the primal dual active set strategy as a semismooth newton method this paper addresses complementarity problems motivated by constrained optimal control problems it is shown that the primal dual active set strategy which is known to be extremely efficient for this class of problems and a specific semismooth newton method lead to identical algorithms the notion of slant differentiability is recalled and it is argued that the max function is slantly differentiable in lp spaces when appropriately combined with a two norm concept this leads to new local convergence results of the primal dual active set strategy global unconditional convergence results are obtained by means of appropriate merit functions

linear preservers of weak majorization on l1 i when i is an infinite set abstract the necessary and sufficient conditions that a bounded linear map on the banach space l 1 i may be considered as a linear preserver of weak majorization on l 1 i where i is an arbitrary infinite set are given also we prove that the set of all linear preservers of weak majorization is closed under the norm topology

boundary elements with mesh refinements for the wave equation the solution of the wave equation in a polyhedral domain in mathbb r 3 admits an asymptotic singular expansion in a neighborhood of the corners and edges in this article we formulate boundary and screen problems for the wave equation as equivalent boundary integral equations in time domain study the regularity properties of their solutions and the numerical approximation guided by the theory for elliptic equations graded meshes are shown to recover the optimal approximation rates known for smooth solutions numerical experiments illustrate the theory for screen problems in particular we discuss the dirichlet and neumann problems as well as the dirichlet to neumann operator and applications to the sound emission of tires

majorization and a schur horn theorem for positive compact operators the nonzero kernel case abstract schur horn theorems focus on determining the diagonal sequences obtainable for an operator under all possible basis changes formally described as the range of the canonical conditional expectation of its unitary orbit following a brief background survey we prove an infinite dimensional schur horn theorem for positive compact operators with infinite dimensional kernel one of the two open cases posed recently by kaftal weiss there they characterized the diagonals of operators in the unitary orbits for finite rank or zero kernel positive compact operators here we show how the characterization problem depends on the dimension of the kernel when it is finite or infinite dimensional we obtain exact majorization characterizations of the range of the canonical conditional expectation of the unitary orbits of positive compact operators with infinite dimensional kernel unlike the approximate characterizations of arveson kadison but extending the exact characterizations of gohberg markus and kaftal weiss recent advances in this subject and related subjects like traces on ideals show the relevance of new kinds of sequence majorization as in the work of kaftal weiss e g strong majorization and another majorization similar to what here we call p majorization and of kalton sukochev e g uniform hardy littlewood majorization and of bownik jasper e g riemann and lebesgue majorization likewise key tools here are new kinds of majorization which we call p and approximate p majorization 0 p

on h p adaptive bem for frictional contact problems in linear elasticity a mixed formulation for a tresca frictional contact problem in linear elasticity is considered in the context of boundary integral equations which is later extended to coulomb friction the discrete lagrange multiplier an approximation of the surface traction on the contact boundary part is a linear combination of biorthogonal basis functions in case of curved isoparametric elements these are the solutions of local problems in particular the biorthogonality allows to rewrite the variational inequality constraints as a simple set of complementarity problems thus enabling an efficient application of a semi smooth newton solver for the discrete mixed problem converging locally super linearly in the frictional case and quadratically in the frictionless case typically the solution of frictional contact problems is of reduced regularity at the interface between contact to non contact and from stick to slip to identify the a priori unknown locations of these interfaces two a posteriori error estimations are introduced in a first step the error is split into specific error contributions resulting from the contact and friction conditions and from the discretization error of a variational equation for the latter a residual and a bubble error estimation are considered explicitly the numerical experiments show the applicability of the derived error estimations and the superiority of h p adaptivity compared to low order uniform and adaptive approaches

modelling unilateral frictionless contact using the null space method and cubic b spline interpolation the analysis of unilateral sliding contact in elasticity is equivalent to a minimisation problem subjected to a set of inequality constraints however the presence of boundary discontinuities such as those stemming from the spatial discretisation appears as a major problem to determine the set of active constraints this work introduces a smoothing technique of the master surface resorting to cubic b spline interpolation which is c 1 continuous in contact situations between elastic and rigid bodies and g 1 continuous in elastic elastic contact problems the technique is applied in conjunction with the null space method where the solution is searched in an unconstrained manifold the resulting formulation eases the contact transition along the master surface and recovers the quadratic convergence of the iterative newton raphson process the robustness of the method is demonstrated using 2d and 3d examples

