regression based specification tests for the multinomial logit model abstract diagnostic tests for omitted variables or functional misspecification in the multinomial logit mnl model can be performed conveniently by testing the significance of auxiliary regressions of residuals on included and excluded variables in particular lagrange multiplier lm and hausman mcfadden hm tests of the independence from irrelevant alternatives iia property of the mnl model can be carried out by the regression method using suitably defined excluded variables using this method it is straightforward to test jointly against several sources of misspecification and to diagnose the structure of deviations from the mnl model

the chain collocation method a spectrally accurate calculus of forms preserving in the discrete realm the underlying geometric topological and algebraic structures at stake in partial differential equations has proven to be a fruitful guiding principle for numerical methods in a variety of fields such as elasticity electromagnetism or fluid mechanics however structure preserving methods have traditionally used spaces of piecewise polynomial basis functions for differential forms yet in many problems where solutions are smoothly varying in space a spectral numerical treatment is called for in an effort to provide structure preserving numerical tools with spectral accuracy on logically rectangular grids over periodic or bounded domains we present a spectral extension of the discrete exterior calculus dec with resulting computational tools extending well known collocation based spectral methods its efficient implementation using fast fourier transforms is provided as well

a spectral chebyshev method for linear stability analysis of one dimensional exact solutions of gas dynamics we present a spectral numerical method for solving one dimensional systems of partial differential equations pdes which arise from linearization of the euler equations about an exact solution depending on space and time a two domain chebyshev collocation method is used matching of quantities is performed in the space of characteristic variables as suggested by kopriva appl numer math 2 1986 221 j comput phys 125 1996 244 time dependent boundary conditions are handled following an approach proposed by thompson j comput phys 68 1987 1 89 1990 439 an exact numerical stability analysis valid for any explicit three step third order nondegenerate runge kutta scheme is provided the numerical method is tested against exact solutions for the three fundamental modes of a compressible flow entropy vorticity and acoustic modes

a quantile regression approach to generating prediction intervals exponential smoothing methods do not involve a formal procedure for identifying the underlying data generating process the issue is then whether prediction intervals should be estimated by a theoretical approach with the assumption that the method is optimal in some sense or by an emp irical procedure in this paper we present an alternative hybrid approach which applies quantile regression to the empirical fit errors to produce forecast error quantile models these models are functions of the lead time as suggested by the theoretical variance expressions in addition to avoiding the optimality assumption the method is nonparametric so there is no need for the common normality assumption application of the new approach to simple holt s and damped holt s exponential smoothing using simulated and real data sets gave encouraging results

specification tests based on artificial regressions abstract many specification tests can be computed with artificial linear regressions designed to be used as calculating devices to obtain test statistics and other quantities of interest this article discusses the general principles that underlie all artificial regressions and the use of such regressions to compute lagrange multiplier and other specification tests based on estimates under the null hypothesis the generality and power of artificial regressions as a means of computing test statistics is demonstrated how durbin wu hausman conditional moment and other tests that are not explicitly lagrange multiplier tests may be computed is shown and several special cases that illustrate the general results and can be useful in practice are discussed these include tests of parameter restrictions in nonlinear regression models and tests of binary choice models such as the logit and probit models

effects of the computational time step on numerical solutions of turbulent flow effects of large computational time steps on the computed turbulence were investigated using a fully implicit method in turbulent channel flow computations the largest computational time step in wall units which led to accurate prediction of turbulence statistics was determined turbulence fluctuations could not be sustained if the computational time step was near or larger than the kolmogorov time scale

a stable penalty method for the compressible navier stokes equations iii multidimensional domain decomposition schemes this paper concluding the trilogy develops schemes for the stable solution of wave dominated unsteady problems in general three dimensional domains the schemes utilize a spectral approximation in each subdomain and asymptotic stability of the semidiscrete schemes is established the complex computational domains are constructed by using nonoverlapping quadrilaterals in the two dimensional case and hexahedrals in the three dimensional space to illustrate the ideas underlying the multidomain method a stable scheme for the solution of the three dimensional linear advection diffusion equation in general curvilinear coordinates is developed the analysis suggests a novel yet simple stable treatment of geometric singularities like edges and vertices the theoretical results are supported by a two dimensional implementation of the scheme the main part of the paper is devoted to the development of a spectral multidomain scheme for the compressible navier stokes equations on conservation form and a unified approach for dealing with the open boundaries and subdomain boundaries is presented well posedness and asymptotic stability of the semidiscrete scheme is established in a general curvilinear volume with special attention given to a hexahedral domain the treatment includes a stable procedure for dealing with boundary conditions at a solid wall the efficacy of the scheme for the compressible navier stokes equations is illustrated by obtaining solutions to subsonic and supersonic boundary layer flows with various types of boundary conditions the results are found to agree with the solution of the compressible boundary layer equations

