sub quadratic convergence of a smoothing newton algorithm for the p 0 and monotone lcp given equation here the linear complementarity problem lcp is to find equation here such that x s 0 s mx q xts 0 by using the chen harker kanzow smale chks smoothing function the lcp is reformulated as a system of parameterized smooth nonsmooth equations as a result a smoothing newton algorithm which is a modified version of the qi sun zhou algorithm mathematical programming vol 87 2000 pp 1 35 is proposed to solve the lcp with m being assumed to be a p0 matrix p0 lcp the proposed algorithm needs only to solve one system of linear equations and to do one line search at each iteration it is proved in this paper that the proposed algorithm has the following convergence properties i it is well defined and any accumulation point of the iteration sequence is a solution of the p0 lcp ii it generates a bounded sequence if the p0 lcp has a nonempty and bounded solution set iii if an accumulation point of the iteration sequence satisfies a nonsingularity condition which implies the p0 lcp has a unique solution then the whole iteration sequence converges to this accumulation point sub quadratically with a q rate 2 t where t 0 1 is a parameter and iv if m is positive semidefinite and an accumulation point of the iteration sequence satisfies a strict complementarity condition then the whole sequence converges to the accumulation point quadratically

structural modal reanalysis methods using homotopy perturbation and projection techniques abstract this paper focuses on the modal reanalysis of structures subjected to multiple modifications of various origins which can greatly affect the mode shapes of these structures the proposed methods are based on the results of a modal analysis of the original structure and on several concepts namely homotopy perturbation projection techniques and taylor series expansion a reduced basis is generated using perturbed eigenvectors and the iterative gram schmidt normalisation algorithm a finite element application highlights the advantages and disadvantages of each of the proposed methods in terms of precision and computational time

convergence of a smoothing type algorithm for the monotone affine variational inequality problem smoothing type algorithms have been applied to solve various optimization problems in the analysis on the global convergence most existing smoothing type algorithms need to assume that the solution set of the problem concerned is nonempty and bounded or some stronger conditions in this paper we investigate a smoothing type algorithm for solving the monotone affine variational inequality problem avip specially we reformulate the avip as a system of parameterized smooth equations and instead of solving the original avip we use a newton type method to solve the smooth equations we show that under mild assumptions the iteration sequence generated by the algorithm is bounded and the algorithm may find a maximally complementary solution to the avip in our analysis on the convergence we do not need to assume that the solution set of the avip is bounded

a combined smoothing and regularization method for monotone second order cone complementarity problems the second order cone complementarity problem soccp is a wide class of problems containing the nonlinear complementarity problem ncp and the second order cone programming problem socp recently fukushima luo and tseng siam j optim 12 2001 pp 436 460 extended some merit functions and their smoothing functions for ncp to soccp moreover they derived computable formulas for the jacobians of the smoothing functions and gave conditions for the jacobians to be invertible in this paper we propose a globally and quadratically convergent algorithm which is based on smoothing and regularization methods for solving monotone soccp in particular we study strong semismoothness and jacobian consistency which play an important role in establishing quadratic convergence of the algorithm furthermore we examine the effectiveness of the algorithm by means of numerical experiments

stochastic free vibration of orthotropic plates using generalized polynomial chaos expansion this paper presents the theory and application of the generalized polynomial chaos expansion for the stochastic free vibration of orthotropic plates specifically the stochastic analysis of orthotropic plates under the uncertainties in elasticity moduli is investigated the uncertain moduli eigen frequencies and eigen modes of the plates are represented by truncated polynomial chaos expansions with arbitrary random basis the expansions are substituted in the governing differential equations to calculating the polynomial chaos coefficients of the eigen frequencies and the eigen modes distribution functions of the uncertain moduli are derived from experimental data where the pearson model is used to identify the type of density functions this realization then is employed to construct random orthogonal basis for each uncertain parameter because of available experimental modal analysis data this paper provides a useful practical example on the efficacy of polynomial chaos where the statistical moments and the probability distributions of modal responses are compared with experimental results

