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

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

fluid structure interaction for non conforming interfaces based on a dual mortar formulation abstract in the present work the problem of fluid structure interaction fsi with independently space discretized fluid and structure fields is addressed in the context of finite elements to be able to deal with non conforming meshes at the fluid structure interface we propose the integration of a dual mortar method into the general fsi framework this method has lately been used successfully to impose interface constraints in other contexts such as finite deformation contact the main focus is set on monolithic coupling algorithms for fsi here in these cases the dual mortar approach allows for the elimination of the additional lagrange multiplier degrees of freedom from the global system by condensation the resulting system matrices have the same block structure as their counterparts for the conforming case and permit the same numerical treatment partitioned dirichlet neumann coupling is also considered briefly and it is shown that the dual mortar approach permits a numerically efficient mapping between fluid and structure quantities at the interface numerical examples demonstrate the efficiency and robustness of the proposed method we present results for a variety of different element formulations for the fluid and the structure field indicating that the proposed method is not limited to any specific formulation furthermore the applicability of state of the art iterative solvers is considered and the convergence behavior is shown to be comparable to standard simulations with conforming discretizations at the interface

consistency based search in feature selection feature selection is an effective technique in dealing with dimensionality reduction for classification it is used to find an optimal subset of relevant features such that the overall accuracy of classification is increased while the data size is reduced and the comprehensibility is improved feature selection methods contain two important aspects evaluation of a candidate feature subset and search through the feature space existing algorithms adopt various measures to evaluate the goodness of feature subsets this work focuses on inconsistency measure according to which a feature subset is inconsistent if there exist at least two instances with same feature values but with different class labels we compare inconsistency measure with other measures and study different search strategies such as exhaustive complete heuristic and random search that can be applied to this measure we conduct an empirical study to examine the pros and cons of these search methods give some guidelines on choosing a search method and compare the classifier error rates before and after feature selection

semismooth newton method for frictional contact between pseudo rigid bodies recently developed semismooth newton approach is adopted in the context of the frictional contact between three dimensional pseudo rigid bodies the signorini coulomb problem is formulated according to the formalism of the contact dynamics method hybrid linearisation penalty scaling and line search techniques are combined as the global convergence enhancements of the newton algorithm quasi static simulations of dry masonry assemblies exemplify performance of the presented framework

a truly variationally consistent and symmetric mortar based contact formulation for finite deformation solid mechanics abstract in this work two mortar based segment to segment contact formulations will be developed for the frictionless finite deformation case while the first one is derived by consistent variation of all active contributions of a scalar valued potential subject to inequality constraints thus resulting in a truly variationally consistent and symmetric formulation the second approach is designed in such a way that it is less computationally expensive but still conserves important quantities such as linear and angular momentum since both formulations are derived side by side the introduced simplifications and errors can be specifically analyzed and quantified based on a lagrange multiplier approach the corresponding inequality constraint terms are introduced in two popular ways firstly in form of a standard lagrangian formulation and secondly via an augmented lagrangian formulation both variational forms as well as both solution procedures will be consistently linearized and discussed finally the obtained results will be compared to each other as well as to a well established yet slightly inconsistent mortar based contact formulation

learning boolean concepts in the presence of many irrelevant features abstract in many domains an appropriate inductive bias is the min features bias which prefers consistent hypotheses definable over as few features as possible this paper defines and studies this bias in boolean domains first it is shown that any learning algorithm implementing the min features bias requires ln l 2 p p ln n e training examples to guarantee pac learning a concept having p relevant features out of n available features this bound is only logarithmic in the number of irrelevant features for implementing the min features bias the paper presents five algorithms that identify a subset of features sufficient to construct a hypothesis consistent with the training examples focus 1 is a straightforward algorithm that returns a minimal and sufficient subset of features in quasi polynomial time focus 2 does the same task as focus 1 but is empirically shown to be substantially faster than focus 1 finally the simple greedy mutual information greedy and weighted greedy algorithms are three greedy heuristics that trade optimality for computational efficiency experimental studies are presented that compare these exact and approximate algorithms to two well known algorithms id3 and fringe in learning situations where many irrelevant features are present these experiments show that contrary to expectations the id3 and fringe algorithms do not implement good approximations of min features the sample complexity and generalization performance of the focus algorithms is substantially better than either id3 or fringe on learning problems where the min features bias is appropriate these experiments also show that among our three heuristics the weighted greedy algorithm provides an excellent approximation to the focus algorithms

