be asymptotically jointly normal with a covariance matrix that can be consistently estimated simultaneous inferential procedures are then proposed extensive monte carlo studies indicate that the normal approximation is adequate for practical use the new methods allow time dependent covariates missing observations and arbitrary patterns of censorship they are illustrat

transient spheroidal elements for unbounded wave problems a wave envelope element numerical scheme is applied to the solution of unbounded wave problems the scheme is based on a fourier transformation of a discrete model formulated in the frequency domain this yields a discrete system of ordinary differential equations in time which are local in space oblate and prolate spheroidal element geometries are used the accuracy of the scheme is demonstrated by a comparison of computed and analytic solutions for axisymmetric test cases time harmonic and transient solution are presented an indirect solution procedure is also presented which permits the sparsity of the transient equations to be utilised more effectively

a coupled fe and boundary integral equation method based on exterior domain decomposition for fluid structure interface problems abstract a coupled finite element and exterior domain decomposition based boundary integral formulations for the solutions of two or three dimensional time harmonic fluid structure interaction problems is described in this paper it is known that the memory limitation of computers has been one of the major obstacles for solving large scale high frequency fluid structure interface systems using various existing nonlocal finite element and boundary integral equation coupling techniques due to the fully populated resultant matrix generated from the boundary integral equation representation the essence of this study is to decompose through domain decomposition of the exterior region the original exterior problem into arbitrary subproblems with data sharing only at the interfaces by decomposing the exterior infinite domain into an appropriate number of infinite subdomains this method not only ensures the validity of the formulation for all frequencies but also leads to a diagonalized blockwise banded system of discretized equations the size of an individual submatrix i e a block that is associated with an exterior subdomain may be decided by the user and may be selected such that the restriction due to the memory limitation of a given computer may be accommodated in addition the method is suited for parallel processing since the data associated with each subdomain impedance matrices load vectors etc may be generated in parallel and the communication needed will be only for the interface values most significantly unlike the existing coupled finite element and boundary integral equation techniques that are valid for all frequencies our method avoids the use of both the hypersingular operator and the double integrals therefore reducing the computational complexity numerical experiments have been performed for elastic cylindrical shells subjected to a plane incident wave the results have demonstrated the accuracy of the method for wavenumbers ranging from 0 to 30 both directly on the shell and in the far field and have confirmed that the procedure is valid for all frequencies

dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment summary a methodology is developed for switching from a continuum to a discrete discontinuity where the governing partial dierential equation loses hyperbolicity the approach is limited to rate independent materials so that the transition occurs on a set of measure zero the discrete discontinuity is treated by the extendednite element method xfem whereby arbitrary discontinuities can be incorporated in the model without remeshing loss of hyperbolicity is tracked by a hyperbolicity indicator that enables both the crack speed and crack direction to be determined for a given material model a new method was developed for the case when the discontinuity ends within an element it facilitates the modelling of crack tips that occur within an element in a dynamic setting the method is applied to several dynamic crack growth problems including the branching of cracks copyright 2003 john wiley sons ltd

an infinite boundary element formulation for three dimensional potential problems an infinite boundary element ibe is presented for the analysis of three dimensional potential problems in an unbounded medium the ibe formulations are done to allow their coupling with the finite element fe matrices for finite domains and to obtain the overall matrices without destroying the banded structure of the fe matrices the infinite body is divided into a number of zones whose contributions are expressed in terms of the nodal quantities at fe nodes by employing suitable decay functions and performing mainly analytical integrations of the boundary element kernels the continuity and compatibility conditions for the potential and the flux at the fe ibe interface are developed the relationships for the contributions of the ibe flux vectors to the fe load vectors are given the final equations for the ibe are obtained in the usual fe stiffness load vector form and are easily assembled with the fe matrices for the finite object a series of numerical examples in heat transfer and electromagnetics were solved and compared with alternative solutions to demonstrate the validity of the present formulations

on generation of lumped mass matrices in partition of unity based methods summary the partition of unity based methods such as the extended finite element method and the numerical manifold method are able to construct global functions that accurately reflect local behaviors through introducing locally defined basis functions beyond polynomials in the dynamic analysis of cracked bodies using an explicit time integration algorithm as a result huge difficulties arise in deriving lumped mass matrices because of the presence of those physically meaningless degrees of freedom associated with those locally defined functions observing no spatial derivatives of trial or test functions exist in the virtual work of inertia force we approximate the virtual work of inertia force in a coarser manner than the virtual work of stresses where we inversely utilize the from local to global skill the proposed lumped mass matrix is strictly diagonal and can yield the results in agreement with the consistent mass matrix but has more excellent dynamic property than the latter meanwhile the critical time step of the numerical manifold method equipped with an explicit time integration scheme and the proposed mass lumping scheme does not decrease even if the crack in study approaches the mesh nodes a very excellent dynamic property copyright 2017 john wiley sons ltd

