reducing spurious dispersion anisotropy and reflection in finite element analysis of time harmonic acoustics abstract galerkin and stabilized galerkin least squares and galerkin gradient least squares finite element methods for solving problems of time harmonic acoustics are presented and analyzed the error of discretization is related to spurious representation of physical phenomena namely dispersion anisotropy and reflection all of which decrease with mesh refinement the performance of the stabilized methods in terms of dispersion and anisotropy is identical both are superior to the galerkin method relaxing wave resolution requirements further insight into the design of these methods is provided by the analyses the stabilized methods differ in the degree of spurious reflection that is engendered by transitions in mesh size the performance of galerkin gradient least squares deteriorates on non uniform meshes however galerkin least squares maintains its enhanced performance exhibiting low sensitivity to transitions in mesh size thereby reducing spurious dispersion anisotropy and reflection in finite element analysis of time harmonic acoustics guidelines for discretization pertaining to mesh orientation and wave resolution are presented

three dimensional element configurations for the discontinuous enrichment method for acoustics hexahedral and tetrahedral elements are proposed for the discontinuous enrichment method dem for boundary value problems governed by the helmholtz equation a procedure for obtaining sets of approximately uniform spherical enrichment directions with high flexibility in the choice of their number is constructed conditioning considerations indicate preferred representations of the oscillatory basis functions dispersion properties are used to rate the performance of different element configurations numerical tests assess accuracy indicating that high order dem elements exhibit little dispersion the dispersion and the numerical results are in a good agreement the proposed configurations of dem elements become more competitive as the number of enrichments and lagrange multipliers is increased copyright 2008 john wiley sons ltd

discontinuous galerkin methods with plane waves for the displacement based acoustic equation several special finite element methods have been proposed to solve helmholtz problems in the mid frequency regime such as the partition of unity method the ultra weak variational formulation and the discontinuous enrichment method the first main purpose of this paper is to present a discontinuous galerkin method with plane waves which is a variant of the discontinuous enrichment method to solve the displacement based acoustic equation the use of the displacement variable is often necessary in the context of fluid structure interactions a well known issue with this model is the presence of spurious vortical modes when one uses standard finite elements such as lagrange elements this problem also known as the locking phenomenon is observed with several other vector based equations such as incompressible elasticity and electromagnetism so this paper also aims at assessing if the special finite element methods suffer from the locking phenomenon in the context of the displacement acoustic equation the discontinuous galerkin method presented in this paper is shown to be very accurate and stable i e no spurious modes are observed the optimal choice of the various parameters are discussed with regards to numerical accuracy and conditioning some interesting properties of the mixed displacement pressure formulation are also presented furthermore the use of the partition of unity method is also presented but it is found that spurious vortical modes may appear with this method

the steinberg component of a finite group with a split b n pair let g g b n r u be a finite group with an unsaturated split b n pair of characteristic p prime and rank n 1 p b b here b uh is a semidirect product where u is a normal p subgroup of b and h is abelian with order prime to p the weyl group w n h is generated by the set r wi w of involutions we allow the intersection of the nconjugates of b to be larger than h i e c nntn n un 1 let v n w be the natural epimorphism with v w w for w e w let f be an algebraically closed field of characteristic y prime or zero we consider y f indc fu fgy where fl is f treated as a trivial umodule and y 10 1 let e end y for any subset t of g 1 ti denotes the cardinality of t t c r t e fg and tr gp tg for g e g in 4 steinberg defines the module fge where e i 1 w b and proves fge is simple when r 0 or r does not divide 1g bi in this paper we find the socle of the steinberg module in arbitrary characteristic by studying the indecomposable components of y in particular by examining what we call the steinberg component the author wishes to thank j a green for his many discussions on the subject matter of this paper