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

stability and resolution analysis for a topological derivative based imaging functional the aim of this paper is to study a topological derivative based anomaly detection algorithm we compare its performance with other imaging approaches such as multiple signal classification backpropagation and kirchhoff migration we also investigate its stability with respect to medium and measurement noises as well as its resolution a simple postprocessing of the data set is introduced and shown to be essential in order to obtain an efficient topological based imaging functional both in terms of resolution and stability

a robust non linear solid shell element based on a mixed variational formulation the paper is concerned with a geometrically non linear solid shell finite element formulation which is based on the hu washizu variational principle for the approximation of the independent displacement stress and strain fields the strain field is additively decomposed into two parts due to the fact that one part of the strain field is interpolated in the same manner as proposed by the enhanced assumed strain eas method it is denoted as eas field the other strain field is approximated with the same interpolation functions as the stress field in contrast to the eas concept the approximation spaces of the stresses and the enhanced assumed strains are not orthogonal consequently the stress field is not eliminated from the finite element equations for the displacements tri linear shape functions are considered shear locking and curvature thickness locking are treated using assumed natural strain interpolations a static condensation leads to a simple low order hexahedral solid shell element numerical tests show that the present model is very robust and allows larger load steps than an eas solid shell element

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

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

music type electromagnetic imaging of a collection of small three dimensional inclusions in this paper we consider the localization of a collection of small three dimensional bounded homogeneous inclusions via time harmonic electromagnetic means typically using arrays of electric or magnetic dipole transmitters and receivers with given polarization s at some distance from the collection possibly also lying in the far field the inclusions somewhat apart or closely spaced are buried within a homogeneous medium and are of arbitrary contrast of permittivity conductivity and permeability vis ag vis this embedding medium the problem is formulated as an inverse scattering problem for the full maxwell equations and it involves a robust asymptotic modeling of the multistatic response matrix no specific application is studied at this stage but characterization of obstacles in subsoils nondestructive evaluation of man made structures and medical imaging are primary fields of application envisaged the proposed approach uses a music multiple signal classification type algorithm and it yields fast numbering accurate localization and estimates of the electromagnetic and geometric parameters polarization tensors of the inclusions the mathematical machinery is detailed first some specific attention being given to triaxial ellipsoidal inclusions and degenerate spherical shapes for the latter known results are retrieved then the viability of this algorithm which would be easily extended to planarly layered environments by introduction of their green s functions is documented by a variety of numerical results from synthetic noiseless and severely noisy field data

two dimensional mortar contact methods for large deformation frictional sliding this paper presents a mortar based formulation for the solution of two dimensional frictional contact problems involving finite deformation and large sliding as is widely recognized traditional node to surface contact formulations have several drawbacks in solution of deformable to deformable contact problems including lack of general patch test passage degradation of spatial convergence rates and robustness issues associated with the faceted representation of contacting surfaces the mortar finite element method initially proposed as a technique to join dissimilarly meshed domains has been shown to preserve optimal convergence rates in tied contact problems see discretization methods and iterative solvers based on domain decomposition springer verlag heidelberg 2001 for a recent review and is examined here as an alternative spatial discretization method for large sliding contact in particular a novel description for frictional sliding conditions in large deformation mortar formulations is proposed in this work in recent years the mortar element method has already been successfully implemented to solve frictional contact problems with linearized kinematics see int j numer meth engng 1993 36 3451 however in the presence of large deformations and finite sliding one must face difficulties associated with the definition and linearization of contact virtual work in the case where the mortar projection has a direct dependence on the tangential relative motion along the interface in this paper such a formulation is presented with particular emphasis on key aspects of the linearization procedure and on the robust description of the friction kinematics some novel techniques are proposed to treat the non smoothness in the contact geometry and the searching required to define mortar segments a number of numerical examples illustrate the performance and accuracy of the proposed formulation copyright 2004 john wiley sons ltd

multi frequency topological derivative for approximate shape acquisition of curve like thin electromagnetic inhomogeneities abstract in this paper we investigate a non iterative imaging algorithm based on the topological derivative in order to retrieve the shape of penetrable electromagnetic inclusions when their dielectric permittivity and or magnetic permeability differ from those in the embedding homogeneous space the main objective is the imaging of crack like thin inclusions but the algorithm can be applied to arbitrarily shaped inclusions for this purpose we apply multiple time harmonic frequencies and normalize the topological derivative imaging function by its maximum value in order to verify its validity we apply it for the imaging of two dimensional crack like thin electromagnetic inhomogeneities completely hidden in a homogeneous material corresponding numerical simulations with noisy data are performed for showing the efficacy of the proposed algorithm

