a mesh based partition of unity method for discontinuity modeling this study explores a numerical analysis scheme the manifold method within the framework of the partition of unity method the manifold method is rooted in the discrete element method and has been used in solving discrete continuum interaction problems at its core two meshes are employed in an analysis the mathematical mesh provides the nodes for building a finite covering of the solution domain and the partition of unity functions while the physical mesh provides the domain of integration after providing a geometric interpretation and giving a construct overview the working of the method is illustrated with a number of examples

robust model based and model assisted predictors of the finite population total the prediction approach to finite population inference has received considerable attention in recent years under this approach the finite population is assumed to be a realization from a superpopulation described by a known probability model usually a linear model the prediction approach is often criticized for its lack of robustness against model misspecification in this article we revisit this important issue and introduce a new robust prediction approach in which the superpopulation model is chosen adaptively from the well known box cox class of probability distributions the richness of the box cox class ensures robustness in our model based prediction approach we explain how our robust model based predictor can be adjusted to handle zero observations for the study variable and to achieve the design unbiasedness and benchmarking properties we demonstrate the robustness of our proposed predictors using a monte carlo simulation study and a real life example

evaluation of the integral terms in reproducing kernel methods reproducing kernel method rkm has its origins in wavelets and it is based on convolution theory being their continuous version rkm is often referred as the general framework for meshless methods in fact since in real computation discretization is inevitable these integrals need to be evaluated numerically leading to the creation of reproducing kernel particle method rkpm and moving least squares mls approximation nevertheless in this paper the integrals in rkm are explicitly evaluated for polynomials basis function and simple geometries in one two and three dimensions even with conforming holes moreover a general formula is provided for complicated shapes also for multiple connected domains this is possible through a boundary formulation where domain integrals involved in rkm are transformed by gauss theorem in circular or flux integrals parallelization is readily enabled since no preliminary arrangements of nodes is needed for the moments matrix furthermore using symbolic inversion computation of shape functions in rkm is considerably speeded up

an h adaptive method in the generalized finite differences abstract this paper describes an h adaptive method in generalized finite difference gfd to solve second order partial differential equations these equations representing the behaviour of many physical processes the explicit difference formulae obtained make it possible to propose an a posteriori error indicator which serves as starting point for an h adaptive method to improve the solution by selectively adding nodes to the domain this paper also analyses the influence of key parameters as the number of nodes to add in each step or the minimum distance between nodes through the analysis of the obtained solutions for different types of differential equations

on the boundedness and continuity of the spectral factorization mapping it is known that the spectral factorization mapping is bounded but not continuous on l infty the space of essentially bounded measurable functions on the unit circle in this article we study the spectral factorization mapping on decomposing banach algebras the most important example of a decomposing banach algebra is the wiener algebra the space of all absolutely convergent fourier series it is shown that the spectral factorization mapping is locally lipschitz continuous but not bounded on all decomposing banach algebras in consideration an application is given to the construction of approximate normalized coprime factorization

adjoint based optimal control using meshfree discretizations the paper at hand presents a combination of optimal control approaches for pdes with meshless discretizations applying a classical lagrangian type particle method to optimization problems with hyperbolic constraints several adjoint based strategies differing in the sequential order of optimization and discretization of the lagrangian or eulerian problem formulation are proposed and compared the numerical results confirm the theoretically predicted independence principle of the optimization approaches and show the expected convergence behavior moreover they exemplify the superiority of meshless methods over the conventional mesh based approaches for the numerical handling and optimization of problems with time dependent geometries and freely moving boundaries

the effect of sampling design and response mechanism on multivariate regression based predictors abstract a general regression procedure for the prediction of a vector of population means in situations of nonresponse is proposed the multivariate treatment of the prediction problem is not computationally complicated and allows the borrowing of information from one target variable to the other even when both variables are subject to nonresponse the predictors are optimal under a general model that specifies the first and second moments of the joint distribution of the survey variables the effects of the sampling design and response mechanism on the properties of the predictors are investigated and appropriate modifications and bias corrections that use the sample inclusion probabilities are proposed the performance of the predictors is illustrated empirically and compared with that of other predictors using simulated and real data data collected in governmental and other large scale surveys is almost always incomplete typical causes for the incompleteness of the data are delays in attaining part

a local least squares method for solving nonlinear partial differential equations of second order in this paper a mesh free method for the treatment of time independent and time dependent nonlinear pdes of second order is presented the basic idea of the discretization is a local least squares approximation similar to the moving least squares approach in data approximation however in our approach the pde is incorporated as an additional minimization constraint the discretization leads to a fixed point problem which is solved by iteration because of the local nature of the method only small dimensional matrix inversions have to be done the approximation error of the discretization even on unstructured meshes is comparable to respective versions of finite elements as a by product the method provides an a posteriori measure for the local approximation error we discuss implementational aspects and present numerical simulations

orbital hp clouds for solving schrodinger equation in quantum mechanics solving schrodinger equation in quantum mechanics presents a challenging task in numerical methods due to the high order behavior and high dimension characteristics in the wave functions in addition to the highly coupled nature between wave functions this work introduces orbital and polynomial enrichment functions to the partition of unity for solution of schrodinger equation under the framework of hp clouds an intrinsic enrichment of orbital function and extrinsic enrichment of monomial functions are proposed due to the employment of higher order basis functions a higher order stabilized conforming nodal integration is developed the proposed methods are implemented using the density functional theory for solution of schrodinger equation analysis of several single and multi electron nucleus structures demonstrates the effectiveness of the proposed method

proper orthogonal decomposition with high number of linear constraints for aerodynamical shape optimization shape optimization involving finite element analysis in engineering design is frequently hindered by the prohibitive cost of function evaluations reduced order models based on proper orthogonal decomposition pod constitute an economical alternative however the truncation of the pod basis implies an error in the calculation of the global values used as objectives and constraints which in turn affects the optimization results in our former contribution xiao and breitkopf 2013 we have introduced a constrained pod projector allowing for exact linear constraint verification for a reduced order model nevertheless this approach was limited a to relatively low numbers constraints therefore in the present paper we propose an approach for a high number of constraints the main idea is to extend the snapshot pod by introducing a new constrained projector in order to reduce both the physical field and the constraint space this allows us to search for the pareto set of best compromises between the projection and the constraint verification errors thereby enabling fine tuning of the reduced model for a particular purpose we illustrate the proposed approach with the reduced order model of the flow around an airfoil parameterized with shape variables

balanced model reduction via the proper orthogonal decomposition a new method for performing a balanced reduction of a high order linear system is presented the technique combines the proper orthogonal decomposition and concepts from balanced realization theory the method of snapshotsisused to obtainlow rank reduced rangeapproximationsto thesystemcontrollability and observability grammiansineitherthetimeorfrequencydomain theapproximationsarethenusedtoobtainabalancedreducedorder model the method is particularly effective when a small number of outputs is of interest it is demonstrated for a linearized high order system that models unsteady motion of a two dimensional airfoil computation of the exact grammians would be impractical for such a large system for this problem very accurate reducedorder models are obtained that capture the required dynamics with just three states the new models exhibit far superiorperformancethanthosederived using a conventionalproperorthogonal decomposition although further development is necessary the concept also extends to nonlinear systems