upwind differencing scheme for the time accurate incompressible navier stokes equations the two dimensional incompressible navier stokes equations are solved in a time accurate manner using the method of pseudocompres sibility using this method subiterations in pseudotime are required to satisfy the continuity equation at each time step an upwind differencing scheme based on flux difference splitting is used to compute the convective terms the upwind differencing is biased based on the sign of the local eigenvalue of the jacobian matrix of the convective fluxes both third order and fifth order differencing schemes are used on the convective fluxes throughout the grid s interior the equations are solved using an implicit line relaxation scheme this solution scheme is stable and is capable of running at large time steps in pseudo time leading to fast convergence for each physical time step a variety of computed results are presented to validate the present scheme results for the flow over an oscillating plate are compared with the exact analytic solution and good agreement is seen excellent comparison is obtained between the computed solution and the analytical results for inviscid channel flow with an oscillating back pressure flow solutions over a circular cylinder with vortex shedding are also presented finally the flow past an airfoil at 90 angle of attack is computed

simulation of incompressible viscous flows past a circular cylinder by hybrid fd scheme and meshless least square based finite difference method in this paper we describe an efficient method for simulating the two dimensional steady and unsteady incompressible flows the method is a hybrid approach which combines the conventional finite difference fd scheme and the meshfree least square based finite difference mlsfd method in this method the mlsfd method is adopted to deal with the complex geometry for its truly mesh free property and it is responsible for the spatial discretization in the region around the complex geometry which represents the stationary solid obstacle correspondingly conventional fd scheme is applied in the rest of the flow domain to take advantage of its high computational efficiency numerical simulation is carried out for the steady flow with reynolds numbers of 10 20 and 40 and unsteady flow with reynolds numbers of 100 and 200 the obtained numerical results agree very well with computational and experimental data available in the literature compared with the fully mlsfd method this new approach greatly improves the computational efficiency 2003 elsevier b v all rights reserved

multidomain spectral solution of the euler gas dynamics equations abstract we present interface treatments for computing the euler gas dynamics equations by a multidomain chebyshev spectral collocation method these treatments are suitable for use at the corners of subdomains and for patched or overlapping subdomains they can be applied to interfaces placed in subsonic supersonic or transonic regions of a flow computed results indicate that the solutions are spectrally accurate can be more accurate and more efficient than a single domain calculation and that reflections of waves at interfaces are not significant

mmc techniques for limited dependent variables models implementation by the branch and bound algorithm we propose a finite sample approach to some of the most common limited dependent variables models the method rests on the maximized monte carlo mmc test technique proposed by dufour 1998 monte carlo tests with nuisance parameters a general approach to finite sample inference and nonstandard asymptotics journal of econometrics this issue we provide a general way for implementing tests and confidence regions we show that the decision rule associated with a mmc test may be written as a mixed integer programming problem the branch and bound algorithm yields a global maximum in finite time an appropriate choice of the statistic yields a consistent test while fulfilling the level constraint for any sample size the technique is illustrated with numerical data for the logit model c 2005 elsevier b v all rights reserved

binary regression models for contaminated data on etudie la nature des observations aberrantes dans le contexte des donnees de regression binaires on propose un modele simple qui permet qu un petit nombre de reponses binaires soit mal enregistre

numerical simulation of transitional flow past a wing using flux reconstruction method in this paper the capabilities of a high order flux reconstruction scheme for the implicit large eddy simulations of a transitional flow at a low reynolds number of 60 000 around the sd7003 wing are examined this is the case posed in the first and second international workshops on the high order computational fluid dynamics method held in 2012 and 2013 the correction function used in the flux reconstruction scheme is the radau polynomial which is equivalent to the discontinuous galerkin scheme a time accurate implicit lower upper symmetric gauss seidel solution algorithm for the application of the flux reconstruction scheme to complex unsteady flows is developed and it is found to be able to produce comparable results to the explicit runge kutta scheme while achieving better computational efficiency simulations are carried out at 4 and 8 deg with polynomials of degree p 1 2 and 3 resulting in second third and fourth order accurate flux reconstruction schemes respectively two structured he