a new lagrangean relaxation approach for the hop constrained minimum spanning tree problem abstract we present a new lagrangean relaxation for the hop constrained minimum spanning tree problem hmst the hmst is np hard and models the design of centralized telecommunication networks with quality of service constraints the linear programming lp relaxation of a hop indexed flow based model recently presented in the literature see gouveia l 1998 using variable redefinition for computing lower bounds for minimum spanning and steiner trees with hop constraints informs journal on computing 10 180 188 produces very tight bounds but has the disadvantage of being very time consuming especially for dense graphs in this paper we present a new lagrangean relaxation which is derived from the hop indexed flow based formulation our computational results indicate that the lower bounds given by the new relaxation dominate the lower bounds given by previous lagrangean relaxations our results also show that for dense graphs the new lagrangean relaxation proves to be a reasonable alternative to solving the lp relaxation of the hop indexed model

energy conserving algorithms for a corotational formulation standard nonlinear schemes for the the simulation of elastodynamic problems have several shortcomings when considering high speed rotations to tackle these problems we use a corotational framework and a corresponding specific linearization to design new energy conserving numerical schemes in the two dimensional case an algorithm preserving also angular momentum is presented the existence of a solution for the fully discrete setting of this algorithm is established numerical results illustrate the flexibility and efficiency of the proposed algorithms

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

energy consistent corotational schemes for frictional contact problems in this paper we consider the unilateral frictional contact problem of a hyperelastic body in the case of large displacements and small strains in order to retain the linear elasticity framework we decompose the deformation into a large global rotation and a small elastic displacement this corotational approach is combined with a primal dual active set strategy to tackle the contact problem the resulting algorithm preserves both energy and angular momentum

finite deformation frictional mortar contact using a semi smooth newton method with consistent linearization a two dimensional finite deformation frictional contact formulation with coulomb s law is presented the approach considers multibody contact and is based on a mortar formulation the enforcement of contact constraints is realized with dual lagrange multipliers these alternative multiplier spaces are constructed in a way that the multipliers can easily be eliminated from the global system of equations by static condensation such that the system size does not increase friction kinematic variables are formulated in an objective way and enter non smooth complementarity functions for expressing the contact constraints an active set strategy is derived by applying a semismooth newton method which treats contact nonlinearities material and geometrical nonlinearities in one single iterative scheme by further carrying out a consistent linearization for both normal and frictional contact forces and constraints a robust and highly efficient algorithm for linear and higher order quadratic interpolation is achieved efficiency of the proposed method and quality of results are demonstrated in serveral exemples

a cal v cycle multigrid approach for mortar finite elements mortar methods based on dual lagrange multipliers provide a flexible tool for the numerical approximation of partial differential equations the associated finite element spaces are in general nonconforming and nonnested optimal multigrid results have previously been established for cal w cycle and the variable cal v cycle multigrid methods in this paper we introduce a new multigrid method based on a nested sequence of modified mortar spaces for which we can establish that the cal v cycle with one smoothing step has contraction numbers uniformly bounded away from one to obtain nested mortar spaces we apply a product form of certain corrections at the interfaces numerical results demonstrate the efficiency of the resulting multigrid solver

multicommodity flow models for spanning trees with hop constraints abstract in this paper we compare the linear programming relaxations of undirected and directed multicommodity flow formulations for the terminal layout problem with hop constraints hop constraints limit the number of hops links between the computer center and any terminal in the network these constraints model delay constraints since a smaller number of hops decreases the maximum delay transmission time in the network they also model reliability constraints because with a smaller number of hops there is a lower route loss probability hop constraints are easily modelled with the variables involved in multicommodity flow formulations we give some empirical evidence showing that the linear programming relaxation of such formulations give sharp lower bounds for this hop constrained network design problem on the other hand these formulations lead to very large linear programming models therefore for bounding purposes we also derive several lagrangean based procedures from a directed multicommodity flow formulation and present some computational results taken from a set of instances with up to 40 nodes

a contractive version of a schur horn theorem in ii1 factors we prove a contractive version of the schur horn theorem for submajorization in ii1 factors that complements some previous results on the schur horn theorem within this context we obtain a reformulation of a conjecture of arveson and kadison regarding a strong version of the schur horn theorem in ii1 factors in terms of submajorization and contractive orbits of positive operators