from a standard factorization to a j spectral factorization for a class of infinite dimensional systems matrix valued functions in the wiener class on the imaginary line are considered in this note this class of functions is large enough to be suitable for many applications in systems and control of infinite dimensional systems for this class of functions three kinds of factorization are discussed right standard factorization canonical factorization and j spectral factorization in particular we focus on an algorithmic procedure to find a right standard factorization and a j spectral factorization for matrix valued functions in the wiener class under the assumption that such factorizations exists in practice the j spectral factors for irrational functions are usually calculated using rational approximations we show that approximation using rational functions may be achieved in the wiener norm

analysis of an augmented moving least squares approximation and the associated localized method of fundamental solutions abstract the localized method of fundamental solutions lmfs is an efficient meshless collocation method that combines the concept of localization and the method of fundamental solutions mfs the resultant system of linear algebraic equations in the lmfs is sparse and banded and thus drastically reduces the storage and computational burden of the mfs in the lmfs the moving least square mls approximation based on fundamental solutions is used to construct approximate solution at each node in this paper this fundamental solutions based mls approximation named as an augmented mls amls approximation is generalized to any point in the computational domain computational formulas theoretical properties and error estimates of the amls approximation are derived then taking laplace equation as an example this paper sets up a framework for the theoretical error analysis of the lmfs finally numerical results are presented to verify the efficiency and theoretical results of the amls approximation and the lmfs convergence and comparison researches are conducted to validate the accuracy convergence and efficiency

a counterexample on continuous coprime factors in georgiou and smith 1992 the following question was raised consider a linear shift invariant system on l sub 2 0 spl infin let the graph of the system have fourier transform mn h sup 2 i e the system has a transfer function p n m where m n are elements of c sub a f spl isin h sup spl infin f is continuous on the compactified right half plane is it possible to normalize m and n i e to ensure m sup 2 n sup 2 1 in c sub a the author shows by example that this is not always possible

relative efficiencies of two stage sampling schemes for mean estimation in multilevel populations when cluster size is informative in multilevel populations there are two types of population means of an outcome variable ie the average of all individual outcomes ignoring cluster membership and the average of cluster specific means to estimate the first mean individuals can be sampled directly with simple random sampling or with two stage sampling tss that is sampling clusters first and then individuals within the sampled clusters when cluster size varies in the population three tss schemes can be considered ie sampling clusters with probability proportional to cluster size and then sampling the same number of individuals per cluster sampling clusters with equal probability and then sampling the same percentage of individuals per cluster and sampling clusters with equal probability and then sampling the same number of individuals per cluster unbiased estimation of the average of all individual outcomes is discussed under each sampling scheme assuming cluster size to be informative furthermore the three tss schemes are compared in terms of efficiency with each other and with simple random sampling under the constraint of a fixed total sample size the relative efficiency of the sampling schemes is shown to vary across different cluster size distributions however sampling clusters with probability proportional to size is the most efficient tss scheme for many cluster size distributions model based and design based inference are compared and are shown to give similar results the results are applied to the distribution of high school size in italy and the distribution of patient list size for general practices in england

the complex variable interpolating moving least squares method abstract in this paper a new method for deriving the moving least squares mls approximation is presented first considering the unclear physical meaning of the functional in the existing complex variable moving least squares cvmls approximation an improved cvmls approximation is presented by constructing a new functional with an explicit physical meaning based on the improved cvmls approximation the complex variable interpolating moving least squares cvimls method is presented and the interpolating property of the corresponding shape function of the cvimls method is proved

improved imputation of non responses to mailback questionnaires poor response rates perhaps as low as 10 to 30 per cent certainly bring into question the validity of any survey suffering such a malady repeated mailouts are capable of providing information on those persons who are resistant to responding if one is willing to assume an exponential drop off in response rates then imputation is possible for the entire group of non responders furthermore a second exponential drop off in favourable or non favourable responses to particular items within the questionnaire leads to closed form estimates of population parameters and their associated standard errors three or more mailouts also provide a test of validity of the model assumed

variational multiscale element free galerkin vmefg and local discontinuous galerkin ldg methods for solving two dimensional brusselator reaction diffusion system with and without cross diffusion abstract the finite element method fem is one of the basic methods for solving deterministic and stochastic partial differential equations this method is proposed in the 19 decade and after years several modifications for this well known technique such as mortal fem discontinuous galerkin fem extended fem least squares fem spectral fem mixed fem immersed fem adaptive fem etc have been proposed also for improving the accuracy and for considering complex domain shape functions of the moving least squares approximation have been replaced with the traditional shape function of the finite element technique the name of this improved method is element free galerkin efg method which is classified in the category of meshless methods the efg method has been applied for solving many problems in engineering in the current paper we select two numerical procedures that are extracted from fem the discontinuous galerkin approach is a useful technique for solving problems that their exact solutions have discontinuity it should be noted that many enriched ideas have been explained for improving accuracy of efg method in the current paper the local discontinuous galerkin and variational multiscale efg methods are applied for obtaining numerical solution of two dimensional brusselator system with and without cross diffusion the brusselator system is a theoretical model for a type of autocatalytic reaction up to best of authors knowledge the accuracy of the obtained numerical solutions using local discontinuous galerkin method is very related to the used time discrete scheme therefore fourth order exponential time differencing method has been employed for discretizing the time variable also to achieve a full discretization scheme the local discontinuous galerkin finite element method is used moreover several test problems are given that show the acceptable accuracy and efficiency of the proposed schemes

modelling complex survey data with population level information an empirical likelihood approach survey data are often collected with unequal probabilities from a stratified population in many modelling situations the parameter of interest is a subset of a set of parameters with the others treated as nuisance parameters we show that in this situation the empirical likelihood ratio statistic follows a chi squared distribution asymptotically under stratified single and multi stage unequal probability sampling with negligible sampling fractions simulation studies show that the empirical likelihood confidence interval may achieve better coverages and has more balanced tail error rates than standard approaches involving variance estimation linearization or resampling

modified moving least squares with polynomial bases for scattered data approximation one common problem encountered in many fields is the generation of surfaces based on values at irregularly distributed nodes to tackle such problems we present a modified robust moving least squares mls method for scattered data smoothing and approximation the error functional used in the derivation of the classical mls approximation is augmented with additional terms based on the coefficients of the polynomial base functions this allows quadratic base functions to be used with the same size of the support domain as linear base functions resulting in better approximation capability the increased robustness of the modified mls method to irregular nodal distributions makes it suitable for use across many fields the analysis is supported by several univariate and bivariate examples

