some aspects of the spline smoothing approach to non parametric regression curve fitting non parametric regression using cubic splines is an attractive flexible and widely applicable approach to curve estimation although the basic idea was formulated many years ago the method is not as widely known or adopted as perhaps it should be the topics and examples discussed in this paper are intended to promote the understanding and extend the practicability of the spline smoothing methodology particular subjects covered include the basic principles of the method the relation with moving average and other smoothing methods the automatic choice of the amount of smoothing and the use of residuals for diagnostic checking and model adaptation the question of providing inference regions for curves and for relevant properties of curves is approached via a finite dimensional bayesian formulation

a comparative study of different sets of variables for solving compressible and incompressible flows a globally conservative galerkin least squares formulation which attains correct shock structure is developed for any choice of variables only the choice of entropy variables satisfies exactly the discrete clausius duhem inequality without any dissipative mechanisms whereas for the rest of the variables artificial diffusion is required to guarantee entropy production the limit of the formulation is well defined for entropy variables and the primitive variables p u t leading to conservative incompressible formulations the approach is stable for any continuous interpolations both for compressible and incompressible flows a comparative study of different variables is performed indicating that entropy variables and the primitive variables p u t possess the most attributes for practical problem solving

a symmetric formulation for computing transient shallow water flows abstract the shallow water equations fall into the category of symmetric advective diffusive systems with source terms these types of equations can be very effectively solved using stabilized methods such as supg and gls a semi discrete finite element method based on these ingredients is presented for the computation of transient shallow water flows special care has been taken in the design of the operators in order to improve the performance for unsteady calculations the solution is advanced in time via a predictor multi corrector algorithm which includes as special cases the second order trapezoidal rule a first order explicit method and a first order implicit method equivalent to the constant in time element of the space time formulation

the ubiquitous kronecker product abstract the kronecker product has a rich and very pleasing algebra that supports a wide range of fast elegant and practical algorithms several trends in scientific computing suggest that this important matrix operation will have an increasingly greater role to play in the future first the application areas where kronecker products abound are all thriving these include signal processing image processing semidefinite programming and quantum computing second sparse factorizations and kronecker products are proving to be a very effective way to look at fast linear transforms researchers have taken the kronecker methodology as developed for the fast fourier transform and used it to build exciting alternatives third as computers get more powerful researchers are more willing to entertain problems of high dimension and this leads to kronecker products whenever low dimension techniques are tensored together

generalized linear array models with applications to multidimensional smoothing summary data with an array structure are common in statistics and the design or regression matrix for analysis of such data can often be written as a kronecker product factorial designs contingency tables and smoothing of data on multidimensional grids are three such general classes of data and models in such a setting we develop an arithmetic of arrays which allows us to define the expectation of the data array as a sequence of nested matrix operations on a coefficient array we show how this arithmetic leads to low storage high speed computation in the scoring algorithm of the generalized linear model we refer to a generalized linear array model and apply the methodology to the smoothing of multidimensional arrays we illustrate our procedure with the analysis of three data sets mortality data indexed by age at death and year of death spatially varying microarray background data and disease incidence data indexed by age at death year of death and month of death

an unstructured finite elements method for solving the compressible rans equations and the spalart allmaras turbulence model this paper deals with a stabilized finite element method for solving the compressible navier stokes equations combined with the spalart allmaras turbulence model the aim is to assess the ability of this formulation to solve high reynolds number turbulent flows over anisotropic meshes this formulation lies in the framework of the stream line upwind petrove galerkin method we propose a simple and efficient formulation for the stabilization matrix and develop a shock capturing operator numerical tests on the 3d boundary layer over a flat plate and on the onera m6 wing show the stability and robustness of the proposed method

the smallest perturbation of a submatrix which lowers the rank and constrained total least squares problems let t left begin array 20 c a b c d end array right be a partitioned rectangular matrix we exhibit perturbations of d of smallest norm which lower the rank of t we apply this result to generalize the total least squares problem sx b when only a rectangular subset of the data s b is considered uncertain