an efficient correction procedure via reconstruction for simulation of viscous flow on moving and deforming domains in this paper we report the development of a new parallel solver using the correction procedure via reconstruction cpr for viscous flows on moving and deforming grids by employing an accurate treatment of flux derivatives for moving and deforming unstructured grids consisting of all quadrilateral cells it is found that the geometric conservation law is not explicitly required the free stream preservation is automatically satisfied the cpr code is verified using a benchmark case for a moving inviscid vortex on moving and deforming grids the optimal orders of accuracy are obtained it is subsequently employed to study viscous flows on moving and deforming grids the cpr method is faster than and nearly as accurate as the sd method for solving viscous flow problems with moving boundaries

towards efficient tracking of inertial particles with high order multidomain methods this paper develops an efficient particle tracking algorithm to be used in fluid simulations approximated by a high order multidomain discretization of the navier stokes equations we discuss how to locate a particle s host subdomain how to interpolate the flow field to its location and how to integrate its motion in time a search algorithm for the nearest subdomain and quadrature point tuned to a typical quadrilateral isoparametric spectral subdomain takes advantage of the inverse of the linear blending equation we show that to compute particle laden flows a sixth order lagrangian polynomial that uses points solely within a subdomain is sufficiently accurate to interpolate the carrier phase variables to the particle position time integration of particles with a lower order adams bashforth scheme rather than the fourth order runge kutta scheme often used for the integration of the carrier phase increases computational efficiency while maintaining engineering accuracy we verify the tracking algorithm with numerical tests on a steady channel flow and an unsteady backward facing step flow

a simple efficient and high order accurate curved sliding mesh interface approach to spectral difference method on coupled rotating and stationary domains this paper presents a simple efficient and high order accurate sliding mesh interface approach to the spectral difference sd method we demonstrate the approach by solving the two dimensional compressible navier stokes equations on quadrilateral grids this approach is an extension of the straight mortar method originally designed for stationary domains 7 8 our sliding method creates curved dynamic mortars on sliding mesh interfaces to couple rotating and stationary domains on the nonconforming sliding mesh interfaces the related variables are first projected from cell faces to mortars to compute common fluxes and then the common fluxes are projected back from the mortars to the cell faces to ensure conservation to verify the spatial order of accuracy of the sliding mesh spectral difference ssd method both inviscid and viscous flow cases are tested it is shown that the ssd method preserves the high order accuracy of the sd method meanwhile the ssd method is found to be very efficient in terms of computational cost this novel sliding mesh interface method is very suitable for parallel processing with domain decomposition it can be applied to a wide range of problems such as the hydrodynamics of marine propellers the aerodynamics of rotorcraft wind turbines and oscillating wing power generators etc

small sample properties of probit model estimators abstract when maximum likelihood estimates of the coefficients in a nonlinear model such as the probit model are obtained there are a number of asymptotically equivalent covariance matrix estimators that can be used these covariance matrix estimators are typically associated with different computer algorithms for example with the newton raphson algorithm the inverse of the negative of the hessian matrix from the log likelihood function is used with the method of scoring the inverse of the information matrix is used and with a procedure proposed by berndt hall hall and hausman 1974 the inverse of the outer product of the first derivatives of the log likelihood function is used although these three estimators are asymptotically equivalent their performance can vary in finite samples the main objective of this article is to use a monte carlo experiment to investigate the finite sample properties of the three covariance matrix estimators in the context of maximum likelihood estimation of the pr

reduced navier stokes equations near a flow boundary we derive a hierarchy of pdes for the leading order evolution of wall based quantities such as the skin friction and the wall pressure gradient in two dimensional fluid flows the resulting reduced navier stokes rns equations are defined on the boundary of the flow and hence have reduced spatial dimensionality compared to the navier stokes equations this spatial reduction speeds up numerical computations and makes the equations attractive candidates for flow control design we prove that members of the rns hierarchy are well posed if appended with boundary conditions obtained from wall based sensors we also derive the lowest order rns equations for three dimensional flows for several benchmark problems our numerical simulations show close finite time agreement between the solutions of rns and those of the full navier stokes equations c 2006 elsevier b v all rights reserved

stable boundary conditions and difference schemas for navier stokes equations the navier stokes equations at high reynolds numbers can be viewed as an incompletely elliptic perturbation of the euler equations by using the entropy function for the euler equations as a measure of energy for the navier stokes equations we are able to obtain nonlinear energy estimates for the mixed initial boundary value problem these estimates are used to derive boundary conditions that guarantee l 2 boundedness even when the reynolds number tends to infinity finally we propose a new difference scheme for modeling the navier stokes equations in multidimensions for which we are able to obtain discrete energy estimates exactly analogous to those we obtained for the differential equation

