a 3d mortar method for solid mechanics a version of the mortar method is developed for tying arbitrary dissimilar 3d meshes with a focus on issues related to large deformation solid mechanics issues regarding momentum conservation large deformations computational efficiency and bending are considered in particular a mortar method formulation that is invariant to rigid body rotations is introduced a scheme is presented for the numerical integration of the mortar surface projection integrals applicable to arbitrary 3d curved dissimilar interfaces here integration need only be performed at problem initialization such that coefficients can be stored and used throughout a quasi static time stepping process even for large deformation problems a degree of freedom reduction scheme exploiting the dual space interpolation method such that direct linear solution techniques can be applied without lagrange multipliers is proposed this provided a significant reduction in factorization times example problems which touch on the aforementioned solid mechanics related issues are presented published in 2003 by john wiley sons ltd

relaxed conditions for stability of time varying delay systems in this paper the problem of delay dependent stability analysis of time varying delay systems is investigated firstly a new inequality which is the modified version of free matrix based integral inequality is derived and then by aid of this new inequality two novel lemmas which are relaxed conditions for some matrices in a lyapunov function are proposed based on the lemmas improved delay dependent stability criteria which guarantee the asymptotic stability of the system are presented in the form of linear matrix inequality lmi two numerical examples are given to describe the less conservatism of the proposed methods

a polynomial time approximation scheme for inferring evolutionary trees from quartet topologies and its application inferring evolutionary trees has long been a challenging problem for both biologists and computer scientists in recent years research has concentrated on the quartet method paradigm for inferring evolutionary trees quartet methods proceed by first inferring the evolutionary history for every set of four species resulting in a set q of inferred quartet topologies and then recombining these inferred quartet topologies to form an evolutionary tree this paper presents two results on the quartet method paradigm the first is a polynomial time approximation scheme ptas for recombining the inferred quartet topologies optimally this is an important result since to date there have been no polynomial time algorithms with performance guarantees for quartet methods to achieve this result the natural denseness of the set q is exploited the second result is a new technique called quartet cleaning that detects and corrects errors in the set q with performance guarantees this result has particular significance since quartet methods are usually very sensitive to errors in the data it is shown how quartet cleaning can dramatically increase the accuracy of quartet methods

mixed fem of higher order for time dependent contact problems abstract in this paper mixed finite element methods of higher order for time dependent contact problems are discussed the mixed methods are based on resolving the contact conditions by the introduction of lagrange multipliers dynamic signorini problems with and without friction are considered involving thermomechanical and rolling contact rothe s method is used to provide a suitable time and space discretization to discretize in time a stabilized newmark method is applied as an adequate time stepping scheme the space discretization relies on finite elements of higher order in each time step the resulting problems are solved by uzawa s method or alternatively by methods of quadratic programming via a suitable formulation in terms of the lagrange multipliers numerical results are presented towards an application in production engineering the results illustrate the performance of the presented techniques for a variety of problem formulations

a note on relationship between two classes of integral inequalities this technical note firstly introduces two classes of integral inequalities with and without free matrices respectively and points out that they although in different forms are actually equivalent in the sense of conservatism i e the two corresponding ones produce the same tight upper bounds secondly the relationship between the method of integral inequalities with free matrices and the free weighting matrix technique is intensively investigated it is shown that these two different methods are actually equivalent in assessing the stability of time delay systems

a mortar segment to segment contact method for large deformation solid mechanics abstract contact modeling is still one of the most difficult aspects of non linear implicit structural analysis most 3d contact algorithms employed today use node on segment approaches for contacting dissimilar meshes two pass node on segment contact approaches have the well known deficiency of locking due to over constraint in this work we develop and demonstrate a segment to segment contact approach based on the mortar method by eliminating the over constraint this method appears to be much more robust than the node on segment approach furthermore node on segment approaches suffer when individual nodes slide out of contact at contact surface boundaries or when contacting nodes slide from facet to facet this causes jumps in the contact forces due to the discrete nature of the constraint enforcement and difficulties in convergence for implicit solution techniques these jumps in forces are avoided in the segment to segment approach since penetration is measured by the occluded weighted volume which varies smoothly with perturbations until now all mortar schemes have been developed for small deformation sliding and have mainly been applied on flat surfaces here we will present the integration scheme and the linearization approach used for handling the contact surface integrals in the event of large sliding the schemes are designed to conserve linear momentum and can be applied to arbitrarily curved 3d surfaces although expensive our numerical examples demonstrate that the approach is far more robust than even smoothed node on segment contact techniques that is problems previously not solvable with node on segment can now be solved with our segment to segment contact

a primal dual active set algorithm for three dimensional contact problems with coulomb friction in this paper efficient algorithms for contact problems with tresca and coulomb friction in three dimensions are presented and analyzed the numerical approximation is based on mortar methods for nonconforming meshes with dual lagrange multipliers using a nonsmooth complementarity function for the three dimensional friction conditions a primal dual active set algorithm is derived the method determines active contact and friction nodes and at the same time resolves the additional nonlinearity originating from sliding nodes no regularization and no penalization are applied and superlinear convergence can be observed locally in combination with a multigrid method it defines a robust and fast strategy for contact problems with tresca or coulomb friction the efficiency and flexibility of the method is illustrated by several numerical examples