finite termination of a smoothing type algorithm for the monotone affine variational inequality problem in this paper we consider the monotone affine variational inequality problem avip for short based on a smooth reformulation of the avip we propose a newton type method to solve the monotone avip where a testing procedure is embedded into our algorithm under mild assumptions we show that the proposed algorithm may find a maximally complementary solution to the monotone avip in a finite number of iterations preliminary numerical results are reported

a hierarchical non iterative extension of the guyan condensation method for damped structures abstract reduction methods are commonly employed for solving the eigenvalue problems of systems with a large number of degrees of freedom these methods are based upon dividing the system s degrees of freedom into masters and slaves and obtaining a reduced system which is in terms of the masters only since 1965 when the guyan condensation method for undamped structures was presented which neglects the dynamic effects of the slaves entirely there have been many efforts to overcome this by proposing various forms of dynamic condensation methods these methods take into account the dynamics of the slaves through an iterative procedure in this paper a hierarchical non iterative reduction method has been proposed for damped dynamic systems the method results in explicit forms of the effective stiffness viscosity and mass and also introduces higher order properties when third and higher order approximations are used furthermore a procedure for the automatic selection of master degrees of freedom has been proposed which assures the convergence and increases the efficiency of the method application of the method for obtaining low frequency eigenvalues of two example structures with and without damping reveals that results with good accuracy are obtained by using higher order approximations as they consider the dynamics of the slaves properly

finite termination of a newton type algorithm based on a new class of smoothing functions for the affine variational inequality problem in this paper we propose a new class of smoothing functions some favorable properties of the functions are investigated by using the proposed functions the affine variational inequality problem avi is reformulated as a system of parameterized smooth equations a newton method with a projection type testing procedure is proposed to solve the equations under mild assumptions we show that the algorithm may find a maximally complementary solution to the monotone avi in a finite number of iterations preliminary numerical results indicate that the proposed smoothing functions are valuable

gaussian model selection with an unknown variance let y be a gaussian vector whose components are independent with a common unknown variance we consider the problem of estimating the mean of y by model selection more precisely we start with a collection mathcal s s m m in mathcal m of linear subspaces of n and associate to each of these the least squares estimator of on sm then we use a data driven penalized criterion in order to select one estimator among these our first objective is to analyze the performance of estimators associated to classical criteria such as fpe aic bic and amdl our second objective is to propose better penalties that are versatile enough to take into account both the complexity of the collection mathcal s and the sample size then we apply those to solve various statistical problems such as variable selection change point detections and signal estimation among others our results are based on a nonasymptotic risk bound with respect to the euclidean loss for the selected estimator some analogous results are also established for the kullback loss

condensed sfes for nonlinear mechanical problems this paper introduces a coupled approach between stochastic finite element methods and an adaptive condensation technique for the analysis of nonlinear mechanical problems under uncertainties this coupling reduces the size of each individual nonlinear problem solved in sfe by the use of an adaptive condensation method the reduced stiffnesses and other quantities necessary for the condensation technique are approximated using a second low order polynomial expansion thus taking advantage of the coupling with sfe this approach also features a semi analytical technique to compute accurately distributions of structural quantities of interest this method is applied on an elasto plastic steel bar with a small defect and on a damaged beam under 4 point bending in both cases it predicts the random behavior of the structure quite accurately and is able to provide higher order models than a state of the art stochastic collocation method for a reduced computation time

efficient computation of eigenvector sensitivities for structural dynamics aniterativeprocedureispresentedforcomputingeigenvectorsensitivitiesdueto e niteelementmodelparameter variations the present method is a preconditioned conjugate projected gradient based technique and is intended to utilize the existing matrix factorizations developed for an iterative eigensolution such as lanczos or subspace iteration as such this technique can be integrated into a coupled eigensolver sensitivity software module and leverage the nonrecurring costs of the solver the use of projection operators in the algorithm is dictated by the indee nite character of the governing coefe cient matrix of the eigenvector derivative two model examples are provided to demonstrate both the accuracy of the present technique and its superior efe ciency as compared to existing techniques with similar accuracy