2d contact smooth formulation based on the mortar method abstract in this paper we apply a smoothing technique to solve contact problems using a segment to segment formulation based on the mortar method in contact smoothing the c 0 finite element description of the geometry is replaced by an improved smoothed one usually with c 1 continuity so far these techniques have been applied to solve contact problems based on node to segment interaction some numerical examples are solved to compare the performance of the smoothing and non smoothing formulations the examples show that the non smoothed mortar formulation is improved mainly for problems with matching curved surfaces discretized with non conforming meshes

representative contact element size determination for micromechanical contact analysis of self affine topographies abstract a generic and straightforward numerical strategy for the determination of the size of representative contact elements rces which are employed in finite element contact homogenization procedures is proposed in this contribution the approach enables the determination of the length height and mesh discretisation of rces that provide a good statistical representation of the contact interface described by a given set of topography properties the case of gaussian self affine and elastic rough profiles under normal frictionless and non adhesive contact is analysed in detail a collection of conditions has been derived for two dimensional problems based on a trade off between the convergence of the real contact area and the computational cost with the increasing width of the roughness power spectrum the restrictions imposed on the length and mesh size can be relaxed allowing to reduce the size of numerical models the corresponding class of problems in three dimensions has also been studied in this case the influence of the numerical scheme adopted for the evaluation of the contact area has been analysed leading to the identification of two bounds which converge for the same value with progressively finer meshes state of the art numerical results fall within the bounded region and the application of the area correction technique proposed by yastrebov et al to the upper node based bound accelerates the convergence of the mesh and renders a good agreement with reference data

parameterized learnability of juntas we study the parameterized complexity of learning k juntas and some variations of juntas we show the hardness of learning k juntas and subclasses of k juntas in the pac model by reductions from a w 2 complete problem on the other hand as a consequence of a more general result we show that k juntas are exactly learnable with improper equivalence queries and access to a w p oracle

topological derivative strategy for one step iteration imaging of arbitrary shaped thin curve like electromagnetic inclusions in this manuscript a fast imaging of thin curve like electromagnetic inclusions completely hidden in the homogeneous domain with smooth boundaries is considered by creating an electromagnetic inclusion of a small diameter and applying the asymptotic expansion formula in the existence of such an inclusion the topological derivative is successfully derived based on this derivative a one step iteration imaging algorithm is designed by solving an adjoint problem various numerical experiments of single and multiple inclusions demonstrate the viability and limitation of the designed algorithm

genetic algorithm based feature set partitioning for classification problems feature set partitioning generalizes the task of feature selection by partitioning the feature set into subsets of features that are collectively useful rather than by finding a single useful subset of features this paper presents a novel feature set partitioning approach that is based on a genetic algorithm as part of this new approach a new encoding schema is also proposed and its properties are discussed we examine the effectiveness of using a vapnik chervonenkis dimension bound for evaluating the fitness function of multiple oblivious tree classifiers the new algorithm was tested on various datasets and the results indicate the superiority of the proposed algorithm to other methods

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

electromagnetic music type imaging of perfectly conducting arc like cracks at single frequency we propose a non iterative music multiple signal classification type algorithm for the time harmonic electromagnetic imaging of one or more perfectly conducting arc like cracks found within a homogeneous space r 2 the algorithm is based on a factorization of the multi static response msr matrix collected in the far field at a single nonzero frequency in either transverse magnetic tm mode dirichlet boundary condition or transverse electric te mode neumann boundary condition followed by the calculation of a music cost functional expected to exhibit peaks along the crack curves each half a wavelength numerical experimentation from exact noiseless and noisy data shows that this is indeed the case and that the proposed algorithm behaves in robust manner with better results in the tm mode than in the te mode for which one would have to estimate the normal to the crack to get the most optimal results