stochastic tamed 3d navier stokes equations existence uniqueness and ergodicity in this paper we prove the existence of a unique strong solution to a stochastic tamed 3d navier stokes equation in the whole space as well as in the periodic boundary case then we also study the feller property of solutions and prove the existence of invariant measures for the corresponding feller semigroup in the case of periodic conditions moreover in the case of periodic boundary and degenerated additive noise using the notion of asymptotic strong feller property proposed by hairer and mattingly ann math 164 993 1032 2006 we prove the uniqueness of invariant measures for the corresponding transition semigroup

modelling transitional and joint marginal distributions in repeated categorical data when a repeated measures endpoint classifies people into several categories marginal and transitional models provide two distinct approaches for data analysis marginal models estimate the probabilities of being in different categories over time transitional models estimate the probability of changing between any two given states during follow up visits this paper develops transitional and marginal models and applies them to a clinical trial of treatments of opiate addiction the primary outcome was the presence or absence of opiates in a thrice weekly urine test administered for 17 weeks subjects frequently miss visits however and in effect respond in one of three ways to a visit missing opiates present or opiates absent thus we have three possible states our transitional model conditions on the current state and models the transition from state k to one of the other 0 k 1 states using a mutinomial logit model this model generalizes previous work of muenz and rubinstein significant covariates in this model are predictive of state changes our marginal model views the state at each time point rather than the transitions as the primary response here we model the probability of being in state k with a multinomial logit model correlation within individuals over visits can be handled by applying the approach of zeger and liang or the bootstrap significant covariates in this model can include more global summaries of a person such as extent of previous opiate use both marginal and transitional models are needed to provide a complete description of an individual s behaviour over time since global summaries might not affect transitions of particular substantive interest is how the opiate treatments affect both the marginal and transition probabilities

mapped infinite elements for exterior wave problems recently a new type of infinite elements which uses r 1 decay was proposed they were applied to exterior wave problems and good results were obtained in two dimensional problems however it was necessary to move the origin of the r 1 decay in order to model the outgoing wave more accurately because it decays roughly as r 1 2 in this paper the mapped infinite elements with r 1 2 decay and the necessary numerical integration procedure are presented these elements do not require any artificial movement of the origin several example problems are solved the results show that the infinite elements with r 1 2 decay here give much more accurate values than the infinite elements with exponential decay and any damper elements

parametric variance function estimation for nonnormal repeated measurement data zeger and liang 1986 biometrics 42 121 130 proposed a procedure for analyzing nonnormal longitudinal data in the context of the generalized linear model this procedure is extended to model variance heterogeneity allowing the observations to come from distributions with different scale parameters loss of efficiency is evaluated when heterogeneity of scale factor is ignored

infinite domain elements a parametric element is formulated which enables the economic modelling of infinite domain type problmes a typical problem is an opening in a stress field in an infinite medium either in two or three dimensions the strategy is to model around the opening with two or three layers of conventional isoparametric finite elements and surround these with a single layer of infinite domain elements several sample problems has been analysed for circular square and spherical openings in infinite media and the results compared with either theoretical or boundary element solutions which include the infinite boundary in their solution technique copyright

the mixed complementarity problem arising from non associative plasticity with non smooth yield surfaces abstract an elastic domain with multiple yield surfaces brings about huge troubles to numerical computations due to singularities while non associative plasticity leads further to the open issue of whether constitutive integration is well posed this study reduces the constitutive integration of non associative plasticity with multiple yield surfaces to a mixed complementarity problem represented by micp a special case of finite dimensional variational inequalities by means of the projection contraction algorithm for finite dimensional variational inequalities and the idea of the gauss seidel method a new projection contraction algorithm for micp is designed and denoted by gspc applying the monotonicity of the mapping of the micp gspc is proved convergent theoretically for associative plasticity for non associative plasticity the sufficient condition for gspc to be convergent is also established if the tension part of the mohr coulomb elastic domain is cut off typical examples are designed to illustrate gspc is highly efficient accurate and stable some of which cannot be solved by the conventional return mapping method in all the cases the computational efficiency of gspc is apparently above the mapping return method

a novel boundary infinite element a new improved infinite element based on mapping is proposed for modelling unbounded domain problems mapping has previously been used in such problems not only for the entire domain but also for the infinite element itself the novelty of the present approach is the simplicity of the mapping and the retention of standard integration abscissae and weights the implementation of these elements is very straightforward and they are ideally suited for the analysis of infinite domain static problems in two and three dimensions

