models for longitudinal data with random effects and ar 1 errors abstract for longitudinal data on several individuals linear models that contain both random effects across individuals and autocorrelation in the within individual errors are studied a score test for autocorrelation in the within individual errors for the conditional independence random effects model is first developed an explicit maximum likelihood estimation procedure using the scoring method for the model with random effects and autoregressive ar 1 errors is then derived empirical bayes estimation of the random effects and prediction of future responses of an individual based on this random effects with ar 1 errors model are also considered a numerical example is presented to illustrate these methods

the construction of preconditioners for elliptic problems by substructuring i in earlier parts of this series of papers we constructed preconditioners for the discrete systems of equations arising from the numerical approximation of elliptic boundary value problems the resulting algorithms are well suited for implementation on computers with parallel architecture in this paper we will develop a technique which utilizes these earlier methods to derive even more efficient preconditioners the iterative algorithms using these new preconditioners converge to the solution of the discrete equations with a rate that is independent of the number of unknowns these preconditioners involve an incomplete chebyshev iteration for boundary interface conditions which results in a negligible increase in the amount of computational work theoretical estimates and the results of numerical experiments are given which demonstrate the effectiveness of the methods

the heteroscedastic graded response model with a skewed latent trait testing statistical and substantive hypotheses related to skewed item category functions the graded response model grm samejima estimation of ability using a response pattern of graded scores psychometric monograph no 17 richmond va the psychometric society 1969 can be derived by assuming a linear regression of a continuous variable z on the trait to underlie the ordinal item scores takane de leeuw in psychometrika 52 393 408 1987 traditionally a normal distribution is specified for z implying homoscedastic error variances and a normally distributed in this paper we present the heteroscedastic grm with skewed latent trait which extends the traditional grm by incorporation of heteroscedastic error variances and a skew normal latent trait an appealing property of the extended grm is that it includes the traditional grm as a special case this enables specific tests on the normality assumption of z we show how violations of normality in z can lead to asymmetrical category response functions the ability to test this normality assumption is beneficial from both a statistical and substantive perspective in a simulation study we show the viability of the model and investigate the specificity of the effects we apply the model to a dataset on affect and a dataset on alexithymia

domain decomposition for least squares finite element methods for the stokes equations in this paper we consider the solutions of the discrete linear system resulting from least squares finite element discretization applied to the stokes equations additive and multiplicative domain decomposition methods are used to solve the linear system and the uniform convergence results are established for both methods

error estimation and anisotropic mesh refinement for 3d laminar aerodynamic flow simulations this article considers a posteriori error estimation and anisotropic mesh refinement for three dimensional laminar aerodynamic flow simulations the optimal order symmetric interior penalty discontinuous galerkin discretization which has previously been developed for the compressible navier stokes equations in two dimensions is extended to three dimensions symmetry boundary conditions are given which allow to discretize and compute symmetric flows on the half model resulting in exactly the same flow solutions as if computed on the full model using duality arguments an error estimation is derived for estimating the discretization error with respect to the aerodynamic force coefficients furthermore residual based indicators as well as adjoint based indicators for goal oriented refinement are derived these refinement indicators are combined with anisotropy indicators which are particularly suited to the discontinuous galerkin dg discretization two different approaches based on either a heuristic criterion or an anisotropic extension of the adjoint based error estimation are presented the performance of the proposed discretization error estimation and adaptive mesh refinement algorithms is demonstrated for 3d aerodynamic flows

testing for ordered group effects with repeated measurements summary in the repeated measures experiment testing procedures for ordered group effects are proposed using the likelihood ratio principle the constrained maximum likelihood estimators of ordered group effects are approximated by the isotonic regression of the unconstrained maximum likelihood estimators based on these constrained maximum likelihood estimators test statistics are constructed and are used for detecting ordered group effects the limiting distributions of the proposed test statistics are shown to be mixtures of chi squared distributions a simulation study shows that the proposed tests have improved powers over the usual chi squared statistic for testing equality of group effects a real data set is analysed to illustrate the proposed statistics

schwarz methods for inequalities with contraction operators we prove the convergence of some multiplicative and additive schwarz methods for inequalities which contain contraction operators the problem is stated in a reflexive banach space and it generalizes the well known fixed point problem in the hilbert spaces error estimation theorems are given for three multiplicative algorithms and two additive algorithms we show that these algorithms are in fact schwarz methods if the subspaces are associated with a decomposition of the domain also for the one and two level methods in the finite element spaces we write the convergence rates as functions of the overlapping and mesh parameters they are similar with the convergence rates of these methods for linear problems besides the direct use of the five algorithms for the inequalities with contraction operators we can use the above results to obtain the convergence rate of the schwarz method for other types of inequalities or nonlinear equations in this way we prove the convergence and estimate the error of the one and two level schwarz methods for some inequalities in hilbert spaces which are not of the variational type and also for the navier stokes problem finally we give conditions of existence and uniqueness of the solution for all problems we consider we point out that these conditions and the convergence conditions of the proposed algorithms are of the same type