lq optimal boundary control of infinite dimensional systems with yosida type approximate boundary observation a class of boundary control systems with boundary observation is considered for which the unbounded operators often lead to technical difficulties an extended model for this class of systems is described and analyzed which involves no unbounded operator except for the dynamics generator a method for the resolution of the lq optimal control problem for this model is described and the solution provides a stabilizing feedback for the nominal system with unbounded operators in the sense that in closed loop the state trajectories converge to zero exponentially fast the model consists of an extended abstract differential equation whose state components are the boundary input the state up to an affine transformation and a yosida type approximation of the output of the nominal system it is shown that under suitable conditions the model is well posed and in particular that the dynamics operator is the generator of a c 0 semigroup moreover the model is shown to be observable and to carry controllability stabilizability and detectability properties from the nominal system a general method of resolution based on the problem of spectral factorization of a multi dimensional operator valued spectral density is described in order to solve a lq optimal control problem for this model it is expected that this approach will lead hopefully to a good trade off between the cost of modeling and the efficiency of methods of resolution of control problems for such systems

new boundary condition treatments in meshfree computation of contact problems due to the loss of kronecker delta properties in the meshfree shape functions the imposition of essential boundary conditions consumes significant cpu time in meshfree computation in this work two boundary condition treatments are proposed to enhance the computational efficiency of meshfree methods for contact problems the mixed transformation method is modified from the previous full transformation method by introducing a node partitioning and a mixed coordinate so that the matrix inversion and multiplication of coordinate transformation involves operations only on the sub degrees of freedom associated with the boundary group the boundary singular kernel method introduces singularities to the kernel functions of the essential and contact boundary nodes so that the corresponding coefficients of the singular kernel shape functions recover nodal values and consequently kinematic constraints can be imposed directly the effectiveness of the proposed methods is demonstrated in several numerical examples

on estimating distribution functions and quantiles from survey data using auxiliary information summary ratio and difference estimators of a population distribution function under a general sampling design are obtained using auxiliary population information the relative mean errors and relative mean square errors of these estimators and a model based estimator of chambers dunstan 1986 are compared through a simulation study the advantages of the design based estimators over the model based estimator under model misspecifications especially for large samples are demonstrated ratio and difference estimators of a population quantile are also studied

a coupled element free galerkin boundary element method for stress analysis of two dimensional solids element free galerkin efg method is a newly developed meshless method for solving partial differential equations using moving least squares interpolants it is however computationally expensive for many problems a coupled efg boundary element be method is proposed in this paper to improve the solution efficiency a procedure is developed for the coupled efg be method so that the continuity and compatibility are preserved on the interface of the two domains where the efg and be methods are applied the present coupled efg be method has been coded in fortran the validity and efficiency of the efg be method are demonstrated through a number of examples it is found that the present method can take the full advantages of both efg and be methods it is very easy to implement and very flexible for computing displacements and stresses of desired accuracy in solids with or without infinite domains

enforcement of essential boundary conditions in meshless approximations using finite elements abstract a technique for easily treating essential boundary conditions for approximations which are not interpolants such as moving least square approximations in the element free galerkin method is presented the technique employs a string of elements along the essential boundaries and combines the finite element shape functions with the approximation in the resulting approximation essential boundary conditions can be treated exactly as in finite elements it is shown that the resulting approximation can exactly reproduce linear polynomials so that it satisfies the patch test numerical studies show that the method retains the high rate of convergence associated with moving least square approximations

spectral factorization and lq optimal regulation for multivariable distributed systems a necessary and sufficient condition is proved for the existence of a bistable spectral factor with entries in the distributed proper stable transfer function algebra x1d49c in the context of distributed multivariable convolution systems with no delays a by product is the existence of a normalized coprime fraction of the transfer function of such a possibly unstable system with entries in the algebra of fractions over x1d49c we next study semigroup state space systems sgb with bounded sensing and control having a transfer function with entries in and consider its standard lq optimal regulation problem having an optimal state feedback operator k0 for a system sgb a formula is given relating any spectral factor of a transfer function coprime fraction power spectral density to k0 a by product is the description of any normalized coprime fraction of the transfer function in terms of k0 finally we describe an alternative way of finding the solution operator k0 of the lq problem using spectral factor

hermite type moving least squares approximations the moving least squares approach first presented by mclain 1 is a method for approximating multivariate functions using scattered data information the method is using local polynomial approximations incorporating weight functions of different types some weights with certain singularities induce c interpolation approximation in n in this work we present a way of generalizing the method to enable hermite type interpolation namely interpolation to derivatives data as well the essence of the method is the use of an appropriate metric in the construction of the local polynomial approximations

an hp proper orthogonal decomposition moving least squares approach for molecular dynamics simulation abstract the application of model order reduction for molecular dynamic systems exhibits intrinsic complexities due to the highly nonlinear and nonlocal properties of such systems the most costly computational part of such work is the calculation of potential energy and inter atomic force fields we introduce the so called hp proper orthogonal decomposition moving least squares hp pod mls method not only to tackle this force computation but also to improve the accuracy of reduced displacement approximations in an adaptive and controllable manner the approach combines the proper orthogonal decomposition pod method with the moving least squares mls one to interpolate the inter atomic force field at an arbitrary time instance this approximated force field is then fed into the reduced molecular dynamic md governing equation to compute the reduced order displacement field in fact this pod mls approach is already able to handle efficiently the force computation in the online computational stage i e the online force computational cost is independent of the dimension of the full md space however its corresponding approximated displacement error will be very large if the considered total time interval is long the proposed hp pod mls algorithm will divide adaptively and automatically the global temporal interval into many smaller local subintervals h refinement and then build the sets of local reduced basis functions over each of these subintervals p refinement the goal is to reduce the corresponding displacement errors to a desired tolerance over these subintervals the effectiveness of the algorithm is demonstrated by performing reduced order simulations of several molecular dynamic systems

frictional contact analysis of functionally graded materials with lagrange finite block method summary based on the one dimensional differential matrix derived from the lagrange series expansion the finite block method was recently developed to solve both the elasticity and transient heat conduction problems of anisotropic and functionally graded materials in this paper the formulation of the lagrange finite block method with boundary type in the strong form is presented and applied to non conforming contact problems for the functionally graded materials subjected to either static or dynamic loads the first order partial differential matrices are only needed both in the governing equations and in the neumann boundary condition by introducing the mapping technique a block of quadratic type is transformed from the cartesian coordinate of global system to the normalized coordinate with eight seeds time dependent partial differential equations are analyzed in the laplace transformed domain and the durbin s inversion method is applied to determine all the physical values in the time domain conforming and non conforming contacts are investigated by using the iterative algorithm with full load technique illustrative numerical examples are given and comparisons have been made with analytical solutions copyright 2015 john wiley sons ltd

