in search of optimal acceleration approach to iterative solution methods of simultaneous algebraic equations this paper presents several new proposals for acceleration of iterative solution methods of both linear and non linear simultaneous algebraic equations sae the main concept is based on the successive over relaxation technique sor a new simple and effective way of evaluation of the relaxation parameter is based on either minimization or annihilation of the subsequent solution residuum the other concept effectively uses features of the infinite geometrical progression its quotient is built using solution increments in several initial series of subsequent iterative steps both acceleration mechanisms were also combined in order to obtain the best acceleration of the solution process for simultaneous linear algebraic equations slae these concepts were tested on many 1d and 2d benchmark problems with banded and or sparse systems for the relaxed gauss seidel g s approach the convergence rates were up to 200 times better when compared with the standard g s one significant convergence improvement was also reached while testing non linear saes with the relaxed newton raphson method the numerical models of the selected engineering problems were based on the meshless approach due to their more sophisticated nature when compared e g with the finite element analysis

on the ill conditioning in the new higher order multipoint method the new higher order approximation multipoint technique in the meshless fdm is considered the method following the original collatz multipoint concept is based on arbitrary irregular meshes moving weighted least squares approximation and the global local or global local formulations of boundary value problems two basic versions of the multipoint meshless fd approach are developed the general and the specific ones unfortunately ill conditioning phenomenon may be encountered when the general multipoint approach is considered therefore several modifications of the multipoint algorithm have been proposed and tested to avoid this problem a variety of tests done show that the proposed concepts work well however efficiency problem in some versions which involves additional calculations is the main issue now alternatively the simplest solution in this situation is to use a regularization term in the weighted error functional numerical results demonstrate the effectiveness of the proposed versions in situation when ill conditioning or singularity could be encountered

element free galerkin methods in combination with finite element approaches element free galerkin efg methods are methods for solving partial differential equations with the help of shape functions coming from moving least squares approximation the efg method is more flexible than the finite element fe method since it requires only nodal data and no element connectivity is needed because the efg method is computationally expensive combinations of the efg method and the fe method are considered implementations based on several weak forms of the problem description are studied numerical examples in elastostatics and fracture mechanics show that the implementations are able to compute both displacement and stress fields accurately

an adaptive finite element meshless coupled method based on local maximum entropy shape functions for linear and nonlinear problems in this paper an automatic adaptive coupling procedure is proposed for the finite element method fem and the element free galerkin method efgm for linear elasticity and for problems with both material and geometrical nonlinearities in this new procedure initially the whole of the problem domain is modelled using the fem during an analysis those finite elements which violate a predefined error measure are automatically converted to an efg zone this efg zone can be further refined by adding nodes thus avoiding computationally expensive fe remeshing local maximum entropy shape functions are used in the efg zone of the problem domain for two reasons their weak kronecker delta property at the boundaries allows straightforward imposition of essential boundary conditions and also provides a natural way to couple the efg and fe regions compared to the use of moving least squares basis functions the zienkiewicz and zhu error estimation procedure with the superconvergent patch method for strains and stresses recovery is used in the fe region of the problem domain while the chung and belytschko error estimation procedure is used in the efg region

assessing the order of dependence for partially exchangeable binary data abstract the problem we consider is how to assess the order of serial dependence within partially exchangeable binary sequences we obtain exact conditional tests comparing any two orders by finding the conditional distribution of data given certain transition counts these tests are facilitated with a new monte carlo scheme asymptotic tests are also discussed in particular we show that the likelihood ratio tests have an asymptotic chi squared distribution thus generalizing the results of billingsley for the particular case of markov chains we apply these methods to several datasets and perform a simulation to study their properties

numerical treatment of acoustic problems with boundary singularities by the singular boundary method abstract the singular boundary method sbm is a novel boundary type meshless method based on the fundamental solution of the given governing equation the sbm employs the origin intensity factors to circumvent the singularities resulting from the fundamental solutions in this paper we investigate the acoustic problems with boundary singularities using the sbm this is achieved by combining the sbm with the singularity subtraction techniques where the solution is decomposed into the singular solution and the regular solution the singular solution is derived analytically which satisfies the governing equation and the corresponding boundary conditions containing the singularities then the regular solution is obtained by the sbm numerical examples show the excellent performance of the proposed technique