improved robustness and consistency of 3d contact algorithms based on a dual mortar approach abstract mortar finite element methods have been successfully applied as discretization scheme to a wide range of contact and impact problems in recent years the 3d finite deformation contact formulation taken up and enhanced in this paper is based on a mortar approach using so called dual lagrange multipliers which substantially facilitate the treatment of interface constraints as compared with standard mortar techniques despite being quite well established in the meantime dual mortar methods may lack robustness or even consistency in certain situations e g when large curvatures occur in the contact zone or when one body slides off another at a sharp edge however since such scenarios are regularly appearing in engineering practice the present contribution provides several new extensions that completely resolve these issues and thus significantly improve the applicability of dual mortar formulations for challenging contact problems the proposed extensions include a consistent biorthogonalization procedure to obtain feasible dual lagrange multiplier shape functions close to boundaries of the contact surfaces an improved conditioning of the global linear system of equations by nodal scaling and a novel approach to unify the advantages of standard and dual mortar methods via a petrov galerkin type of lagrange multiplier interpolation several numerical examples demonstrate the achievable improvements in terms of consistency and robustness for 3d contact analysis including finite deformations

stability of linear systems with time varying delays using bessel legendre inequalities this paper addresses the stability problem of linear systems with a time varying delay hierarchical stability conditions based on linear matrix inequalities are obtained from an extensive use of the bessel inequality applied to legendre polynomials of arbitrary orders while this inequality has been only used for constant discrete and distributed delays this paper generalizes the same methodology to time varying delays we take advantages of the dependence of the stability criteria on both the delay and its derivative to propose a new definition of allowable delay sets a light and smart modification in their definition leads to relevant conclusions on the numerical results

wirtinger based multiple integral inequality for stability of time delay systems abstractnote that the conservatism of the delay dependent stability criteria can be reduced by increasing the integral terms in lyapunov krasovskii functional lkf this brief revisits the stability problem for a class of linear time delay systems via multiple integral approach the novelty of this brief lies in that a wirtinger based multiple integral inequality is employed to estimate the derivative of a class of lkf with multiple integral terms based on these innovations a new delay dependent stability criterion is derived in terms of linear matrix inequalities two numerical examples are exploited to demonstrate the effectiveness and superiority of the proposed method

affine bessel legendre inequality application to stability analysis for systems with time varying delays abstract recently some novel inequalities have been proposed such as the auxiliary function based integral inequality and the bessel legendre inequality which can be obtained from the former by choosing legendre polynomials as auxiliary functions these inequalities have been successfully applied to systems with constant delays but there have been some difficulties in application to systems with time varying delays since the resulting bounds contain the reciprocal convexity which may not be tractable as it is this paper proposes an equivalent form of the bessel legendre inequality which has the advantage of being easily applied to systems with time varying delays without the reciprocal convexity

technical communique sliding mode control with bounded l 2 gain performance of markovian jump singular time delay systems in this paper we investigate the problem of sliding mode control smc of markovian jump singular time delay systems the aim is to consider the bounded 2 gain performance in the analysis of sliding mode dynamics thus to improve the transient performance of the smc system firstly a delay dependent bounded real lemma is proposed for the underlying system to be stochastically admissible while achieving the prescribed bounded 2 gain performance condition an integral type switching surface function is designed by taking the singular matrix into account thus the resulting sliding mode dynamics is a full order singular markovian jump time delay system then the sliding mode dynamics is analyzed and the solvability condition for the desired switching surface function is derived moreover an smc law is synthesized to drive the system trajectories onto the predefined switching surface in a finite time finally a numerical example is provided to illustrate the effectiveness of the proposed techniques

multiplier spaces for the mortar finite element method in three dimensions we consider the construction of multiplier spaces for use with the mortar finite element method in three spatial dimensions on globally or locally quasi uniform meshes a set of abstract conditions is given for the multiplier spaces which are sufficient to guarantee a stable and convergent mortar approximation three examples of multipliers satisfying these conditions are presented the first one is a dual basis example while the remaining two are based on finite volumes finally the results of computational examples illustrating the theory are reported

stability and stabilization of t s fuzzy systems with two additive time varying delays abstract in this paper new stability and stabilization conditions are proposed for a novel t s fuzzy system the novel t s fuzzy model considered contains two additive time varying delays and has strong application background in networked control systems in contrast to earlier models new lyapunov krasovskii functionals and integral inequalities are used to investigate these criteria as a result new stability and stabilization conditions involving two delay components are established in terms of linear matrix inequalities numerical examples are provided to demonstrate the effectiveness of the criteria

inferring a tree from lowest common ancestors with an application to the optimization of relational expressions we present an algorithm for constructing a tree to satisfy a set of lineage constraints on common ancestors we then apply this algorithm to synthesize a relational algebra expression from a simple tableau a problem arising in the theory of relational databases

recent developments on the stability of systems with aperiodic sampling an overview this article presents basic concepts and recent research directions about the stability of sampled data systems with aperiodic sampling we focus mainly on the stability problem for systems with arbitrary time varying sampling intervals which has been addressed in several areas of research in control theory systems with aperiodic sampling can be seen as time delay systems hybrid systems input output interconnections discrete time systems with time varying parameters etc the goal of the article is to provide a structural overview of the progress made on the stability analysis problem without being exhaustive which would be neither possible nor useful we try to bring together results from diverse communities and present them in a unified manner for each of the existing approaches the basic concepts fundamental results converse stability theorems when available and relations with the other approaches are discussed in detail results concerning extensions of lyapunov and frequency domain methods for systems with aperiodic sampling are recalled as they allow to derive constructive stability conditions furthermore numerical criteria are presented while indicating the sources of conservatism the problems that remain open and the possible directions of improvement at last some emerging research directions such as the design of stabilizing sampling sequences are briefly discussed

multiscale coupling in function space weak coupling between molecular dynamics and continuum mechanics we present a function space oriented coupling approach for the multiscale simulation of non linear processes in mechanics using finite elements and molecular dynamics concurrently the key idea is to construct a transfer operator between the different scales on the basis of weighted local averaging instead of using point wise taken values the local weight functions are constructed by assigning a partition of unity to the molecular degrees of freedom shepard s approach this allows for decomposing the micro scale displacements into a low frequency and a high frequency part by means of a weighted l2 projection numerical experiments illustrating the stabilizing effect of our coupling approach are given copyright 2009 john wiley sons ltd

