comparative study on accuracy and conservation properties of two particle regularization schemes and proposal of an optimized particle shifting scheme in isph context abstract the paper provides a comparative investigation on accuracy and conservation properties of two particle regularization schemes namely the dynamic stabilization ds 1 and generalized particle shifting ps 2 schemes in simulations of both internal and free surface flows in isph incompressible sph context the paper also presents an optimized ps ops scheme for accurate and consistent implementation of particle shifting for free surface flows in contrast to ps the ops does not contain any tuning parameters for free surface consistently resulting in perfect elimination of shifting normal to an interface and resolves the unphysical discontinuity beneath the interface seen in ps results

unconditional stability of corrected explicit implicit domain decomposition algorithms for parallel approximation of heat equations a class of corrected explicit implicit domain decomposition ceidd methods is investigated for the parallel approximation of linear heat equations explicit implicit domain decomposition eidd methods are computationally and communicationally efficient for each time step but always suffer from small time step size restrictions by adding an interface correction step to kuznetsov s eidd the one dimensional ceidd procedure achieves unconditional stability without discarding the time stepwise efficiency of the eidd method in order to maintain the virtues of the ceidd method and improve the flexibility in domain partitioning for solving multidimensional problems special zigzag shaped interfaces are suggested in the ceidd method based on noncrossover and crossover types of zigzag interfaces the resulting ceidd zi algorithms are studied for two strategies of subdomain partition by the energy method it shows that the proposed algorithms including their degenerate cases the corrected explicit hopscotch schemes are convergent in the discrete h1 semi norm and l2 norm numerical experiments confirm the results in our analysis

smoothness priors and nonlinear regression abstract smoothness priors represent prior information that an unknown function does not change slope quickly and hence that the function describes a simple curve e g wahba 1978 in this article such priors for the multiple nonlinear regression model are developed in such a way that estimates and standard errors can be obtained as a natural and conceptually straightforward extension of linear multiple regression estimation with the addition of dummy variables and dummy observations relations to spline and polynomial interpolation are described an illustrative example of cost function estimation is provided

unconditional stability of parallel difference schemes with second order accuracy for parabolic equation in this paper we investigate the parallel difference schemes of parabolic equation in particular two kinds of difference schemes with intrinsic parallelism are constructed firstly we combine the values of previous two time levels at the interface points to get the dirichlet boundary condition for the sub domain problems then the values in the sub domains are calculated by fully implicit scheme and then finally the values at the interface points are computed by fully implicit scheme the unconditional stability of these schemes is proved and the convergence rate of second order is also obtained numerical results are presented to examine the accuracy stability and parallelism of the parallel schemes

efficient statistical inference procedures for partially nonlinear models and their applications motivated by an analysis of a real data set in ecology we consider a class of partially nonlinear models where both a nonparametric component and a parametric component are present we develop two new estimation procedures to estimate the parameters in the parametric component consistency and asymptotic normality of the resulting estimators are established we further propose an estimation procedure and a generalized f test procedure for the nonparametric component in the partially nonlinear models asymptotic properties of the newly proposed estimation procedure and the test statistic are derived finite sample performance of the proposed inference procedures are assessed by monte carlo simulation studies an application in ecology is used to illustrate the proposed methods

estimation for a partial linear single index model in this paper we study the estimation for a partial linear single index model a two stage estimation procedure is proposed to estimate the link function for the single index and the parameters in the single index as well as the parameters in the linear component of the model asymptotic normality is established for both parametric components for the index a constrained estimating equation leads to an asymptotically more efficient estimator than existing estimators in the sense that it is of a smaller limiting variance the estimator of the nonparametric link function achieves optimal convergence rates and the structural error variance is obtained in addition the results facilitate the construction of confidence regions and hypothesis testing for the unknown parameters a simulation study is performed and an application to a real dataset is illustrated the extension to multiple indices is briefly sketched