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

the multi level hp method for three dimensional problems dynamically changing high order mesh refinement with arbitrary hanging nodes abstract one main challenge of the h p version of the finite element method is the high implementational complexity of the method resulting from the added need of handling hanging nodes appropriately the multi level h p formulation recently introduced for two dimensional applications aims at alleviating these difficulties without compromising the approximation quality this is achieved by changing from the conventional refine by replacement approach to a refine by superposition idea the current work shows that the multi level h p approach can be extended naturally to three dimensional refinement without increasing the complexity of the rule set ensuring linear independence and compatibility of the shape functions in this way a three dimensional h p refinement scheme is formulated in which hanging nodes are avoided by definition this ease of complexity allows for a highly flexible discretization kernel featuring arbitrary irregular meshes and a continuous refinement and coarsening throughout the simulation runtime different numerical examples demonstrate that even in the presence of singularities this novel refinement scheme yields exponential convergence with respect to both the number of unknowns and the computational time it is further shown that the refinement scheme is able to capture complex solution features that demand for three dimensional refinement patterns the dynamic discretization properties of the approach are demonstrated by continuously refining and coarsening the mesh during the simulation runtime to keep the refinement zone local to a moving singularity finally it is shown that the high approximation power of the multi level h p scheme also carries over to curved geometries common in engineering practice without a significant detrimental effect on the conditioning of the stiffness matrix

higher order meshless schemes applied to the finite element method in elliptic problems abstract this paper presents selected approximation techniques typical for the meshless finite difference method mfdm although applied to the finite element method fem finite elements with standard or hierarchical shape functions are coupled with higher order meshless schemes based upon the correction terms of a simple difference operator those terms consist of higher order derivatives which are evaluated by means of the appropriate formulas composition as well as a numerical solution which corresponds to the primary interpolation order assigned to element shape functions correction terms modify the right hand sides of algebraic fe equations only yielding an iterative procedure therefore neither re generation of the stiffness matrix nor introduction of any additional nodes and or degrees of freedom is required such improved fe mfd solution approach allows for the optimal application of advantages of both methods for instance a high accuracy of the nodal fe solution and a derivatives super convergence phenomenon at arbitrary domain points typical for the meshless fdm existing and proposed higher order techniques applied in the fem are compared with each other in terms of the solution accuracy algorithm efficiency and computational complexity in order to examine the considered algorithms numerical results of several two dimensional benchmark elliptic problems are presented both the accuracy of a solution and the solution s derivatives as well as their convergence rates evaluated on irregular and structured meshes as well as arbitrarily irregular adaptive clouds of nodes are taken into account

misspecification tests in econometrics based on ranks abstract this paper introduces a class of rank statistics for use in testing econometric models for misspecification these statistics are ideally suited to survey data since endogenous and exogenous variables in econometric models may therefore be considered exchangeable thus residuals from a wide class of models e g linear regression non linear regression simultaneous equations etc are also exchangeable since rank statistics are distribution free when based on exchangeable data it follows the rank statistics based on these residuals are also distribution free simulation studies in the linear regression case suggest that they have good power characteristics and are distributionally robust in comparison to the usual classical procedures

conforming boundary elements in plane elasticity for shape design sensitivity the structural design sensitivity analysis of a two dimensional continuum using conforming continuous boundary elements is investigated implicit differentiation of the discretized boundary integral equations is performed to obtain design sensitivities in an efficient manner by avoiding the factorization of the perturbed matrices a singular formulation of the boundary element method is used implicit differentiation of the boundary integral equations produces terms that contain derivatives of the fundamental solutions employed in the analysis the behaviour of the singularity of these derivatives of the boundary element kernel functions with respect to the design variables is investigated a rigid body motion technique is presented to obtain the singular terms in the resulting sensitivity matrices thus avoiding the problems associated with their numerical integration a formulation for obtaining the design sensitivities of the continua under body forces of the gravitational and centrifugal types is also presented the design sensitivity results are seen to be of the same order of accuracy as the boundary element analysis results numerical data comparing the performance of conforming and non conforming formulations in the calculation of design sensitivities are also presented the accuracy of the present results is demonstrated through comparisons with existing analytical results

mixed finite element methods reduced and selective integration techniques a unification of concepts the equivalence of certain classes of mixed finite element methods with displacement methods which employ reduced and selective integration techniques is established this enables one to obtain the accuracy of the mixed formulation without incurring the additional computational expense engendered by the auxiliary field of the mixed method applications and numerical examples are presented for problems with constraints which can be difficult to enforce in finite element approximations and have often dictated the use of mixed principles these include thin beams and plates and linear and nonlinear incompressible and nearly incompressible continuum problems in solid and fluid mechanics