analysis of repeated ordered categorical outcomes with possibly missing observations and time dependent covariates abstract this article describes a method for comparing responses in two groups of subjects observed repeatedly at a common set of observation times when the response is an ordered categorical outcome the method which allows both time dependent covariates and missing observations consists of two analytic steps in the first step the data are analyzed separately at each occasion using a regression model chosen from the class of models for ordinal data proposed by mccullagh 1980 the joint asymptotic distribution of the estimates of these occasion specific regression coefficients and a consistent estimator of their asymptotic covariance matrix are obtained without imposing any parametric model of dependence on the repeated observations in the second step this asymptotic distribution together with appropriate simultaneous inference procedures is used to characterize the overall difference between groups and the variation in group differences over time the missing data process may differ between gro

new strategies for some issues of numerical manifold method in simulation of crack propagation summary aiming to solve in a unified way continuous and discontinuous problems in geotechnical engineering the numerical manifold method introduces two covers namely the mathematical cover and the physical cover in order to reach the goal some issues in the simulation of crack propagation have to be solved among which are the four issues to be treated in this study 1 to reduce the rank deficiency induced by high degree polynomials as local approximation a new variational principle is formulated which suppresses the gradient dependent dofs 2 to evaluate the integrals with singularity of 1 r a new numerical quadrature scheme is developed which is simpler but more efficient than the existing duffy transformation 3 to analyze kinked cracks a sign convention for argument in the polar system at the crack tip is specified which leads to more accurate results in a simpler way than the existing mapping technique and 4 to demonstrate the mesh independency of numerical manifold method in handling strong singularity a mesh deployment scheme is advised which can reproduce all singular locations of the crack with regard to the mesh corresponding to the four issues typical examples are given to demonstrate the effectiveness of the proposed schemes copyright 2013 john wiley sons ltd

some general methods for the analysis of categorical data in longitudinal studies this paper is concerned with the analysis of multivariate categorical data from epidemiologic and clinical studies with longitudinal designs an expository discussion of pertinent hypotheses for such situations is provided within the context of two relevant data sets appropriate large sample tests of these hypotheses are developed through the application of weighted least squares to generate wald statistics these procedures are illustrated with extensive analyses of one of these data sets in some situations the resulting cross classification of the response variables leads to extremely sparse frequency data especially when the number of subjects is not large for such repeated measurement designs in which a single variable is measured repeatedly over time this paper considers the use of a generalized mantel haenszel strategy for tests of marginal homogeneity symmetry these randomization model methods are illustrated for data in which the repeated measurement variable is reported on an ordinal scale this paper also focuses on the available computing software to implement these methods within the version 5 release of the sas system the randomization model approach can be implemented within the freq procedure and a broad range of models and hypotheses can be investigated within the catmod procedure

some large sample distribution free estimators and tests for multivariate partially incomplete data from two populations the most common instance of multivariate observations is the case of repeated measures over time the two most widely used methods for the analysis of k repeated measures for two groups are the k degrees of freedom d f t2 manova f test and the within subjects 1 degree of freedom anova f test both require complete samples from normally distributed populations in this paper i describe alternative k and 1 d f distribution free procedures which allow for randomly missing observations these include a large sample analysis of means the wei and lachin multivariate wilcoxon test with estimates of the mann whitney parameter and a multivariate hodges lehmann location shift estimator based on the multivariate u statistic of wei and johnson each of these methods provides a distribution free k variate estimate of the magnitude of group differences which can be used as the basis for an overall test of group differences these tests include the k d f omnibus t2 like test 1 d f tests of restricted hypotheses such as the wei lachin multivariate one sided test of stochastic ordering and the test of general association based on a minimum variance generalized least squares gls estimate of the average group difference i then describe covariate stratified adjusted gls estimates and tests of group differences this approach also provides tests of homogeneity interaction for within subjects and between subjects effects i illustrate these analyses with an analysis of repeated cholesterol measurements in two groups of patients stratified by sex such analyses provide an overall distribution free summary estimate and test of the treatment effect obtained by combining the group differences over both time repeated measures and strata

the design and analysis of the generalized finite element method abstract in this paper we introduce the generalized finite element method gfem as a combination of the classical finite element method fem and the partition of unity method pum the standard finite element spaces are augmented by adding special functions which reflect the known information about the boundary value problem and the input data e g the singular functions obtained from the local asymptotic expansion of the exact solution in the neighborhood of a corner point etc the special functions are multiplied with the partition of unity corresponding to the standard linear vertex shape functions and pasted together with the existing finite element basis to construct an augmented conforming finite element space in this way the local approximability afforded by the special functions is included in the approximation while maintaining the existing infrastructure of finite element codes the major features of the gfem are 1 the essential boundary conditions can be imposed exactly as in the standard fem unlike other partition of unity based methods where this is a major issue 2 the accuracy of the numerical integration of the entries of the stiffness matrix and load vector is controlled adaptively so that the errors in integration of the special functions do not affect the accuracy of the constructed approximation this issue also has not been sufficiently addressed in other implementations of partition of unity or meshless methods and 3 linear dependencies in the system of equations are resolved by employing an easy modification of the direct linear solver the power of the gfem for solving problems in domains with complex geometry with less error and less computer resources than the standard fem is illustrated by numerical examples