a dual lagrange method for contact problems with regularized contact conditions this paper presents an algorithm for solving quasi static non linear elasticity contact problems without friction in the context of rough surfaces here we want to model the transition from soft to hard contact in case of rough surfaces on the micro scale the popular dual mortar method is used to enforce the contact constraints in a variationally consistent way without increasing the algebraic system size the algorithm is deduced from a perturbed lagrange formulation and combined with mass lumping techniques to exploit the full advantages of the duality pairing this leads to a regularized saddle point problem for which a nonlinear complementary function and thus a semi smooth newton method can be derived numerical examples demonstrate the applicability to industrial problems and show a good agreement to experimentally obtained results copyright 2014 john wiley sons ltd

an exact method for the stability analysis of time delayed linear time invariant lti systems a general class of linear time invariant systems with time delay is studied recently they attracted considerable interest in the systems and control community the complexity arises due to the exponential type transcendental terms in their characteristic equation the transcendentality brings infinitely many characteristic roots which are cumbersome to elaborate as evident from the literature a number of methodologies have been suggested with limited ability to assess the stability in the parametric domain of time delay this study offers an exact structured and robust methodology to bring a closure to the question at hand ultimately we present a unique explicit analytical expression in terms of the system parameters which not only reveals the stability regions pockets in the domain of time delay but it also declares the number of unstable characteristic roots at any given pocket the method starts with the determination of all possible purely imaginary resonant characteristic roots for any positive time delay to achieve this a simplifying substitution is used for the transcendental terms in the characteristic equation it is proven that the number of such resonant roots for a given dynamics is finite each one of these roots is created by infinitely many time delays which are periodically distributed an interesting property is also claimed next that the root crossing directions at these locations are invariant with respect to the delay and dependent only on the crossing frequency these two unique findings facilitate a simple and practical stability method which is the highlight of the work

convergence and equivalence results for the jensen s inequality application to time delay and sampled data systems the jensen s inequality plays a crucial role in the analysis of time delay and sampled data systems its conservatism is studied through the use of the gruss inequality it has been reported in the literature that fragmentation or partitioning schemes allow to empirically improve the results we prove here that the jensen s gap can be made arbitrarily small provided that the order of uniform fragmentation is chosen sufficiently large nonuniform fragmentation schemes are also shown to speed up the convergence in certain cases finally a family of bounds is characterized and a comparison with other bounds of the literature is provided it is shown that the other bounds are equivalent to jensen s and that they exhibit interesting well posedness and linearity properties which can be exploited to obtain better numerical results

technical communique improved delay range dependent stability criteria for linear systems with time varying delays this paper is concerned with the stability analysis of linear systems with time varying delays in a given range a new type of augmented lyapunov functional is proposed which contains some triple integral terms in the proposed lyapunov functional the information on the lower bound of the delay is fully exploited some new stability criteria are derived in terms of linear matrix inequalities without introducing any free weighting matrices numerical examples are given to illustrate the effectiveness of the proposed method

algorithms for combining rooted triplets into a galled phylogenetic network this paper considers the problem of determining whether a given set t of rooted triplets can be merged without conflicts into a galled phylogenetic network and if so constructing such a network when the input t is dense we solve the problem in o t time which is optimal since the size of the input is theta t in comparison the previously fastest algorithm for this problem runs in o t 2 time we also develop an optimal o t time algorithm for enumerating all simple phylogenetic networks leaf labeled by l that are consistent with t where l is the set of leaf labels in t which is used by our main algorithm next we prove that the problem becomes np hard if extended to nondense inputs even for the special case of simple phylogenetic networks we also show that for every positive integer n there exists some set t of rooted triplets on n leaves such that any galled network can be consistent with at most 0 4883 cdot t of the rooted triplets in t on the other hand we provide a polynomial time approximation algorithm that always outputs a galled network consistent with at least a factor of frac 5 12 0 4166 of the rooted triplets in t

stability and stabilization of t s fuzzy systems with variable delays via new bessel legendre polynomial based relaxed integral inequality abstract this paper investigates the delay range dependent drd stability problem in regards to continuous time takagi sugeno t s fuzzy system with variable delays first a new integral inequality lemma referred herein as higher order polynomial based relaxed integral inequality hopbrii is proposed to reduce the estimation gap of the current work with that of bessel legendre polynomial based inequality blpbi next a suitable lyapunov krasovskii functional lkf is constructed with delay product terms and then using the proposed inequality suitable condition for drd stability and stabilization condition of the considered t s fuzzy system are derived in a linear matrix inequality lmi framework to analyse the advantage theoretically and less conservatism of the proposed method a new drd stability condition using similar lkfs and the blpbi approach is further derived herein finally the efficacy of the proposed stability and stabilization conditions are validated through the solutions of four numerical examples

brief paper passivity based sliding mode control of uncertain singular time delay systems in this paper the problem of sliding mode control smc with passivity of a class of uncertain nonlinear singular time delay systems is studied an integral type switching surface function is designed by taking the singular matrix into account thus the resulting sliding mode dynamics is a full order uncertain singular time delay system by introducing some slack matrices a delay dependent sufficient condition is proposed in terms of linear matrix inequality lmi which guarantees the sliding mode dynamics to be generalized quadratically stable and robustly passive the passification solvability condition is then established moreover a smc law and an adaptive smc law are synthesized to drive the system trajectories onto the predefined switching surface in a finite time finally a numerical example is provided to illustrate the effectiveness of the proposed theory