a parallel domain decomposition algorithm of mixed element equation for second order elliptic dirichlet boundary value problem a parallel domain decomposition algorithm of schwarz type is introduced to solve the mixed finite element equation for the dirichlet boundary value problem of a second order partial differential equation of elliptic type and convergence of this algorithm is analyzed

a two level schwarz method for a finite element approximation of a nonlinear biharmonic equation in this paper we consider a finite element approximation of a nonlinear biharmonic equation which is related to the well known two dimensional navier stokes equations first optimal energy and h 1 norm estimates are obtained second a two level additive schwarz method is presented for the discrete nonlinear algebraic system it is shown that if the reynolds number is sufficiently small the two level schwarz method is optimal i e the convergence rate of the schwarz method is independent of the mesh size and the number of subdomains

an approach to the analysis of repeated measurements summary a linear model for repeated measurements is proposed in which the correlation structure within each time sequence of measurements includes parameters for measurement error variation between experimental units and serial correlation within units an approach to data analysis is presented which involves preliminary analysis by ordinary least squares use of the empirical semi variogram of residuals to suggest a suitable correlation structure and formal inference using likelihood based methods applications to two biological data sets are described

a goal oriented hp adaptive finite element method with electromagnetic applications part i electrostatics we describe the development and application of a finite element fe self adaptive hp goal oriented algorithm for elliptic problems the algorithm delivers without any user interaction a sequence of optimal hp grids this sequence of grids minimizes the error of a prescribed quantity of interest with respect to the problem size the refinement strategy is an extension of a fully automatic energy norm based hp adaptive algorithm we illustrate the efficiency of the method with 2d numerical results among other problems we apply the goal oriented hp adaptive strategy to simulate direct current dc resistivity logging instruments including through casing resistivity tools in a borehole environment and for the assessment of rock formation properties copyright 2005 john wiley sons ltd

arma covariance structures with time heteroscedasticity for repeated measures experiments abstract rochon and helms 1989 presented a model for analyzing repeated measures experiments the general linear model was used to assess the influence of covariate information and arma time series models were put forward to characterize the covariance matrix among the repeated measures practical experience has suggested however that the arma assumption of constant variances and autocovariances over time is too restrictive for many applications for example observations may be relatively stable toward the beginning of the study but become more variable toward the end this article presents a modification to this structure which provides for heteroscedasticity over time maximum likelihood ml estimation procedures are considered and the estimators are found to enjoy optimal large sample properties a scoring algorithm is described for iterating to a solution of the ml equations the model is illustrated with data from a clinical trial investigating human erythropoietin for treating anemia in end

new convergence estimates for multigrid algorithms in this paper new convergence estimates are proved for both symmetric and nonsymmetric multigrid algorithms applied to symmetric positive definite problems our theory relates the convergence of multigrid algorithms to a regularity and approximation parameter cap alpha epsilon 0 1 and the number of relaxations m we show that for the symmetric and nonsymmetric nu cycles the multigrid iteration converges for any positive m at a rate which deteriorates no worse than 1 cj sup 1 sup cap alpha sup sup cap alpha where j is the number of grid levels we then define a generalized nu cycle algorithm which involves exponentially increasing for example doubling the number of smoothings on successively coarser grids we show that the resulting symmetric and nonsymmetric multigrid iterations converge for any cap alpha with rates that are independent of the mesh size the theory is presented in an abstract setting which can be applied to finite element multigrid and finite difference multigrid methods

general methods for analysing repeated measures we present an overview of issues and methods for analysing repeated measures of a continuous random variable we discuss modelling the mean vector and covariance structure statistical efficiency regression diagnostics and discrepancies between longitudinal and cross sectional methods we illustrate key points with examples and discuss areas requiring further development

convergence estimates for multigrid algorithms without regularity assumptions a new technique for proving rate of convergence estimates of multi grid algorithms for symmetric positive definite problems will be given in this paper the standard multigrid theory requires a regularity and approxima tion assumption in contrast the new theory requires only an easily verified approximation assumption this leads to convergence results for multigrid re finement applications problems with irregular coefficients and problems whose coefficients have large jumps in addition the new theory shows why it suffices to smooth only in the regions where new nodes are being added in multigrid refinement applications

an application of the abstract multilevel theory to nonconforming finite element methods a multilevel product algorithm and its additive version or a multilevel preconditioner are proposed for the crouzeix raviart nonconforming finite element methods for second order elliptic equations the authors show that the preconditioned matrix has a condition number bounded uniformly from above if the domain can be partitioned into overlapping convex subdomains a uniform convergence for the multilevel product algorithm is also established the results are regularity free for the continuous problem and can be applied to problems with rough solutions and local grid refinement numerical results that illustrate the theory are presented

on schwarz alternating methods for the incompressible navier stokes equations the schwarz alternating method can be used to solve linear elliptic boundary value problems on domains which consist of two or more overlapping subdomains the solution is approximated by an infinite sequence of functions which result from solving a sequence of elliptic boundary value problems in each of the subdomains this paper considers four schwarz alternating methods for the n dimensional steady viscous incompressible navier stokes equations n leq 4 it is shown that the schwarz sequences converge to the true solution provided that the reynolds number is sufficiently small