gibbsian dynamics and ergodicity for the stochastically forced navier stokes equation we study stationary measures for the two dimensional navier stokes equation with periodic boundary condition and random forcing we prove uniqueness of the stationary measure under the condition that all determining modes are forced the main idea behind the proof is to study the gibbsian dynamics of the low modes obtained by representing the high modes as functionals of the time history of the low modes

some covariance models for longitudinal count data with overdispersion a family of covariance models for longitudinal counts with predictive covariates is presented these models account for overdispersion heteroscedasticity and dependence among repeated observations the approach is a quasi likelihood regression similar to the formulation given by liang and zeger 1986 biometrika 73 13 22 generalized estimating equations for both the covariate parameters and the variance covariance parameters are presented large sample properties of the parameter estimates are derived the proposed methods are illustrated by an analysis of epileptic seizure count data arising from a study of progabide as an adjuvant therapy for partial seizures

the performance of spheroidal infinite elements a number of spheroidal and ellipsoidal infinite elements have been proposed for the solution of unbounded wave problems in the frequency domain i e solutions of the helmholtz equation these elements are widely believed to be more effective than conventional spherical infinite elements in cases where the radiating or scattering object is slender or flat and can therefore be closely enclosed by a spheroidal or an ellipsoidal surface the validity of this statement is investigated in the current article the radial order which is required for an accurate solution is shown to depend strongly not only upon the type of element that is used but also on the aspect ratio of the bounding spheroid and the non dimensional wave number the nature of this dependence can partially be explained by comparing the non oscillatory component of simple source solutions to the terms available in the trial solution of spheroidal elements numerical studies are also presented to demonstrate the rates at which convergence can be achieved in practice by unconjugated burnett and conjugated astley leis type elements it will be shown that neither formulation is entirely satisfactory at high frequencies and high aspect ratios

a new mapped infinite wave element for general wave diffraction problems and its validation on the ellipse diffraction problem the theory for an improved infinite element for wave diffraction is presented the improvement is on the original wave element presented by bettess zienkiewicz and others the modification involves the introduction of one extra term in the original shape function derivatives and a change in the numerical integration sequence the modification enables the element to be used with elliptical and other non circular meshes similar mappings have already been used with wave envelope infinite elements by astley and others as a test of the element accurate results are demonstrated for a range of elliptical cylinder diffraction problems the element has not yet been tested for other non circular problems

infinite elements with 1 rn type decay this paper presents a method of developing a family of 1 rn type infinite elements for the analysis of problems definite in unbounded media the proposed method is a direct extension of the conventional finite element method the resulting improper integrals are integrated exactly over the infinite element domains two numerical examples in elastic half space static problems are investigated to illustrate the applicability and accuracy of the method the use of the proposed infinite elements yields excellent results and preserves all the advantages of the finite element method

the numerical methods for oscillating singularities in elliptic boundary value problems the singularities near the crack tips of homogeneous materials are monotone of type r and r log r depending on the boundary conditions along nonsmooth domains however the singularities around the interfacial cracks of the heterogeneous bimaterials are oscillatory of type r sin e log r the method of auxiliary mapping mam introduced by babuska and oh was proven to be successful in dealing with r type singularities however the effectiveness of mam is reduced in handling oscillating singularities this paper deals with oscillating singularities as well as the monotone singularities by extending mam through introducing the power auxiliary mapping and the exponential auxiliary mapping

the ill conditioning of infinite element stiffness matrices abstract in this paper a method for improving the conditioning of infinite element stiffness matrices is proposed and examined for one dimensional and two dimensional infinite elements this method is a preconditioning technique which is based on a gram schmidt like transformation induced by general sesquilinear forms although the preconditioning method can be applied to many types of infinite elements it will be applied to improve the conditioning of the popular multipole infinite element the paper is concluded with numerical examples demonstrating improved conditioning and convergence properties of the preconditioned multipole infinite elements