a high order solver for unsteady incompressible navier stokes equations using the flux reconstruction method on unstructured grids with implicit dual time stepping we report development of a high order compact flux reconstruction method for solving unsteady incompressible flow on unstructured grids with implicit dual time stepping the method falls under the class of methods now referred to as flux reconstruction correction procedure via reconstruction the governing equations employ chorin s classic artificial compressibility formulation with dual time stepping to solve unsteady flow problems an implicit non linear lower upper symmetric gauss seidel scheme with backward euler discretization is used to efficiently march the solution in pseudo time while a second order backward euler discretization is used to march in physical time we verify and validate implementation of the high order method coupled with our implicit time stepping scheme using both steady and unsteady incompressible flow problems the current implicit time stepping scheme is proven effective in satisfying the divergence free constraint on the velocity field in the artificial compressibility formulation within the context of the high order flux reconstruction method this compact high order method is very suitable for parallel computing and can easily be extended to moving and deforming grids

a staggered grid multidomain spectral method for the compressible navier stokes equations we present a flexible non conforming staggered grid chebyshev spectral multidomain method for the solution of the compressible navier stokes equations in this method subdomain corners are not included in the approximation thereby simplifying the subdomain connectivity to allow for local refinement of the polynomial order or subdomain subdivision non conforming subdomains are treated by a mortar method spectral accuracy is shown in one and two dimensional linear and non linear problems application is made to four compressible flow problems the couette flow a steady boundary layer over a flat plate steady transonic flow in a nozzle and unsteady flow over a cylinder at a reynolds number of 75

a weak legendre collocation spectral method for the solution of the incompressible navier stokes equations in unstructured quadrilateral subdomains a weak legendre spectral method is developed for the solution of the primitive variable formulation of the unsteady incompressible navier stokes equations in general two dimensional and axisymmetric geometries a semi implicit projection method is utilized for the temporal approximation and for decoupling the velocity field from the pressure field a series of elliptic boundary value problems arises from the above procedure each of which is spatially discretized by a weak collocation method in multiple nonoverlapping subdomains in particular a modified variational formulation of the partial differential equations is presented which leads after discretization to a weak multidomain approximation of the corresponding problems a weak formalism for the influence matrix technique is also developed which is consistent with the spatial discretization scheme and successfully separate the equations for the internal nodes from the ones governing the interface unknowns a method of dealing with the singularity problem faced by the weak formulation at axisymmetric problems is proposed while a combination of direct methods is studied for tackling effectively the linear algebraic systems resulting from the full discretization exponential convergence is demonstrated for a plethora of stokes and navier stokes simulations

a maximum entropy approach to recovering information from multinomial response data abstract the classical maximum entropy me approach to estimating the unknown parameters of a multinomial discrete choice problem which is equivalent to the maximum likelihood multinomial logit ml estimator is generalized the generalized maximum entropy gme model includes noise terms in the multinomial information constraints each noise term is modeled as the mean of a finite set of a priori known points in the interval 1 1 with unknown probabilities where no parametric assumptions about the error distribution are made a gme model for the multinomial probabilities and for the distributions associated with the noise terms is derived by maximizing the joint entropy of multinomial and noise distributions under the assumption of independence the gme formulation reduces to the me in the limit as the sample grows large or when no noise is included in the entropy maximization further even though the gme and the logit estimators are conceptually different the dual gme model is related to a gener

an adaptive filtering procedure for estimating regression quantiles applications of reliability theory and some forms of chance constrained programming need real time nonstationary estimates of regression quantiles to trigger preventive actions thereby avoiding undesirable system states we have designed the quantile estimation procedure qep for this purpose qep is a new adaptive filter that nonparametrica11y estimates time varying parameters of multivariate regression quantiles results of monte carlo tests show that qep provides accurate estimates for a range of stochastic processes falling within this range is the case study of this paper on monitoring compliance with short term air quality standards

unsteady solution of incompressible navier stokes equations abstract a new time accurate finite difference numerical method for solving incompressible navier stokes equations is presented with primitive variables as the unknowns the numerical scheme is a crank nicolson implicit treatment of all terms of the equations with central differencing for space derivatives the pressure and the nonlinearities in convection terms are not lagged to obtain the incompressible solution at the advanced time level a continuous auxiliary system is introduced in pseudo time with artificial compressibility time accurate solutions are presented for two dimensional fluid flows in a square cavity with an impulsively starting lid and with an oscillating lid