the ultra weak variational formulation for elastic wave problems the ultra weak variational formulation has been used effectively to solve time harmonic acoustic and electromagnetic wave propagation in inhomogeneous media we develop the ultra weak variational formulation for elastic wave propagation in two space dimensions in order to improve the accuracy and stability of the method we find it necessary to approximate the s and p wave components of the solution in a balanced way some preliminary analysis is provided and numerical evidence is presented for the efficiency of the scheme in comparison to piecewise linear finite elements

estimation of type 3 tobit models using symmetric trimming and pairwise comparisons abstract this paper considers estimation of the semiparametric type 3 tobit model we construct two step estimators that use the ideas of symmetric trimming and pairwise comparisons which have been proposed for the censored regression model by powell 1986 and honore and powell 1994 the estimators are consistent and asymptotically normal under two identifying assumptions conditional symmetry and independence between the errors and regressors the ideas and techniques are also implementable in other selection models that are variations of the basic type 3 tobit model we demonstrate this by applying the proposed method in estimating an empirical model considered by udry 1994

discontinuous galerkin methods with plane waves for time harmonic problems a general framework for discontinuous galerkin methods in the frequency domain with numerical flux is presented the main feature of the method is the use of plane waves instead of polynomials to approximate the solution in each element the method is formulated for a general system of linear hyperbolic equations and is applied to problems of aeroacoustic propagation by solving the two dimensional linearized euler equations it is found that the method requires only a small number of elements per wavelength to obtain accurate solutions and that it is more efficient than high order drp schemes in addition the conditioning of the method is found to be high but not critical in practice it is shown that the ultra weak variational formulation is in fact a subset of the present discontinuous galerkin method a special extension of the method is devised in order to deal with singular solutions generated by point sources like monopoles or dipoles aeroacoustic problems with non uniform flows are also considered and results are presented for the sound radiated from a two dimensional jet

properties of optimal forecasts under asymmetric loss and nonlinearity abstract evaluation of forecast optimality in economics and finance has almost exclusively been conducted under the assumption of mean squared error loss under this loss function optimal forecasts should be unbiased and forecast errors serially uncorrelated at the single period horizon with increasing variance as the forecast horizon grows using analytical results we show that standard properties of optimal forecasts can be invalid under asymmetric loss and nonlinear data generating processes and thus may be very misleading as a benchmark for an optimal forecast we establish instead that a suitable transformation of the forecast error known as the generalized forecast error possesses an equivalent set of properties the paper also provides empirical examples to illustrate the significance in practice of asymmetric loss and nonlinearities and discusses the effect of parameter estimation error on optimal forecasts

special short wave elements for flow acoustics a numerical formulation based on the partition of unity method pum is proposed for modelling the propagation of short acoustic waves on irrotational mean flows the method seeks to reduce the pollution error which exists in conventional fe schemes at high frequencies by using a local basis which is enriched by plane wave solutions of the convected helmholtz equation initially the method is demonstrated with reference to a one dimensional model consisting of a variable area converging diverging duct with mean flow next a simple two dimensional model of a straight duct with uniform flow is considered in both cases the accuracy and the conditioning of the numerical solution is investigated for ranges of frequency and mach number characteristic of aero engine bypass ducts

higher order extensions of a discontinuous galerkin method for mid frequency helmholtz problems recently a discontinuous galerkin method with plane wave basis functions and lagrange multiplier degrees of freedom was proposed for the efficient solution of helmholtz problems in the mid frequency regime in this paper this method is extended to higher order elements performance results obtained for various two dimensional problems highlight the advantages of these elements over classical higher order galerkin elements such as q2 and q4 for the discretization of interior and exterior helmholtz problems copyright 2004 john wiley sons ltd

an analysis of housing expenditure using semiparametric models and panel data in this paper we model expenditure on housing for owners and renters by means of endogenous switching regression models for panel data we explain the share of housing in total expenditure from a household specific effect family characteristics constant quality prices and total expenditure where the latter is allowed to be endogenous we consider both random and fixed effects panel data models we compare estimates for the random effects model with estimates for the linear panel data model in which selection only enters through the fixed effects and with estimates allowing for fixed effects and a more general type of selectivity differences appear to be substantial the results imply that the random effects model as well as the linear panel data model are too restrictive