breakout local search for the steiner tree problem with revenue budget and hop constraints the steiner tree problem stp is one of the most popular combinatorial optimization problems with various practical applications in this paper we propose a breakout local search bls algorithm for an important generalization of the stp the steiner tree problem with revenue budget and hop constraints stprbh which consists of determining a subtree of a given undirected graph which maximizes the collected revenues subject to both budget and hop constraints starting from a probabilistically constructed initial solution bls uses a neighborhood search ns procedure based on several specifically designed move operators for local optimization and employs an adaptive diversification strategy to escape from local optima the diversification mechanism is implemented by adaptive perturbations guided by dedicated information of discovered high quality solutions computational results based on 240 benchmarks show that bls produces competitive results with respect to several previous approaches for the 56 most challenging instances with unknown optimal results bls succeeds in improving 49 and matching one best known results within reasonable time for the 184 instances which have been solved to optimality bls can also match 167 optimal results

design of energy conserving algorithms for frictionless dynamic contact problems this paper proposes a formulation of dynamic contact problems which enables exact algorithmic conservation of linear momentum angular momentum and energy in finite element simulations it is seen that a lagrange multiplier enforcement of an appropriate contact rate constraint produces these conservation properties a related method is presented in which a penalty regularization of the aforementioned rate constraint is utilized this penalty method sacrifices the energy conservation property but is dissipative under all conditions of changing contact so that the global algorithm remains stable notably it is also shown that augmented lagrangian iteration utilizing this penalty kernel reproduces the energy conserving i e lagrange multiplier solution to any desired degree of accuracy the result is a robust stable method even in the context of large deformations as is shown by some representative numerical examples in particular the ability of the formulation to produce accurate results where more traditional integration schemes fail is emphasized by the numerical simulations 1997 by john wiley sons ltd

fast heuristics for the steiner tree problem with revenues budget and hop constraints this article describes and compares three heuristics for a variant of the steiner tree problem with revenues which includes budget and hop constraints first a greedy method which obtains good approximations in short computational times is proposed this initial solution is then improved by means of a destroy and repair method or a tabu search algorithm computational results compare the three methods in terms of accuracy and speed

a unified formulation of small strain corotational finite elements i theory this paper presents a unified theoretical framework for the corotational cr formulation of finite elements in geometrically nonlinear structural analysis the key assumptions behind cr are i strains from a corotated configuration are small while ii the magnitude of rotations from a base configuration is not restricted following a historical outline the basic steps of the element independent cr formulation are presented the element internal force and consistent tangent stiffness matrix are derived by taking variations of the internal energy with respect to nodal freedoms it is shown that this framework permits the derivation of a set of cr variants through selective simplifications this set includes some previously used by other investigators the different variants are compared with respect to a set of desirable qualities including self equilibrium in the deformed configuration tangent stiffness consistency invariance symmetrizability and element independence we discuss the main benefits of the cr formulation as well as its modeling limitations

the local average contact lac method abstract the local average contact lac method allows the handling of nonmatching meshes in an easy way by averaging locally the interpenetration between the contacting bodies in this paper we consider the frictionless unilateral contact problem and several numerical experiments involving two and three dimensional bodies discretized with various linear and quadratic finite elements we also present a convergence analysis of the method in the geometrical nonconforming case in which the boundary points of the candidate contact areas do not coincide

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

an infinite dimensional schur horn theorem and majorization theory the main result of this paper is the extension of the schur horn theorem to infinite sequences for two nonincreasing nonsummable sequences and that converge to 0 there exists a positive compact operator a with eigenvalue list and diagonal sequence if and only if j 1n j j 1n j for every n if and only if q for some orthostochastic matrix q when and are summable requiring additionally equality of their infinite series obtains the same conclusion extending a theorem by arveson and kadison our proof depends on the construction and analysis of an infinite product of t transform matrices

hybrid finite element methods for the signorini problem we study three mixed linear finite element methods for the numerical simulation of the two dimensional signorini problem applying falk s lemma and saddle point theory to the resulting discrete mixed variational inequality allows us to state the convergence rate of each of them two of these finite elements provide optimal results under reasonable regularity assumptions on the signorini solution and the numerical investigation shows that the third method also provides optimal accuracy