on monotone iteration and schwarz methods for nonlinear parabolic pdes the schwarz alternating method can be used to solve elliptic boundary value problems on domains which consist of two or more overlapping subdomains the solution is approximated by an infinite sequence of functions which results from solving a sequence of elliptic boundary value problems in each of the subdomains in this paper proofs of convergence of some schwarz alternating methods for nonlinear parabolic problems which are known to have solutions by the monotone method also known as the method of subsolutions and supersolutions are given in particular an additive schwarz method for scalar as well some coupled nonlinear pdes are shown to converge to the solution on finitely many subdomains in the coupled system case each subdomain pde is linear decoupled and can be solved concurrently with other subdomain pdes these results are applicable to several models in population biology the convergence behavior is illustrated by two numerical examples

the post processing approach in the finite element method part 1 calculation of displacements stresses and other higher derivatives of the displacements this is the first in a series of three papers in which we discuss a method for post processing a finite element solution to obtain high accuracy approximations for displacements stresses stress intensity factors etc rather than take the values of these quantities directly from the finite element solution we evaluate certain weighted averages of the solution over the entire region these yield approximations are of the same order of accuracy as the strain energy we obtain error estimates and also present some numerical examples to illustrate the practical effectiveness of the technique in the third paper of this series we address the matters of adaptive mesh selection and a posteriori error estimation

rate of convergence for some constraint decomposition methods for nonlinear variational inequalities some general subspace correction algorithms are proposed for a convex optimization problem over a convex constraint subset one of the nontrivial applications of the algorithms is the solving of some obstacle problems by multilevel domain decomposition and multigrid methods for domain decomposition and multigrid methods the rate of convergence for the algorithms for obstacle problems is of the same order as the rate of convergence for jump coefficient linear elliptic problems in order to analyse the convergence rate we need to decompose a finite element function into a sum of functions from the subspaces and also satisfying some constraints a special nonlinear interpolation operator is introduced for decomposing the functions

maximum likelihood estimation for incomplete repeated measures experiments under an arma covariance structure a stochastic model is presented for the analysis of incomplete repeated measures experiments the general linear model is used to relate the response measures to other variables which are thought to account for inherent variation an autoregressive moving average arma time series representation is used to model disturbance terms maximum likelihood estimation procedures are considered and the properties of these estimators are derived it is concluded that while the assumptions underpinning the arma covariance models may be somewhat restrictive they provide a useful inferential vehicle particularly in the presence of missing values

repeated measurement split plot trend analysis versus analysis of first differences summary for studies with repeated measurement of experimental units ad hod claims e g box 1950 biometrics 6 362 389 that analysis of increments of response is superior to trend analysis of the original data with a split plot model are shown to be spurious reduction of interperiod correlation by using first differences does not necessarily eliminate problems with heterogeneity of the variancecovariance matrix over time for the homogeneous condition the expected variance of a simple trend contrast between two treatments for adjacent periods is shown to be the same for either analysis but the analysis of increments incurs a loss of degrees of freedom that can be critical in studies with few experimental units per treatment an example from mammary physiology is given

accounting for covariates observed post randomization for discrete and continuous repeated measures data adjusting for covariates observed post randomization is a difficult issue in randomized clinical trials one approach is to enter these covariates as time dependent covariates in a general linear model however this approach fails to account for interactions between the primary end point and confounding variable as they evolve over time in this paper we adopt the view that since the confounder is observed following randomization it should be treated as an outcome and analysed accordingly we consider the repeated measures design where both the primary end point and the confounding measure are observed repeatedly over patient follow up a generalized estimating equation model is applied to allow each set of repeated measures to be modelled in terms of important explanatory variables seemingly unrelated regression combines the two models into an overall framework for analysis inference is then performed by imposing restrictions on the confounder regression parameters to reflect the behaviour profile of interest estimation and identification procedures are described and the methodology is illustrated with an example

maximum likelihood computations with repeated measures application of the em algorithm abstract the purpose of this article is to consider the use of the em algorithm dempster laird and rubin 1977 for both maximum likelihood ml and restricted maximum likelihood reml estimation in a general repeated measures setting using a multivariate normal data model with linear mean and covariance structure anderson 1973 several models and methods of analysis have been proposed in recent years for repeated measures data ware 1985 presented an overview because the em algorithm is a general purpose iterative method for computing ml estimates with incomplete data it has often been used in this particular setting dempster et al 1977 andrade and helms 1984 jennrich and schluchter 1985 there are two apparently different approaches to using the em algorithm in this setting in one application each experimental unit is observed under a standard protocol specifying measurements at each of n occasions or under n conditions and incompleteness implies that the number of measurements actua

adjoint consistency analysis of discontinuous galerkin discretizations this paper is concerned with the adjoint consistency of discontinuous galerkin dg discretizations adjoint consistency in addition to consistency is the key requirement for dg discretizations to be of optimal order in l 2 as well as measured in terms of target functionals we provide a general framework for analyzing the adjoint consistency of dg discretizations which is also useful for the derivation of adjoint consistent methods this analysis will be performed for the dg discretizations of the linear advection equation the interior penalty dg method for elliptic problems and the dg discretization of the compressible euler equations this framework is then used to derive an adjoint consistent dg discretization of the compressible navier stokes equations numerical experiments demonstrate the link of adjoint consistency to the accuracy of numerical flow solutions and the smoothness of discrete adjoint solutions