an improved partition of unity finite element model for diffraction problems the partition of unity finite element method pufem is explored and improved to deal with practical diffraction problems efficiently the use of plane waves as an external function space allows an efficient implementation of an approximate exterior non reflective boundary condition improving the original proposed by higdon for general diffraction problems a virtually analytical integration procedure is introduced for multi dimensional high frequency problems which exhibits a dramatic decrease in the number of operations for a given error compared with standard integration methods suitable conjugate gradient type solvers for the whole range of wavenumbers are used including such cases in which pufem can produce nearly singular matrices caused by round off limits copyright 2001 john wiley sons ltd

application of an ultra weak variational formulation of elliptic pdes to the two dimensional helmholtz problem a new technique to solve elliptic linear pdes called ultra weak variational formulation uwvf in this paper is introduced in b despres c r acad sci paris 318 1994 pp 939 944 this paper is devoted to an evaluation of the potentialities of this technique it is applied to a model wave problem the two dimensional helmholtz problem the new method is presented in three parts following the same style of presentation as the classical one of the finite elements method even though they are definitely conceptually different methods the first part is committed to the variational formulation and to the continuous problem the second part defines the discretization process using a galerkin procedure the third part actually studies the efficiency of the technique from the order of convergence point of view this is achieved using theoretical proofs and a series of numerical experiments in particular it is proven and shown the order of convergence is lower bounded by a linear function of the number of degrees of freedom an application to scattering problems is presented in a fourth part

residual analysis in the grouped and censored normal linear model graphical and numerical analysis of residual can be informative about model misspecification even when data are censored or grouped this paper provides simple procedures for calculating diagnostic statistics to detect model misspecification when grouped or censored data are analysed using a normal linear model graphs can reveal the nature of the correlations that these statistics pick up but when grouping or censoring is severe they can be difficult to interpret we discuss the processing of graphs so that they are more easily interpreted and provide examples based on artificial data and on grouped data relating to unemployment durations

modelling of short wave diffraction problems using approximating systems of plane waves this paper describes a finite element model for the solution of helmholtz problems at higher frequencies that offers the possibility of computing many wavelengths in a single finite element the approach is based on partition of unity isoparametric elements at each finite element node the potential is expanded in a discrete series of planar waves each propagating at a specified angle these angles can be uniformly distributed or may be carefully chosen they can also be the same for all nodes of the studied mesh or may vary from one node to another the implemented approach is used to solve a few practical problems such as the diffraction of plane waves by cylinders and spheres the wave number is increased and the mesh remains unchanged until a single finite element contains many wavelengths in each spatial direction and therefore the dimension of the whole problem is greatly reduced issues related to the integration and the conditioning are also discussed

displacement pressure based mixed finite element formulations for acoustic fluid structure interaction problems summary we present reliable finite element discretizations based on displacement pressure interpolations for the analysis of acoustic fluid structure interaction problems the finite element interpolations are selected using the inf sup condition and emphasis is given to the fact that the boundary conditions must satisfy the mass and momentum conservation we show that with our analysis procedure no spurious non zero frequencies are encountered as heretofore calculated with other displacement based discretizations 1997 by john wiley sons ltd

score tests for zero covariances in recursive linear models for grouped or censored data abstract the score test statistic for testing whether an error covariance is zero is derived for a normal linear recursive model for fully observed censored or grouped data the test which is obtained by regarding non zero error covariances as arising from correlated random parameter variation is shown to be closely related to the information matrix test it turns out that the statistic which is asymptotically n 0 1 under the null examines the sample covariance of appropriately defined residuals