unilateral non linear dynamic contact of thin walled structures using a primal dual active set strategy the efficient modelling of three dimensional contact problems is still a challenge in non linear implicit structural analysis we use a primal dual active set strategy siam j optim 2003 13 865 888 based on dual lagrange multipliers siam j numer anal 2000 38 989 1012 to handle the non linearity of the contact conditions this allows us to enforce the contact constraints in a weak integral sense without any additional parameter due to the biorthogonality condition of the basis functions the lagrange multipliers can be locally eliminated we perform a static condensation to achieve a reduced system for the displacements the lagrange multipliers representing the contact pressure can be easily recovered from the displacements in a variationally consistent way for the application to thin walled structures we adapt a three dimensional non linear shell formulation including the thickness stretch of the shell to contact problems a reparametrization of the geometric description of the shell body gives us a surface oriented shell element which allows the application of contact conditions directly to nodes lying on the contact surface shell typical locking phenomena are treated with the enhanced assumed strain method and the assumed natural strain method the discretization in time is done with the implicit generalized method j appl mech 1993 60 371 375 and the generalized energy momentum method comp methods appl mech eng 1999 178 343 366 to compare the development of energies within a frictionless contact description in order to conserve the total energy within the discretized frictionless contact framework we follow an approach from laursen and love int j numer methods eng 2002 53 245 274 who introduced a discrete contact velocity to update the velocity field in a post processing step various examples show the good performance of the primal dual active set strategy applied to the implicit dynamic analysis of thin walled structures

an infinite dimensional version of the schur horn convexity theorem the schur horn convexity theorem states that forain rnp u diag a u u u n conv sna wherepdenotes the projection on the diagonal in this paper we generalize this result to the setting of arbitrary separable hilbert spaces it turns out that the theorem still holds if we take thel closure on both sides we will also give a description of the left hand side for nondiagonalizable hermitian operators in the last section we use this result to get an extension theorem for invariant closed convex subsets of the diagonal operators

a posteriori error estimates of discontinuous galerkin methods for the signorini problem a reliable and efficient a posteriori error estimator is derived for a class of discontinuous galerkin dg methods for the signorini problem a common property shared by many dg methods leads to a unified error analysis with the help of a constraint preserving enriching map the error estimator of dg methods is comparable with the error estimator of the conforming methods numerical experiments illustrate the performance of the error estimator

an interior point method for isogeometric contact abstract the interior point method is applied to frictionless contact mechanics problems and is shown to be a viable alternative to the augmented lagrangian approach the method is derived from a mixed formulation which induces a contact discretization scheme in the spirit of the mortar method and naturally delivers slack variables that help constrain the solution to the feasible region the derivation of the algorithm as well as its robustness benefits from the contact interface description that is induced by nurbs based isogeometric volume discretizations various interior point algorithms are discussed including a primal dual approach that satisfies the unilateral contact constraints exactly in addition to two primal approaches that retain an arbitrary barrier parameter the developed algorithms can easily be pursued starting from an augmented lagrangian implementation numerical investigations on benchmark problems demonstrate the efficiency and the robustness of the framework but also highlight current limitations that suggest paths for future research overall the results indicate that the interior point method can challenge the augmented lagrangian method in contact mechanics even displaying potential for higher efficiency and robustness

a posteriori error estimator and error control for contact problems in this paper we consider two error estimators for one body contact problems the first error estimator is defined in terms of h div conforming stress approximations and equilibrated fluxes while the second is a standard edge based residual error estimator without any modification with respect to the contact we show reliability and efficiency for both estimators more over the error is bounded by the first estimator with a constant one plus a higher order data oscillation term plus a term arising from the contact that is shown numerically to be of higher order the second estimator is used in a control based afem refinement strategy and the decay of the error in the energy is shown several numerical tests demonstrate the performance of both estimators

path following and augmented lagrangian methods for contact problems in linear elasticity a certain regularization technique for contact problems leads to a family of problems that can be solved efficiently using infinite dimensional semismooth newton methods or in this case equivalently primal dual active set strategies we present two procedures that use a sequence of regularized problems to obtain the solution of the original contact problem first order augmented lagrangian and path following methods the first strategy is based on a multiplier update while path following with respect to the regularization parameter uses theoretical results about the path value function to increase the regularization parameter appropriately comprehensive numerical tests investigate the performance of the proposed strategies for both a 2d as well as a 3d contact problem