convergence acceleration methods the past decade abstract the aim of this paper is to present a review of the most significant results obtained the past ten years on convergence acceleration methods it is divided into four sections dealing respectively with the theory of sequence transformations the algorithms for such transformations the practical problems related to their implementation and their applications to various subjects of numerical analysis

parallel solution methods for stochastic finite element analysis using monte carlo simulation in the present paper innovative solution strategies for parallel computer implementation have been developed in connection with the monte carlo simulation mcs and the weighted integral method to produce efficient numerical handling of stochastic finite element analysis for 2d plane stress strain problems furthermore mcs in conjunction with the local average method is also used to extend the stochastic finite element analysis to 3d solid structures although mcs approaches have the major advantage that accurate solutions can be obtained for any type of problem whose deterministic solution is known either numerically or analytically their applicability is hindered by the high computational effort that is required the implementation of innovative parallel solution techniques in this study resulted in cost effective treatment of these highly computationally demanding problems one and two level domain decomposition methods have been implemented numerical results revealed that the proposed approaches permit an efficient treatment of stochastic finite element analysis for real scale 2d plane stress strain and 3d solid structures

the stochastic finite element method past present and future a powerful tool in computational stochastic mechanics is the stochastic finite element method sfem sfem is an extension of the classical deterministic fe approach to the stochastic framework i e to the solution of static and dynamic problems with stochastic mechanical geometric and or loading properties the considerable attention that sfem received over the last decade can be mainly attributed to the spectacular growth of computing power rendering possible the efficient treatment of large scale problems this article aims at providing a state of the art review of past and recent developments in the sfem area and indicating future directions as well as some open issues to be examined by the computational mechanics community in the future

stress based nonlocal damage model abstract progressive microcracking in brittle or quasi brittle materials as described by damage models presents a softening behavior that in turn requires the use of regularization methods in order to maintain objective results such regularization methods which describe interactions between points provide some general properties including objectivity and the non alteration of a uniform field as well as drawbacks damage initiation free boundary a modification of the nonlocal integral regularization method that takes the stress state into account is proposed in this contribution the orientation and intensity of nonlocal interactions are modified in accordance with the stress state the fundamental framework of the original nonlocal method has been retained making it possible to maintain the method s advantages the modification is introduced through the weight function which in this modified version depends not only on the distance between two points as for the original model but also on the stress state at the remote point the efficiency of this novel approach is illustrated using several examples the proposed modification improves the numerical solution of problems observed in numerical simulations involving regularization techniques damage initiation and propagation in mode i as well as shear band formation are analyzed herein

numerical solution of spectral stochastic finite element systems abstract this paper addresses the issues involved in solving systems of linear equations which arise in the context of the spectral stochastic finite element ssfem formulation two efficient solution procedures are presented that dramatically reduce the amount of computations involved in numerically solving these problems a brief review is first provided of the underlying spectral approach which highlights the peculiar structure of the matrices generated and how their properties are related to both the level of approximation involved as well as to the convergence behavior of the proposed solution procedure the differences between these matrices from their deterministic finite element counterparts are illustrated an iterative solution scheme is proposed which utilizes their specific properties for efficient memory management and enhanced convergence behavior results from numerical tests are presented comparisons with standard algorithms illustrate the efficiency of the proposed algorithm the second solution procedure presented in this paper is based on hierarchical basis concepts results from numerical tests are again provided and the limitations of this approach are assessed the performance of both proposed algorithms indicates that the linear algebraic systems from the underlying ssfem formulation can be solved with considerably less effort in memory and computation time than their size suggests furthermore the data structures and the hierarchical concept introduced in this study are found to have great potential for the future development of adaptive procedures in stochastic fem