testing for omitted variables and non linearity in regression models for longitudinal data when fitting regression models to investigate the relationship between an outcome variable and independent variables of primary interest there is often concern whether omitted variables or assuming a different functional relationship could have changed the conclusion or interpretation of the results in longitudinal studies of aging the concern with omitted variables is well known in the context of cohort and period effects which refer to unmeasured variables systematically related to the individual s year of birth and secular trends in outcome respectively we present and compare three approaches to detecting omitted confounders and non linearity in the random effects model for longitudinal data laird and ware 1982 with random slope and intercept across individuals the first approach compares simple unweighted within and between regression coefficients the second is the hausman specification test for regression models and the third approach involves testing directly the significance of functions of individual specific covariate means means i in the random effects regression model this last approach is motivated by the models that arise when cohort or period effects are ignored we compare the three approaches and illustrate their application

complementarity problem arising from static growth of multiple cracks and mls based numerical manifold method abstract the full response of a brittle structure containing multiple cracks to loading under the servo control is of vital importance in the evaluation of properties of the structure during crack growth the fracture toughness condition at all the crack tips as well as the equilibrium condition should be obeyed leading to a nonlinear complementarity problem ncp the vector valued function in the ncp depends implicitly on the cracking increments which in turn determine the stress field the stress field can be obtained through solving a mixed variational problem since the degrees of freedom in the discrete variational problem vary with cracking not only in magnitude but also in number the jacobian matrix of the ncp is hard to compute and it cannot be expected to be solved by the newton methods that involve the calculation of jacobian matrices therefore a well scaled projection contraction algorithm is designed the proposed procedure is able to simulate growth of multiple cracks in a natural way allowing the crack tips to stop anywhere with no sensitivity to node configuration or cracking increments through the analysis of some examples that have been widely tested many interesting and profound phenomena are found which have never been revealed

a coupling approach to randomly forced nonlinear pde s ii we consider a class of discrete time random dynamical systems and establish the exponential convergence of its trajectories to a unique stationary measure the result obtained applies in particular to the 2d navier stokes system and multidimensional complex ginzburg landau equation with random kick force

prediction of rank deficiency in partition of unity based methods with plane triangular or quadrilateral meshes in the partition of unity pu based methods the global approximation is built by multiplying a partition of unity by local approximations within this framework high order approximations are achieved by directly adopting high order polynomials as local approximations and therefore nodes along sides or inside elements which are usually adopted in the conventional finite element methods are no more required however the pu based approximation constructed in this way may suffer from rank deficiency due to the linear dependence of the global degrees of freedom in this paper the origin of the rank deficiency in the pu based approximation space is first dissected at an element level and then an approach to predict the rank deficiency for a mesh is proposed together with the principle of the increase of rank deficiency finally examples are investigated to validate the present approach the current work indicates such a fact that the rank deficiency is an unrelated issue to the nullity of the global matrix it can be resolved in its own manner

an infinite element and a formula for numerical quadrature over an infinite interval in this publication we present a new infinite element and discuss a formula for numerical quadrature over infinite regions both the element and the formula are based on the properties of a set of orthonormal functions obtained by mapping the legendre polynomials on the infinite interval the element can represent any physical function over the entire infinite region and the formula can integrate most integrands over the infinite interval they are thus very convenient for implementation in a general computer program which could then be used to solve different problems with no restrictions concerning the asymptotic behaviour of the solutions or the form of integrands to be integrated over the infinite interval however the element and the formula will perform at their best when used in conjunction and for problems of electrostatic magnetostatic etc potential the formula was compared with other existing formulae and found to be either superior or satisfactory in practically all cases as shown by the results of many numerical experiments expressions of shape functions are given for the element a test problem was solved using the element and the formula and the results are shown to be more accurate than those obtained when solving the same problem using infinite elements with exponential decay and gauss laguerre numerical quadrature

the numerical manifold method for exterior problems abstract the numerical manifold method nmm a galerkin type numerical method has been successful in the solution of problems with finite definition domains yet it has never been applied to problems with unbounded domains or exterior problems this study aims to fill the big gap by constructing infinite patches together with the finite patches to cover the unbounded domain the local approximations of infinite patches can take the asymptotic estimations of the solutions at infinity which are available for all those well established boundary value problems compared with the infinite element methods in the finite element method fem the construction of the trial functions by nmm is more elegant in theory and more systematical in methodology resulting in more accurate solutions some typical examples in potential and half space elasticity problems are investigated to illustrate the applicability and accuracy of the proposed method

improved xfem an extra dof free well conditioning and interpolating xfem abstract although its unprecedentedly success in approximating the singular field around a crack tip independent of mesh discretization xfem still has been long hindered in engineering applications by its ill conditioning and the difficulty in mass lumping corresponding to extra dofs an improved xfem i xfem is developed to overcome those difficulties from three aspects 1 to eliminate the linear dependence and the ill conditioning issues of the standard and the corrected xfems 2 to get rid of extra dofs in crack tip enrichment to facilitate optimal mass lumping in dynamic analyses 3 to be interpolating at enriched nodes to enable direct essential contact boundary treatments the core of i xfem is a globally interpolating approximation based on local least squares fitting the new method is numerically examined with comprehensive comparisons with the standard xfem and the corrected xfem fries 2008 the new method s excellent performance in terms of accuracy convergence and conditioning stability are demonstrated