a stable energy conserving approach for frictional contact problems based on quadrature formulas a common approach for the numerical simulation of non linear multi body contact problems is the use of lagrange multipliers to model the contact conditions the stability of standard algorithms is improved by introducing a modified mass matrix which assigns no mass to the potential contact nodes by this the spurious algorithmic oscillations in the multiplier do not occur any more which facilitates the application of the primal dual active set strategy to dynamical contact problems the new mass matrix is calculated via a modified quadrature formula that needs no extra computational cost in addition the conservation properties of the underlying algorithm are transferred to the modified mass version different numerical examples for frictional two body contact problems illustrate the improvement in the results for the contact stresses copyright 2007 john wiley sons ltd

a discontinuous stabilized mortar method for general 3d elastic problems first the present paper is concerned with the extension to linearized elastodynamics of the optimal results known in statics for the mortar method it also analyzes and tests a new couple of displacements lagrange multipliers for the method as proposed independently by ben belgacem f ben belgacem a stabilized domain decomposition method with non matching grids for the stokes problem in three dimensions siam j numer anal 42 2 2004 667 685 and the authors p hauret methodes numeriques pour la dynamique des structures non lineaires incompressibles a deux echelles numerical methods for the dynamic analysis of two scale incompressible nonlinear structures ph d thesis ecole polytechnique 2004 finally questions of practical implementation in the presence of curved interfaces are addressed and validated from the numerical point of view

a steiner arborescence model for the feeder reconfiguration in electric distribution networks in this paper we address the problem of finding the radial configuration of an electric distribution network that minimizes the total losses due to the joule effect we propose an interpretation of the feeder reconfiguration problem as a steiner arborescence problem formulated through a model with a separable quadratic objective function the problem is then solved by a mixed integer quadratic programming solver computational experience on test networks is reported showing the effectiveness of the formulation

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

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

an accurate local average contact method for nonmatching meshes the present paper deals with linear and quadratic finite element approximations of the two and three dimensional unilateral contact problems between two elastic bodies with nonmatching meshes we propose a simple noninterpenetration condition on the displacements which is local as the well known node to segment and node to face conditions and accurate like the mortar approach this condition consists of averaging locally on a few elements the noninterpenetration we prove optimal convergence rates in 2d and 3d using various linear and quadratic elements the taylor patch test and the hertzian contact test illustrate the theoretical results and show the capabilities of the method

incorporation of contact for high order finite elements in covariant form the covariant contact description is applied to incorporate the treatment of contact problems into a high order finite element technique a hierarchical enrichment of the shape functions space allows to construct a contact layer finite element combining both exact geometry representation for contact surfaces and a mesh with linear shape functions for the interior of the contacting bodies the developed contact approach can be viewed as a smoothing technique for linear meshes as well as a general application of high order fem the good approximation property for the developed contact layer elements is shown for the classical hertz problem even within a few contact elements discretizing the contact zone

solution of contact problems by feti domain decomposition with natural coarse space projections abstract an efficient non overlapping domain decomposition algorithm of the neumann neumann type for solving both coercive and semicoercive contact problems is presented the discretized problem is first turned by the duality theory of convex programming to the quadratic programming problem with bound and equality constraints and the latter is further modified by means of orthogonal projectors to the natural coarse space introduced by farhat and roux in the framework of their feti method the resulting problem is then solved by an augmented lagrangian type algorithm with an outer loop for the lagrange multipliers for the equality constraints and an inner loop for the solution of the bound constrained quadratic programming problems the projectors are shown to guarantee fast convergence of iterative solution of auxiliary linear problems and to comply with efficient quadratic programming algorithms proposed earlier reported theoretical results and numerical experiments indicate high numerical scalability of the algorithm which preserves the parallelism of the feti methods

a segment to segment mortar contact method for quadratic elements and large deformations abstract this paper describes a new extension of mortar based segment to segment algorithms for large deformation contact analysis permitting their use when quadratic interpolations are used in the underlying finite element method the work builds upon results previously described by puso and laursen m a puso t a laursen a mortar segment to segment contact method for large deformation solid mechanics comput methods appl mech engrg 193 2004 601 629 m a puso t a laursen a mortar segment to segment frictional contact method for large deformations comput methods appl mech engrg 193 2004 601 629 where methods were developed for quasistatic and implicit dynamic analysis in the context of linear element interpolations here we see that many algorithmic ideas from the linear case can be adopted for use with quadratic elements along with different alternative interpolations of the mortar contact multipliers the result is a class of methods appropriate for use for either mesh tying true large sliding simulation frictionless or frictional and readily admits mixing of element types several numerical examples are given to demonstrate the effectiveness of the approach

