the h text p version of the finite element method for domains with curved boundaries this paper analyzes the convergence of the h text p version of the finite element method for elliptic problems on curved domains it proves that when the boundary of the domain is piecewise analytic boundary conditions are piecewise analytic and the sides of the elements are analytic the h text p version has an exponential rate of convergence numerical computations are included the paper generalizes the results previously obtained by the authors the h text p version of finite element method part 1 the basic approximation results comp mech 1 1986 pp 21 41 the h text p version of finite element method part 2 general results and applications comp mech 1 1986 pp 203 220

asymptotic distributions of quasi maximum likelihood estimators for spatial autoregressive models this paper investigates asymptotic properties of the maximum likelihood estimator and the quasi maximum likelihood estimator for the spatial autoregressive model the rates of convergence of those estimators may depend on some general features of the spatial weights matrix of the model it is important to make the distinction with dif ferent spatial scenarios under the scenario that each unit will be influenced by only a few neighboring units the estimators may have n rate of convergence and be asymp totically normal when each unit can be influenced by many neighbors irregularity of the information matrix may occur and various components of the estimators may have different rates of convergence

adaptive cfd analysis for rotorcraft aerodynamics abstract an adaptive parallel computational fluid dynamics cfd technique is developed to compute rotor blade aerodynamics for this purpose an error indicator is formulated and coded into an adaptive finite element framework it is shown that the error indicator is effective in resolving the global features of the flow field furthermore for efficiency and problem size considerations once the interpolation errors are reduced to acceptable levels the adaptive refinement is done only in regions affected by the vortical flows to accomplish this a novel vortex core detection technique is used to capture vortex tubes the combination of interpolation error estimate and vortex core detection technique proved to be very effective in computing vortical flow field of rotor blades example adaptive parallel calculations of hovering rotor blades requiring 1 3 million tetrahedral elements are presented

toward a universal adaptive finite element strategy part 3 design of meshes abstract in this third paper in our series the issue of designing h p meshes which are optimal in some sense is addressed criteria for h p meshes are derived which are based on the idea of minimizing the estimated error over a mesh with a fixed number of degrees of freedom an optimization algorithm is developed based on these criteria and is applied to several model one dimensional and two dimensional elliptic boundary value problems numerical results indicate that the approach can lead to exponential rates of convergence

the sr approach a new estimation procedure for non linear and non gaussian dynamic term structure models abstract this paper suggests a new approach for estimating linear and non linear dynamic term structure models with latent factors we impose no distributional assumptions on the factors which therefore may be non gaussian the novelty of our approach is to use many observables yields or bond prices in the cross section dimension this implies that the latent factors can be determined quite accurately by a sequence of cross section regressions we also show how output from these regressions can be used to obtain model parameters by a two or three step moment based estimation procedure

hac estimation in a spatial framework abstract we suggest a non parametric heteroscedasticity and autocorrelation consistent hac estimator of the variance covariance vc matrix for a vector of sample moments within a spatial context we demonstrate consistency under a set of assumptions that should be satisfied by a wide class of spatial models we allow for more than one measure of distance each of which may be measured with error monte carlo results suggest that our estimator is reasonable in finite samples we then consider a spatial model containing various complexities and demonstrate that our hac estimator can be applied in the context of that model

reliability of automatic 3d mesh generation abstract this paper considers issues critical to ensuring the reliability of automatic three dimensional mesh generators building on basic concepts from geometric modeling consideration is given to i the definition and assurance of a valid finite element mesh ii the use of topological adjacency information to improve the reliability and efficiency of a meshing process and iii how the geometric approximations used during the construction of a geometric model must be explicitly considered if the mesh generator s reliability is to be ensured

geometrically accurate efficient and flexible quadrature techniques for the tetrahedral finite cell method abstract we illustrate the importance of geometrically accurate volume quadrature for obtaining optimal accuracy with non boundary fitted finite element discretizations when the problem domain is defined by sharp boundaries we consider the tetrahedral finite cell method tetfcm and replace its recursive subdivision based integration approach with geometrically accurate quadrature rules that emanate from higher order geometric parametrizations of cut tetrahedral elements the element wise parametrization procedure relies on the identification of the intersection topology and a series of higher order mappings based on lagrange polynomials we demonstrate with several 3d examples that geometrically faithful local parametrization ensures optimal accuracy while significantly reducing the number of quadrature points with respect to recursive subdivision on the other hand we highlight the strength of subdivision quadrature in the context of a patient specific workflow for the simulation based performance analysis of coupled bone implant configurations in particular we show that accuracy flexibility and computational efficiency of the tetfcm critically depend on flexibly applying the two different quadrature variants for fuzzy imaging data and sharp boundary representations respectively