a second order projection method for the incompressible navier stokes equations in this paper we describe a second order projection method for the time dependent incom pressible navier stokes equations as in the original projection method developed by chorin we first solve diffusion convection equations to predict intermediate velocities which are then projected onto the space of divergence free vector fields by introducing more coupling between the diffusion onvection step and the projection step we obtain a temporal discretiza tion that is second order accurate our treatment of the diffusion convection step uses a specialized higher order godunov method for differencing the nonlinear convective terms that provides a robust treatment of these terms at high reynolds number the godunov procedure is second order accurate for smooth flow and remains stable for discontinuous initial data even in the zero viscosity limit we approximate the projection directly using a galerkin procedure that uses a local basis for discretely divergence free vector fields numerical results are presented validating the convergence properties of the method we also apply the method to doubly periodic shear layers to assess the performance of the method on more difficult

estimation and testing in the random effects probit model abstract this paper examines the finite sample properties of the random effects probit estimator in comparison to the standard probit estimator and the standard probit estimator with a corrected asymptotic covariance matrix the monte carlo experiment considers data generating processes consistent with longitudinal data and also data from sample surveys the probit estimator with corrected asymptotic covariance matrix works surprisingly well over a wide range of parametric configurations and is recommended as long as an estimate of the error correlation is not of high importance

a spectrally accurate method for overlapping grid solution of incompressible navier stokes equations an overlapping mesh methodology that is spectrally accurate in space and up to third order accurate in time is developed for solution of unsteady incompressible flow equations in three dimensional domains the ability to decompose a global domain into separate but overlapping subdomains eases mesh generation procedures and increases flexibility of modeling flows with complex geometries the methodology employs implicit spectral element discretization of equations in each subdomain and explicit treatment of subdomain interfaces with spectrally accurate spatial interpolation and high order accurate temporal extrapolation and requires few if any iterations yet maintains the global accuracy and stability of the underlying flow solver the overlapping mesh methodology is thoroughly validated using two dimensional and three dimensional benchmark problems in laminar and turbulent flows the spatial and temporal convergence is documented and is in agreement with the nominal order of accuracy of the solver the influence of long integration times as well as inflow outflow global boundary conditions on the performance of the overlapping grid solver is assessed in a turbulent benchmark of fully developed turbulent pipe flow the turbulent statistics with the overlapping grids is validated against published available experimental and other computation data scaling tests are presented that show near linear strong scaling even for moderately large processor counts a novel overlapping grid method for incompressible flow equations is developed the overlapping grid method is based on spectral element discretization the method maintains global spectral accuracy with polynomial refinement an explicit interface extrapolation scheme for temporal coupling is proposed the scheme allows for high order temporal accuracy with only a few iterations

bayesian analysis of binary and polychotomous response data abstract a vast literature in statistics biometrics and econometrics is concerned with the analysis of binary and polychotomous response data the classical approach fits a categorical response regression model using maximum likelihood and inferences about the model are based on the associated asymptotic theory the accuracy of classical confidence statements is questionable for small sample sizes in this article exact bayesian methods for modeling categorical response data are developed using the idea of data augmentation the general approach can be summarized as follows the probit regression model for binary outcomes is seen to have an underlying normal regression structure on latent continuous data values of the latent data can be simulated from suitable truncated normal distributions if the latent data are known then the posterior distribution of the parameters can be computed using standard results for normal linear models draws from this posterior are used to sample new latent data and t

duration response measurement error the impact of response measurement error in duration data is investigated using small parameter asymptotic approximations and compared with the effect of hazard function heterogeneity the approximations lead to a specification test to detect measurement error which is shown to be related to the class of information matrix tests it is shown that in a commonly used class of models the test statistic is exactly pivotal the second order asymptotic properties of the alternative forms of the test statistic are derived and the quality of the approximations and the performance of the test are investigated via monte carlo experimentation

a direct solver for variable coefficient elliptic pdes discretized via a composite spectral collocation method a numerical method for variable coefficient elliptic problems on two dimensional domains is presented the method is based on high order spectral approximations and is designed for problems with smooth solutions the resulting system of linear equations is solved using a direct solver with o n 1 5 complexity for the pre computation and o nlogn complexity for the solve the fact that the solver is direct is a principal feature of the scheme and makes it particularly well suited to solving problems for which iterative solvers struggle in particular for problems with highly oscillatory solutions numerical examples demonstrate that the scheme is fast and highly accurate for instance using a discretization with 12 points per wavelength a helmholtz problem on a domain of size 100x100 wavelengths was solved to ten correct digits the computation was executed on a standard laptop it involved 1 6m degrees of freedom and required 100 s for the pre computation and 0 3 s for the actual solve