assessment of methods for computing the closest point projection penetration and gap functions in contact searching problems summary in computational contact mechanics problems local searching requires calculation of the closest point projection of a contactor point onto a given target segment it is generally supposed that the contact boundary is locally described by a convex region however because this assumption is not valid for a general curved segment of a three dimensional quadratic serendipity element an iterative numerical procedure may not converge to the nearest local minimum to this end several unconstrained optimization methods are tested the newton raphson method the least square projection the sphere and torus approximation method the steepest descent method the broyden method the broyden fletcher goldfarb shanno method and the simplex method the effectiveness and robustness of these methods are tested by means of a proposed benchmark problem it is concluded that the newton raphson method in conjunction with the simplex method significantly increases the robustness of the local contact search procedure of pure penalty contact methods whereas the torus approximation method can be recommended for contact searching algorithms which employ the lagrange method or the augmented lagrangian method copyright 2015 john wiley sons ltd

an augmented lagrangian algorithm for contact mechanics based on linear regression summary the penalty method for the solution of contact problems yields an approximate satisfaction of the contact constraints augmentation schemes which can be adopted to improve the solution either include the contact forces as additional unknowns or are strongly affected by the penalty parameter and display a poor convergence rate in a previous investigation an unconventional augmentation scheme was proposed on the basis of estimating the exact values of the contact forces through linear interpolation of a database extracted by the previous converged states an enhanced version of this method is proposed herein with respect to the original method the enhanced one eliminates some numerical problems and improves the regularity of the convergence path by carrying out the estimate through linear regression methods the resulting convergence rate is superlinear and the method is quite insensitive to the penalty parameter the main underlying concept is that within the iterative solution of a non linear problem linear regression techniques may be used as a tool to shoot faster to the final solution on the basis of a set of intermediate data the generality of this concept makes it potentially applicable to contact problems in more general settings as well as to other categories of non linear problems copyright 2012 john wiley sons ltd

a semi smooth newton method for orthotropic plasticity and frictional contact at finite strains abstract a new approach for the unified treatment of frictional contact and orthotropic plasticity at finite strains using semi smooth newton methods is presented the contact discretization is based on the well known mortar finite element method using dual lagrange multipliers to facilitate the handling of the additional lagrange multiplier degrees of freedom exploiting the similarity of the typical inequality constraints of plasticity and friction all involved discrete inequalities are reformulated as nonlinear non smooth equations using complementarity functions the resulting set of discrete semi smooth equations can be solved efficiently by a variant of newton s method where all additionally introduced variables are condensed from the global system so that a linear system only consisting of the displacement degrees of freedom has to be solved in each iteration step in contrast to classical radial return mapping methods for computational plasticity the plastic constraints are not required to hold at every iterate in the nonlinear solution procedure but only at convergence this relaxation in the pre asymptotic behavior results in an increased flexibility regarding algorithm design and a potentially higher robustness compared to radial return mapping algorithms the presented elasto plasticity algorithm includes arbitrary isotropic hyperelasticity an anisotropic hill type yield function with isotropic and kinematic hardening plastic spin and appropriate finite element technology for nearly incompressible materials therefore it is well suited for the modeling of sheet metal forming and similar processes several numerical examples underline the robustness of the proposed plasticity algorithm and the efficient treatment of elasto plastic contact problems

crack reconstruction using a level set strategy we present a level set based technique to recover key characteristics of a defect or crack e g location length and shape in a two dimensional material from boundary electrical measurements the key feature of this work is to extend the usual level set technique for modeling volumetric objects to very thin objects two level set functions are employed the first one models the location and form of the crack and the second one models its length and connectivity an efficient gradient based method is derived in order to define evolution laws for these two level set functions which minimize the least squares data misfit numerical experiments show the utility of this method even in the presence of a significant noise level in the measurements a finite element method is used to simulate the electric field behavior in the presence of very thin objects

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

feature selection based on a modified fuzzy c means algorithm with supervision in this paper we propose a new approach to feature selection based on a modified fuzzy c means algorithm with supervision mfcms mfcms completes the unsupervised learning of classical fuzzy c means with labeled patterns the labeled patterns allow mfcms to accurately model the shape of each cluster and consequently to highlight the features which result to be particularly effective to characterize a cluster these features are distinguished by a low variance of their values for the patterns with a high membership degree to the cluster if with respect to these features the distance between the prototype of the cluster and the prototypes of the other clusters is high then these features have the property of discriminating between the cluster and the other clusters to take these two aspects into account for each cluster and each feature we introduce a purposely defined index the higher the value of the index the higher the discrimination capability of the feature for the cluster we execute mfcms on the training set considering all patterns as labeled then we retain the features which are associated at least for one cluster with an index larger than a threshold we applied mfcms to several real world pattern classification benchmarks we used the well known k nearest neighbors as learning algorithm we show that feature selection performed by mfcms achieved an improvement in generalization on all data sets