spatial heteroskedasticity and autocorrelation consistent estimation of covariance matrix this paper considers spatial heteroskedasticity and autocorrelation consistent spatial hac estimation of covariance matrices of parameter estimators we generalize the spatial hac estimator introduced by kelejian and prucha 2007 to apply to linear and nonlinear spatial models with moment conditions we establish its consistency rate of convergence and asymptotic truncated mean squared error mse based on the asymptotic truncated mse criterion we derive the optimal bandwidth parameter and suggest its data dependent estimation procedure using a parametric plug in method the finite sample performances of the spatial hac estimator are evaluated via monte carlo simulation

inference on difference in differences average treatment effects a fixed b approach abstract this paper provides an analysis of the standard errors proposed by driscoll and kraay 1998 dk in linear difference in differences dd models with fixed effects and individual specific time trends the analysis is accomplished within the fixed b asymptotic framework developed by kiefer and vogelsang 2005 for heteroskedasticity and autocorrelation consistent hac covariance matrix estimator based tests for both the fixed n large t and large n large t cases it is shown that fixed b asymptotic distributions of test statistics constructed using the dd estimator and the dk standard errors are different from the results found by kiefer and vogelsang 2005 and vogelsang 2012 the newly derived fixed b asymptotic distributions depend on the date of policy change individual specific trend functions as well as the choice of kernel and bandwidth monte carlo simulations illustrate the performance of the fixed b approximations in practice

a straightforward structure to construct shape functions for variable p order meshes this paper describes a method for specifying variable p order meshes based on the topological hierarchy of mesh entities defining the finite elements a decomposition of p version mesh entity shape functions into a product of a function defined over the mesh entity and a blending function defined over the elements that the mesh entity bounds is presented the decomposed shape functions allow the effective construction of the shape functions and derivatives needed to construct element matrices for variable p enrichment

optimal finite element interpolation on curved domains this paper is devoted to a general theory of approximation of functions in finite element spaces in particular the case is considered where the functions to be interpolated are on the one hand not very smooth and on the other are defined on curved domains thus a number of well known optimal interpolation results are generalized

the h p and h p versions of the finite element methods in 1 dimension part iii the adaptive h p version abstract the paper is the third and final part in the series of three devoted to the detailed analysis of the three basic versions of the finite element method in one dimension the first part analyzed the p version and the second part concentrated on the h and h p version this paper analyzes a theoretical frame of the adaptive h p version and based on it the authors provide concrete algorithm for the one dimensional problem it is proven that in the case that the solution has x sub alpha type singularity the adaptive algorithm give an exponential rate of convergence very close to the optimal one analyzed in the second part of the paper additional keyword error analysis

approximate optimal points for polynomial interpolation of real functions in an interval and in a triangle the main results of this paper are the analysis of the quality of approximation of polynomial interpolation and the computation of the approximate optimal interpolation points in the triangle we introduce various norms for the interpolation operator computational results indicate that for a given polynomial degree the set that minimizes the mean l2 norm of the interpolation operator is close to the smallest lebesgue constant interpolation set in particular for the triangle this set gives the smallest lebesgue constant currently known

the generation of triangular meshes for nurbs enhanced fem summary this paper presents the first method that enables the fully automatic generation of triangular meshes suitable for the so called non uniform rational b spline nurbs enhanced finite element method nefem the meshes generated with the proposed approach account for the computer aided design boundary representation of the domain given by nurbs curves the characteristic element size is completely independent of the geometric complexity and of the presence of very small geometric features the proposed strategy allows to circumvent the time consuming process of de featuring complex geometric models before a finite element mesh suitable for the analysis can be produced a generalisation of the original definition of a nefem element is also proposed enabling to treat more complicated elements with an edge defined by several nurbs curves or more than one edge defined by different nurbs three examples of increasing difficulty demonstrate the applicability of the proposed approach and illustrate the advantages compared with those of traditional finite element mesh generators finally a simulation of an electromagnetic scattering problem is considered to show the applicability of the generated meshes for finite element analysis 2016 the authors international journal for numerical methods in engineering published by john wiley sons ltd