estimating incidence and diagnostic error rates for bivariate progressive processes estimating the times until incidences of bivariate progressive processes that are categorical is a common problem in ophthalmology audiology pulmonary medicine and other fields of medical research we consider study designs in which diagnoses of subject s bivariate status are performed repeatedly across time and when diagnosis is subject to error in such situations error confounds the interpretation of the time until an event a composite model is proposed for parameterizing both the incidence and error distributions which allows for correlation between sites with respect to both incidence and diagnostic error an em algorithm is described for this model which allows categorical covariates for both incidence and error the methodology is applied to two examples the first represents a situation in which bivariate incidence and error can reasonably be assumed symmetric prospective data concerning the development of ocular lens opacities in a large pharmaceutical clinical trial the second example represents a situation in which bivariate incidence and error may not be symmetric clinical evaluations of sexual maturation status with respect to two different anatomical indices in the cooperative study of sickle cell disease the methodology described in this paper is used in each case to estimate incidence characterize error rates and assess bivariate correlations

a finite element alternative to infinite elements abstract in this paper a simple idea based on midpoint integration rule is utilized to solve a particular class of mechanics problems namely static problems defined on unbounded domains where the solution is required to be accurate only in an interior and not in the far field by developing a finite element mesh that approximates the stiffness of an unbounded domain directly without approximating the far field displacement profile first the current formulation provides a superior alternative to infinite elements ies that have long been used to incorporate unbounded domains into the finite element method fem in contrast to most ies the present formulation a requires no new shape functions or special integration rules b is proved to be both accurate and efficient and c is versatile enough to handle a large variety of domains including those with anisotropic stratified media and convex polygonal corners in addition to this the proposed model leads to the derivation of a simple error expression that provides an explicit correlation between the mesh parameters and the accuracy achieved this error expression can be used to calculate the accuracy of a given mesh a priori this in turn allows one to generate the most efficient mesh capable of achieving a desired accuracy by solving a mesh optimization problem we formulate such an optimization problem solve it and use the results to develop a practical mesh generation methodology this methodology does not require any additional computation on the part of the user and can hence be used in practical situations to quickly generate an efficient and near optimal finite element mesh that models an unbounded domain to the required accuracy numerical examples involving practical problems are presented at the end to illustrate the effectiveness of this method

consistency and asymptotic normality of the maximum likelihood estimator in generalized linear models generalized linear models are used for regression analysis in a number of cases including categorical responses where the classical assumptions are violated the statistical analysis of such models is based on the asymptotic properties of the maximum likelihood estimator we present mild general conditions which respectively assure weak or strong consistency or asymptotic normality most of the previous work has been concerned with natural link functions in this case our normality condition though obtained by a different approach is closely related to a condition of haberman 1977a examples show how the general conditions reduce to weak requirements for special exponential families further for regressors with a compact range sufficient conditions are given which do not involve the unknown parameter and are therefore easy to check in practice responses with a bounded range e g categorical responses and stochastic regressors also are treated

on two dimensional infinite elements utilizing basis functions with compact support in this paper improvements are made in the numerical conditioning of infinite element stiffness matrices by replacing the characteristic eigenfunction basis functions which have global support with basis functions which have local support and appropriate preconditioning the conditioning and convergence properties of these new infinite elements are presented in solving two dimensional exterior problems for the helmholtz equation

comparison of methods for the analysis of longitudinal interval count data longitudinal studies are often concerned with estimating the recurrence rate of a non fatal event in many cases only the total number of events occurring during successive time intervals is known we compared a mixed poisson gamma regression method proposed by thall and a quasi likelihood method proposed by zeger and liang for the analysis of such data in the case where the mean was correctly specified using simulation techniques with large samples both methods produced similar standard errors in most situations except in the case of time dependent covariates with non poisson gamma data where they were seriously underestimated by the thall method a simple method for discriminating between the variance forms of the two methods is described the findings are applied to the analyses of clinical trials of non melanoma skin cancer and familial polyposis this study extends the findings of breslow concerning variance misspecification in overdispersed poisson and quasi likelihood models to the longitudinal setting