efficient simulation of multi body contact problems on complex geometries a flexible decomposition approach using constrained minimization we consider the numerical simulation of non linear multi body contact problems in elasticity on complex three dimensional geometries in the case of warped contact boundaries and non matching finite element meshes particular emphasis has to be put on the discretization of the transmission of forces and the non penetration conditions at the contact interface we enforce the discrete contact constraints by means of a non conforming domain decomposition method which allows for optimal error estimates here we develop an efficient method to assemble the discrete coupling operator by computing the triangulated intersection of opposite element faces in a locally adjusted projection plane but carrying out the required quadrature on the faces directly our new element based algorithm does not use any boundary parameterizations and is also suitable for isoparametric elements the emerging non linear system is solved by a monotone multigrid method of optimal complexity several numerical examples in 3d illustrate the effectiveness of our approach copyright 2008 john wiley sons ltd

a dual lagrange method for contact problems with regularized frictional contact conditions modelling micro slip abstract this paper presents an algorithm for solving quasi static non linear elasticity contact problems with friction in the context of rough surfaces here we want to model the transition from sticking to slipping also called micro slip in a physically correct way in order to reproduce measured frictional damping the popular dual mortar method is used to enforce the contact constraints in a variationally consistent way without increasing the algebraic system size the algorithm is deduced from a perturbed lagrange formulation and combined with a serial parallel iwan model this leads to a regularized saddle point problem for which a non linear complementary function and thus a semi smooth newton method can be derived numerical examples demonstrate the applicability to industrial problems and show good agreement to experimentally obtained results

robust h state feedback control for linear systems this paper investigates the problem of robust h control for linear systems first the state feedback closed loop control algorithm is designed second by employing the geometric progression theory a modified augmented lyapunov krasovskii functional lkf with the geometric integral interval is established then parameter uncertainties and the derivative of the delay are flexibly described by introducing the convex combination skill this technique can eliminate the unnecessary enlargement of the lkf derivative estimation which gives less conservatism in addition the designed controller can ensure that the linear systems are globally asymptotically stable with a guaranteed h performance in the presence of a disturbance input and parameter uncertainties a liquid monopropellant rocket motor with a pressure feeding system is evaluated in a simulation example it shows that this proposed state feedback control approach achieves the expected results for linear systems in the sense of the prescribed h performance

wirtinger based integral inequality application to time delay systems in the last decade the jensen inequality has been intensively used in the context of time delay or sampled data systems since it is an appropriate tool to derive tractable stability conditions expressed in terms of linear matrix inequalities lmis however it is also well known that this inequality introduces an undesirable conservatism in the stability conditions and looking at the literature reducing this gap is a relevant issue and always an open problem in this paper we propose an alternative inequality based on the fourier theory more precisely on the wirtinger inequalities it is shown that this resulting inequality encompasses the jensen one and also leads to tractable lmi conditions in order to illustrate the potential gain of employing this new inequality with respect to the jensen one two applications on time delay and sampled data stability analysis are provided

technical communique absolute stability of time delay systems with sector bounded nonlinearity this paper deals with the problem of absolute stability of time delay systems with sector bounded nonlinearity some new delay dependent stability criteria are obtained and formulated in the form of linear matrix inequalities lmis neither model transformation nor bounding technique for cross terms is involved through derivation of the stability criteria numerical examples show that the results obtained in this paper improve the estimate of the stability limit over some existing result

free matrix based integral inequality for stability analysis of systems with time varying delay the free weighting matrix and integral inequality methods are widely used to derive delay dependent criteria for the stability analysis of time varying delay systems because they avoid both the use of a model transformation and the technique of bounding cross terms this technical note presents a new integral inequality called a free matrix based integral inequality that further reduces the conservativeness in those methods it includes well known integral inequalities as special cases using it to investigate the stability of systems with time varying delays yields less conservative delay dependent stability criteria which are given in terms of linear matrix inequalities two numerical examples demonstrate the effectiveness and superiority of the method

a generalized free matrix based integral inequality for stability analysis of time varying delay systems abstract this paper focuses on the delay dependent stability problem of time varying delay systems a generalized free matrix based integral inequality gfmbii is presented this inequality is able to deal with time varying delay systems without using the reciprocal convexity lemma it overcomes the drawback that the bessel legendre inequality is inconvenient to cope with a time varying delay system as the resultant bound contains a reciprocal convexity through the use of the derived inequality and by constructing a suitable lyapunov krasovskii function lkf improved stability criteria are presented in the form of linear matrix inequalities lmis two numerical examples are carried out to demonstrate that the results outperform the state of the art in the literature

computing the maximum agreement of phylogenetic networks we introduce the maximum agreement phylogenetic subnetwork problem masn for finding branching structure shared by a set of phylogenetic networks we prove that the problem is np hard even if restricted to three phylogenetic networks and give an o n2 time algorithm for the special case of two level 1 phylogenetic networks where n is the number of leaves in the input networks and where n is called a level f phylogenetic network if every biconnected component in the underlying undirected graph induces a subgraph of n containing at most f nodes with indegree 2 we also show how to extend our technique to yield a polynomial time algorithm for any two level f phylogenetic networks n1 n2 satisfying f o log n more precisely its running time is o v n1 v n2 2f1 f2 where v ni and fi denote the set of nodes in ni and the level of ni respectively for i 1 2

comparison of some bounding inequalities applied in stability analysis of time delay systems abstract this paper gives comparisons of several bounding inequalities proposed recently for the estimation of integrals and sums of quadratic functions which plays an important role in stability analysis of time delay systems via the lyapunov krasovskii approach the equivalences of several known variants of the free matrix based inequalities and their generalized and simplified forms are shown secondly the relationship between the simplified free matrix based inequality and the combination of the bessel based inequality with different bounding inequalities affine in the length of the intervals are investigated finally we shall demonstrate the theoretical results with the application of the various estimations for the stability analysis of a linear system with time varying delay using the same lyapunov krasovskii functional