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

an artificial compressibility flux for the discontinuous galerkin solution of the incompressible navier stokes equations discontinuous galerkin dg methods have proved to be well suited for the construction of robust high order numerical schemes on unstructured and possibly nonconforming grids for a variety of problems their application to the incompressible navier stokes ins equations has also been recently considered although the subject is far from being fully explored in this work we propose a new approach for the dg numerical solution of the ins equations written in conservation form the inviscid numerical fluxes both in the continuity and in the momentum equation are computed using the values of velocity and pressure provided by the exact solution of the riemann problem associated with a local artificial compressibility perturbation of the equations unlike in most of the existing methods artificial compressibility is here introduced only at the interface flux level therefore resulting in a consistent discretization of the ins equations irrespectively of the amount of artificial compressibility introduced the discretization of the viscous term follows the well established dg scheme named br2 the performance and the accuracy of the method are demonstrated by computing the kovasznay flow and the two dimensional lid driven cavity flow for a wide range of reynolds numbers and for various degrees of polynomial approximation

preconditioned multigrid methods for unsteady incompressible flows a highly efficient numerical approach based on multigrid and preconditioning methods is developed for modeling 3d steady and time dependent incompressible flows thek turbulence model is used to estimate the effects of turbulence the model equations are solved together with the n s equations in a strongly coupled way and acceleration techniques like the multigrid method are also used for the turbulence model equations for unsteady problems a dual time stepping procedure is adopted to satisfy the divergence free constraint and to obtain a time accurate solution to improve the performance of this approach for small physical time steps a modification to residual smoothing parameters is proposed the numerical algorithm and the turbulence model are validated first by calculating unsteady inviscid flow around an oscillating cylinder unsteady laminar flow past a circular cylinder and steady high reynolds number turbulent flow over a 6 1 prolate spheroid then the three dimensional time dependent turbulent flow over a spheroid when it is undergoing a pitch up maneuver is calculated and compared with experimental data

empirically relevant critical values for hypothesis tests a bootstrap approach tests of statistical hypotheses can be based on either of two critical values the type i critical value or the size corrected critical value the former usually depends on unknown population parameters and cannot be evaluated exactly in applications but it can often be estimated very accurately by using the bootstrap the latter does not depend on unknown population parameters but is likely to yield a test with low power the critical values used in most monte carlo studies of the powers of tests are neither type i nor size corrected they are irrelevant to empirical research

the power of bootstrap and asymptotic tests the bootstrap discrepancy measures the difference in rejection probabilities between a bootstrap test and one based on the true distribution the order of magnitude of the bootstrap discrepancy is the same under the null hypothesis and under non null processes described by pitman drift if the test statistic is not an exact pivot critical values depend on which data generating process dgp is used to determine the null distribution we propose using the dgp which minimizes the bootstrap discrepancy we also show that under an asymptotic independence condition the power of both bootstrap and asymptotic tests can be estimated cheaply by simulation

a stable penalty method for the compressible navier stokes equations i open boundary conditions the purpose of this paper is to present asymptotically stable open boundary conditions for the numerical approximation of the compressible navier stokes equations in three spatial dimensions the treatment uses the conservation form of the navier stokes equations and utilizes linearization and localization at the boundaries based on these variables the proposed boundary conditions are applied through a penalty procedure thus ensuring correct behavior of the scheme as the reynolds number tends to infinity the versatility of this method is demonstrated for the problem of a compressible flow past a circular cylinder

convenient specification tests for logit and probit models abstract we propose several lagrange multiplier tests of logit and probit models which may be inexpen sively computed by means of artificial linear regressions these maybe used to test for various forms of model inadequacy including the omission of specified variables and heteroskedasticity of known form we perform a number of sampling experiments in which we compare the small sam ple properties of these tests and of likelihood ratio tests one of the lm tests turns out to have better small sample properties than any of the others we then investigate the power of the tests against local alternatives and conduct a further series of sampling experiments to compare the power of various tests

dynamic mode extrapolation to improve the efficiency of dual time stepping method abstract this work proposes a methodology to improve the computational efficiency of unsteady flow simulations with dual time stepping scheme the methodology is developed on the combination of dynamic mode extrapolation and dual time stepping scheme it accelerates the convergence speed of the inner iterations by using dynamic mode extrapolation to provide an initial solution for each physical time step the validation and verification are demonstrated by three cases including unsteady flow past a stationary circular cylinder at re 200 transonic flow over periodic and non periodic pitching naca 0012 airfoil and buffeting flow around nasa sc 0714 airfoil for comparison lagrange extrapolation initial condition and natural initial condition are also applied the results confirm that the proposed methodology is very successful in reducing computational time for both incompressible and transonic unsteady flow