enrichment and coupling of the finite element and meshless methods a mixed hierarchical approximation based on finite elements and meshless methods is presented two cases are considered the first one couples regions where finite elements or meshless methods are used to interpolate continuity and consistency is preserved the second one enriches a finite element mesh with particles thus there is no need to remesh in adaptive refinement processes in both cases the same formulation is used convergence is studied and examples are shown copyright 2000 john wiley sons ltd

coupling finite element method with meshless finite difference method in thermomechanical problems this paper focuses on coupling two different computational approaches namely finite element method fem and meshless finite difference method mfdm in one domain the coupled approach is applied in solving thermomechanical initialboundary value problem where the heat transport in the domain is non stationary in this method the domain is divided into two subdomains for fem and mfdm respectively contrary to other coupling techniques the approach presented in this paper is defined in terms of mathematical problem formulation rather than at the approximation level in the weak form of thermomechanical initialboundary value problem variational principle the appropriate additional coupling integrals are defined a priori subsequently the fem and the mfdm approximations which may differ from each other are provided to the formulation it is assumed that there exists a very thin layer of material between the subdomains which is not spatially discretized the width of this layer may be considered the coupling parameter and it is the same for both thermal and mechanical parts similar approach is applied to essential boundary conditions e g prescribed temperature and displacements consequently the consistent formulation of the mixed problem for the coupled femmfdm method is derived the analysis is illustrated with two and three dimensional examples of mechanical and thermomechanical problems

high order fem for multigrid homogenization the high order fem was applied to the multigrid based homogenization and proved to be an efficient method for upscaled solution approximation of problems with rapidly varying possibly noncontinuous coefficients as well as non coherent porous domains that may or may not depict a periodic micro structure and do not have to satisfy the separation condition our main contribution is an improved appropriate for bubble functions inter grid mapping consequently a fast exponential convergence of both displacements and stresses was observed in the conducted numerical experiments with respect to the number of degrees of freedom as well as the time of computation particularly the high accuracy of solution derivatives is an important advantage of this homogenization technique that is equivalent to the multiscale fem

the effective interface approach for coupling of the fe and meshless fd methods and applying essential boundary conditions the paper presents a new effective technique for coupling two computational methods with different types of discretization and approximation it is based on a concept of two adjacent subdomains which are connected with each other by means of a thin layer of material each of the subdomain may have a different discretization structure and approximation base the standard finite element method fem as well as the meshless finite difference method mfdm are applied here to be coupled however the coupling can be used for any other methods the same concept is used for applying the essential boundary conditions for both of the methods the width of the interface layer depending on discretization density is evaluated by means of several heuristic assumptions the paper is illustrated with selected two and three dimensional examples

critical phenomena in sequence matching we give a generalization of the result of erdos and renyi on the length r n of the longest head run in the first n tosses of a coin consider two independent sequences x 1 x 2 cdots x m and y 1y 2 cdots y n suppose that x 1 x 2 cdots are i i d mu and y 1 y 2 cdots are i i d nu where mu and nu are possibly different distributions on a common finite alphabet s let p equiv p x 1 y 1 in 0 1 the length of the longest matching consecutive subsequence is m m n equiv max k x i r y j r for r 1 to k for some 0 leq i leq m k 0 leq j leq n k for m and n rightarrow infty with log m log mn rightarrow lambda in 0 1 our result is that there is a constant k equiv k mu nu lambda in 0 1 rbrack such that p lim m m n log 1 p mn k 1 the proof uses large deviation methods the constant k is determined from a variational formula involving the kullback liebler distance or relative entropy a simple necessary and sufficient condition for k 1 is given for the case m n lambda 1 2 and mu nu k 1 the set of mu nu lambda for which k 1 has nonempty interior the boundary of this set is the location of a phase transition the results generalize to more than two sequences and to markov chains a strong law of large numbers is given for the proportion of letters within the longest matching word the limiting proportion exhibits critical behavior similar to that of k

p fem for finite deformation powder compaction the simulation of powder compaction problems die compaction and cold isostatic pressing is considered herein by an implicit high order p version finite element method in this class of problems use is made of a finite strain viscoplasticity model with evolution equations for internal variables developed for the highly compressible behavior in powder compaction processes the classical approach of implicit finite elements applies the combination of backward euler integration scheme and the multilevel newton algorithm to solve the system of differential algebraic equations resulting from the space discretized weak formulation by means of p version finite elements this approach requires on gauss point level a robust stress algorithm the challenging investigations are the incorporation of the applied highly non linear viscoplasticity model into a p version finite element formulation using follower load applications several axisymmetric numerical examples show the feasibility and good performance of this p version approach