delay dependent stabilization of linear systems with time varying state and input delays the integral inequality method is a new way of tackling the delay dependent stabilization problem for a linear system with time varying state and input delays email protected t ax t a 1x t h 1 t b 1u t b 2u t h 2 t in this paper a new integral inequality for quadratic terms is first established then it is used to obtain a new state and input delay dependent criterion that ensures the stability of the closed loop system with a memoryless state feedback controller finally some numerical examples are presented to demonstrate that control systems designed based on the criterion are effective even though neither a b 1 nor a a 1 b 1 is stabilizable

stability analysis of systems with time varying delay via novel augmented lyapunov krasovskii functionals and an improved integral inequality abstract delay dependent stability analysis of linear systems with a time varying delay is investigated in this paper firstly instead of developing a lyapunov krasovskii functional lkf including augmented non integral quadratic terms as usual this paper proposes two augmented integral function based lkfs which can reflect closer relationships among system states secondly to bound the derivative of lkf more accurately a new integral inequality with several free matrices is developed compared with the free matrix based integral inequality this inequality can provide additional freedom due to the free matrices introduced then by employing those lkfs and the improved integral inequality several delay dependent stability criteria are established for two types of delays finally two numerical examples are given to demonstrate the superiority of the proposed method

dual quadratic mortar finite element methods for 3d finite deformation contact mortar finite element methods allow for a flexible and efficient coupling of arbitrary nonconforming interface meshes and are by now quite well established in nonlinear contact analysis in this pa

efficient numerical methods for the large scale parallel solution of elastoplastic contact problems parts of the work of the first author were supported by the deutsche forschungsgemeinschaft dfg within priority program 1480 modelling simulation and compensation of thermal effects for complex machining processes through grant number bl 256 11 3 the third author is supported by the national science foundation through award no oci 1148116 the second and third authors are supported in part by the computational infrastructure in geodynamics initiative cig through the national science foundation under award no ear 0949446 and the university of california davis this publication is based in part on the work supported by award no kus c1 016 04 made by king abdullah university of science and technology kaust some computations for this paper were performed on the brazos and hurr clusters at the institute for applied mathematics and computational science iamcs at texas a m university part of brazos was supported by nsf award dms 0922866 hurr is supported by award no kus c1 016 04 made by king abdullah university of science and technology kaust

equilibration techniques for solving contact problems with coulomb friction abstract in this paper we consider residual and equilibrated error indicators for contact problems with coulomb friction the contact problem is handled within the abstract framework of saddle point problems more precisely the non penetration constraint and the friction law is realized as a variationally consistent weak formulation in terms of a localized dual lagrange multiplier space thus from the displacement we can easily compute in a local post process the lagrange multiplier which acts as a neumann condition on the possible contact zone having computed the discrete lagrange multiplier we can apply standard error estimators by replacing the unknown neumann data by its approximation as it is shown in 1 this results in an error estimator for a one sided contact problem without friction here we consider more general situations and discuss two additional contact terms which measure the non conformity of the discrete lagrange multiplier numerical results in two and three dimensions illustrate the flexibility of the approach and show the influence of the material parameters on the adaptive refinement process

a new dual mortar method for curved interfaces 2d elasticity dual mortar method formulations have shown to be a very effective and efficient way for interfacing e g tying contacting dissimilar meshes on the other hand we have recently found that they can sometimes perform quite poorly when applied to curved surfaces in some solid mechanics applications a new modified two dimensional dual mortar method for piecewise linear finite elements is developed that overcomes this deficiency and is demonstrated on a model problem furthermore mathematical analysis is provided to demonstrate the optimal convergence and stability of the new method copyright 2005 john wiley sons ltd

semi smooth newton methods for mixed fem discretizations of higher order for frictional elasto plastic two body contact problems in this article a semi smooth newton method for frictional two body contact problems and a solution algorithm for the resulting sequence of linear systems are presented it is based on a mixed variational formulation of the problem and a discretization by finite elements of higher order general friction laws depending on the normal stresses and elasto plastic material behavior with linear isotropic hardening are considered numerical results show the efficiency of the presented algorithm

the mortar finite element method with lagrange multipliers the present paper deals with a variant of a non conforming domain decomposition technique the mortar finite element method in the opposition to the original method this variant is never conforming because of the relaxation of the matching constraints at the vertices and the edges in 3d of subdomains it is shown that written under primal hybrid formulation the approximation problem issued from a discretization of a second order elliptic equation in 2d is nonetheless well posed and provides a discrete solution that satisfies optimal error estimates with respect to natural norms finally the parallelization advantages consequence of this variant are also addressed

numerical implementation of two nonconforming finite element methods for unilateral contact we consider the finite element approximation of the unilateral contact problem between elastic bodies we are interested in a practical problem which often occurs in finite element computations concerning two independently discretized bodies in unilateral contact it follows that the nodes of both bodies located on the contact surface do not fit together we present two different approaches in order to define unilateral contact on nonmatching meshes the first is an extension of the mortar finite element method to variational inequalities that defines the contact in a global way on the contrary the second one expresses local node on segment contact conditions in both cases the theoretical approximation properties are given then we implement and compare the two methods

stable lagrange multipliers for quadrilateral meshes of curved interfaces in 3d for the discretization of coupled problems by means of mortar finite elements the choice of the discrete lagrange multiplier space is of crucial importance for the performance of the resulting numerical scheme dual lagrange multipliers offer several advantages since they can be locally eliminated in this paper the lowest order dual lagrange multipliers are extended to arbitrary quadrilateral or triangular surface grids in a first step two alternatives are provided for the case of planar interfaces for the approximation of vector fields two more modifications are given for use on curvilinear interfaces a priori results are obtained and several numerical examples are shown