a goal oriented hp adaptive discontinuous galerkin approach for biharmonic problems summary a goal oriented algorithm is developed and applied for hp adaptive approximations given by the discontinuous galerkin finite element method for the biharmonic equation the methodology is based on the dual problem associated with the target functional we consider three error estimators and analyse their properties as basic tools for the design of the hp adaptive algorithm to improve adaptation the combination of two different error estimators is used each one at its best efficiency to guide the tasks of where and how to adapt the approximation spaces the performance of the resulting hp adaptive schemes is illustrated by numerical experiments for two benchmark problems copyright 2013 john wiley sons ltd

multilevel schwarz methods we consider the solution of the algebraic system of equations which result from the discretization of second order elliptic equations a class of multilevel algorithms are studied using the additive schwarz framework we establish that the condition number of the iteration operators are bounded independent of mesh sizes and the number of levels this is an improvement on dryja and widlund s result on a multilevel additive schwarz algorithm as well as bramble pasciak and xu s result on the bpx algorithm some multiplicative variants of the multilevel methods are also considered we establish that the energy norms of the corresponding iteration operators are bounded by a constant less than one which is independent of the number of levels for a proper ordering the iteration operators correspond to the error propagation operators of certain v cycle multigrid methods using gauss seidel and damped jacobi methods as smoothers respectively

hp fem for a stabilized three field formulation of the biharmonic problem abstract in this paper a three field formulation for the biharmonic equation is considered that consists of the potential u the flux and a lagrange multiplier the use of stabilization techniques circumvents the discrete inf sup condition and thus enables the application of arbitrary conforming finite element spaces for the three fields a priori error estimates as well as reliable and efficient a posteriori error estimates are derived the proof of the latter is based on an implicit never to be computed h 2 reconstruction of the discrete potential several numerical experiments underline the theoretical results and show the existence of discretization spaces for which the a posteriori error estimate is p robust with an efficiency index tending towards the optimal value of one the numerical experiments indicate that the proposed method is applicable even if the theoretically required minimal regularity of the lagrange multiplier for the a priori error estimate is not fulfilled in particular h and h p adaptivity recover optimal algebraic and exponential converge rates respectively

on linear monotone iteration and schwarz methods for nonlinear elliptic pdes the schwarz alternating method can be used to solve elliptic boundary value problems on domains which consist of two or more overlapping subdomains the solution is approximated by an infinite sequence of functions which results from solving a sequence of elliptic boundary value problems in each subdomain in this paper proofs of convergence of some schwarz alternating methods for nonlinear elliptic problems which are known to have solutions by the monotone method also known as the method of subsolutions and supersolutions are given in particular an additive schwarz method for scalar as well some coupled nonlinear pdes are shown to converge to some solution on finitely many subdomains even when multiple solutions are possible in the coupled system case each subdomain pde is linear decoupled and can be solved concurrently with other subdomain pdes these results are applicable to several models in population biology

convergence rate of a schwarz multilevel method for the constrained minimization of nonquadratic functionals in l badea convergence rate of a multiplicative schwarz method for strongly nonlinear inequalities v barbu i lasiecka d tiba and c varsan eds kluwer academic publishers boston 2003 the convergence of a subspace correction method applied to the constrained minimization of a functional in a general reflexive banach space has been proved provided that the convex set verifies a certain assumption this assumption is weaker than that in which the convex set is decomposed according to the space decomposition as a sum of subsets in the sobolev spaces the proposed method becomes a multiplicative schwarz method for the solution of the variational inequalities coming from the minimization of nonquadratic functionals we prove in this paper that this assumption holds for the one two and multilevel multiplicative schwarz methods in the finite element space and we explicitly write the constants in the error estimations depending on the overlapping and mesh parameters our error estimates are similar with those obtained for the minimization of quadratic functionals in l badea x c tai and j wang siam j numer anal 2003 pp 1052 1073 or with those obtained for the one obstacle problem in x c tai numer math 93 2003 pp 755 786

on schwarz alternating methods for nonlinear elliptic pdes the schwarz alternating method can be used to solve elliptic boundary value problems on domains which consist of two or more overlapping subdomains the solution is approximated by an infinite sequence of functions which results from solving a sequence of elliptic boundary value problems in each of the subdomains this paper considers several schwarz alternating methods for nonlinear elliptic problems we show that schwarz alternating methods can be embedded in the framework of common techniques such as banach and schauder fixed point methods and global inversion methods used to solve these nonlinear problems

two level additive schwarz methods for a discontinuous galerkin approximation of second order elliptic problems we present some two level nonoverlapping and overlapping additive schwarz methods for a discontinuous galerkin method for solving second order elliptic problems it is shown that the condition numbers of the preconditioned systems are of the order o frac h h for the nonoverlapping schwarz methods and of the order o frac h delta for the overlapping schwarz methods where h and h stand for the fine mesh size and the coarse mesh size respectively and delta denotes the size of the overlaps between subdomains numerical experiments are provided to gauge the efficiency of the methods and to validate the theory