semiparametric inference in a partial linear model in a partial linear model the dependence of a response variate y on covariates w x is given by y w x e where e is independent of w x with densities g and f respectively in this paper an asymptotically efficient estimator of is constructed solely under mild smoothness assumptions on the unknown f and g thereby removing the assumption of finite residual variance on which all least squares type estimators available in the literature are based

a stabilized explicit lagrange multiplier based domain decomposition method for parabolic problems a fully explicit stabilized domain decomposition method for solving moderately stiff parabolic partial differential equations pdes is presented writing the semi discretized equations as a differential algebraic equation dae system where the interface continuity constraints between subdomains are enforced by lagrange multipliers the method uses the runge kutta chebyshev projection scheme to integrate the dae explicitly and to enforce the constraints by a projection with mass lumping techniques and node to node matching grids the method is fully explicit without solving any linear system a stability analysis is presented to show the extended stability property of the method the method is straightforward to implement and to parallelize numerical results demonstrate that it has excellent performance

towards consistence and convergence of conservative sph approximations typical conservative smoothed particle hydrodynamics sph approximations of the gradient of a scalar field introduce two errors one smoothing error is due to smoothing of the gradient by an integration associated with a kernel function the other integration error is due to approximating the integration by summation over all particles within the kernel support when particles are not on a uniform grid the integration error leads to violation of zero order consistency i e the inability to reproduce a constant field in this paper we confirm that partition of unity is the condition under which the conservative sph approximation achieves both consistence and convergence we show that this condition can be achieved by relaxing a particle distribution under a constant pressure field and invariant particle volume the resulting particle distribution is very similar to that is typical for liquid molecules we further show that with two different typical kernel functions the sph approximation upon satisfying the partition of unity property is able to achieve very high order of the integration error which previously could be shown only with particles on a uniform grid the background pressure used in a weakly compressible sph simulation implies a self relaxation mechanism which explains that convergence with respect to increasing particle numbers could be obtained in sph simulations although not predicted by previous numerical analysis furthermore by relating the integration error to the background pressure we explain why the previously proposed transport velocity formulation of sph s adami et al 2013 1 is able to achieve unprecedented accuracy and stability

positive shrinkage improved pretest and absolute penalty estimators in partially linear models shrinkage estimators of a partially linear regression parameter vector are constructed by shrinking estimators in the direction of the estimate which is appropriate when the regression parameters are restricted to a linear subspace we investigate the asymptotic properties of positive stein type and improved pretest semiparametric estimators under quadratic loss under an asymptotic distributional quadratic risk criterion their relative dominance picture is explored analytically it is shown that positive stein type semiparametric estimators perform better than the usual stein type and least square semiparametric estimators and that an improved pretest semiparametric estimator is superior to the usual pretest semiparametric estimator we also consider an absolute penalty type estimator for partially linear models and give a monte carlo simulation comparisons of positive shrinkage improved pretest and the absolute penalty type estimators the comparison shows that the shrinkage method performs better than the absolute penalty type estimation method when the dimension of the parameter space is much larger than that of the linear subspace

sliced inverse regression for dimension reduction abstract modern advances in computing power have greatly widened scientists scope in gathering and investigating information from many variables information which might have been ignored in the past yet to effectively scan a large pool of variables is not an easy task although our ability to interact with data has been much enhanced by recent innovations in dynamic graphics in this article we propose a novel data analytic tool sliced inverse regression sir for reducing the dimension of the input variable x without going through any parametric or nonparametric model fitting process this method explores the simplicity of the inverse view of regression that is instead of regressing the univariate output variable y against the multivariate x we regress x against y forward regression and inverse regression are connected by a theorem that motivates this method the theoretical properties of sir are investigated under a model of the form y f 1 x k x e where the k s are the unknown

second order approximation in the partially linear regression model we examine the second order properties of various quantities of interest in the partially linear regression model we obtain a stochastic expansion with remainder op n 2 4 where u 1 2 for the standardized semiparametric least squares estimator a standard error estimator and a studentized statistic we use the second order expansions to correct the standard error estimates for second order effects and to define a method of bandwidth choice a monte carlo experiment provides favorable evidence on our method of bandwidth choice