multidomain spectral solution of compressible viscous flows abstract we develop a nonoverlapping multidomain spectral collocation method to solve compressible viscous flows at the interfaces the advection terms are treated with a characteristic correction method the diffusion terms are treated with a penalty method spectral accuracy is demonstrated on linear model problems in one and two space dimensions the method is applied to a subsonic and a supersonic flow over a flat plate the results are compared to solutions of the boundary layer equations which show that two digit accuracy in the adiabatic plate temperature is obtained with 16 points in the boundary layer for a freestream mach number of two a second application is to a transonic flow in a two dimensional converging diverging nozzle where the computed results are compared to experimental data

a strategy for the efficient simulation of viscous compressible flows using a multi domain pseudospectral method abstract a new multi domain pseudospectral method is developed to simulate viscous compressible flow in a quasi one dimensional nozzle the flow variables at the interface points are advanced in time using the same second order time marching scheme as the interior points the spatial derivatives of the inviscid flux vector are evaluated at the interface points using a spectrally accurate modification of van leer s flux vector splitting method the derivatives of the viscous flux vector are evaluated alternately from neighboring sub domains the scheme is found to be spectrally accurate shock waves are resolved without oscillations for moderate reynolds numbers

a direct solver with o n complexity for variable coefficient elliptic pdes discretized via a high order composite spectral collocation method a numerical method for solving elliptic pdes with variable coefficients on two dimensional domains is presented the method is based on high order composite spectral approximations and is designed for problems with smooth solutions the resulting system of linear equations is solved using a direct as opposed to iterative solver that has optimal o n complexity for all stages of the computation when applied to problems with nonoscillatory solutions such as the laplace and the stokes equations numerical examples demonstrate that the scheme is capable of computing solutions with a relative accuracy of 10 10 or better for challenging problems such as highly oscillatory helmholtz problems and convection dominated convection diffusion equations in terms of speed it is demonstrated that a problem with a nonoscillatory solution that was discretized using 10 8 nodes can be solved in 115 minutes on a personal workstation with two quad core 3 3 ghz cpus since the solver is direct and the solution

computation of electromagnetic scattering with a non conforming discontinuous spectral element method in this paper we solve electromagnetic scattering problems by approximating maxwell s equations in the time domain with a high order quadrilateral discontinuous spectral element method dsem the method is a collocation form of the discontinuous galerkin method for hyperbolic systems where the solution is approximated by a tensor product legendre expansion and inner products are replaced with gauss legendre quadratures to increase flexibility of the method we use a mortar element method to couple element faces mortars provide a means for coupling element faces along which the polynomial orders differ which allows the flexibility to choose the approximation order within an element by considering only local resolution requirements mortars also permit local subdivision of a mesh by connecting element faces that do not share a full side we present evidence showing that the convergence of the non conforming approximations is spectral along with examples of their use copyright 2001 john wiley sons ltd

a high order discontinuous galerkin method for the unsteady incompressible navier stokes equations we present a high order discontinuous galerkin discretization of the unsteady incompressible navier stokes equations in convection dominated flows using triangular and tetrahedral meshes the scheme is based on a semi explicit temporal discretization with explicit treatment of the nonlinear term and implicit treatment of the stokes operator the nonlinear term is discretized in divergence form by using the local lax friedrichs fluxes thus local conservativity is inherent spatial discretization of the stokes operator has employed both equal order p k p k and mixed order p k p k 1 velocity and pressure approximations a second order approximate algebraic splitting is used to decouple the velocity and pressure calculations leading to an algebraic helmholtz equation for each component of the velocity and a consistent poisson equation for the pressure the consistent poisson operator is replaced by an equivalent in stability and convergence operator namely that arising from the interior penalty discretization of the standard poisson operator with appropriate boundary conditions this yields a simpler and more efficient method characterized by a compact stencil size we show the temporal and spatial behavior of the method by solving some popular benchmarking tests for an unsteady stokes problem second order temporal convergence is obtained while for the taylor vortex test problem on both semi structured and fully unstructured triangular meshes spectral convergence with respect to the polynomial degree k is obtained by studying the orr sommerfeld stability problem we demonstrate that the p k p k method yields a stable solution while the p k p k 1 formulation leads to unphysical instability the good performance of the method is further shown by simulating vortex shedding in flow past a square cylinder we conclude that the proposed discontinuous galerkin method with the p k p k formulation is an efficient scheme for accurate and stable solution of the unsteady navier stokes equations in convection dominated flows