a monte carlo investigation of the sampling behavior of conditional moment tests in tobit and probit models this paper provides a monte carlo examination of conditional moment tests for several forms of misspecification in tobit and probit models the experimental design is based on actual data taken from a study of labor supply our results indicate that the tests work well in terms of size and power for the tobit model whereas they perform poorly for the probit model the major conclusion is that although there is little to choose between the various forms of the tests the degree of censoring of the latent dependent variable is crucial

contracting in space an application of spatial statistics to discrete choice models abstract we develop tests for spatial error correlation and methods of estimation in the presence of such correlation for discrete choice models the tests which are based on the notion of a generalized residual are a set of orthogonality conditions that should be satisfied under the null when the restrictions are rejected the full model can be estimated by generalized method of moments these techniques are used to evaluate spatial patterns in retail gasoline contracts we examine whether the spatial configuration is random or whether there is a tendency towards clustering or dispersion of contract types the data consist of all contracts between integrated oil companies and their branded service stations in the city of vancouver six metrics or measures of closeness are examined euclidean distance competition along streets a combination of the first two nearest neighbors along streets nearest neighbors in euclidean distance and neighbors that share a common marked boundary

the discontinuous enrichment method for multiscale analysis computation naturally separates scales of a problem according to the mesh size a variety of improved numerical methods are described by multiscale considerations differing in the treatment of the unresolved fine scales the discontinuous enrichment method provides a unique multiscale approach to computation by employing fine scales that contain solutions of the homogeneous partial differential equation in a discontinuous framework the method thus combines relative ease of implementation with improved numerical performance these properties are demonstrated for both multiscale wave and transport problems pointing to the potential of considerable savings in computational resources

a discontinuous galerkin method with lagrange multipliers for the solution of helmholtz problems in the mid frequency regime we present a discontinuous galerkin method dgm for the solution of the helmholtz equation in the mid frequency regime our approach is based on the discontinuous enrichment method in which the standard polynomial field is enriched within each finite element by a non conforming field that contains free space solutions of the homogeneous partial differential equation to be solved hence for the helmholtz equation the enrichment field is chosen here as the superposition of plane waves we enforce a weak continuity of these plane waves across the element interfaces by suitable lagrange multipliers preliminary results obtained for two dimensional model problems discretized by uniform meshes reveal that the proposed dgm enables the development of elements that are far more competitive than both the standard linear and the standard quadratic galerkin elements for the discretization of helmholtz problems

likelihood ratio specification tests misspecification tests for parametric models f y that examine data for failure of moment conditions implied by the maintained parametric distribution are interpreted as score tests of h 0 0 in the context of a parametric family of distributions r y this family contains the maintained distribution as a special case 0 and has the property that only in that special case do the chosen moment conditions hold a likelihood ratio test of h 0 0 therefore constitutes an alternative test of the validity of the moment conditions this test admits a bartlett correction unlike conventional moment tests for which adjustments based on second order asymptotic theory may behave badly the dependence of the bartlett correction and of the o n 1 2 local power of the test on the way in which r y is constructed is studied in many cases the correction can be made to vanish leading to a specification test whose distribution is chi square to order o p n 2

finite element computation of three dimensional elastoacoustic vibrations abstract in this paper the interior elastoacoustic problem in a 3d domain is solved displacement variables are used for both the fluid and the solid to avoid the typical spurious modes of this formulation a non standard discretization is used consisting of classical linear tetrahedral finite element for the solid and raviart thomas elements of lowest order for the fluid a new unknown is introduced on the interface between solid and fluid to impose the transmission conditions

computational aspects of the ultra weak variational formulation the ultra weak variational formulation uwvf approach has been proposed as an effective method for solving helmholtz problems with high wave numbers however for coarse meshes the method can suffer from instability in this paper we consider computational aspects of the ultra weak variational formulation for the inhomogeneous helmholtz problem we introduce a method to improve the uwvf scheme and we compare iterative solvers for the resulting linear system computations for the acoustic transmission problem in 2d show that the new approach enables helmholtz problems to be solved on a relatively coarse mesh for a wide range of wave numbers