testing the parametric null model hypothesis in semiparametric partial and generalized spline models on etend les resultats de cox et koh 1986 aux modeles generalises de wahba 1985 et a divers autres modeles splines partiels on montre que la statistique de test a une relation etroite avec le comportement de la fonction de validation croisee generalisee

stabilized explicit implicit domain decomposition methods for the numerical solution of parabolic equations we report a class of stabilized explicit implicit domain decomposition seidd methods for the numerical solution of parabolic equations explicit implicit domain decomposition eidd methods are globally noniterative nonoverlapping domain decomposition methods which when compared with schwarz algorithm based parabolic solvers are computationally and communicationally efficient for each simulation time step but suffer from small time step size restrictions by adding a stabilization step to eidd the seidd methods retain the time stepwise efficiency in computation and communication of the eidd methods but exhibit much better numerical stability three seidd algorithms are presented in this paper which are experimentally tested to show excellent stability computation and communication efficiencies and high parallel speedup and scalability

the new mass conserving s ddm scheme for two dimensional parabolic equations with variable coefficients abstract in the article a new and efficient mass conserving operator splitting domain decomposition method s ddm is proposed and analyzed for solving two dimensional variable coefficient parabolic equations with reaction term the domain is divided into multiple non overlapping block divided subdomains on each block divided subdomain the interface fluxes are first computed explicitly by local multi point weighted schemes and the solutions in the interior of subdomain are computed by the one directional operator splitting implicit schemes at each time step the scheme is proved to satisfy mass conservation over the whole domain of domain decomposition by combining with some auxiliary lemmas and applying the energy method we analyze theoretically the stability of our scheme and prove it to have second order accuracy in space step in the l2 norm numerical experiments are performed to illustrate its accuracy conservation stability efficiency and parallelism our scheme not only keeps the excellent advantages of the non overlapping domain decomposition and the operator splitting technique but also preserves the global mass

explicit implicit conservative domain decomposition procedures for parabolic problems based on block centered finite differences domain decomposition procedures for solving parabolic equations are considered the underlying discretization consists of block centered finite differences in these procedures fluxes at subdomain interfaces are calculated from the solution at the previous time level these fluxes serve as neumann boundary data for implicit block centered discretizations in the subdomains a priori error estimates are presented and numerical results examining the stability accuracy and parallelism of the scheme are presented

an efficient s ddm iterative approach for compressible contamination fluid flows in porous media in this paper we develop an efficient splitting domain decomposition method s ddm for compressible contamination fluid flows in porous media over multiple block divided sub domains by combining the non overlapping domain decomposition splitting linearization and extrapolation techniques the proposed s ddm iterative approach divides the large domain into multiple block sub domains in each time interval the s ddm scheme is applied to solve the water head equation in which an efficient local multilevel scheme is used for computing the values of water head on the interfaces of sub domains and the splitting implicit scheme is used for computing the interior values of water head in sub domains and the s ddm scheme is then proposed to solve the concentration equation by combining the upstream volume technique numerical experiments are performed and analyzed to illustrate the efficiency of the s ddm iterative approach for simulating compressible contamination fluid flows in porous media the developed method takes the excellent attractive advantages of both the non overlapping domain decomposition and the splitting technique and reduces computational complexities large memory requirements and long computational durations

a quasi optimal non overlapping domain decomposition algorithm for the helmholtz equation this paper presents a new non overlapping domain decomposition method for the helmholtz equation whose effective convergence is quasi optimal these improved properties result from a combination of an appropriate choice of transmission conditions and a suitable approximation of the dirichlet to neumann operator a convergence theorem of the algorithm is established and numerical results validating the new approach are presented in both two and three dimensions

semiparametric estimates of the relation between weather and electricity sales abstract a nonlinear relationship between electricity sales and temperature is estimated using a semiparametric regression procedure that easily allows linear transformations of the data this accommodates introduction of covariates timing adjustments due to the actual billing schedules and serial correlation the procedure is an extension of smoothing splines with the smoothness parameter estimated from minimization of the generalized cross validation criterion introduced by craven and wahba 1979 estimates are presented for residential sales for four electric utilities and are compared with models that represent the weather using only heating and cooling degree days or with piecewise linear splines