reciprocally convex approach to stability of systems with time varying delays whereas the upper bound lemma for matrix cross product introduced by park 1999 and modified by moon park kwon and lee 2001 plays a key role in guiding various delay dependent criteria for delayed systems the jensen inequality has become an alternative as a way of reducing the number of decision variables it directly relaxes the integral term of quadratic quantities into the quadratic term of the integral quantities resulting in a linear combination of positive functions weighted by the inverses of convex parameters this paper suggests the lower bound lemma for such a combination which achieves performance behavior identical to approaches based on the integral inequality lemma but with much less decision variables comparable to those based on the jensen inequality lemma

brief paper wirtinger s inequality and lyapunov based sampled data stabilization discontinuous lyapunov functionals appeared to be very efficient for sampled data systems fridman 2010 naghshtabrizi hespanha teel 2008 in the present paper new discontinuous lyapunov functionals are introduced for sampled data control in the presence of a constant input delay the construction of these functionals is based on the vector extension of wirtinger s inequality these functionals lead to simplified and efficient stability conditions in terms of linear matrix inequalities lmis the new stability analysis is applied to sampled data state feedback stabilization and to a novel sampled data static output feedback problem where the delayed measurements are used for stabilization

multiple integral inequalities and stability analysis of time delay systems abstract this paper is devoted to stability analysis of continuous time delay systems based on a set of lyapunov krasovskii functionals new multiple integral inequalities are derived that involve the famous jensen s and wirtinger s inequalities as well as the recently presented bessel legendre inequalities of seuret and gouaisbaut 2015 and the wirtinger based multiple integral inequalities of park et al 2015 and lee et al 2015 the present paper aims at showing that the proposed set of sufficient stability conditions can be arranged into a bidirectional hierarchy of lmis establishing a rigorous theoretical basis for comparison of conservatism of the investigated methods numerical examples illustrate the efficiency of the method

finite time h fuzzy control of nonlinear markovian jump delayed systems with partly uncertain transition descriptions abstract this paper addresses a finite time h fuzzy control problem for a class of nonlinear markovian jump delayed systems with partly uncertain transition descriptions which is represented as a takagi sugeno t s fuzzy model a new homogeneous polynomial of partly uncertain transition rates is chosen free matrix based and double integral forms of the wirtinger based integral inequalities are employed to make the proposed approach less conservative then sufficient conditions are derived such that the fuzzy nonlinear makovian jump delayed system exhibits stochastic finite time boundedness finally two numerical examples are given to illustrate the effectiveness of the proposed design methodology

improved delay dependent stability criteria for time delay systems this note provides an improved asymptotic stability condition for time delay systems in terms of a strict linear matrix inequality unlike previous methods the mathematical development avoids bounding certain cross terms which often leads to conservatism when time varying norm bounded uncertainties appear in a delay system an improved robust delay dependent stability condition is also given examples are provided to demonstrate the reduced conservatism of the proposed conditions

stability analysis of systems with uncertain time varying delays stability of systems in the presence of bounded uncertain time varying delays in the feedback loop is studied the delay parameter is assumed to be an unknown time varying function for which the upper bounds on the magnitude and the variation are given the stability problem is treated in the integral quadratic constraint iqc framework criteria for verifying robust stability are formulated as feasibility problems over a set of frequency dependent linear matrix inequalities the criteria can be equivalently formulated as semi definite programs sdp using kalman yakubovich popov lemma as such checking robust stability can be performed in a computationally efficient fashion

on equivalence and efficiency of certain stability criteria for time delay systems in recent years there have been a number of new delay dependent stability criteria based on linear matrix inequalities published in the literature this note aims to theoretically establish the equivalence of seven of these stability criteria moreover the efficiency of these stability criteria is assessed based on the number of unknowns in the linear matrix inequalities

stability analysis of sampled data systems via free matrix based time dependent discontinuous lyapunov approach in this paper a new time dependent discontinuous lyapunov functional namely free matrix based time dependent discontinuous fmbtdd lyapunov functional is introduced for stability analysis of sampled data systems first a modified free matrix based integral inequality mfmbii is derived based on the existing free matrix based integral inequality 1 and it is applied to develop a stability criterion for sampled data systems and then inspired by mfmbii fmbtdd term is established that leads to efficient stability conditions four numerical examples are given to demonstrate the effectiveness of the proposed methods

improved delay dependent stability criteria for generalized neural networks with time varying delays abstract this paper is concerned with the problem of stability analysis for generalized neural networks with time varying delays a novel integral inequality which includes several existing inequalities as special cases is presented by employing a suitable lyapunov krasovskii functional lkf and using the proposed integral inequality to estimate the derivative of the lkf improved delay dependent stability criteria expressed in terms of linear matrix inequalities are derived finally four numerical examples are provided to demonstrate the effectiveness and the improvement of the proposed method

mixed finite element methods for unilateral problems convergence analysis and numerical studies in this paper we propose and study different mixed variational methods in order to approximate with finite elements the unilateral problems arising in contact mechanics the discretized unilateral conditions at the candidate contact interface are expressed by using either continuous piecewise linear or piecewise constant lagrange multipliers in the saddle point formulation a priori error estimates are established and several numerical studies corresponding to the different choices of the discretized unilateral conditions are achieved

a time discretization scheme based on rothe s method for dynamical contact problems with friction abstract we present a new dissipative and contact stabilized time discretization scheme for dynamic frictional contact problems which is based on rothe s method especially for the case of coulomb friction the stability of the contact stresses is of crucial importance as they directly influence the frictional behavior in our approach we obtain an accurate description of the frictional stresses by a time discretized friction law allowing for an implicit treatment of the contact forces in the framework of the newmark scheme moreover undesirable oscillations at the contact interface are removed by employing an additional l 2 projection within the predictor step since the implicit treatment of the material behavior and the frictional response requires a quasi variational inequality to be solved in each time step we derive a non smooth multiscale method which allows for the efficient and robust solution of these highly non linear problems the convergence of this multiscale method is proven for the case of tresca friction for the case of coulomb friction an inexact fixed point iteration in the normal stresses is used we furthermore consider the case of two body contact here the information transfer at the contact interface is realized by means of mortar methods which provide a stable discretization of the relative displacements and the stresses at the contact boundary numerical results for the resulting fully discrete scheme in 3d are presented showing the high accuracy of the proposed method