spatial correlation robust inference with errors in location or distance this paper presents results from a monte carlo study concerning inference with spatially dependent data we investigate the impact of location distance measurement errors upon the accuracy of parametric and nonparametric estimators of asymptotic variances nonparametric estimators are quite robust to such errors method of moments estimators perform surprisingly well and mle estimators are very poor we also present and evaluate a specification test based on a parametric bootstrap that has good power properties for the types of measurement error we consider

robustness of isogeometric structural discretizations under severe mesh distortion abstract this paper investigates higher order and higher continuity functions in isogeometric structural analysis under distortion of the control and physical meshes first the concepts behind isogeometric analysis are briefly reviewed the effect of perturbing control points upon the geometrical mapping is observed in the one dimensional setting the concept is extended to multiple dimensions with a series of cases where the interior of a cube is distorted in different ways and patch tests are performed to assess accuracy a circular fillet patch is introduced through the appropriate degeneration of a control mesh in order to address the problem of modeling small features in finite element models the fillet patch is tested with two problems of linear elasticity and is shown to be accurate the investigation is further extended to the setting of large deformation nearly incompressible nonlinear elasticity with two examples which make use of the recently proposed f projection method

toward a universal h p adaptive finite element strategy part 1 constrained approximation and data structure abstract this is the first of a series of papers devoted to the development of an adaptive finite element method to solve various boundary value problems arising in solid and fluid mechanics the paper deals with the general concepts of h p finite element methods constrained approximation and data structure and related issues several numerical examples illustrate the main ideas of the method

approximation properties of the h p version of the finite element method abstract the paper surveys the approximation and convergence properties of the h p version of the finite element method the basic theoretical results together with the main ideas of the proofs numerical examples are given

a likelihood ratio test for spatial model selection abstract this paper develops a nondegenerate likelihood ratio test for model selection between two competitive spatial econometrics models it generalizes the test of vuong 1989 to models with spatial near epoch dependent ned data we do not make any structural assumption on the true model specification and allow for the cases where both or one of the two competing models are mis specified the test is valid whether two models are nested or non nested as a prerequisite of the test we first show that quasi maximum likelihood estimators qmle of spatial econometrics models are consistent estimators of their pseudo true values and are asymptotically normal under regularity conditions in particular we study spatial autoregressive models with spatial autoregressive errors sarar and matrix exponential spatial specification mess models we derive the limiting null distribution of the test statistic a spatial heteroskedastic and autoregressive consistent estimator of asymptotic variance of the test statistic under the null which is necessary to implement the test is constructed monte carlo experiments are designed to investigate finite sample performance of qmles for sarar and mess models as well as the size and power of the proposed test

conservative multimoment transport along characteristics for discontinuous galerkin methods a set of algorithms based on characteristic discontinuous galerkin methods is presented for tracer transport on the sphere the algorithms are designed to reduce message passing interface communica

the effect of numerical quadrature in the p version of the finite element method we investigate the use of numerical quadrature in the p version of the finite element method we describe a set of minimal conditions that the quadrature rules should satisfy for various types of elements under sufficient assumptions of smoothness we establish optimality of the asymptotic rate of convergence some computational results are presented which illustrate under what conditions overintegration may be useful

the p version of the finite element method for three dimensional curved thin walled structures in this paper we present an implementation of a three dimensional p version for structural problems of solids with almost arbitrarily curved surfaces applying the blending function method complex structures can often be modelled by a few p elements being the basis for a higher order approximation numerical examples will demonstrate that the p version with anisotropic ansatz spaces allows to predict the structural behaviour of three dimensional plates and shells with approximately the same amount of degrees of freedom as in the two dimensional case yet significantly more accurate due to the three dimensional model furthermore it is advantageous to compute complex structures exclusively with three dimensional discretizations as no special elements are needed to model the transition from dimensionally reduced formulations like plates or shells to fully three dimensional solid elements using the p version with anisotropic ansatz spaces the whole structure can be efficiently discretized with solid elements even if the aspect ratio of the elements becomes very large copyright 2001 john wiley sons ltd