an efficient parallel algorithm with application to computational fluid dynamics abstract when solving time dependent partial differential equations on parallel computers using the nonoverlapping domain decomposition method one often needs numerical boundary conditions on the boundaries between subdomains these numerical boundary conditions can significantly affect the stability and accuracy of the final algorithm in this paper a stability and accuracy analysis of the existing methods for generating numerical boundary conditions will be presented and a new approach based on explicit predictors and implicit correctors will be used to solve convection diffusion equations on parallel computers with application to aerospace engineering for the solution of euler equations in computational fluid dynamics simulations both theoretical analyses and numerical results demonstrate significant improvement in stability and accuracy by using the new approach

spline smoothing in a partly linear model on donne des estimations qui minimisent la somme des sommes residuelles des carres et une penalite de difficulte

a cartesian grid embedded boundary method for poisson s equation on irregular domains we present a numerical method for solving poisson s equation with variable coefficients and dirichlet boundary conditions on two dimensional regions the approach uses a finite volume discretization which embeds the domain in a regular cartesian grid we treat the solution as a cell centered quantity even when those centers are outside the domain cells that contain a portion of the domain boundary use conservative differencing of second order accurate fluxes on each cell volume the calculation of the boundary flux ensures that the conditioning of the matrix is relatively unaffected by small cell volumes this allows us to use multigrid iterations with a simple point relaxation strategy we have combined this with an adaptive mesh refinement amr procedure we provide evidence that the algorithm is second order accurate on various exact solutions and compare the adaptive and nonadaptive calculations

conservative domain decomposition procedure with unconditional stability and second order accuracy a new derivation of the conservative domain decomposition procedure for solving the parabolic equation is presented in this procedure fluxes at subdomain interfaces are calculated from the solution at the previous time level then these fluxes serve as neumann boundary data for implicit block centered discretization in the subdomain the unconditional stability and the second order accuracy of solution values as well as fluxes are proved numerical results examining the stability accuracy and parallelism of the procedure are also presented

bootstrap test for difference between means in nonparametric regression abstract a bootstrap test is proposed for detecting a difference between two mean functions in the setting of nonparametric regression error distributions in the regression model are permitted to be arbitrary and unequal the test enjoys power properties akin to those in a parametric setting in the sense that it can distinguish between regression functions distant only n 1 2 apart where n is the sample size it has exceptional level accuracy with level error of only n 2 and uses a very accurate estimate of the critical point of an exact test being in error by only n 3 2 under the null hypothesis the test admits several generalizations for example to the case of testing for differences between several regression means this is a nonparametric regression analog of analysis of variance a simulation study using n as small as 15 corroborates the asymptotic result on level accuracy of the bootstrap test applications are illustrated with an example involving acid rain data

a new insight into the consistency of the sph interpolation formula abstract in this paper the consistency of the smoothed particle hydrodynamics sph interpolation formula is investigated by analytical means a novel error analysis is developed in n dimensional space using the poisson summation formula which enables the simultaneous treatment of both the kernel and particle approximation errors for arbitrary particle distributions new consistency integral relations are derived for the particle approximation which correspond to the cosine fourier transform of the kernel consistency conditions the functional dependence of the error bounds on the sph interpolation parameters namely the smoothing length h and the number of particles within the kernel support n is demonstrated explicitly from which consistency conditions arise as n the particle approximation converges to the kernel approximation independently of h provided that the particle mass scales with h as m h with n where n is the spatial dimension this implies that as h 0 the joint limit m 0 n and n is necessary for complete convergence to the continuum where n is the total number of particles the analysis also reveals a dominant error term of the form ln n n n for finite n as it has long been conjectured based on the similarity between the sph and the quasi monte carlo estimates when n 1 the error of the sph interpolant decays as n 1 independently of the dimension this ensures approximate partition of unity of the kernel volume