a perturbation method for stochastic meshless analysis in elastostatics a stochastic meshless method is presented for solving boundary value problems in linear elasticity that involves random material properties the material property was modelled as a homogeneous random field a meshless formulation was developed to predict stochastic structural response unlike the finite element method the meshless method requires no structured mesh since only a scattered set of nodal points is required in the domain of interest there is no need for fixed connectivities between nodes in conjunction with the meshless equations classical perturbation expansions were derived to predict second moment characteristics of response numerical examples based on one and two dimensional problems are presented to examine the accuracy and convergence of the stochastic meshless method a good agreement is obtained between the results of the proposed method and monte carlo simulation since mesh generation of complex structures can be a far more time consuming and costly effort than the solution of a discrete set of equations the meshless method provides an attractive alternative to finite element method for solving stochastic mechanics problems copyright 2001 john wiley sons ltd

surfaces generated by moving least squares methods an analysis of moving least squares m l s methods for smoothing and interpolating scattered data is presented in particular theorems are proved concerning the smoothness of interpolants and the description of m l s processes as projection methods some properties of compositions of the m l s projector with projectors associated with finiteelement schemes are also considered the analysis is accompanied by examples of univariate and bivariate problems

a meshfree enriched finite element method for compressible and near incompressible elasticity summary in this paper a two dimensional displacement based meshfree enriched fem me fem is presented for the linear analysis of compressible and near incompressible planar elasticity the me fem element is established by injecting a first order convex meshfree approximation into a low order finite element with an additional node the convex meshfree approximation is constructed using the generalized meshfree approximation method and it possesses the kronecker delta property on the element boundaries the gradient matrix of me fem element satisfies the integration constraint for nodal integration and the resultant me fem formulation is shown to pass the constant stress test for the compressible media the me fem interpolation is an element wise meshfree interpolation and is proven to be discrete divergence free in the incompressible limit to prevent possible pressure oscillation in the near incompressible problems an area weighted strain smoothing scheme incorporated with the divergence free me fem interpolation is introduced to provide the smoothing on strains and pressure with this smoothed strain field the discrete equations are derived based on a modified hu washizu variational principle several numerical examples are presented to demonstrate the effectiveness of the proposed method for the compressible and near incompressible problems copyright 2012 john wiley sons ltd

a note on variance estimation for the regression estimator in double sampling abstract double sampling of a finite population occurs when a sample from the population is itself sampled with the intent of measuring varites in the subsample not already available in the sample an important example is the regression estimator for means or totals which uses values of an auxiliary variable from the full sample to estimate the mean of a variable of interest that is available only on the subsample this article concerns estimation of the variance of the regression estimator the estimators of variance recommended by cochran rely solely on the subsample data at least to first order this article note proposes variance estimators that make better use of the entire sample

the analysis of categorical data from complex sample surveys chi squared tests for goodness of fit and independence in two way tables abstract the effect of stratification and clustering on the asymptotic distributions of standard pearson chi squared test statistics for goodness of fit simple hypothesis and independence in a two way contingency table denoted as x 2 and xi 2 respectively is investigated it is shown that both x 2 and xi 2 are asymptotically distributed as weighted sums of independent 1 2 random variables the weights are then related to the familiar design effects deffs used by survey samplers a simple correction to x 2 which requires only the knowledge of variance estimates or deffs for individual cells in the goodness of fit problem is proposed and empirical results on the performance of corrected x 2 provided empirical work on xi 2 indicated that the distortion of nominal significance level is substantially smaller with xi 2 than with x 2 some results under simple models for clustering are also given

an evaluation of model dependent and probability sampling inferences in sample surveys abstract in this paper we are concerned with inferences from a sample survey to a finite population we contrast inferences that are dependent on an assumed model with inferences based on the randomization induced by the sample selection plan randomization consistency for finite population estimators is defined and adopted as a requirement of probability sampling a numerical example is examined to illustrate the dangers in the use of model dependent estimators even when the model is apparently consonant with the sample data the paper concludes with a summary of principles that we believe should guide the practitioner of sample surveys of finite populations

to model or not to model competing modes of inference for finite population sampling finite population sampling is perhaps the only area of statistics in which the primary mode of analysis is based on the randomization distribution rather than on statistical models for the measured variables this article reviews the debate between design based and model based inference the basic features of the two approaches are illustrated using the case of inference about the mean from stratified random samples strengths and weakness of design based and model based inference for surveys are discussed it is suggested that models that take into account the sample design and make weak parametric assumptions can produce reliable and efficient inferences in surveys settings these ideas are illustrated using the problem of inference from unequal probability samples a model based regression analysis that leads to a combination of design based and model based weighting is described

a kernel method for estimating finite population distribution functions using auxiliary information summary this paper considers the use of auxiliary information to improve the estimation of the distribution function of a finite population a method is proposed which combines the known distribution of the auxiliary variable with a kernel estimate of the conditional distribution of the survey variable given the value of the auxiliary variable the resulting estimator compares favourably with existing estimators in terms of efficiency conditional behaviour and robustness the proposed method also has the advantage of producing estimates which are bona fide distribution functions this is not the case for many calibration type estimators suggested in the literature finally the proposed method is applicable under any probability sampling scheme

constrained proper orthogonal decomposition based on qr factorization for aerodynamical shape optimization while performing numerical simulations for design optimization one of the major issues is reaching a good compromise between accuracy and computational effort simulation methods such as finite elements finite volumes etc provide high fidelity numerical solutions at a cost which may be prohibitive in optimization problems requiring frequent calls to the discretized equations solver the proper orthogonal decomposition pod constitutes an economical and efficient option to decrease the cost of the solution however the truncation of the pod basis implies an error in the calculation of the global quantities used as objectives and optimization constraints which in turn might bias the optimization results our idea is thus to improve the snapshot pod by means of a reduced basis constructed to provide an exact interpolation of the quantities of interest obtained by integration of the physical fields to this end we reformulate the pod as a minimization problem where the desired properties are expressed as a set of constraints impacting the calculation of both the modes and the coefficients the main contribution of this paper is to provide a detailed mathematical justification for our constrained variant of the pod including a graphical interpretation of the proposed approach the constrained pod method is then applied to the problem of representing the pressure field around a 2d wing and is compared with the traditional pod

lq optimal control of infinite dimensional systems by spectral factorization abstract we consider the standard lq optimal control of an exponentially stabilizable and detectable infinite dimensional semigroup state space system with bounded sensing and control it is reported that the reachable restriction of the lq optimal state feedback operator can be identified 1 by solving a spectral factorization problem delivering a bistable spectral factor with entries in the distributed proper stable transfer function algebra and 2 by obtaining any constant solution of an operator diophantine equation over the properties of the restricted solution feedback operator are discussed it is shown in particular that the lq optimal state feedback operator and its reachable restriction coincide whenever the unreachable state components are unobservable these theoretical results are applied to a simple model of heat diffusion with collocated sensor and actuator leading to an approximation procedure converging exponentially fast to the lq optimal state feedback operator this procedure is based on approximate spectral factorization by symmetric extraction and on simple residue calculus