a distortion measure to validate and generate curved high order meshes on cad surfaces with independence of parameterization the first author was sponsored by cur from diue of the generalitat de catalunya and the european social fund grants fi dgr 11 and be dgr 12 and by the ferran sunyer i balaguer foundation grant fsb 13 the work of the corresponding author was partially supported by the boeing co us air force office of scientific research european commission through the boeing mit alliance the computational math program marie sklodowska curie actions hipermegaflows individual fellowship grant

geometry representation issues associated with p version finite element computations this paper addresses issues related to accurate geometry representation for p version finite elements on curved three dimensional domains specific options to account for domain geometry information during element level computation are identified accuracy requirements on the geometry related approximations to preserve the optimal rate of finite element error convergence for second order elliptic boundary value problems are given an element geometric mapping scheme based on blending the exact shape of the domain boundary is described that can either be used directly during element integrations or used to construct element level geometric approximations of required accuracy smoothness issues of the rational blends on simplex topologies are discussed and a numerical example based on the solution of poisson s equation in three dimensions is presented to illustrate the impact of the rational blends on the optimal rate of finite element error convergence

heteroskedasticity autocorrelation and spatial correlation robust inference in linear panel models with fixed effects abstract this paper develops an asymptotic theory for test statistics in linear panel models that are robust to heteroskedasticity autocorrelation and or spatial correlation two classes of standard errors are analyzed both are based on nonparametric heteroskedasticity autocorrelation hac covariance matrix estimators the first class is based on averages of hac estimators across individuals in the cross section i e averages of hacs this class includes the well known cluster standard errors analyzed by arellano 1987 as a special case the second class is based on the hac of cross section averages and was proposed by driscoll and kraay 1998 the hac of averages standard errors are robust to heteroskedasticity serial correlation and spatial correlation but weak dependence in the time dimension is required the averages of hacs standard errors are robust to heteroskedasticity and serial correlation including the nonstationary case but they are not valid in the presence of spatial correlation the main contribution of the paper is to develop a fixed b asymptotic theory for statistics based on both classes of standard errors in models with individual and possibly time fixed effects dummy variables the asymptotics is carried out for large time sample sizes for both fixed and large cross section sample sizes extensive simulations show that the fixed b approximation is usually much better than the traditional normal or chi square approximation especially for the driscoll kraay standard errors the use of fixed b critical values will lead to more reliable inference in practice especially for tests of joint hypotheses

shell finite cell method a high order fictitious domain approach for thin walled structures abstract this article presents a generalization of the recently proposed finite cell method to thin walled structures this approach uses a combination of well known fictitious domain methods with high order hierarchical ansatz spaces known from the p version of the finite element method whereas the original concept embeds a three dimensional structure in a simple domain being meshed into a grid of cube shaped cells the extension presented in this paper applies the fictitious domain approach to a two dimensional master domain defined in the parameter plane of the geometric model implementation details are discussed and numerical benchmark problems show the high accuracy and computational efficiency of the new approach it is also remarked that the present approach can easily be carried over to isogeometric analysis opening an attractive possibility to simulate trimmed nurbs surfaces

the cross quantilogram measuring quantile dependence and testing directional predictability between time series this paper proposes the cross quantilogram to measure the quantile dependence between two time series we apply it to test the hypothesis that one time series has no directional predictability to another time series we establish the asymptotic distribution of the cross quantilogram and the corresponding test statistic the limiting distributions depend on nuisance parameters to construct consistent confidence intervals we employ the stationary bootstrap procedure we show the consistency of this bootstrap also we consider the self normalized approach which is shown to be asymptotically pivotal under the null hypothesis of no predictability we provide simulation studies and two empirical applications first we use the cross quantilogram to detect predictability from stock variance to excess stock return compared to existing tools used in the literature of stock return predictability our method provides a more complete relationship between a predictor and stock return second we investigate the systemic risk of individual financial institutions such as jp morgan chase goldman sachs and aig this article has supplementary materials online