performance analysis of multi frequency topological derivative for reconstructing perfectly conducting cracks abstract this paper concerns a fast one step iterative technique of imaging extended perfectly conducting cracks with dirichlet boundary condition in order to reconstruct the shape of cracks from scattered field data measured at the boundary we introduce a topological derivative based electromagnetic imaging functional operated at several nonzero frequencies the structure of the imaging functionals is carefully analyzed by establishing relationships with infinite series of bessel functions for the configurations of both symmetric and non symmetric incident field directions identified structure explains why the application of incident fields with symmetric direction operated at multiple frequencies guarantees a successful reconstruction various numerical simulations with noise corrupted data are conducted to assess the performance effectiveness robustness and limitations of the proposed technique

higher order mortar finite element methods in 3d with dual lagrange multiplier bases mortar methods with dual lagrange multiplier bases provide a flexible efficient and optimal way to couple different discretization schemes or nonmatching triangulations here we generalize the concept of dual lagrange multiplier bases by relaxing the condition that the trace space of the approximation space at the slave side with zero boundary condition on the interface and the lagrange multiplier space have the same dimension we provide a new theoretical framework within this relaxed setting which opens a new and simpler way to construct dual lagrange multiplier bases for higher order finite element spaces as examples we consider quadratic and cubic tetrahedral elements and quadratic serendipity hexahedral elements numerical results illustrate the performance of our approach

optimization algorithm for reconstructing interface changes of a conductivity inclusion from modal measurements we propose an original optimization approach for reconstructing interface changes of a conductivity inclusion from measurements of eigenvalues and eigenvectors associated with the transmission problem for the laplacian let be a smooth domain and d be an inclusion contained in whose boundary is also assumed to be smooth shape deformation of d causes a perturbation of modal parameters the aim of this work is to show how this information can be used to reconstruct the unknown deformation for doing so we rigorously derive an asymptotic formula for the perturbations in the eigenvalues of the transmission problem for the laplacian that are due to small deformations of the interface of an inclusion based on this formula we design an efficient reconstruction algorithm from modal measurements our algorithm consists on minimizing a functional whose minimizer yields certain geometric properties of the unknown inclusion it naturally follows from a key identity that is in some sense dual to the asymptotic formula numerical experiments showing the viability of our algorithm are presented our results in this paper extend those established in the context of small volume inclusions as well as those for the conductivity interface problem in fact on one hand in a series of recent papers 5 3 1 2 we have derived high order asymptotic expansions of the eigenvalue perturbations due to the presence of small inclusions and used them for locating the inclusions and identifying some of their geometric features on the other hand in 4 we have derived highorder terms in the asymptotic expansions of the boundary perturbations of steady state voltage potentials resulting from small perturbations of the shape of a conductivity inclusion based on these derivations we have designed an effective algorithm to determine some geometric features of the shape perturbation of the inclusion based on boundary measurements

a fast and robust iterative solver for nonlinear contact problems using a primal dual active set strategy and algebraic multigrid for extending the usability of implicit fe codes for large scale forming simulations the computation time has to be decreased dramatically in principle this can be achieved by using iterative solvers in order to facilitate the use of this kind of solvers one needs a contact algorithm which does not deteriorate the condition number of the system matrix and therefore does not slow down the convergence of iterative solvers like penalty formulations do additionally an algorithm is desirable which does not blow up the size of the system matrix like methods using standard lagrange multipliers the work detailed in this paper shows that a contact algorithm based on a primal dual active set strategy provides these advantages and therefore is highly efficient with respect to computation time in combination with fast iterative solvers especially algebraic multigrid methods copyright 2006 john wiley sons ltd