on stabilized finite element methods for linear systems of convection diffusion reaction equations abstract a stabilized finite element method for solving systems of convection diffusion reaction equations is studied in this paper the method is based on the subgrid scale approach and an algebraic approximation to the subscales after presenting the formulation of the method it is analyzed how it behaves under changes of variables showing that it relies on the law of change of the matrix of stabilization parameters associated to the method an expression for this matrix is proposed for the case of general coupled systems of equations that is an extension of the expression proposed for a one dimensional 1d model problem applications of the stabilization technique to the stokes problem with convection and to the bending of reissner mindlin plates are discussed next the design of the matrix of stabilization parameters is based on the identification of the stability deficiencies of the standard galerkin method applied to these two problems

use of finite element methods in frequency domain aeroacoustics the linearized euler equations are used widely in many aerodynamic noise prediction schemes the linearized euler equations also support instability waves which can obscure the acoustic solution an approach to suppress the instability waves is to solve the linearized euler equations in the frequency domain also the frequency domain approach is far less expensive compared to the time domain approach in terms of the computational time though only a single frequency can be computed at one time the application and comparison of two unstructured grid methods for the solution of aeroacoustic problems in the frequency domain are presented algorithms are developed using the discontinuous galerkin and the streamline upwind petrov galerkin finite element methods in two spatial dimensions on conforming triangular meshes using nodal polynomial basis sets unlike other existing frequency domain solvers no assumption is made regarding the nature of the mean flow the application of the two methods to a two dimensional benchmark problem involving the suppression of instability waves is presented the two methods are compared in terms of the computational cost it is concluded that the discontinuous galerkin method is prohibitively more expensive compared to the streamline upwind petrov galerkin method for aeroacoustic applications in the frequency domain using conforming meshes and nodal polynomials

supg finite element computation of compressible flows with the entropy and conservation variables formulations abstract supg stabilized finite element formulations of compressible euler equations based on the conservation and entropy variables are investigated and compared the formulation based on the conservation variables consists of the formulation introduced by tezduyar and hughes plus a shock capturing term the formulation based on the entropy variables is the same as the one by hughes franca and mallet which has a shock capturing term built in these formulations are tested on several subsonic transonic and supersonic compressible flow problems it is shown that the stabilized formulation based on the conservation variables gives solutions which are just as good as those obtained with the entropy variables furthermore the solutions obtained using the two formulations are very close and in some cases almost indistinguishable consequently it can be deduced that the relative merits of these two formulations will continue to remain under debate

a unified finite element formulation for compressible and incompressible flows using augmented conservation variables abstract a unified approach to computing compressible and incompressible flows is proposed the governing equation for pressure is selected based on the local mach number in the incompressible limit the divergence free constraint on velocity field determines the pressure while it is the equation of state that governs the pressure solution for the compressible flows stabilized finite element formulations based on the space time and semi discrete methods with the augmented conservation variables are employed the augmented conservation variables consist of the usual conservation variables and pressure as an additional variable the formulation is applied to various test problems involving steady and unsteady flows over a large range of mach and reynolds numbers

a variational multiscale stabilized finite element method for the solution of the euler equations of nonhydrostatic stratified flows we present a compressible version of the variational multiscale stabilization vms method applied to the finite element fe solution of the euler equations for nonhydrostatic stratified flows this paper is meant to verify how the algorithm performs when solving problems in the framework of nonhydrostatic atmospheric dynamics this effort is justified by the previously observed good performance of vms and by the advantages that a compact galerkin formulation offers on massively parallel architectures a paradigm for both computational fluid dynamics cfd and numerical weather prediction nwp practitioners we also propose a simple technique to construct a well balanced approximation of the dominant hydrostatics that if not properly discretized may cause unacceptable vertical oscillations this is a relevant problem in nwp especially in the proximity of steep topography to evaluate the performance of the method for stratified environments six standard 2d and two 3d test cases are selected of these two admit a semi analytic solution while the remaining six are non steady and non linear thermal problems with dominant buoyancy effects that challenge the algorithm in terms of stability