a mortar method for energy momentum conserving schemes in frictionless dynamic contact problems summary in the present work the mortar method is applied to planar large deformation contact problems without friction in particular the proposed form of the mortar contact constraints is invariant under translations and rotations these invariance properties lay the foundation for the design of energy momentum timestepping schemes for contact impact problems the iterative solution procedure is embedded into an active set algorithm lagrange multipliers are used to enforce the mortar contact constraints the solution of generalized saddle point systems is circumvented by applying the discrete null space method numerical examples demonstrate the robustness and enhanced numerical stability of the newly developed energymomentum scheme copyright q 2008 john wiley sons ltd

optimal relay node placement in delay constrained wireless sensor network design abstract the delay constrained relay node placement problem dcrnpp frequently arises in the wireless sensor network wsn design in wsn sensor nodes are placed across a target geographical region to detect relevant signals these signals are communicated to a central location known as the base station for further processing the dcrnpp aims to place the minimum number of additional relay nodes at a subset of candidate relay node locations in such a manner that signals from various sensor nodes can be communicated to the base station within a pre specified delay bound in this paper we study the structure of the projection polyhedron of the problem and develop valid inequalities in form of the node cut inequalities we also derive conditions under which these inequalities are facet defining for the projection polyhedron we formulate a branch and cut algorithm based upon the projection formulation to solve dcrnpp optimally a lagrangian relaxation based heuristic is used to generate a good initial solution for the problem that is used as an initial incumbent solution in the branch and cut approach computational results are reported on several randomly generated instances to demonstrate the efficacy of the proposed algorithm

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

a mortar finite element method using dual spaces for the lagrange multiplier the mortar finite element method allows the coupling of different discretization schemes and triangulations across subregion boundaries in the original mortar approach the matching at the interface is realized by enforcing an orthogonality relation between the jump and a modified trace space which serves as a space of lagrange multipliers in this paper this lagrange multiplier space is replaced by a dual space without losing the optimality of the method the advantage of this new approach is that the matching condition is much easier to realize in particular all the basis functions of the new method are supported in a few elements the mortar map can be represented by a diagonal matrix in the standard mortar method a linear system of equations must be solved the problem is considered in a positive definite nonconforming variational as well as an equivalent saddle point formulation

a tabu search heuristic for the vehicle routing problem the purpose of this paper is to describe taburoute a new tabu search heuristic for the vehicle routing problem with capacity and route length restrictions the algorithm considers a sequence of adjacent solutions obtained by repeatedly removing a vertex from its current route and reinserting it into another route this is done by means of a generalized insertion procedure previously developed by the authors during the course of the algorithm infeasible solutions are allowed numerical tests on a set of benchmark problems indicate that tabu search out performs the best existing heuristics and taburoute often produces the best known solutions

the schur horn theorem for operators with three point spectrum abstract we characterize the set of diagonals of the unitary orbit of a self adjoint operator with three points in the spectrum our result gives a schur horn theorem for operators with three point spectrum analogous to kadison s pythagorean theorem and carpenter s theorem which characterize the diagonals of orthogonal projections

weak supermajorization and families as doubly superstochastic operators on lp i abstract we present necessary and sufficient conditions that a family a a i j i j i of real numbers may be considered as a bounded linear operator on banach spaces l 1 i and l i where i is an arbitrary non empty set moreover we get that these conditions are sufficient for a family to be a bounded linear operator on l p i for each p 1 within this class of operators the notion of doubly superstochastic operator is introduced as an extension of the doubly superstochastic matrix and some of its essentially properties are presented in the second part we extend the notion of weak supermajorization relation on the banach space l p i using doubly superstochastic operators and present close relationship between this relation and superstochastic operators as generalisation well known results in the theory of majorization among others for two functions f g l 1 i we show that relations f w s g and g w s f hold if and only if there exist a permutation p such that g p f

adaptive finite elements for elastic bodies in contact to avoid interpenetration of matter under the small strain assumption the linear contact condition is frequently applied where the distance of bodies is controlled only along a certain direction the standard direction is the normal on the surface where interpenetration might occur in this paper we allow other directions as well we address questions such as the correct mathematical model existence of solutions the penalty method for regularization of the variational inequality finite element discretization and a priori and a posteriori error estimates but exclude the error of penalization the computable upper error bound leads to a criterion for automatic mesh refinements within a finite element method numerical simulations of the hertzian contact problem and a supported cantilever beam are included

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