mesh generation in curvilinear domains using high order elements the ability to construct suitable computational meshes is currently a significant limiting factor in the development of compact high order algorithms in very complex geometries compact high order algorithms such as spectral element or p type finite element techniques offer the potential of high accuracy if the solution is smooth and a well behaved mapping exists between the local sub domains and a standard region in this paper we address the problem of coupling high order algorithms with unstructured mesh generation and cad representation techniques we present three complementary strategies to alleviate the problem of generation of elemental regions with singular elemental mappings the first strategy investigates the influence of an anisometric parametric surface representation on the quality of high order unstructured meshes we show that a straightforward splitting of a standard linear mesh for use in a high order method can lead to the generation of distorted possibly invalid meshes even for simple computational domains such as cubes the second strategy uses hybrid meshes applying prismatic elements near curvilinear boundaries in the third and final strategy we investigate the use of curvature driven surface discretization to incorporate higher order information about the surface into the mesh generation using the computational reconstruction of the arterial bypass graft as an example computational domain we demonstrate how the combination of all three strategies leads to a valid high order discretization of the computational domain copyright 2001 john wiley sons ltd

optimal bandwidth selection in heteroskedasticity autocorrelation robust testing the paper considers studentized tests in time series regressions with nonparametrically autocorrelated errors the studentization is based on robust standard errors with truncation lag m bt for some constant b 2 0 1 and sample size t it is shown that the nonstandard xed b limit distributions of such nonparametrically studentized tests provide more accurate approximations to the nite sample distributions than the standard small b limit distribution we further show that for typical economic time series the optimal bandwidth that minimizes a weighted average of type i and type ii errors is larger by an order of magnitude than the bandwidth that minimizes the asymptotic mean squared error of the corresponding long run variance estimator a plug in procedure for implementing this optimal bandwidth is suggested and simulations not reported here con rm that the new plug in procedure works well in nite samples

heteroskedasticity and spatiotemporal dependence robust inference for linear panel models with fixed effects abstract this paper studies robust inference for linear panel models with fixed effects in the presence of heteroskedasticity and spatiotemporal dependence of unknown forms we propose a bivariate kernel covariance estimator that nests existing estimators as special cases our estimator improves upon existing estimators in terms of robustness efficiency and adaptiveness for distributional approximations we considered two types of asymptotics the increasing smoothing asymptotics and the fixed smoothing asymptotics under the former asymptotics the wald statistic based on our covariance estimator converges to a chi square distribution under the latter asymptotics the wald statistic is asymptotically equivalent to a distribution that can be well approximated by an f distribution simulation results show that our proposed testing procedure works well in finite samples

a parallel hp fem infrastructure for three dimensional structural acoustics this paper describes a parallel three dimensional numerical infrastructure for the solution of a wide range of time harmonic problems in structural acoustics and vibration high accuracy and rate of error convergence in the mid frequency regime is achieved by the use of hp finite and infinite element approximations the infrastructure supports parallel computation in both single and multi frequency settings multi frequency solves utilize concurrent factoring of the frequency dependent linear algebraic systems and are naturally scalable scalability of large scale single frequency problems is realized by using feti dp an iterative domain decomposition scheme numerical examples are presented to cover applications in vibratory response of fluid filled elastic structures as well as radiation and scattering from elastic structures submerged in an infinite acoustic medium we demonstrate both the numerical accuracy as well as parallel scalability of the infrastructure in terms of problem parameters that include wavenumber and number of frequencies polynomial degree of finite infinite element approximations as well as the number of processors scalability and accuracy is evaluated for both single and multiple frequency sweeps on four high performance parallel computing platforms sgi altix sgi origin ibm p690 sp and linux cluster results show good performance on shared as well as distributed memory architecture copyright 2006 john wiley sons ltd

the h p and h p versions of the finite element method in 1 dimension this paper is the first one in the series of three which are addressing in detail the properties of the three basic versions of the finite element method in the one dimensional setting the main emphasis is placed on the analysis when the exact solution has singularity of x type the first part analyzes thep version the second theh version and generalh p version and the final third part addresses the problems of the adaptiveh p version

the h p and h p versions of the finite element method in 1 dimension part ii the error analysis of the h and h p versions the paper is the second in the series of three devoted to the detailed analysis of the three basic versions of the finite element method in one dimensional setting the first part 1 analyzed thep version the present one concentrates on theh andh p versions