a singularity avoiding moving least squares scheme for two dimensional unstructured meshes moving least squares interpolation schemes are in widespread use as a tool for numerical analysis on scattered data in particular they are often employed when solving partial differential equations on unstructured meshes which are typically needed when the geometry defining the domain is complex it is known that such schemes can be singular if the data points in the stencil happen to be in certain special geometric arrangements however little research has specifically addressed this issue in this paper a moving least squares scheme is presented which is an appropriate tool for use when solving partial differential equations in two dimensions and the precise conditions under which singularities occur are identified the theory is used to develop a stencil building algorithm which automatically detects singular stencils and corrects them in an efficient manner while attempting to maintain stencil symmetry as closely as possible finally the scheme is applied in a convection diffusion equation solver and an incompressible navier stokes solver and the results are shown to compare favourably with known analytical solutions and previously published results

element free galerkin methods for static and dynamic fracture abstract element free galerkin efg methods are presented and applied to static and dynamic fracture problems efg methods which are based on moving least square mls interpolants require only nodal data no element connectivity is needed the description of the geometry and numerical model of the problem consists only of a set of nodes and a description of exterior boundaries and interior boundaries from any cracks this makes the method particularly attractive for growing crack problems since only minimal remeshing is needed to follow crack growth in moving least square interpolants the dependent variable at any point is obtained by minimizing a function in terms of the nodal values of the dependent variable in the domain of influence of the point numerical examples involving fatigue crack growth and dynamic crack propagation are presented to illustrate the performance and potential of this method

optimal sampling and estimation strategies under the linear model in some cases model based and model assisted inferences can lead to very different estimators these two paradigms are not so different if we search for an optimal strategy rather than just an optimal estimator a strategy being a pair composed of a sampling design and an estimator we show that under a linear model the optimal model assisted strategy consists of a balanced sampling design with inclusion probabilities that are proportional to the standard deviations of the errors of the model and the horvitz thompson estimator if the heteroscedasticity of the model is fully explainable by the auxiliary variables then this strategy is also optimal in a model based sense moreover under balanced sampling and with inclusion probabilities that are proportional to the standard deviation of the model the best linear unbiased estimator and the horvitz thompson estimator are equal finally it is possible to construct a single estimator for both the design and model variance the inference can thus be valid under the sampling design and under the model

non linearly stable reduced order models for incompressible flow with energy conserving finite volume methods abstract a novel reduced order model rom formulation for incompressible flows is presented with the key property that it exhibits non linearly stability independent of the mesh of the full order model the time step the viscosity and the number of modes the two essential elements to non linear stability are 1 first discretise the full order model and then project the discretised equations and 2 use spatial and temporal discretisation schemes for the full order model that are globally energy conserving in the limit of vanishing viscosity for this purpose as full order model a staggered grid finite volume method in conjunction with an implicit runge kutta method is employed in addition a constrained singular value decomposition is employed which enforces global momentum conservation the resulting velocity only rom is thus globally conserving mass momentum and kinetic energy for non homogeneous boundary conditions a one time poisson equation is solved that accounts for the boundary contribution the stability of the proposed rom is demonstrated in several test cases furthermore it is shown that explicit runge kutta methods can be used as a practical alternative to implicit time integration at a slight loss in energy conservation

the generalized finite element method this paper describes a pilot design and implementation of the generalized finite element method gfem as a direct extension of the standard finite element method sfem or fem which makes possible the accurate solution of engineering problems in complex domains which may be practically impossible to solve using the fem the development of the gfem is illustrated for the laplacian in two space dimensions in domains which may include several hundreds of voids and or cracks for which the construction of meshes used by the fem is practically impossible the two main capabilities are 1 it can construct the approximation using meshes which may overlap part or all of the domain boundary 2 it can incorporate into the approximation handbook functions which are known analytically or are generated numerically and approximate well the solution of the boundary value problem in the neighborhood of corner points voids cracks etc the main tool is a special integration algorithm which we call the fast remeshing approach which is robust and works for any domain with arbitrary complexity the incorporation of the handbook functions into the gfem is done by employing the partition of unity method pum the presented formulations and implementations can be easily extended to the multi material medium where the voids are replaced by inclusions of various shapes and sizes and to the case of the elasticity problem this work can also be understood as a pilot study for the feasibility and demonstration of the capabilities of the gfem which is needed before analogous implementations are attempted in the three dmensional and nonlinear cases which are the cases of main interest for future work

realisation and approximation of linear infinite dimensional systems with error bounds the class of linear infinite dimensional systems with finite dimensional inputs and outputs whose impulse response h satisfies h in l 1 cap l 2 0 infty mathbb c p times m and induces a nuclear hankel operator is said to be of nuclear type for this class of systems it is shown that balanced or output normal realisations always exist and their truncations converge to the original system in various topologies furthermore explicit l infty bounds on the transfer function errors l 1 and l 2 bounds on the impulse response errors and hilbert schmidt and nuclear bounds on the hankel operator errors are obtained these truncations also generate an approximating sequence to the optimal hankel norm approximations to the original system and various error bounds of these approximants are deduced

a marginal model for analyzing discrete outcomes from longitudinal surveys with outcomes subject to multiple cause nonresponse techniques for analyzing categorical outcomes obtained from longitudinal survey samples with outcomes subject to multiple cause nonresponse are developed within the framework of weighted generalized estimating equations development of these techniques was motivated by disability data obtained from the longitudinal study of aging lsoa a longitudinal survey sample containing missing follow up for many elderly participants we posit a model that combines different multivariate link functions to permit fitting markov models to an outcome with categories represented by a mixture of ordinal success states and multiple failure states extending the missing data approach of robins rotnitzky and zhao to longitudinal survey sample settings we use multiple logit models to model the probability of multiple reasons for missing success or failure outcomes given the assumption that the probability of nonresponse depends only on observed responses and covariates specified in the missing data model weighted est

a total lagrangian framework for simulation of powder compaction process based on a smooth three surface cap model and a mesh free method this paper presents a detailed framework for simulation of cold powder compaction process this framework consists of the following main assumptions the total lagrangian description is employed the powder is assumed to be isotropic and it is modeled by a complete smooth three surface cap model the constitutive formulation is based on the multiplicative decomposition of the deformation gradient and on stress strain pair formed by the hencky logarithmic strain and the rotated kirchhoff stress tensor the elastic constitutive relationship considers that some parameters are dependent upon the relative density of the powder the contact formulation is based on the signorini condition and the friction is modeled by using a regularized coulomb model and the spatial discretization is made by the element free galerkin method where the essential boundary conditions are enforced via an augmented lagrangian method details concerning the discretization and the linearization of the weak form are presented and a master algorithm is proposed some key examples already investigated by other authors but with somewhat different approaches are revisited in this paper in order to investigate the adequacy of the proposed model and attest the performance of the proposed numerical scheme copyright 2008 john wiley sons ltd