statistical inference of a time to failure distribution derived from linear degradation in the study of semiconductor degradation records of transconductance loss or threshold voltage shift over time are useful in constructing the cumulative distribution function cdf of the time until the degradation reaches a specified level in this article we propose a model with random regression coefficients and a standard deviation function for analyzing linear degradation data both analytical and empirical motivations of the model are provided we estimate the model parameters the cdf and its quantiles by the maximum likelihood ml method and construct confidence intervals from the bootstrap from the asymptotic normal approximation and from inverting likelihood ratio tests simulations are conducted to examine the properties of the ml estimates and the confidence intervals analysis of an engineering dataset illustrates the proposed procedures

an anisotropic h adaptive finite element method for compressible navier stokes equations abstract application of the finite element method with significantly stretched elements to solve compressible navier stokes equations is presented stretched elements are introduced in an adaptive process as a result of selective directional subsecting of elements an adaptive strategy of such anisotropic h type refinements was developed it is based on minimization of the interpolation errors reduction of the residual error indicators and an adaptive recovery of the viscous fluxes with the possibility to control their accuracy an iterative solver with the convergence characteristics independent of the aspect ratio of elements is presented the solver is the gmres algorithm with the domain decomposition schwarz type preconditioner the proposed techniques are used to solve a benchmark problem a hypersonic high reynolds number flow with strong shock boundary layer interaction

goal oriented error estimation and adaptivity for the finite element method abstract in this paper we study a new approach in a posteriori error estimation in which the numerical error of finite element approximations is estimated in terms of quantities of interest rather than the classical energy norm these so called quantities of interest are characterized by linear functionals on the space of functions to where the solution belongs we present here the theory with respect to a class of elliptic boundary value problems and in particular show how to obtain accurate estimates as well as upper and lower bounds on the error we also study the new concept of goal oriented adaptivity which embodies mesh adaptation procedures designed to control error in specific quantities numerical experiments confirm that such procedures greatly accelerate the attainment of local features of the solution to preset accuracies as compared to traditional adaptive schemes based on energy norm error estimates

the matrix logarithmic covariance model abstract a flexible method is introduced to model the structure of a covariance matrix c and study the dependence of the covariances on explanatory variables by observing that for any real symmetric matrix a the matrix exponential transformation c exp a is a positive definite matrix because there is no constraint on the possible values of the upper triangular elements on a any possible structure of interest can be imposed on them the method presented here is not intended to replace the existing special models available for a covariance matrix but rather to provide a broad range of further structures that supplements existing methodology maximum likelihood estimation procedures are used to estimate the parameters and the large sample asymptotic properties are obtained a simulation study and two real life examples are given to illustrate the method introduced

preconditioning in h div and applications we consider the solution of the system of linear algebraic equations which arises from the finite element discretization of boundary value problems associated to the differential operator i grad div the natural setting for such problems is in the hilbert space h div and the variational formulation is based on the inner product in h div we show how to construct preconditioners for these equations using both domain decomposition and multigrid techniques these preconditioners are shown to be spectrally equivalent to the inverse of the operator as a consequence they may be used to precondition iterative methods so that any given error reduction may be achieved in a finite number of iterations with the number independent of the mesh discretization we describe applications of these results to the efficient solution of mixed and least squares finite element approximations of elliptic boundary value problems

unbalanced repeated measures models with structured covariance matrices the question of how to analyze unbalanced or incomplete repeated measures data is a common problem facing analysts we address this problem through maximum likelihood analysis using a general linear model for expected responses and arbitrary structural models for the within subject covariances models that can be fit include standard univariate and multivariate models with incomplete data random effects models and models with time series and factor analytic error structures we describe newton raphson and fisher scoring algorithms for computing maximum likelihood estimates and generalized em algorithms for computing restricted and unrestricted maximum likelihood estimates an example fitting several models to a set of growth data is included

uniform convergence of the schwarz alternating method for solving singularly perturbed advection diffusion equations our purpose in this paper is to study the convergence rate of some variants of the schwarz alternating method for solving two types of singularly perturbed advection diffusion equations one in which the advection term first order term dominates and the other in which the lowest order term zeroth order term dominates for such problems boundary or other layer regions may be present for singular perturbation problems in which the advection dominates we choose two overlapping subregions one corresponding to an outer or elliptic region and the other corresponding to an inner or hyperbolic region our main result for this problem shows that if the subdomains can be chosen to follow the flow i e if the boundary interface of one of the subdomains corresponds to an outflow boundary for the streamlines of the flow then the schwarz iterates converge in the maximum norm with an error reduction factor per iteration that exponentially decays with increasing overlap or decreasing diffusion for the singular perturbation problem in which the lowest order term dominates we consider many overlapping subregions with no special requirement on outflow or inflow boundaries our main result here which is valid for two variants of the classical schwarz algorithm shows that the error reduction factor per iteration decays exponentially in the maximum norm with increasing overlap and increasing dominance of the zeroth order term for both problems our proofs rely on the maximum principle and the construction of barrier functions