stabilized residual distribution for shallow water simulations we propose a stabilized residual distribution rd scheme for the simulation of shallow water flows the final discretization is obtained combining the stabilized rd approach proposed in abgrall j comp phys 214 2006 and ricchiuto and abgrall iccfd4 springer verlag 2006 with the conservative formulation already used in ricchiuto et al j comp phys 222 2007 to simulate shallow water flows the scheme proposed is a nonlinear variant of a lax friedrichs type discretization it is well balanced it actually yields second order of accuracy in smooth areas and it preserves the positivity of the height of the water in presence of dry areas this is made possible by the residual character of the discretization by properly adapting the stabilization operators proposed in abgrall j comp phys 214 2006 and ricchiuto and abgrall iccfd4 springer verlag 2006 and thanks to the positivity preserving character of the underlying lax friedrichs scheme we demonstrate the properties of the discretization proposed on a wide variety of tests

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

a taylor galerkin method for convective transport problems a method is described to derive finite element schemes for the scalar convection equation in one or more space dimensions to produce accurate temporal differencing the method employs forward time taylor series expansions including time derivatives of second and third order which are evaluated from the governing partial differential equation this yields a generalized time discretized equation which is successively discretized in space by means of the standard bubnov galerkin finite element method the technique is illustrated first in one space dimension with linear elements and euler leap frog and crank nicolson time stepping several interesting relations with standard galerkin and recently developed petrov galerkin methods emerge and the new taylor galerkin schemes are found to exhibit particularly high phase accuracy with minimal numerical damping the method is successively extended to deal with variable coefficient problems and multi dimensional situations

bayesian confidence intervals for the cross validated smoothing spline summary we consider the model y t g ti ei i 17 2 n where g t t 0 1 is a smooth function and the ei are independent n 0 a2 errors with g2 unknown the cross validated smoothing spline can be used to estimate g non parametrically from

approximate inference in generalized linear mixed models statistical approaches to overdispersion correlated errors shrinkage estimation and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model glmm given an unobserved vector of random effects observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function known prior weights and a scale factor the random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components for problems involving time series spatial aggregation and smoothing the dispersion may be specified in terms of a rank deficient inverse covariance matrix approximation of the marginal quasi likelihood using laplace s method leads eventually to estimating equations based on penalized quasilikelihood or pql for the mean parameters and pseudo likelihood for the variances im

linear models for field trials smoothing and cross validation abstract spatial methods for the analysis of agricultural field experiments are represented here as smoothing methods applied simultaneously with the estimation of treatment effects selection of both the form of the smoother and the degree of smoothing required may be based on cross validation particular emphasis is placed in this paper on generalized least squares estimation ion linear models but the principle applies quite generally keywords agricultural field experiments generalized least squares incomplete block designs neighbour methods papadakis method recovery of inter block formation smoothing and spatial models

conditional transformation models the ultimate goal of regression analysis is to obtain information about the conditional distribution of a response given a set of explanatory variables this goal is however seldom achieved because most established regression models only estimate the conditional mean as a function of the explanatory variables and assume that higher moments are not aected by the regressors the underlying reason for such a restriction is the assumption of additivity of signal and noise we propose to relax this common assumption in the framework of transformation models the novel class of semiparametric regression models proposed herein allows transformation functions to depend on explanatory variables these transformation functions are estimated by regularised optimisation of scoring rules for probabilistic forecasts e g the continuous ranked probability score the corresponding estimated conditional distribution functions are consistent based on applications from dierent domains we show that these conditional transformation models are useful for describing possible heteroscedasticity comparing spatially varying distributions identifying extreme events deriving prediction intervals and selecting variables beyond mean regression eects an empirical investigation based on a heteroscedastic varying coecient simulation model demonstrates that semiparametric estimation of conditional distribution functions can be more benecial than kernel based non parametric approaches or parametric generalised additive models for location scale and shape