technical communique stability and robust stability for systems with a time varying delay to concern the stability and robust stability criteria for systems with time varying delays this note uses not only the time varying delayed state x t h t but also the delay upper bounded state x email protected to exploit all possible information for the relationship among a current state x t an exactly delayed state x t h t a marginally delayed state x email protected and the derivative of the state email protected t when constructing lyapunov krasovskii functionals and some appropriate integral inequalities originally suggested by park 1999 a delay dependent stability criterion for systems with uncertain time invariant delays ieee transactions on automatic control 44 4 876 877 two fundamental criteria are provided for the cases where no bound of delay derivative is assumed and where an upper bound of delay derivative is assumed examples show the resulting criteria outperform all existing ones in the literature

stability analysis of linear systems with interval time varying delays utilizing multiple integral inequalities this paper is devoted to stability analysis of continuous time delay systems with interval time varying delays having known bounds on the delay derivatives a parameterized family of lyapunov krasovskii functionals involving multiple integral terms is introduced and novel multiple integral inequalities are utilized to derive sufficient stability condition for systems with time varying delays the efficiency of the proposed method is illustrated by numerical examples

monotone multigrid methods on nonmatching grids for nonlinear multibody contact problems nonconforming domain decomposition techniques provide a powerful tool for the numerical approximation of partial differential equations we use a generalized mortar method based on dual lagrange multipliers for the discretization of a nonlinear contact problem between linear elastic bodies in the case of unilateral contact problems pointwise constraints occur and monotone multigrid methods yield efficient iterative solvers here we generalize these techniques to nonmatching triangulations where the constraints are realized in terms of weak integral conditions the basic new idea is the construction of a nested sequence of nonconforming constrained spaces we use suitable basis transformations and a multiplicative correction in contrast to other approaches no outer iteration scheme is required the resulting monotone method is of optimal complexity and can be implemented as a multigrid method numerical results illustrate the performance of our approach in two and three dimensions

quantitative approximations of evolving probability measures and sequential markov chain monte carlo methods we study approximations of evolving probability measures by an interacting particle system the particle system dynamics is a combination of independent markov chain moves and importance sampling resampling steps under global regularity conditions we derive non asymptotic error bounds for the particle system approximation in a few simple examples including high dimensional product measures bounds with explicit constants of feasible size are obtained our main motivation are applications to sequential mcmc methods for monte carlo integral estimation

domain decomposition with nonmatching grids augmented lagrangian approach we propose and study a domain decomposition method which treats the constraint of displacement continuity at the interfaces by augmented la grangian techniques and solves the resulting problem by a parallel version of the peaceman rachford algorithm we prove that this algorithm is equivalent to the fictitious overlapping method introduced by p l lions we also prove its linear convergence independently of the discretization step h even if the finite element grids do not match at the interfaces a new preconditioner using fictitious overlapping and well adapted to three dimensional elasticity problems is also introduced and is validated on several numerical examples

further improvement of free weighting matrices technique for systems with time varying delay a novel method is proposed in this note for stability analysis of systems with a time varying delay appropriate lyapunov functional and augmented lyapunov functional are introduced to establish some improved delay dependent stability criteria less conservative results are obtained by considering the additional useful terms which are ignored in previous methods when estimating the upper bound of the derivative of lyapunov functionals and introducing the new free weighting matrices the resulting criteria are extended to the stability analysis for uncertain systems with time varying structured uncertainties and polytopic type uncertainties numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

inferring a level 1 phylogenetic network from a dense set of rooted triplets we consider the following problem given a set j of rooted triplets with leaf set l determine whether there exists a phylogenetic network consistent with j and if so construct one we show that if no restrictions are placed on the hybrid nodes in the solution the problem is trivially solved in polynomial time by a simple sorting network based construction for the more interesting and biologically more motivated case where the solution is required to be a level 1 phylogenetic network we present an algorithm solving the problem in o t 2 time when t is dense i e when t contains at least one rooted triplet for each cardinality three subset of l we also give an o t 5 3 time algorithm for finding the set of all phylogenetic networks having a single hybrid node attached to exactly one leaf and having no other hybrid nodes that are consistent with a given dense set of rooted triplets

an optimal a priori error estimate for nonlinear multibody contact problems nonconforming domain decomposition methods provide a powerful tool for the numerical approximation of partial differential equations for the discretization of a nonlinear multibody contact problem we use linear mortar finite elements based on dual lagrange multipliers under some regularity assumptions on the solution an optimal convergence order of h 0 5 nu 0 nu leq 0 5 can be established in two dimensions 2d and three dimensions 3d compared with a standard linear saddle point formulation two additional terms which provide a measure for the nonconformity and the nonlinearity of the approach have to be taken in account numerical examples illustrating the performance of the nonconforming method and confirming our theoretical result are presented

note on stability of linear systems with time varying delay this note considers the stability of linear systems with a time varying delay we are interested in a simple lyapunov krasovskii functional lkf approach without delay decomposition in this category all recent tractable results had a fixed bound on the allowable maximum size of the delay for years we propose a new simple lkf including the cross terms of variables and quadratic terms multiplied by a higher degree scalar function and present a new result expressed in the form of lmis we show by two well known examples that our result overcomes the previous allowable maximum size of delay and it is less conservative than the previous results having a relatively small upper bound in the derivative of time delay