asymptotic theory with hierarchical autocorrelation ornstein uhlenbeck tree models hierarchical autocorrelation in the error term of linear models arises when sampling units are related to each other according to a tree the residual covariance is parametrized using the tree distance between sampling units when observations are modeled using an ornstein uhlenbeck ou process along the tree the autocorrelation between two tips decreases exponentially with their tree distance these models are most often applied in evolutionary biology when tips represent biological species and the ou process parameters represent the strength and direction of natural selection for these models we show that the mean is not microergodic no estimator can ever be consistent for this parameter and provide a lower bound for the variance of its mle for covariance parameters we give a general sufficient condition ensuring microergodicity this condition suggests that some parameters may not be estimated at the same rate as others we show that indeed maximum likelihood estimators of the autocorrelation parameter converge at a slower rate than that of generally microergodic parameters we showed this theoretically in a symmetric tree asymptotic framework and through simulations on a large real tree comprising 4507 mammal species

detection of adaptive shifts on phylogenies by using shifted stochastic processes on a tree summary comparative and evolutive ecologists are interested in the distribution of quantitative traits between related species the classical framework for these distributions consists of a random process running along the branches of a phylogenetic tree relating the species we consider shifts in the process parameters which reveal fast adaptation to changes of ecological niches we show that models with shifts are not identifiable in general constraining the models to be parsimonious in the number of shifts partially alleviates the problem but several evolutionary scenarios can still provide the same joint distribution for the extant species we provide a recursive algorithm to enumerate all the equivalent scenarios and to count the number of effectively different scenarios we introduce an incomplete data framework and develop a maximum likelihood estimation procedure based on the expectation maximization algorithm finally we propose a model selection procedure based on the cardinal of effective scenarios to estimate the number of shifts and for which we prove an oracle inequality

galerkin finite element approximations of stochastic elliptic partial differential equations we describe and analyze two numerical methods for a linear elliptic problem with stochastic coefficients and homogeneous dirichlet boundary conditions here the aim of the com putations is to approximate statistical moments of the solution and in particular we give a priori error estimates for the computation of the expected value of the solution the first method gener ates independent identically distributed approximations of the solution by sampling the coefficients of the equation and using a standard galerkin finite element variational formulation the monte carlo method then uses these approximations to compute corresponding sample averages the sec ond method is based on a finite dimensional approximation of the stochastic coefficients turning the original stochastic problem into a deterministic parametric elliptic problem a galerkin finite element method of either the h o rp version then approximates the corresponding deterministic solution yielding approximations of the desired statistics we present a priori error estimates and include a comparison of the computational work required by each numerical approximation to achieve a given accuracy this comparison suggests intuitive conditions for an optimal selection of the numerical approximation

on finite termination of an iterative method for linear complementarity problems based on a well known reformulation of the linear complementarity problem lcp as a nondifferentiable system of nonlinear equations a newton type method will be described for the solution of lcps under certain assumptions it will be shown that this method has a finite termination property i e if an iterate is sufficiently close to a solution of lcp the method finds this solution in one step this result will be applied to a recently proposed algorithm by harker and pang in order to prove that their algorithm also has the finite termination property

a modified augmented lagrangian method for a class of monotone variational inequalities abstract the augmented lagrangian method is an attractive approach for solving linearly constrained convex optimization problems ccop the method is iterative and the task in each iteration is to solve a convex optimization sub problem whose dimension is equal to the number of variables for large problems solving such a sub problem can be still very expensive in this paper we propose a modified augmented lagrangian method for a class of monotone variational inequalities which include ccop the computational load in each iteration of the proposed method is quite small in order to demonstrate the ability and efficiency of the proposed method we present some numerical results for convex nonlinear programming and traffic network equilibrium problems