modelling and smoothing parameter estimation with multiple quadratic penalties summary penalized likelihood methods provide a range of practical modelling tools including spline smoothing generalized additive models and variants of ridge regression selecting the correct weights for penalties is a critical part of using these methods and in the single penalty case the analyst has several well founded techniques to choose from however many modelling problems suggest a formulation employing multiple penalties and here general methodology is lacking a wide family of models with multiple penalties can be fitted to data by iterative solution of the generalized ridge regression problem minimise kw 1 2 xp a y k 2 o p m i 1 iip 0 s i p p is a parameter vector x a design matrix si a non negative definite coefficient matrix defining the i th penalty with associated smoothing parameter ii w a diagonal weight matrix y a vector of data or pseudodata and o an overall smoothing parameter included for reasons of computational efficiency this paper shows how smoothing parameter selection can be performed efficiently by applying generalized cross validation to this problem and how this allows non linear generalized linear and linear models to be fitted using multiple penalties substantially increasing the scope of penalized modelling methods examples of non linear modelling generalized additive modelling and anisotropic smoothing are given

local preconditioning and variational multiscale stabilization for euler compressible steady flow abstract this paper introduces a preconditioned variational multiscale stabilization p vms method for compressible flows in this introductory paper we focus on inviscid flow and steady state problems the euler equations are solved on fully unstructured grids and discretized using the finite element method the p vms method can be decomposed into three parts first a local preconditioner is applied to the continuous equations to reduce the stiffness while covering a wide range of mach numbers then the resulting preconditioned system is discretized in space using finite elements and stabilized with a variational multiscale stabilization method adapted for the preconditioned equations in this paper the solution is advanced in time using a fully explicit time discretization although p vms is general and can be applied to fully implicit solvers the proposed method is assessed by comparing convergence and accuracy of the solutions between the non preconditioned and preconditioned cases in particular for van leer lee roe s 1991 and choi merkle s 1993 preconditioners in some selected examples covering a large range of mach numbers

modelling covariance structure in bivariate marginal models for longitudinal data summary it can be more challenging to efficiently model the covariance matrices for multivariate longitudinal data than for the univariate case due to the correlations arising between multiple responses the positive definiteness constraint and the high dimensionality are further obstacles in covariance modelling in this paper we develop a data based method by which the parametersinthecovariancematricesarereplacedbyunconstrainedandinterpretableparameterswith reduced dimensions the maximum likelihood estimators for the mean and covariance parameters are shown to be consistent and asymptotically normally distributed simulations and real data analysis show that the new approach performs very well even when modelling bivariate nonstationary dependence structures

a first order hyperbolic framework for large strain computational solid dynamics part i total lagrangian isothermal elasticity abstract this paper introduces a new computational framework for the analysis of large strain fast solid dynamics the paper builds upon previous work published by the authors gil et al 2014 48 where a first order system of hyperbolic equations is introduced for the simulation of isothermal elastic materials in terms of the linear momentum the deformation gradient and its jacobian as unknown variables in this work the formulation is further enhanced with four key novelties first the use of a new geometric conservation law for the co factor of the deformation leads to an enhanced mixed formulation advantageous in those scenarios where the co factor plays a dominant role second the use of polyconvex strain energy functionals enables the definition of generalised convex entropy functions and associated entropy fluxes for solid dynamics problems moreover the introduction of suitable conjugate entropy variables enables the derivation of a symmetric system of hyperbolic equations dual of that expressed in terms of conservation variables third the new use of a tensor cross product 61 greatly facilitates the algebraic manipulations of expressions involving the co factor of the deformation fourth the development of a stabilised petrov galerkin framework is presented for both systems of hyperbolic equations that is when expressed in terms of either conservation or entropy variables as an example a polyconvex mooney rivlin material is used and for completeness the eigen structure of the resulting system of equations is studied to guarantee the existence of real wave speeds finally a series of numerical examples is presented in order to assess the robustness and accuracy of the new mixed methodology benchmarking it against an ample spectrum of alternative numerical strategies including implicit multi field fraeijs de veubeke hu washizu variational type approaches and explicit cell and vertex centred finite volume schemes