a resampling procedure for complex survey data abstract in complex survey data often the sampling design induces a non iid structure to the data e g without replacement sampling stratification multistage or unequal probability of selection though techniques for variance estimation and confidence intervals do exist they often are cumbersome to implement or do not extend to complex designs it would be desirable to have resampling methods that reuse the existing estimation system repeatedly using computing power to avoid theoretical work and that can be applied to such data in recognition of this need various resampling procedures for variance estimation and confidence intervals in sample survey data where the sampling is without replacement have been proposed in the literature these include the jackknife the with replacement bootstrap bwr the without replacement bootstrap bwo and the rescaling bootstrap the bwr and bwo are applicable only to simple sampling designs others have shown the asymptotic consistency of jackknife vari

a noninformative bayesian approach to interval estimation in finite population sampling abstract a noninformative bayesian approach to interval estimation in finite population sampling is discussed given the sample this method introduces the polya distribution as a pseudo posterior distribution over the unobserved members of the population in many cases this distribution yields interval estimates similar to those of standard frequentist theory in addition it can be used in situations where the standard methods are difficult to apply for example in producing an interval estimate for the ratio of two medians we also consider related point estimation problems and observe that estimators derived from the pseudo posterior often perform better than classical alternatives

continuity of the spectral factorization on a vertical strip the continuity of the mapping which associates a spectral factor to a spectral density is investigated this mapping can be defined on several classes of spectral densities and spectral factors for the usual largest class of spectral densities i e essential bounded functions on the imaginary axis that are bounded away from zero it is known that this mapping is not continuous it is shown here that for slightly smaller but still generic class the mapping becomes continuous

efg approximation with discontinuous derivatives a technique for incorporating discontinuities in derivatives into meshless methods is presented the technique enriches the approximation by adding special shape functions that contain discontinuities in derivatives the special shape functions have compact support which results in banded matrix equations the technique is described in element free galerkin context but is easily applicable to other meshless methods and projections numerical results for problems in one and two dimensions are reported 1998 john wiley sons ltd

resolution of computational aeroacoustics problems on unstructured grids with a higher order finite volume scheme computational fluid dynamics cfd has become increasingly used in the industry for the simulation of flows nevertheless the complex configurations of real engineering problems make the application of very accurate methods that only work on structured grids difficult from this point of view the development of higher order methods for unstructured grids is desirable the finite volume method can be used with unstructured grids but unfortunately it is difficult to achieve an order of accuracy higher than two and the common approach is a simple extension of the one dimensional case the increase of the order of accuracy in finite volume methods on general unstructured grids has been limited due to the difficulty in the evaluation of field derivatives this problem is overcome with the application of the moving least squares mls technique on a finite volume framework in this work we present the application of this method fv mls to the solution of aeroacoustic problems

robust estimation for finite populations based on a working model a common scenario in finite population inference is that it is possible to find a working superpopulation model which explains the main features of the population but which may not capture all the fine details in addition there are often outliers in the population which do not follow the assumed superpopulation model in situations like these it is still advantageous to make use of the working model to estimate finite population quantities provided that we do it in a robust manner the approach that we suggest is first to fit the working model to the sample and then to fine tune for departures from the model assumed by estimating the conditional distribution of the residuals as a function of the auxiliary variable this is a more direct approach to handling outliers and model misspecification than the huber approach that is currently being used two simple methods stratification and nearest neighbour smoothing are used to estimate the conditional distributions of the residuals which result in two modifications to the standard model based estimator of the population distribution function the estimators suggested perform very well in simulation studies involving two types of model departure and have small variances due to their model based construction as well as acceptable bias the potential advantage of the proposed robustified model based approach over direct nonparametric regression is also demonstrated

conditional properties of some estimators in stratified sampling abstract the prediction properties of the stratified expansion estimator the separate and combined ratio estimators and the separate and combined regression estimators are studied under a model appropriate to a population stratified on a size variable several estimators of variance for each total estimator are considered including standard ones from probability sampling theory alternative choices derived from a superpopulation model and the jackknife the theory is tested in an empirical study using a real population earlier studies of the ratio and regression estimators under simple random sampling plans have illustrated that conditional properties of those estimators and of the linearization variance estimators that are often used with them can be much different and less desirable than unconditional properties whether similar results hold for stratified samples and estimators has been the subject of some debate this article illustrates both theoretically and empirically that the use of stratifi

enhancement of the material point method using b spline basis functions the mpm material point method enhanced with b spline basis functions referred to as bsmpm b spline mpm is developed and demonstrated using representative quasi static and dynamic example problems smooth b spline basis functions could significantly reduce the cell crossing error as known for the original mpm a gauss quadrature scheme is designed and shown to be able to diminish the quadrature error in the bsmpm analysis of large deformation problems for the improved accuracy and convergence especially with the quadratic b splines moreover the increase in the order of the b spline basis function is also found to be an effective way to reduce the quadrature error and to improve accuracy and convergence for plate impact examples it is demonstrated that the bsmpm outperforms the generalized interpolation material point gimp and convected particle domain interpolation cpdi methods in term of the accuracy of representing stress waves thus the bsmpm could become a promising alternative to the mpm gimp and cpdi in solving certain types of transient problems

estimation in survey sampling robustness and optimality abstract it is shown how the criteria of efficiency and robustness can be integrated fruitfully in a single optimality criterion within the framework of the unified theory godambe 1955 this is achieved by extending the scope of the usual model based estimation using appropriate sampling designs some situations of common occurrence in survey practice are discussed with a numerical study

spectral factorization by symmetric extraction for distributed parameter systems the spectral factorization problem of a scalar coercive spectral density is considered in the framework of the callier desoer algebra of distributed parameter system transfer functions criteria are given for the infinite product representation of a meromorphic coercive spectral density of finite order and for the convergence of infinite product representations of spectral factors i e for the convergence of the symmetric extraction method for solving the spectral factorization problem of such spectral density these convergence criteria are applied to the solution of the linear quadratic optimal control problem by spectral factorization for a specific class of semigroup hilbert state space systems with a riesz spectral generator the speed of convergence of the symmetric extraction method is also considered as an example a damped vibrating string model is handled

the prediction approach to robust variance estimation in two stage cluster sampling abstract robust statistics are derived for estimating the error variance when a finite population total or a ratio of totals is estimated from a two stage cluster sample in which the first stage sampling fraction is small the analysis is based on prediction superpopulation models that allow for very general correlation structure within clusters results are obtained for when all cluster sizes are known and for when sizes are known only for sample clusters ratio regression and mean of ratios statistics are in the class of population total estimators considered