a conservative staggered grid chebyshev multidomain method for compressible flows we present a new multidomain spectral collocation method that uses a staggered grid for the solution of compressible flow problems the solution unknowns are defined at the nodes of a gauss quadrature rule the fluxes are evaluated at the nodes of a gauss lobatto rule the method is conservative free stream preserving and exponentially accurate a significant advantage of the method is that subdomain corners are not included in the approximation making solutions in complex geometries easier to compute

short note a comparison of computational efficiencies of spectral difference method and correction procedure via reconstruction we report computational efficiencies of two types of numerical solvers the first type uses the spectral difference sd method and the second one uses the correction procedure via reconstruction cpr in this paper we employ the lumped g 2 scheme proposed by huynh as an example of the cpr approach the solvers deal with both inviscid euler equations and navier stokes equations on 2d unstructured grids which are comprised of all quadrilateral cells both types of solvers are programmed using fortran 90 with similar management of data structures we employ identical time marching schemes for both sd and cpr methods spatial 3rd and 4th order of accuracy for both methods is demonstrated by a study of a moving inviscid vortex the comparisons were directed to measure the computational efficiency of both sd and cpr methods in spatial discretization with respect to the fourth order methods cpr is 27 faster than sd for inviscid flow and more promisingly cpr is over 40 faster than sd for viscous flow

the compact discontinuous galerkin cdg method for elliptic problems we present a compact discontinuous galerkin cdg method for an elliptic model problem the problem is first cast as a system of first order equations by introducing the gradient of the primal unknown or flux as an additional variable a standard discontinuous galerkin dg method is then applied to the resulting system of equations the numerical interelement fluxes are such that the equations for the additional variable can be eliminated at the element level thus resulting in a global system that involves only the original unknown variable the proposed method is closely related to the local discontinuous galerkin ldg method b cockburn and c w shu siam j numer anal 35 1998 pp 2440 2463 but unlike the ldg method the sparsity pattern of the cdg method involves only nearest neighbors also unlike the ldg method the cdg method works without stabilization for an arbitrary orientation of the element interfaces the computation of the numerical interface fluxes for the cdg method is slightly more involved than for the ldg method but this additional complication is clearly offset by increased compactness and flexibility compared to the br2 f bassi and s rebay j comput phys 131 1997 pp 267 279 and ip j douglas jr and t dupont in computing methods in applied sciences second internat sympos versailles 1975 lecture notes in phys 58 springer berlin 1976 pp 207 216 methods which are known to be compact the present method produces fewer nonzero elements in the matrix and is computationally more efficient

an entropy stable discontinuous galerkin approximation for the incompressible navier stokes equations with variable density and artificial compressibility abstract we present a provably stable discontinuous galerkin spectral element method for the incompressible navier stokes equations with artificial compressibility and variable density stability proofs which include boundary conditions that follow a continuous entropy analysis are provided we define a mathematical entropy function that combines the traditional kinetic energy and an additional energy term for the artificial compressibility and derive its associated entropy conservation law the latter allows us to construct a provably stable split form nodal discontinuous galerkin dg approximation that satisfies the summation by parts simultaneous approximation term sbp sat property the scheme and the stability proof are presented for general curvilinear three dimensional hexahedral meshes we use the exact riemann solver and the bassi rebay 1 br1 scheme at the inter element boundaries for inviscid and viscous fluxes respectively and an explicit low storage runge kutta rk3 scheme to integrate in time we assess the accuracy and robustness of the method by solving a manufactured solution the kovasznay flow a lid driven cavity the inviscid taylor green vortex and the rayleigh taylor instability

a conservative staggered grid chebyshev multidomain method for compressible flows ii a semi structured method we present a chebyshev multidomain method that can solve systems of hyperbolic equations in conservation form on an unrestricted quadrilateral subdivision of a domain within each subdomain the solutions and fluxes are approximated by a staggered grid chebyshev method thus the method is unstructured in terms of the subdomain decomposition but strongly structured within the subdomains communication between subdomains is done by a mortar method in such a way that the method is globally conservative the method is applied to both linear and nonlinear test problems and spectral accuracy is demonstrated

predicting binary outcomes we address the issue of using a set of covariates to categorize or predict a binary outcome this is a common problem in many disciplines including economics in the context of a prespecified utility or cost function we examine the construction of forecasts suggesting an extension of the manski 1975 1985 maximum score approach we provide analytical properties of the method and compare it to more common approaches such as forecasts or classifications based on conditional probability models the results are informative for both forecasting environments as well as program allocation where the value of including the participant in the program depends on how useful the program turns out to be for that participant