automatic generation of evolutionary hypotheses using mixed gaussian phylogenetic models phylogenetic comparative methods are widely used to understand and quantify the evolution of phenotypic traits based on phylogenetic trees and trait measurements of extant species such analyses depend crucially on the underlying model gaussian phylogenetic models like brownian motion and ornstein uhlenbeck processes are the workhorses of modeling continuous trait evolution however these models fit poorly to big trees because they neglect the heterogeneity of the evolutionary process in different lineages of the tree previous works have addressed this issue by introducing shifts in the evolutionary model occurring at inferred points in the tree however for computational reasons in all current implementations these shifts are intramodel meaning that they allow jumps in 1 or 2 model parameters keeping all other parameters global for the entire tree there is no biological reason to restrict a shift to a single model parameter or even to a single type of model mixed gaussian phylogenetic models mgpms incorporate the idea of jointly inferring different types of gaussian models associated with different parts of the tree here we propose an approximate maximum likelihood method for fitting mgpms to comparative data comprising possibly incomplete measurements for several traits from extant and extinct phylogenetically linked species we applied the method to the largest published tree of mammal species with body and brain mass measurements showing strong statistical support for an mgpm with 12 distinct evolutionary regimes based on this result we state a hypothesis for the evolution of the brain body mass allometry over the past 160 million y

modal approaches for the stochastic finite element analysis of structures with material and geometric uncertainties this paper presents two efficient modal approaches as an alternative to direct formulations for the time harmonic dynamic analysis of structures with random material and shape parameters in both approaches the structural eigenproblem is solved and complemented by a sensitivity analysis to the random parameters the modal perturbation stochastic finite element method sfem then condenses the response sensitivities to assess the response variability the mixed perturbation monte carlo sfem assesses the response statistics by sampling the structural eigenmodes according to the perturbation estimation of their probability distribution functions pdfs geometric uncertainties are handled through an appropriate shape parameterisation and a shape design sensitivity analysis two numerical applications examine both approaches in terms of accuracy variability level and computational requirements the applications involve a plate bending problem with random young modulus or edge length and a plate with a random flatness default particular observations related to the influence of the parameter pdfs in simulation based methods are also provided

sensitivity analysis of discrete structural systems methods for calculating sensitivity derivatives for discrete structural systems are surveyed primarily covering literature published during the past two decades methods are described for calculating derivatives of static displacements and stresses eigenvalues and eigenvectors transient structural response and derivatives of optimum structural designs with respect to problem parameters the survey is focused on publications developed in nonstructural fields such as electronics controls and physical chemistry which are directly applicable to structural problems most notable among the nonstructural based methods are the adjoint variable technique from control theory and the green s function and fast methods from physical chemistry

reduction of the stochastic finite element models using a robust dynamic condensation method abstract one of the ways in which models of structural dynamics can be improved is by taking the various uncertainties that exist into consideration this would also increase the reliability of predicted calculation trends in these models here an original robust multi level dynamic condensation method of stochastic models is proposed the first level condensation is based on a strategy that combines the stochastic finite element method sfem with the robust condensation model it is based on a discretization technique of random fields that was established using the karhunen loeve procedure in addition the use of dynamic condensation was aided by random residual static responses the consequent loads are representative of local modifications per zone or component of the mechanical structure for the second level condensation use of the polynomial chaos pc approach allows the presence of uncertainties in the design parameters to be taken into account and also the variability of the response can be analysed in a less costly manner than by using the monte carlo method alternatively a modal perturbation mp approach allows rapid synthesis of the random response we show how either of these can be used to give an accurate prediction of the condensed model and a considerable reduction of the calculation costs two numerical examples are presented to illustrate the performance of the proposed method

an efficient sfe method using lagrange polynomials application to nonlinear mechanical problems with uncertain parameters designing efficient numerical methods for the solution of stochastic partial differential equations with random inputs or random coefficients is meeting growing interest so far the stochastic galerkin method has been successfully used for various problems with small number of independent random variables the drawback of this method lies in its difficulty of implementation for nonlinear problems in this paper we propose a high order stochastic collocation method to solve nonlinear mechanical systems whose uncertain parameters can be modeled as random variables similar to the stochastic galerkin methods fast convergence can be achieved when the solution in random space is smooth however the numerical implementation of stochastic collocation method is as easy as the monte carlo method since it only requires repetitive runs of an existing deterministic solver we illustrate the efficiency of this method on two nonlinear mechanical problems in which the random parameters are modeled as correlated lognormal random variables