a test of the missing data mechanism for repeated categorical data due to the occurrence of missing observations longitudinal data are rarely balanced and complete weighted least squares analyses described by grizzle starmer and koch 1969 biometrics 25 489 504 have been developed for the analysis of incomplete longitudinal categorical data stanish gillings and koch 1978 biometrics 34 305 317 woolson and clarke 1984 journal of the royal statistical society series a 147 87 99 however all these analyses have assumed that missing observations are missing completely at random in the sense of rubin 1976 biometrika 63 581 592 when the occurrence of missing observations is related to the unobserved response values these analyses may result in biased results in this paper we develop a simple and practical test of the missing mechanism in incomplete repeated categorical data the proposed test is an extension of the test of little 1988 journal of the american statistical association 83 1198 1202 and uses a test criterion given in general form by wald the test is illustrated using data from a longitudinal investigation of obesity in school age children

dual form of discontinuous deformation analysis abstract discontinuous deformation analysis dda is a numerical method for analyzing dynamic behaviors of an assemblage of distinct blocks with the block displacements as the basic variables the contact conditions are approximately satisfied by the open close iteration which needs to fix or remove repeatedly the virtual springs between blocks in contact the results from dda are strongly dependent upon stiffness of these virtual springs excessively hard or soft springs all incur numerical problems this is believed to be the biggest obstacle to more extensive application of dda to avoid the introduction of virtual springs huge efforts have been made with little progress related to low efficiency in solution in this study the contact forces instead of the block displacements are taken as the basic variables stemming from the equations of momentum conservation of each block the block displacements can be expressed in terms of the contact forces acting on the block from the contact conditions a finite dimensional quasi variational inequality is derived with the contact forces as the independent variables on the basis of the projection contraction algorithm for the standard finite dimensional variational inequalities an iteration algorithm called the compatibility iteration is designed for the quasi variational inequality the main processes can be highly parallelized with no need to assemble the global stiffness matrix a number of numerical tests including those very challenging suggest that the proposed procedure has reached practical level in accuracy robustness and efficiency and the goal to abandon completely virtual springs has been reached

diffraction of short waves modelled using new mapped wave envelope finite and infinite elements we consider a two dimensional wave diffraction problem from a closed body such that the complex progressive wave potential satisfies the sommerfield condition and the helmholtz equation we are interested in the case where the wavelength is much smaller than any other length dimensions of the problem we introduce new mapped wave envelope infinite elements to model the potential in the far field and test them for some simple dirichlet boundary condition problems they are used in conjuction with wave envelope finite elements developed earlier 1 to model the potential in the near field an iterative procedure is used in which an initial estimate of the phase is iteratively improved the iteration scheme by which the wave envelope and phase are recovered is described in detail copyright 1999 john wiley sons ltd

majorizing kernels and stochastic cascades with applications to incompressible navier stokes equations a general method is developed to obtain conditions on initial data and forcing terms for the global existence of unique regular solutions to incompressible 3d navier stokes equations the basic idea generalizes a probabilistic approach introduced by lejan and sznitman 1997 to obtain weak solutions whose fourier transform may be represented by an expected value of a stochastic cascade a functional analytic framework is also developed which partially connects stochastic iterations and certain picard iterates some local existence and uniqueness results are also obtained by contractive mapping conditions on the picard iteration

detection of outlying data in bioavailability bioequivalence studies this paper considers the problem of detecting outlying data in bioavailability bioequivalence studies we define outlying subjects as those whose responses in bioavailability to all formulations differ from the rest of the subjects we also define an outlying observation as the response in bioavailability of a subject to a particular formulation which is grossly different from the average bioavailability of that formulation calculated from all subjects we propose two test procedures the first based on two sample hotelling t2 is to detect possible outlying subjects the second based on residuals from formulation means is to identify possible outlying observations within subjects both procedures take into account the covariance structure of the responses to formulations dependence of test statistics and multiplicity of test procedures we apply the monte carlo or bootstrap simulation to evaluate the sampling distributions of test statistics an example from a 3 way crossover bioequivalence study illustrates the two procedures

the analysis of correlated panel data using a continuous time markov model we consider the analysis of correlated panel data in which two or more correlated multistate processes are periodically observed on each individual and the exact transition times between states are unknown we describe a procedure that models each process marginally under a time homogeneous markov model allowing for covariates the resulting estimators are shown to be asymptotically jointly normal with a covariance matrix that can be consistently estimated simultaneous inference procedures are also proposed methods are illustrated using data from an aids clinical trial to compare the toxic effects of two treatments on two hematologic variables hemoglobin and absolute neutrophil count

numerical manifold space of hermitian form and application to kirchhoff s thin plate problems summary for second order problems where the behavior is described by second order partial differential equations the numerical manifold method nmm has gained great success because of difficulties in the construction of the h 2 regular lagrangian partition of unity subordinate to the finite element cover however few applications of the nmm have been found to fourth order problems such as kirchhoff s thin plate problems parallel to the finite element methods this study constructs the numerical manifold space of the hermitian form to solve fourth order problems from the minimum potential principle meanwhile the mixed primal formulation and the penalized formulation fitted to the nmm for kirchhoff s thin plate problems are derived the typical examples indicate that by the proposed procedures even those earliest developed elements in the finite element history such as zienkiewicz s plate element regain their vigor copyright 2013 john wiley sons ltd