a note on equivalence between two integral inequalities for time delay systems jensen s inequality and extended jensen s inequality are two important integral inequalities when problems of stability analysis and controller synthesis for time delay systems are considered the extended jensen s inequality introduces two additional free matrices and is generally regarded to be less conservative than jensen s inequality the equivalence between jensen s inequality and extended jensen s inequality in bounding the quadratic term h t h t x t s z x s d s in lyapunov functional of time delay systems is presented and theoretically proved it is shown that the extended jensen s inequality does not decrease the lower bound of this quadratic term obtained using jensen s inequality and then it does not reduce the conservativeness though two additional free matrices m 1 and m 2 are involved

a new model transformation of discrete time systems with time varying delay and its application to stability analysis this technical note focuses on analyzing a new model transformation of uncertain linear discrete time systems with time varying delay and applying it to robust stability analysis the uncertainty is assumed to be norm bounded and the delay intervally time varying a new comparison model is proposed by employing a new approximation for delayed state and then lifting method and simple lyapunov krasovskii functional method are used to analyze the scaled small gain of this comparison model this new approximation results in a much smaller error than the existing ones based on the scaled small gain theorem new stability criteria are proposed in terms of linear matrix inequalities moreover it is shown that the obtained conditions can be established through direct lyapunov method two numerical examples are presented to illustrate the effectiveness and superiority of our results over the existing ones

concurrently coupled atomistic and xfem models for dislocations and cracks a method for the modeling of dislocations and cracks by atomistic continuum models is described the methodology combines the extended finite element method with the bridging domain method bdm the former is used to model crack surfaces and slip planes in the continuum whereas the bdm is used to link the atomistic models with the continuum the bdm is an overlapping domain decomposition method in which the atomistic and continuum energies are blended so that their contributions decay to their boundaries on the overlapping subdomain compatibility between the continua and atomistic domains is enforced by a continuous lagrange multiplier field the methodology allows for simulations with atomistic resolution near crack fronts and dislocation cores while retaining a continuum model in the remaining part of the domain and so a large reduction in the number of atoms is possible it is applied to the modeling of cracks and dislocations in graphene sheets energies and energy distributions compare very well with direct numerical simulations by strictly atomistic models copyright 2008 john wiley sons ltd

a posteriori error estimates of higher order finite elements for frictional contact problems abstract in this paper a posteriori estimates are derived for higher order finite element methods and frictional contact problems the discretization is based on a mixed approach where the geometrical and frictional constraints are captured by lagrange multipliers the use of higher order polynomials leads to a certain non conformity in the discretization which requires special attention in the error analysis as a main result an error estimation is proposed which consists of the dual norm of a residual plus some computable remainder terms the residual is estimated by well known a posteriori error estimates for variational equations the remainder terms represent typical sources resulting from the non conforming mixed discretization numerical experiments confirm the applicability of the a posteriori estimates to adaptive mesh refinements

a primal dual active set strategy for non linear multibody contact problems abstract non conforming domain decomposition methods provide a powerful tool for the numerical approximation of partial differential equations for the discretization of a non linear multibody contact problem we use the mortar approach with a dual lagrange multiplier space to handle the non linearity of the contact conditions we apply a primal dual active set strategy to find the actual contact zone the algorithm can be easily generalized to multibody contact problems a suitable basis transformation guarantees the same algebraic structure in the multibody situation as in the one body case using an inexact primal dual active set strategy in combination with a multigrid method yields an efficient iterative solver different numerical examples for one and multibody contact problems illustrate the performance of the method

optimized general sparse grid approximation spaces for operator equations this paper is concerned with the construction of optimized sparse grid approximation spaces for elliptic pseudodifferential operators of arbitrary order based on the framework of tensor product biorthogonal wavelet bases and stable subspace splittings we construct operator adapted subspaces with a dimension smaller than that of the standard full grid spaces but which have the same approximation order as the standard full grid spaces provided that certain additional regularity assumptions on the solution are fulfilled specifically for operators of positive order their dimension is o 2 j independent of the dimension n of the problem compared to o 2 jn for the full grid space also for operators of negative order the overall cost is significantly in favor of the new approximation spaces we give cost estimates for the case of continuous linear information we show these results in a constructive manner by proposing a galerkin method together with optimal preconditioning the theory covers elliptic boundary value problems as well as boundary integral equations

notes on stability of time delay systems bounding inequalities and augmented lyapunov krasovskii functionals the bounding inequalities and the lyapunov krasovskii functionals lkfs are important for the stability analysis of time delay systems much attention has been paid to develop tighter inequalities for improving stability criteria while the contribution of the lkfs has not been considered when discussing the relationship between the tightness of inequalities and the conservatism of criteria this note is concerned with this issue firstly it is proved that when a simple lkf is applied the stability criteria obtained by the wirtinger based inequality and the jensen inequality are equivalent although the wirtinger based inequality is tighter it means that the tighter inequality does not always lead to a less conservative criterion secondly it is found that a suitable augmented lkf with necessary integral vectors in its derivative is required to achieve the advantage of the wirtinger based inequality based on this observation two delay product type terms are introduced into the lkf to establish new stability criteria finally a numerical example is given to verify the equivalence statements and to show the benefit of the proposed criteria

improved delay dependent stabilization for a class of networked control systems with nonlinear perturbations and two delay components abstract this paper focuses on the problem of delay dependent state feedback control for a class of networked control systems ncss with nonlinear perturbations and two delay components based on the dynamic delay interval ddi method and the wirtinger integral inequality some improved delay dependent stability analysis are obtained furthermore the results are extended to the conditions of ncss with one time delay and the corresponding stability analysis results and state feedback controller are obtained finally some numerical examples and simulations are given to show the effectiveness of the proposed methods

a note on wirtinger type integral inequalities for time delay systems different integral inequalities play important role when problems of stability analysis and controller synthesis for time delay systems are considered the connection of jensen s inequality and extended jensen s inequality is well understood now to reduce the conservativeness introduced by the application of jensen s inequality several versions of the wirtinger integral inequality have been published recently this note presents a comparison between some of these inequalities