the perfectly matched layer for the ultra weak variational formulation of the 3d helmholtz equation we investigate the feasibility of using the perfectly matched layer pml as an absorbing boundary condition for the ultra weak variational formulation uwvf of the 3d helmholtz equation the pml is derived using complex stretching of the spatial variables this leads to a modified helmholtz equation for which the uwvf can be derived in the standard discrete uwvf the approximating subspace is constructed from local solutions of the helmholtz equation in previous studies plane wave basis functions have been advocated because they simplify the building of the uwvf matrices for the pml domain we propose a special set of plane wave basis functions which allow fast computations and efficiently reduce spurious numerical reflections the method is validated by numerical experiments in comparison to a low order absorbing boundary condition the pml shows superior performance copyright 2004 john wiley sons ltd

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

the discontinuous enrichment method we propose a finite element based discretization method in which the standard polynomial field is enriched within each element by a nonconforming field that is added to it the enrichment contains free space solutions of the homogeneous differential equation that are not represented by the underlying polynomial field continuity of the enrichment across element interfaces is enforced weakly by lagrange multipliers in this manner we expect to attain high coarse mesh accuracy without significant degradation of conditioning assuring good performance of the computation at any mesh resolution examples of application to acoustics and advection diffusion are presented

graphical methods for assessing logistic regression models abstract in ordinary linear regression graphical diagnostic displays can be very useful for detecting and examining anomalous features in the fit of a model to data for logistic regression models the discreteness of binary data makes it difficult to interpret such displays modifications and extensions of linear model displays lead to three methods for diagnostic checking of logistic regression models local mean deviance plots are useful for detecting overall lack of fit empirical probability plots help point out isolated departures from the fitted model partial residual plots when smoothed to show underlying structure help identify specific causes of lack of fit these methods are illustrated through the analyses of simulated and real data

dispersion and pollution of the fem solution for the helmholtz equation in one two and three dimensions for high wave numbers the helmholtz equation suffers the so called pollution effect this effect is directly related to the dispersion a method to measure the dispersion on any numerical method related to the classical galerkin fem is presented this method does not require to compute the numerical solution of the problem and is extremely fast numerical results on the classical galerkin fem p method is compared to modified methods presented in the literature a study of the influence of the topology triangles is also carried out the efficiency of the different methods is compared the numerical results in two of the mesh and for square elements show that the high order elements control the dispersion well the most effective modified method is the qsfem 1 2 but it is also very complicated in the general setting the residual free bubble 3 4 is effective in one dimension but not in higher dimensions the least square method 1 5 approach lowers the dispersion but relatively little the results for triangular meshes show that the best topology is the criss cross pattern copyright 1999 john wiley sons ltd

estimation of a censored regression panel data model using conditional moment restrictions efficiently honore has introduced a semiparametric estimator for the censored regression panel data model with fixed individual effects newey has shown how to obtain efficient estimators under a given conditional moment restriction we apply newey s approach to obtain a two step gmm estimator which is more efficient than the honore estimator we compare this estimator to the honore estimator and to parametric estimators including chamberlain s quasi fixed effects estimator in a monte carlo experiment we also extend the honore estimator and the two step gmm estimator to the case of a balanced or unbalanced panel of more than two waves we apply the estimators to an empirical example concerning earnings of married females using data from the dutch socio economic panel

a note on maximum likelihood estimation for regression models using grouped data summary the estimation of parameters for a class of regression models using grouped or censored data is considered it is shown that with a simple reparameterization some commonly used distributions such as the normal and extreme value result in a log likelihood which is concave with respect to the transformed parameters apart from its theoretical implications for the existence and uniqueness of maximum likelihood estimates this result suggests minor changes to some commonly used algorithms for maximum likelihood estimation from grouped data two simple examples are given