an enriched meshless method for non linear fracture mechanics this paper presents an enriched meshless method for fracture analysis of cracks in homogeneous isotropic non linear elastic two dimensional solids subject to mode i loading conditions the method involves an element free galerkin formulation and two new enriched basis functions types i and ii to capture the hutchinson rice rosengren singularity field in non linear fracture mechanics the type i enriched basis function can be viewed as a generalized enriched basis function which degenerates to the linear elastic basis function when the material hardening exponent is unity the type ii enriched basis function entails further improvements of the type i basis function by adding trigonometric functions four numerical examples are presented to illustrate the proposed method the boundary layer analysis indicates that the crack tip field predicted by using the proposed basis functions matches with the theoretical solution very well in the whole region considered whether for the near tip asymptotic field or for the far tip elastic field numerical analyses of standard fracture specimens by the proposed meshless method also yield accurate estimates of the j integral for the applied load intensities and material properties considered also the crack mouth opening displacement evaluated by the proposed meshless method is in good agreement with finite element results furthermore the meshless results show excellent agreement with the experimental measurements indicating that the new basis functions are also capable of capturing elastic plastic deformations at a stress concentration effectively copyright 2003 john wiley sons ltd

improved xfem an extra dof free well conditioning and interpolating xfem abstract although its unprecedentedly success in approximating the singular field around a crack tip independent of mesh discretization xfem still has been long hindered in engineering applications by its ill conditioning and the difficulty in mass lumping corresponding to extra dofs an improved xfem i xfem is developed to overcome those difficulties from three aspects 1 to eliminate the linear dependence and the ill conditioning issues of the standard and the corrected xfems 2 to get rid of extra dofs in crack tip enrichment to facilitate optimal mass lumping in dynamic analyses 3 to be interpolating at enriched nodes to enable direct essential contact boundary treatments the core of i xfem is a globally interpolating approximation based on local least squares fitting the new method is numerically examined with comprehensive comparisons with the standard xfem and the corrected xfem fries 2008 the new method s excellent performance in terms of accuracy convergence and conditioning stability are demonstrated

voronoi cell finite difference method for the diffusion operator on arbitrary unstructured grids voronoi cells and the notion of natural neighbours are used to develop a finite difference method for the diffusion operator on arbitrary unstructured grids natural neighbours are based on the voronoi diagram which partitions space into closest point regions the sibson and the laplace non sibsonian interpolants which are based on natural neighbours have shown promise within a galerkin framework for the solution of partial differential equations in this paper we focus on the laplace interpolant with a two fold objective first to unify the previous developments related to the laplace interpolant and to indicate its ties to some well known numerical methods and secondly to propose a voronoi cell finite difference scheme for the diffusion operator on arbitrary unstructured grids a conservation law in integral form is discretized on voronoi cells to derive a finite difference scheme for the diffusion operator on irregular grids the proposed scheme can also be viewed as a point collocation technique a detailed study on consistency is conducted and the satisfaction of the discrete maximum principle stability is established owing to symmetry of the laplace weight a symmetric positive definite stiffness matrix is realized which permits the use of efficient linear solvers on a regular rectangular or hexagonal grid the difference scheme reduces to the classical finite difference method numerical examples for the poisson equation with dirichlet boundary conditions are presented to demonstrate the accuracy and convergence of the finite difference scheme copyright 2003 john wiley sons ltd

mls moving least square based finite elements for three dimensional nonmatching meshes and adaptive mesh refinement abstract with the aid of moving least square mls approximation a new class of three dimensional finite elements are proposed for treating nonmatching meshes and adaptive mesh refinement for which the existing finite elements are hardly efficient with a special choice of the weight function supports and the base functions the method results in useful elements with the polynomial shape function for which the c 1 continuity breaks down on the boundaries between the neighboring subdomains comprising one element the effectiveness of the new elements in handling the discontinuities due to nonmatching interfaces and automatic mesh refinement is demonstrated via three dimensional examples

new concepts in meshless methods meshless methods have been extensively popularized in literature in recent years due to their flexibility in solving boundary value problems two kinds of truly meshless methods the meshless local boundary integral equation mlbie method and the meshless local petrov galerkin mlpg approach are presented and discussed both methods use the moving least squares approximation to interpolate the solution variables while the mlbie method uses a local boundary integral equation formulation and the mlpg employs a local symmetric weak form the two methods are truly meshless ones as both of them do not need a finite element or boundary element mesh either for purposes of interpolation of the solution variables or for the integration of the energy all integrals can be easily evaluated over regularly shaped domains in general spheres in three dimensional problems and their boundaries numerical examples presented in the paper show that high rates of convergence with mesh refinement are achievable in essence the present meshless method based on the lswf is found to be a simple efficient and attractive method with a great potential in engineering applications copyright 2000 john wiley sons ltd

the boundary node method for potential problems the element free galerkin efg method allows one to use a nodal data structure usually with an underlying cell structure within the domain of a body of arbitrary shape the usual efg combines moving least squares mls interpolants with a variational principle weak form and has been used to solve two dimensional 2 d boundary value problems in mechanics such as in potential theory elasticity and fracture this paper proposes a combination of mls interpolants with boundary integral equations bie in order to retain both the meshless attribute of the former and the dimensionality advantage of the latter this new method called the boundary node method bnm only requires a nodal data structure on the bounding surface of a body whose dimension is one less than that of the domain itself an underlying cell structure is again used for numerical integration in principle the bnm for 3 d problems should be extremely powerful since one would only need to put nodes points on the surface of a solid model for an object numerical results are presented in this paper for the solution of laplace s equation in 2 d dirichlet neumann and mixed problems have been solved some on bodies with piecewise straight and others with curved boundaries results from these numerical examples are extremely encouraging 1997 by john wiley sons ltd

does simple random sampling provide adequate balance une etude empirique montre que sous un echantillonnage aleatoire simple les intervalles de confiance du total peuvent avoir des probabilites de recouvrement conditionnelles qui sont imposantes de facon persistante lorsque la taille de l echantillon croit

model based multiplicity estimation of population size a survey is conducted at w of k selection units or lists e g health care institutions or weeks in a year to estimate n the total number of individuals with particular characteristics our estimator utilizes two items determined for each survey participant the number u among the w lists in s and the number j among all k lists on which each survey participant appears in its traditional form selection units are chosen using probability sampling and the statistical properties of the estimator derive from the sampling mechanism here selection units are purposively chosen to maximize the chance that they are typical and a model based analysis is used for inference if the sample is typical the ml estimators of n and e j are unbiased if a condition on the second moment of u j is satisfied the model based variance of the estimator of n based on a purposively chosen typical sample is smaller than one based on a randomly chosen sample methods to test whether the typical assumption is valid using data from the survey are not yet available the importance of proper selection of the sample to maximize the chance that it is typical and model breakdown does not occur must be emphasized

model based direct adjustment abstract direct adjustment or standardization applies population weights to subclass means in an effort to estimate population quantities from a sample that is not representative of the population direct adjustment has several attractive features but when there are many subclasses it can attach large weights to small quantities of data often in a fairly erratic manner in the extreme direct adjustment can attach infinite weight to nonexistent data a noticeable inconvenience in practice this article proposes a method of model based direct adjustment that preserves the attractive features of conventional direct adjustment while stabilizing the weights attached to small subclasses the sample mean and conventional direct adjustment are both special cases of model based direct adjustment under two different extreme models for the subclass specific selection probabilities the discussion of this method provides some insights into the behavior of true and estimated propensity scores the estimated scores