parallel galerkin domain decomposition procedures based on the streamline diffusion method for convection diffusion problems based upon the streamline diffusion method parallel galerkin domain decomposition procedures for convection diffusion problems are given these procedures use implicit method in the sub domains and simple explicit flux calculations on the inter boundaries of sub domains by integral mean method or extrapolation method to predict the inner boundary conditions thus the parallelism can be achieved by these procedures the explicit nature of the flux calculations induces a time step limitation that is necessary to preserve stability artificial diffusion parameters d are given by analysis optimal order error estimate is derived in a norm which is stronger than l 2 norm for these procedures this error estimate not only includes the optimal h 1 norm error estimate but also includes the error estimate along the streamline direction b u u which cannot be achieved by standard finite element method experimental results are presented to confirm theoretical results

generalizations and accelerations of lions nonoverlapping domain decomposition method for linear elliptic pde in this paper a one parameter generalization of lions nonoverlapping domain decomposition method for linear elliptic pdes is proposed and studied the generalized methods are shown to be descent direction methods for minimizing an interface bias functional iteration convergence of both the continuous and finite element versions of the proposed methods is established it is theoretically and numerically demonstrated that for generic choices of the parameter the generalized methods converge faster than lions original method algorithms are given and numerical results are presented

an additive analysis of multiplicative schwarz methods we present an analysis of multiplicative schwarz methods for symmetric positive definite problems that is based on the theory of additive schwarz preconditioners and discuss applications to multigrid methods and domain decomposition methods

global and uniform convergence of subspace correction methods for some convex optimization problems this paper gives some global and uniform convergence estimates for a class of subspace correction based on space decomposition iterative methods applied to some unconstrained convex optimization problems some multigrid and domain decomposition methods are also discussed as special examples for solving some nonlinear elliptic boundary value problems

hp adaptive discontinuous galerkin finite element methods for first order hyperbolic problems we consider the a posteriori error analysis of hp discontinuous galerkin finite element approximations to first order hyperbolic problems in particular we discuss the question of error estimation for linear functionals such as the outflow flux and the local average of the solution based on our a posteriori error bound we design and implement the corresponding adaptive algorithm to ensure reliable and efficient control of the error in the prescribed functional to within a given tolerance this involves exploiting both local polynomial degree variation and local mesh subdivision the theoretical results are illustrated by a series of numerical experiments

maximum likelihood estimation of variance components in repeated measures designs assuming autoregressive errors summary linear models used for estimation of variance components are generally formulated under the assumption of independent errors herein we consider a two way mixed model with errors assumed to follow a first order nonstationary autoregressive process maximum likelihood techniques are employed to estimate the variance components and also a parameter for the autoregression an example using lactational yield of cows is given along with some monte carlo results

convergence estimates for product iterative methods with applications to domain decomposition in this paper we consider iterative methods for the solution of symmetric positive definite problems on a space which are defined in terms of products of operators defined with respect to a number of subspaces the simplest algorithm of this sort has an error reducing operator which is the product of orthogonal projections onto the complement of the subspaces new normreduction estimates for these iterative techniques will be presented in an abstract setting applications are given for overlapping schwarz algorithms with many subregions for finite element approximation of second order elliptic problems

c1 macroelements in adaptive finite element methods some interesting properties of composite basis functions for c1 macroelements are investigated including their use for constructing conforming c1 function spaces on non conforming adaptively refined meshes of particular interest is the classical cubic hsieh clough tocher 3 split triangle because of its simplicity and convergence properties in fourth order problems as compared with the powell sabin heindl 6 split and 12 split triangles a posteriori error indicators for adaptive refinement are developed numerical experiments demonstrate convergence rates and adaptive refinement performance based on a simplified error indicator is tested extensibility to analogous three dimensional tetrahedral elements is briefly discussed copyright 2006 john wiley sons ltd

autoregressive growth curves and kalman filtering the first part of this paper describes how a kalman filter can be used to construct maximum likelihood ml estimates of autoregressive ar and polynomial parameters in polynomial growth curves with ar 1 errors and irregularly spaced data the second part introduces a disturbed highest derivative polynomial dhdp as a model for growth curves this model does not depend on regression coefficients variances of the highest derivative disturbance and the observation error are estimated by ml using a kalman filter the estimated dhdp growth curve is obtained by optimally smoothing the output of the filter equally spaced data is not required the dhdp model and analysis are developed for an individual and extended to a population growth curve using data from many individuals with covariates

parallel galerkin domain decomposition procedures for wave equation parallel galerkin domain decomposition procedures for wave equation are given these procedures use implicit method in the sub domains and simple explicit flux calculation on the inter boundaries of sub domains by integral mean method or extrapolation method thus the parallelism can be achieved by these procedures the explicit nature of the flux prediction induces a time step constraint that is necessary to preserve the stability l 2 norm error estimates are derived for these procedures experimental results are presented to confirm the theoretical results

modelling the covariance structure of repeated measurements models for repeated measurements used by wilson hebel and sherwin 1981 biometrics 37 553565 and mansour nordheim and rutledge 1985 biometrics 41 287 294 are considered these two models are generalized by the a p e k model obtained by introducing an extra parameter k a more general class of models described by kenward unpublished ph d thesis university of reading 1981 is briefly discussed simulation results are presented in which model parameters are estimated by maximum likelihood and likelihood ratios are used as criteria for choosing between models a set of blood pressure data is used to illustrate model fitting