gmm estimation with cross sectional dependence this paper presents a spatial model of dependence among agents using a metric of economic distance measurements of this economic distance provide cross sectional data with a structure similar to that provided by the time index in time series data generalized method of moments estimators using such dependent data are shown to be consistent and asymptotically normal this paper presents a class of non parametric positive semi definite covariance matrix estimators that allow for general forms of dependence characterized by economic distance these covariance matrix estimators are shown to remain consistent when economic distances are not precisely observed

autoregressive spatial spectral estimates abstract nonparametric spectral density estimates find many uses in econometrics for stationary random fields on a regular spatial lattice we propose an autoregressive nonparametric spectral density estimate that is guaranteed positive even when suitable edge effect correction is employed and is simple to compute using least squares our estimate is based on truncating a true half plane infinite autoregressive representation while also allowing the truncation length to diverge in all dimensions to avoid the potential bias due to truncation at a fixed lag length uniform consistency of the proposed estimate is established and new criteria for order selection are also suggested and studied in practical settings the asymptotic distribution of the estimate is shown to be zero mean normal and independent at fixed distinct frequencies mirroring the behaviour for time series a small monte carlo experiment examines finite sample performance technically the key to the results is the covariance structure of stationary random fields defined on regularly spaced lattices we show the covariance matrix to satisfy a generalization of the toeplitz property familiar from time series analysis

bootstrap procedures under some non i i d models it is shown in this article that the classical i i d bootstrap remains a valid procedure for estimating the sampling distributions of certain symmetric estimators of location as long as the random observations are independently drawn from distributions with essentially a common location this may be viewed as a robust property of the classical i i d bootstrap also included is a study of the second order properties of a different bootstrap procedure proposed by wu in the context of heteroscedasticity in regression

the p version of the finite element method in the p version of the finite element method the triangulation is fixed and the degree p of the piecewise polynomial approximation is progressively increased until some desired level of precision is reached in this paper we first establish the basic approximation properties of some spaces of piecewise polynomials defined on a finite element triangulation these properties lead to an a priori estimate of the asymptotic rate of convergence of the p version the estimate shows that the p version gives results which are not worse than those obtained by the conventional finite element method called the h version in which h represents the maximum diameter of the elements when quasi uniform triangulations are employed and the basis for comparison is the number of degrees of freedom furthermore in the case of a singularity problem we show under conditions which are usually satisfied in practice that the rate of convergence of the p version is twice that of the h version with quasi uniform mesh inve

optimization of a regularized distortion measure to generate curved high order unstructured tetrahedral meshes we present a robust method for generating high order nodal tetrahedral curved meshes the approach consists of modifying an initial linear mesh by first introducing high order nodes second displacing the boundary nodes to ensure that they are on the cad surface and third smoothing and untangling the mesh obtained after the displacement of the boundary nodes to produce a valid curved high order mesh the smoothing algorithm is based on the optimization of a regularized measure of the mesh distortion relative to the original linear mesh this means that whenever possible the resulting mesh preserves the geometrical features of the initial linear mesh such as shape stretching and size we present several examples to illustrate the performance of the proposed algorithm furthermore the examples show that the implementation of the optimization problem is robust and capable of handling situations in which the mesh before optimization contains a large number of invalid elements we consider cases with polynomial approximations up to degree ten large deformations of the curved boundaries concave boundaries and highly stretched boundary layer elements the meshes obtained are suitable for high order finite element analyses

nurbs enhanced finite element method nefem the development of nurbs enhanced finite element method nefem is revisited this technique allows a seamless integration of the cad boundary representation of the domain and the finite element method fem the importance of the geometrical model in finite element simulations is addressed and the benefits and potential of nefem are discussed and compared with respect to other curved finite element techniques

sign changing saddle point abstract in this paper the saddle point theorems are generalized to a new version by showing that there exists a sign changing saddle point besides zero the abstract result is applied to the semilinear elliptic boundary value problem u f x u in u 0 on and the schrodinger equation u v x u f x u x r n u x 0 as x where r n is a bounded domain with smooth boundary the schrodinger operator v has both eigenvalues and essential spectrum the asymptotically linear case is considered which permits double resonance to be happened some existence results of sign changing solutions are established

h p adaptive finite element methods in computational fluid dynamics the principal ideas of h p adaptive finite element methods for fluid dynamics problems are discussed applications include acoustics compressible euler and both compressible and incompressible navier stokes equations several numerical examples illustrate the presented concepts