combination of the meshless finite difference approach with the monte carlo random walk technique for solution of elliptic problems abstract this paper proposes a stochastic approach for the fast and effective numerical analysis of the second order elliptic differential equations it is based upon the well known monte carlo mc method with a random walk rw technique carried out on the grid of points this method allows for accurate estimation of the solution of the differential equation at selected point s of the domain and or its boundary it extends the standard formulation of the monte carlo random walk mc rw approach by means of its appropriate combination with the meshless version of the finite difference method in this manner the proposed approach may deal with elliptic equations in more general non homogeneous form as well as boundary conditions of both essential and natural types moreover arbitrarily irregular clouds of nodes may be used with no a priori imposed nodes structure therefore the meshless mc rw approach may be applied to the significantly wider class of problems with more complex geometry this concept was examined on variety of 2d boundary value problems selected numerical results are presented and discussed a simple matlab code is included as well

enrichment of the method of finite spheres using geometry independent localized scalable bubbles summary in this paper we report the development of two new enrichment techniques for the method of finite spheres a truly meshfree method developed for the solution of boundary value problems on geometrically complex domains in the first method the enrichment functions are multiplied by a weight function with compact support while in the second one a floating enrichment node is introduced the scalability of the enrichment bubbles offers flexibility in localizing the spatial extent to which the enrichment field is applied the bubbles are independent of the underlying geometric discretization and therefore provide a means of achieving convergence without excessive refinement several numerical examples involving problems with singular stress fields are provided demonstrating the effectiveness of the enrichment schemes and contrasting them to traditional geometry dependent enrichment strategies in which one or more nodes associated with the geometric discretization of the domain are enriched an additional contribution of this paper is the use of a meshfree numerical integration technique for computing the j integral using the domain integral method copyright 2006 john wiley sons ltd

a coupled interpolating meshfree method for computing sound radiation in infinite domain summary in this paper the coupling of the improved interpolating element free galerkin iiefg method and the variable order infinite acoustic wave envelope element wee method is studied a coupled iiefg wee method for computing sound radiation is proposed to make use of their advantages while evading their disadvantages the coupling is achieved by constructing the hybrid shape function of continuity and compatibility on the interface between the iiefg and wee domains in the iiefg domain the improved interpolating moving least squares iimls method is employed to form the shape functions satisfying the kronecker delta condition while nonsingular weight functions can be used the impacts of the size of the influence domain and the shape parameter on the performance of this coupled method are investigated the numerical results show that the coupled iiefg wee method can take full advantage of both the iiefg and wee methods and that it not only can achieve higher accuracy but also has a faster convergence speed than the conventional method of the finite element coupled with the wee the experimental results show that the method is very flexible for acoustic radiation prediction in the infinite domain this article is protected by copyright all rights reserved

a novel meshless scheme for solving surface integral equations with flat integral domains numerical solutions for electromagnetic em integral equations rely on the discretization of integral domains and the use of meshes for geometric description meshing geometries is very tedious especially for complicated structures with many details tiny parts and geometric discontinuities corners or edges and remeshing could be required in many scenarios to reduce the costs of generating quality meshes meshless or mesh free methods were developed and they have been extensively studied in mechanical engineering though there are less obvious interests in em community the meshless methods employ discrete nodes to replace meshes in the description of geometries but the background meshes for integrations are still needed traditionally in this work we first address the traditional meshless scheme for solving em integral equations based on the moving least square mls approximation for unknown currents and the use of background meshes for integrations and then develop a novel meshless scheme by applying the green s lemma to the em surface integral equations with flat domains the novel scheme transforms a surface integral over a flat domain into a line integral along its boundaries when excluding a singular patch in the domain since only the domain boundaries are discretized and no background meshes are needed the scheme is truly meshless numerical examples for em scattering by flat surface objects are presented to demonstrate the effectiveness of the novel scheme

an empirical study of the ratio estimator and estimators of its variance abstract this paper reports results from an empirical study of the ratio estimator for a finite population total from each of six real populations 1 000 simple random samples 1 000 restricted random samples and three nonrandom samples of size 32 are drawn performance of the ratio estimator and of five estimators of its variance is compared with theoretical results generated using a prediction superpopulation models and b probability sampling distributions the results presented graphically show that theory based on prediction models can reveal relationships that are essential in making inferences but that are concealed in probability sampling analyses

reproducing kernel hierarchical partition of unity part i formulation and theory this work is concerned with developing the hierarchical basis for meshless methods a reproducing kernel hierarchical partition of unity is proposed in the framework of continuous representation as well as its discretized counterpart to form such hierarchical partition a class of basic wavelet functions are introduced based upon the built in consistency conditions the differential consistency conditions for the hierarchical kernel functions are derived it serves as an indispensable instrument in establishing the interpolation error estimate which is theoretically proven and numerically validated for a special interpolant with different combinations of the hierarchical kernels a synchronized convergence effect may be observed being different from the conventional legendre function based p type hierarchical basis the new hierarchical basis is an intrinsic pseudo spectral basis which can remain as a partition of unity in a local region because the discrete wavelet kernels form a partition of nullity these newly developed kernels can be used as the multi scale basis to solve partial differential equations in numerical computation as a p type refinement copyright 1999 john wiley sons ltd

interpolating element free galerkin method for the regularized long wave equation and its error analysis abstract combining the simplified interpolating moving least squares imls method with the galerkin weak form an interpolating element free galerkin iefg method is presented for the numerical study of the regularized long wave rlw equation the trial function in the imls method has one less unknown coefficient than in the traditional mls approximation and the shape functions satisfy the interpolating property at nodes then the iefg method can apply the essential boundary conditions naturally and directly and has high computational accuracy and then this paper studies the error estimates of the iefg method for rlw equation the error estimate of the semi discrete iefg method for the rlw equation on the influence domain radius is first studied and then the convergence rate of the full discrete scheme of the method on the influence domain radius and time step is studied the theoretical results show that the iefg method for rlw equation has good convergence rate for the purpose of demonstration three selected numerical examples are given to demonstrate the method and the mathematical theory of this paper

meshless local petrov galerkin mlpg approximation to the two dimensional sine gordon equation during the past few years the idea of using meshless methods for numerical solution of partial differential equations pdes has received much attention throughout the scientific community and remarkable progress has been achieved on meshless methods the meshless local petrov galerkin mlpg method is one of the truly meshless methods since it does not require any background integration cells the integrations are carried out locally over small sub domains of regular shapes such as circles or squares in two dimensions and spheres or cubes in three dimensions in this paper the mlpg method for numerically solving the non linear two dimensional sine gordon sg equation is developed a time stepping method is employed to deal with the time derivative and a simple predictor corrector scheme is performed to eliminate the non linearity a brief discussion is outlined for numerical integrations in the proposed algorithm some examples involving line and ring solitons are demonstrated and the conservation of energy in undamped sg equation is investigated the final numerical results confirm the ability of proposed method to deal with the unsteady non linear problems in large domains