a constant density approach for incompressible multi phase sph a constant density approach which corrects intermediate density errors by adjusting the half time step velocity with exact projection is proposed for the multi phase sph method developed in our previous work x y hu n a adams an incompressible multi phase sph method j comput phys 227 2007 264 278 as no prescribed reference pressure is required the present approach introduces smaller numerical viscosity and allows to simulate flows with unprecedentedly high density ratios by the projection sph method numerical examples for taylor green flow capillary waves and for rayleigh taylor instability are presented and compared to theoretical solutions or references from the literature

a domain decomposition discretization of parabolic problems in recent years domain decomposition methods have attracted much attention due to their successful application to many elliptic and parabolic problems domain decomposition methods treat problems based on a domain substructuring which is attractive for parallel computation due to the independence among the subdomains in principle domain decomposition methods may be applied to the system resulting from a standard discretization of the parabolic problems or directly be carried out through a discretization of parabolic problems in this paper a direct domain decomposition method is introduced to discretize the parabolic problems the stability and convergence of this algorithm are analyzed

the euler maclaurin formula for simple integral polytopes we give a euler maclaurin formula with remainder for the sum of a smooth function on the integral points in a simple integral lattice polytope our proof uses elementary methods

a note on smoothness priors and nonlinear regression abstract a generalization of a nonparametric estimator proposed by shiller 1984 is considered the estimator is shown to be directly related to penalized least squares estimation and spline smoothing some simplifications concerning the computation of shiller s estimator and corresponding posterior covariances are indicated

an efficient characteristic finite difference s ddm scheme for convection diffusion equations abstract in this paper an efficient splitting domain decomposition method scheme for solving time dependent convection diffusion reaction equations is analyzed a three step method along each direction is used to solve the solution over each block divided sub domain at every time interval the new solutions are firstly solved by the quadratic interpolation then the intermediate fluxes on the interfaces of sub domains are computed by local multi point weighted average from the new solutions lastly the solutions and fluxes in the interiors of sub domains are computed by the splitting implicit characteristic difference method by some auxiliary lemmas and the defined intermediate exact solution the stability and error estimate are given in discrete l 2 norm we further prove that our scheme is of second order convergence in space and of first order convergence in time numerical experiments are presented to validate theoretical result

analysis of field experiments by least squares smoothing summary assuming a smooth trend plus independent error model for the environmental effects in the yields of a field plot experiment least squares smoothing methods are developed to estimate both the treatment effects and the unknown trend treatment estimates are closely related to those resulting from a generalized least squares analysis in which the covariance structure for the environmental effects has a particular form however the main emphases are on the accuracy of treatment estimates under a fixed smooth trend plus error model and the exploratory power of the basic method to isolate trend effects of unknown form although the detailed development is for the one dimensional case generalizations of the smoothness concept and extensions to two dimensions are also discussed application of the basic method is illustrated on three data sets and the results compared with other analyses

ipic domain decomposition algorithm for parabolic problems a domain decomposition algorithm which is based on a semi implicit prediction and then a fully implicit correction at the interface for solving parabolic partial differential equations is presented the numerical results show that the algorithm is unconditionally stable and very efficient in this paper high speed up is analyzed with respect to the spectral radius and operation counts

some nonoverlapping domain decomposition methods the purpose of this paper is to give a unified investigation of a class of nonoverlapping domain decomposition methods for solving second order elliptic problems in two and three dimensions the methods under scrutiny fall into two major categories the substructuring type methods and the neumann neumann type methods the basic framework used for analysis is the parallel subspace correction method or additive schwarz method and other technical tools include local global and global local techniques the analyses for both two and three dimensional cases are carried out simultaneously some internal relationships between various algorithms are observed and several new variants of the algorithms are also derived

efficient parallel algorithms for parabolic problems domain decomposition algorithms for parallel numerical solution of parabolic equations are studied for steady state or slow unsteady computation implicit schemes are used in order to march with large time steps parallelization is realized by approximating interface values using explicit computation various techniques are examined including a multistep second order explicit scheme and a one step high order scheme we show that the resulting schemes are of second order global accuracy in space and stable in the sense of osher or in l infty they are optimized with respect to the parallel efficiency