goal oriented hp adaptivity for elliptic problems we propose and test a fully automatic goal oriented hp adaptive strategy for elliptic problems the method combines two techniques the standard goal oriented adaptivity based on a simultaneous solution of a dual problem and a recently proposed hp strategy based on minimizing the projection based interpolation error of a reference solution the proposed strategy is illustrated with two numerical examples laplace equation in l shape domain and an axisymmetric maxwell problem involving radiation of a loop antenna wrapped around a metallic cylinder into a conductive medium

multigrid convergence for second order elliptic problems with smooth complex coefficients the finite element method when applied to a second order partial differential equation in divergence form can generate operators that are neither hermitian nor definite when the coefficient function is complex valued for such problems under a uniqueness assumption we prove the continuous dependence of the exact solution and its finite element approximations on data provided that the coefficients are smooth and uniformly bounded away from zero then we show that a multigrid algorithm converges once the coarse mesh size is smaller than some fixed number providing an efficient solver for computing discrete approximations numerical experiments while confirming the theory also reveal pronounced sensitivity of gauss seidel iterations on the ordering of the unknowns for certain problems

random effects models for longitudinal data models for the analysis of longitudinal data must recognize the relationship between serial observations on the same unit multivariate models with general covariance structure are often difficult to apply to highly unbalanced data whereas two stage random effects models can be used easily in two stage models the probability distributions for the response vectors of different individuals belong to a single family but some random effects parameters vary across individuals with a distribution specified at the second stage a general family of models is discussed which includes both growth models and repeated measures models as special cases a unified approach to fitting these models based on a combination of empirical bayes and maximum likelihood estimation of model parameters and using the em algorithm is discussed two examples are taken from a current epidemiological study of the health effects of air pollution

convergence of algebraic multigrid based on smoothed aggregation we prove aconvergence estimate for the algebraic multigrid method with prolongations defined by aggregation using zero energy modes followed by a smoothing the method input is the problem matrix and a matrix of the zero energy modes the estimate depends only polylogarithmically on the mesh size and requires only a weak approximation property for the aggregates which can be a priori verified computationally construction of the prolongator in the case of a general second order system is described and the assumptions of the theorem are verified for a scalar problem discretized by linear conforming finite elements

schwarz methods of neumann neumann type for three dimensional elliptic finite element problems several domain decomposition methods of neumann neumann type are considered for solving the large linear systems of algebraic equations that arise from discretizations of elliptic problems by finite elements we will only consider problems in three dimensions several new variants of the basic algorithm are introduced in a schwarz method framework that provides tools which have already proven very useful in the design and analysis of other domain decomposition and multi level methods the neumann neumann algorithms have several advantages over other domain decomposition methods the subregions which define the subproblems only share the boundary degrees of freedom with their neighbors the subregions can also be of quite arbitrary shape and many of the major components of the preconditioner can be constructed from subprograms available in standard finite element program libraries in its original form however the algorithm lacks a mechanism for global transportation of information and its performance therefore suffers when the number of subregions increases in the new variants of the algorithms considered in this paper the preconditioners include global components of low rank to overcome this difficulty bounds are established for the condition number of the iteration operator which are independent of the number of subregions and depend only polylogarithmically on the number of degrees of freedom of individual local subproblems results are also given for problems with arbitrarily large jumps in the coefficients across the interfaces separating the subregions 1995 john wiley sons inc

the post processing approach in the finite element method part 2 the calculation of stress intensity factors abstract in the context of a model problem the authors describe post processing techniques for the calculation of generalized stress intensity factors they discuss two broad classes of methods one involving an influence function and the other related to the well known energy release principle of fracture mechanics an error analysis is sketched and two numerical examples are given to illustrate the effectivity of the techniques this is the second in a series of three papers author

convergence rate analysis of an asynchronous space decomposition method for convex minimization we analyze the convergence rate of an asynchronous space decomposition method for constrained convex minimization in a reflexive banach space this method includes as special cases parallel domain decomposition methods and multigrid methods for solving elliptic partial differential equations in particular the method generalizes the additive schwarz domain decomposition methods to allow for asynchronous updates it also generalizes the bpx multigrid method to allow for use as solvers instead of as preconditioners possibly with asynchronous updates and is applicable to nonlinear problems applications to an overlapping domain decomposition for obstacle problems are also studied the method of this work is also closely related to relaxation methods for nonlinear network flow accordingly we specialize our convergence rate results to the above methods the asynchronous method is implementable in a multiprocessor system allowing for communication and computation delays among the processors

newton raphson and em algorithms for linear mixed effects models for repeated measures data abstract we develop an efficient and effective implementation of the newton raphson nr algorithm for estimating the parameters in mixed effects models for repeated measures data we formulate the derivatives for both maximum likelihood and restricted maximum likelihood estimation and propose improvements to the algorithm discussed by jennrich and schluchter 1986 to speed convergence and ensure a positive definite covariance matrix for the random effects at each iteration we use matrix decompositions to develop efficient and computationally stable implementations of both the nr algorithm and an em algorithm laird and ware 1982 for this model we compare the two methods em vs nr in terms of computational order and performance on two sample data sets and conclude that in most situations a well implemented nr algorithm is preferable to the em algorithm or em algorithm with aitken s acceleration the term repeated measures refers to experimental designs where there are several individuals and several