ergodicity of the 2 d navier stokes equation under random perturbations a 2 dimensional navier stokes equation perturbed by a sufficiently distributed white noise is considered existence of invariant measures is known from previous works the aim is to prove uniqueness of the invariant measures strong law of large numbers and convergence to equilibrium

group sequential distribution free methods for the analysis of multivariate observations many studies involve the collection of multivariate observations such as repeated measures on two groups of subjects who are recruited over time i e with staggered entry of subjects various marginal distribution free multivariate methods have been proposed for the analyses of such multivariate observations where some measures may be missing at random using the multivariate u statistic of wei and johnson 1985 biometrika 72 359 364 we describe the group sequential analysis of such a study where the multivariate observations are observed sequentially both within and among subjects we describe a multivariate generalization of the hodges and lehmann 1963 annals of mathematical statistics 34 598 611 estimator of a location shift that can be obtained via the multivariate u statistic with the mann whitney wilcoxon kernel we then describe large sample group sequential interval estimators and tests based on an aggregate estimate of the location shift combined over all of the repeated measures we also describe how the same steps could be employed to perform a group sequential analysis based on any one of the variety of marginal multivariate methods that have been proposed these methods are applied to a real life example

the weighted finite element method for elasticity equations on unbounded domains abstract by introducing the weighted riesz galerkin method with a special weight function oh jou 23 made it possible to apply mam the method of auxiliary mapping introduced by babuska oh to general elliptic boundary value problems on unbounded domains in this paper this method is further generalized to yield highly accurate approximate solutions for linear elasticity problems on unbounded domains with bounded or unbounded boundaries it is shown that in the framework of the p version of the fem this method does efficiently handle elasticity problems on unbounded domains and yields accurate solutions at low cost

an ellipsoidal acoustic infinite element abstract in previous papers the authors presented new 3 d time harmonic prolate and oblate spheroidal acoustic infinite elements based on new prolate and oblate spheroidal multipole expansions for modeling acoustic fields in unbounded domains here we present the development of an ellipsoidal infinite element which is the logical generalization of those elements this development is also based on a new multipole expansion as well as a new system of ellipsoidal coordinates the element stiffness radiation damping and mass matrices are developed and presented in sufficient detail to enable their software implementation both the new coordinate system and the new element include the previous spheroidal coordinate systems and spheroidal elements as limiting cases therefore all the previously reported performance data for the spheroidal elements apply to this ellipsoidal element when used in spheroidal form since the three axes of an ellipsoid can be chosen independently an ellipsoid can circumscribe any structural shape at least as closely and generally more closely than a prolate or oblate spheroid the resulting reduction in size of the finite computational domain will result in even greater computational speeds than those already reported for the spheroidal elements the element may be used to model problems in free space 4 steradians half space 2 quarter space or eighth space 2 since this infinite element provides maximum computational efficiency for structures of all shapes software element libraries would need only this one element for all problems in unbounded domains

an axisymmetric infinite element a parametric infinite element is presented for solving axisymmetric problems under non axisymmetric forcing functions where the considered domain is assumed infinite the element accuracy is compared against the exact solution for two classical problems boussinesq s and cerruti s boussinesq s problem for a rigid circular plate is also presented for these problems using relatively simple displacement functions the element provides a reasonable infinite domain representation

a static infinite element reference lmaf article 1983 001view record in web of science record created on 2005 09 14 modified on 2017 05 10

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

analyzing repeated measures on generalized linear models via the bootstrap the analysis of longitudinal data for which the response variables have nonnormal error distributions previously has been complex and or dependent on restrictive assumptions in this paper simple methods are introduced for the class of generalized linear models glms regressions are fit to the data at each observation time functions of the resulting coefficients may be bootstrapped or the coefficients combined through closed form estimation of their covariances application is made to a data set on xerophthalmia in indonesian children

existence and uniqueness of stationary solutions for 3d navier stokes system with small random forcing via stochastic cascades we consider the 3d navier stokes system in the fourier space with regular forcing given by a stationary in time stochastic process satisfying a smallness condition we explicitly construct a stationary solution of the system and prove a uniqueness theorem for this solution in the class of functions with fourier transform majorized by a certain function h moreover we prove the following one force one solution principle the unique stationary solution at time t is presented as a functional of the realization of the forcing in the past up to t our explicit construction of the solution is based upon the stochastic cascade representation