the efficient s ddm scheme and its analysis for solving parabolic equations abstract in this paper we develop and analyze the efficient splitting domain decomposition method for solving parabolic equations the domain is divided into non overlapping multi block subdomains on interfaces of sub domains the local multilevel explicit scheme is proposed to solve the interface values of solution and then the splitting implicit scheme is proposed to solve the solution in interiors of subdomains on the theoretical aspect analyzing the s ddm scheme over non overlapping multi block sub domains is much challenging we strictly prove the stability and convergence of the s ddm scheme and obtain the optimal error estimates over non overlapping multi block subdomains numerical experiments are given to illustrate the accuracy and efficiency of the s ddm scheme the developed method takes the most attractive advantages of both the non overlapping domain decomposition and the splitting technique which overcomes the limitation of the stripe divided sub domains for parabolic equations in the previous methods the developed s ddm scheme reduces computational complexities large memory requirements and computational costs

truncation error in mesh free particle methods a truncation error analysis has been developed for the approximation of spatial derivatives in smoothed particle hydrodynamics sph and related first order consistent methods such as the first order form of the reproducing kernel particle method error is shown to depend on both the smoothing length h and the ratio of particle spacing to smoothing length x h for uniformly spaced particles in one dimension analysis shows that as h is reduced while maintaining constant x h error decays as h2 until a limiting discretization error is reached which is independent of h if x h is reduced while maintaining constant h i e if the number of neighbours per particle is increased error decreases at a rate which depends on the kernel function s smoothness when particles are distributed non uniformly error can grow as h is reduced with constant x h first order consistent methods are shown to remove this divergent behaviour numerical experiments confirm the theoretical analysis for one dimension and indicate that the main results are also true in three dimensions this investigation highlights the complexity of error behaviour in sph and shows that the roles of both h and x h must be considered when choosing particle distributions and smoothing lengths copyright 2005 john wiley sons ltd

semiparametric regression in likelihood based models abstract a weighted likelihood is used to estimate the parameters in a semiparametric model involving two covariates and allowing an association between the covariates the development is for arbitrary but specified densities of the observations the estimators are consistent and asymptotically normal hypothesis testing of the parametric component can be performed using a wald test simulations and analysis of data with bernoulli observations demonstrate the estimators application speckman developed kernel estimators where the conditional density of the observations is normal with p parametric covariates speckman s estimators and the new estimators are asymptotically equivalent with the bias of speckman s estimators being smaller as an example we study the relationship between a binary response indicating the occurrence of an intraoperative cardiac complication icc in vascular surgery patients and two risk factors duration of the operation or and asa score which is an evaluation of the patien

a finite difference domain decomposition algorithm for numerical solution of the heat equation a domain decomposition algorithm for numerically solving the heat equation in one and two space dimensions is presented in this procedure interface values between subdomains are found by an explicit finite difference formula once these values are calculated interior values are determined by backward differencing in time a natural extension of this method allows for the use of different time steps in different subdomains maximum norm error estimates for these procedures are derived which demonstrate that the error incurred at the interfaces is higher order in the discretization parameters

modeling low reynolds number incompressible flows using sph the method of smoothed particle hydrodynamics sph is extended to model incompressible flows of low reynolds number for such flows modification of the standard sph formalism is required to minimize errors associated with the use of a quasi incompressible equation of state treatment of viscosity state equation kernel interpolation and boundary conditions are described simulations using the method show close agreement with series solutions for couette and poiseuille flows furthermore comparison with finite element solutions for flow past a regular lattice of cylinders shows close agreement for the velocity and pressure fields the sph results exhibit small pressure fluctuations near curved boundaries further improvements to the boundary conditions may be possible which will reduce these errors a similar method to that used here may permit the simulation of other flows at low reynolds numbers using sph further development will be needed for cases involving free surfaces or substantially different equations of state