rate of convergence of some space decomposition methods for linear and nonlinear problems convergence of a space decomposition method is proved for a class of convex programming problems a space decomposition refers to a method that decomposes a space into a sum of subspaces which could be a domain decomposition or a multilevel method when applied to partial differential equations two algorithms are proposed both can be used for linear as well as nonlinear elliptic problems and they reduce to the standard additive and multiplicative schwarz methods for linear elliptic problems

local multilevel methods for adaptive finite element methods for nonsymmetric and indefinite elliptic boundary value problems in this paper we propose some local multilevel algorithms for solving linear systems arising from adaptive finite element approximations of nonsymmetric and indefinite elliptic boundary value problems two types of local smoothers are constructed one is based on the original nonsymmetric problems and the other is defined in terms of the associated symmetric problems it is shown that the local multilevel methods for the nonsymmetric and indefinite elliptic boundary value problems are optimal which means that the convergence rates of the local multilevel methods are independent of mesh sizes and mesh levels provided that the coarsest grid is sufficiently fine numerical experiments are reported to confirm our theory

analysis of incomplete multivariate data using linear models with structured covariance matrices incomplete and unbalanced multivariate data often arise in longitudinal studies due to missing or unequally timed repeated measurements and or the presence of time varying covariates a general approach to analysing such data is through maximum likelihood analysis using a linear model for the expected responses and structural models for the within subject covariances two important advantages of this approach are 1 the generality of the model allows the analyst to consider a wider range of models than were previously possible using classical methods developed for balanced and complete data and 2 maximum likelihood estimates obtained from incomplete data are often preferable to other estimates such as those obtained from complete cases from the standpoint of bias and efficiency a variety of applications of the model are discussed including univariate and multivariate analysis of incomplete repeated measures data analysis of growth curves with missing data using random effects and time series models and applications to unbalanced longitudinal data

numerical analysis of vanka type solvers for steady stokes and navier stokes flows we consider vanka type smoothers for solving stokes and navier stokes problems in each iteration step this smoother requires the solution of several small local subproblems over finite element blocks it is shown that for particular choices for the blocks the algorithm always converges to the solution of the stokes problem and under suitable conditions to the solution of the navier stokes problem the convergence properties are analyzed and numerical examples are presented

domain decomposition for a least square finite element method for second order elliptic problem in this paper we consider the solutions of the discrete linear system resulting from least square mixed finite element discretization applied to a second order elliptic problems additive and multiplicative domain decomposition methods are used to solve the linear system and the uniform convergence results are established for both methods

an additive schwarz method for variational inequalities this paper proposes an additive schwarz method for variational inequalities and their approximations by finite element methods the schwarz domain decomposition method is proved to converge with a geometric rate depending on the decomposition of the domain the result is based on an framework of convergence analysis established for general variational inequalities in hilbert spaces

analysis of a parallel schwarz algorithm for elliptic problems a parallel algorithm which is derived directly from the schwarz alternating algorithm with an overlapping domain decomposition for solving boundary value problems of elliptic partial differential equations is analyzed a new general analysis framework different from lions ones is established to describe the recursive relations of error functions between approximate solutions and the exact solution at the different iterative steps some abstract theories on convergence and convergent rate of the synchronously parallel algorithm are established under different conditions

nested analysis of variance with autocorrelated errors summary in this paper we consider the problem where there is a randomized experimental design with several successive time measurements on each experimental unit one approach to the analysis of such data is to treat time as the subplot treatment and to use a split plot analysis of variance alternatively the problem may be considered in a more general multivariate framework here we recognize the timeinduced correlations and apply an autoregressive time series modelling approach estimation and testing are addressed two examples are presented to illustrate the practicality of our procedure some extensions are also considered briefly frequently data arise from a randomized experimental design where several successive measurements over time are made on each experimental unit there are many examples such as the following i in medical trials observations may be taken on each subject at regular time intervals ii in wildlife radio telemetry studies the distance moved by each animal may be tracked during successive periods of a day iii in plant animal experiments observations may be taken on the same plant animal as it grows and changes over time in all cases there will be a correlation between observations taken on the same experimental unit at different time points it is also likely that there is a decay in the correlation with increasing time lags in other words observations on the same experimental unit which are close together should be more highly correlated than those that are far apart in time this is contrary to the assumption of constant correlation between all time points subplots within a unit whole plot made by the traditional split plot analysis an alternative approach is to consider a general multivariate analysis of variance manova model which assumes an arbitrary covariance matrix for the observations see timm 1980 however we believe that the multivariate model is overparametrized and also it cannot easily incorporate missing values therefore we consider a time series modelling approach to the problem which serves as a compromise we now present the time series model that we consider for analyzing such data we denote the variable under study by the letter y with two subscripts where the first subscript refers to the individual experimental units and the second subscript refers to the successive measurements for the particular individual we assume that n individuals are selected at random and that measurements are taken at ti consecutive time points on the ith individual we consider a linear model r