a conservative nodal variational multiscale method for lagrangian shock hydrodynamics abstract a new method based on a continuous piece wise linear approximation of the equations for lagrangian shock hydrodynamics is presented numerical instabilities are controlled by a stabilizing operator derived using the paradigm of the variational multiscale analysis encouraging numerical comparisons with existing methods in the case of quadrilateral and hexahedral elements indicate that the proposed method is capable of preventing hourglass patterns in the solution while maintaining accuracy in regions of smooth flow the proposed approach satisfies galilean invariance properties and hinges upon the interpretation of the lagrangian shock hydrodynamics equations as a system of nonlinear wave equations a specific implementation in terms of a predictor multi corrector version of the mid point time integrator guarantees global conservation of mass momentum and total energy for each iterate stability and formal order of accuracy are investigated applying the von neumann analysis to the linearized shock hydrodynamics equations in one dimension this approach yields tight bounds for stable time step estimation formal second order accuracy of the method in time and space and valuable indications on the choice of the most appropriate values for the stabilization parameters present in the formulation

modulation models for seasonal time series and incidence tables we model monthly disease counts on an age time grid using the two dimensional varying coefficient poisson regression since the marginal profile of counts shows a very strong and varying annual cycle sine and cosine regressors model periodicity but their coefficients are allowed to vary smoothly over the age and time plane the coefficient surfaces are estimated using a relatively large tensor product b spline basis smoothness is tuned using difference penalties on the rows and columns of the tensor product coefficients heavy over dispersion occurs making it impossible to use akaike s information criterion or bayesian information criterion based on a poisson likelihood it is handled by selective weighting of part of the data and by the use of extended quasi likelihood very efficient computation is achieved with fast array algorithms the model is applied to monthly deaths due to respiratory diseases for u s females during 1959 1998 and for ages 51 100

finite element methods for first order hyperbolic systems with particular emphasis on the compressible euler equations a petrov galerkin finite element formulation is presented for first order hyperbolic systems of conservation laws with particular emphasis on the compressible euler equations applications of the methodology are made to one and two dimensional steady and unsteady flows with shocks results obtained suggest the potential of the type of methods developed

modelling function valued stochastic processes with applications to fertility dynamics summary we introduce a simple and interpretable model for functional data analysis for situations where the observations at each location are functional rather than scalar this new approach is based on a tensor product representation of the function valued process and utilizes eigenfunctions of marginal kernels the resulting marginal principal components and product principal components are shown to have nice properties given a sample of independent realizations of the underlying function valued stochastic process we propose straightforward fitting methods to obtain the components of this model and to establish asymptotic consistency and rates of convergence for the estimates proposed the methods are illustrated by modelling the dynamics of annual fertility profile functions for 17 countries this analysis demonstrates that the approach proposed leads to insightful interpretations of the model components and interesting conclusions

modeling and testing differential item functioning in unidimensional binary item response models with a single continuous covariate a functional data analysis approach differential item functioning dif referring to between group variation in item characteristics above and beyond the group level disparity in the latent variable of interest has long been regarded as an important item level diagnostic the presence of dif impairs the fit of the single group item response model being used and calls for either model modification or item deletion in practice depending on the mode of analysis methods for testing dif with continuous covariates rather than categorical grouping variables have been developed however they are restrictive in parametric forms and thus are not sufficiently flexible to describe complex interaction among latent variables and covariates in the current study we formulate the probability of endorsing each test item as a general bivariate function of a unidimensional latent trait and a single covariate which is then approximated by a two dimensional smoothing spline the accuracy and precision of the proposed procedure is evaluated via monte carlo simulations if anchor items are available we proposed an extended model that simultaneously estimates item characteristic functions icfs for anchor items icfs conditional on the covariate for non anchor items and the latent variable density conditional on the covariate all using regression splines a permutation dif test is developed and its performance is compared to the conventional parametric approach in a simulation study we also illustrate the proposed semiparametric dif testing procedure with an empirical example

fast bivariate p splines the sandwich smoother national science foundation dms 0805975 national institutes of health r01 ns060910 national center for research resources ul1 rr024996 national natural science foundation of china 11201390

on a parabolic quadrilateral finite element for compressible flows abstract we present a 9 node finite element for compressible flow solutions a high order derivative upwind term and a shock capturing term are employed for stability and accuracy of the formulation we give the solutions of various example problems to illustrate our experiences with the element

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100