a finite element approach for the line to line contact interaction of thin beams with arbitrary orientation abstract the objective of this work is the development of a novel finite element formulation describing the contact interaction of slender beams in complex 3d configurations involving arbitrary beam to beam orientations it is shown in a mathematically concise manner that standard beam contact models based on a point wise contact force fail to describe a considerable range of configurations which are however likely to occur in practical applications on the contrary the formulation proposed here models beam to beam contact by means of distributed line forces a procedure that is shown to be applicable for arbitrary geometrical configurations the proposed formulation is based on a gauss point to segment type contact discretization and a penalty regularization of the contact constraint by means of detailed theoretical and numerical investigations it is shown that this approach is more suitable for beam contact than possible alternatives based on mortar type contact discretizations or constraint enforcement by means of lagrange multipliers the proposed formulation is enhanced by a consistently linearized integration interval segmentation avoiding numerical integration across strong discontinuities in combination with a smoothed contact force law and the employed c 1 continuous beam elements this procedure drastically reduces the numerical integration error an essential prerequisite for optimal spatial convergence rates the resulting line to line contact algorithm is supplemented by contact contributions of the beam endpoints which represent boundary minima of the underlying minimal distance problem finally a series of numerical test cases is analyzed in order to investigate the accuracy and consistency of the proposed formulation regarding integration error spatial convergence behavior and resulting contact force distributions for one of these test cases an analytical solution based on the kirchhoff theory of thin rods is derived which can serve as valuable benchmark for the proposed model but also for future beam to beam contact formulations

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

isogeometric dual mortar methods for computational contact mechanics in recent years isogeometric analysis iga has received great attention in many fields of computational mechanics research especially for computational contact mechanics an exact and smooth surface representation is highly desirable as a consequence many well known finite element methods and algorithms for contact mechanics have been transferred to iga in the present contribution the so called dual mortar method is investigated for both contact mechanics and classical domain decomposition using nurbs basis functions in contrast to standard mortar methods the use of dual basis functions for the lagrange multiplier based on the mathematical concept of biorthogonality enables an easy elimination of the additional lagrange multiplier degrees of freedom from the global system this condensed system is smaller in size and no longer of saddle point type but positive definite a very simple and commonly used element wise construction of the dual basis functions is directly transferred to the iga case the resulting lagrange multiplier interpolation satisfies discrete inf sup stability and biorthogonality however the reproduction order is limited to one in the domain decomposition case this results in a limitation of the spatial convergence order to o h3 2 in the energy norm whereas for unilateral contact due to the lower regularity of the solution optimal convergence rates are still met numerical examples are presented that illustrate these theoretical considerations on convergence rates and compare the newly developed isogeometric dual mortar contact formulation with its standard mortar counterpart as well as classical finite elements based on first and second order lagrange polynomials

imaging schemes for perfectly conducting cracks we consider the problem of locating perfectly conducting cracks and estimating their geometric features from multistatic response matrix measurements at a single or multiple frequencies a main objective is to design specific crack detection rules and to analyze their receiver operating characteristics and the associated signal to noise ratios in this paper we introduce an analytic framework that uses asymptotic expansions which are uniform with respect to the wavelength to crack size ratio in combination with a hypothesis test based formulation to construct specific procedures for detection of perfectly conducting cracks a central ingredient in our approach is the use of random matrix theory to characterize the signal space associated with the multistatic response matrix measurements we present numerical experiments to illustrate some of our main findings

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

learnability and the vapnik chervonenkis dimension valiant s learnability model is extended to learning classes of concepts defined by regions in euclidean space e n the methods in this paper lead to a unified treatment of some of valiant s results along with previous results on distribution free convergence of certain pattern recognition algorithms it is shown that the essential condition for distribution free learnability is finiteness of the vapnik chervonenkis dimension a simple combinatorial parameter of the class of concepts to be learned using this parameter the complexity and closure properties of learnable classes are analyzed and the necessary and sufficient conditions are provided for feasible learnability

feature selection with ensembles artificial variables and redundancy elimination predictive models benefit from a compact non redundant subset of features that improves interpretability and generalization modern data sets are wide dirty mixed with both numerical and categorical predictors and may contain interactive effects that require complex models this is a challenge for filters wrappers and embedded feature selection methods we describe details of an algorithm using tree based ensembles to generate a compact subset of non redundant features parallel and serial ensembles of trees are combined into a mixed method that can uncover masking and detect features of secondary effect simulated and actual examples illustrate the effectiveness of the approach

a cut cell finite volume finite element coupling approach for fluid structure interaction in compressible flow we present a loosely coupled approach for the solution of fluid structure interaction problems between a compressible flow and a deformable structure the method is based on staggered dirichlet neumann partitioning the interface motion in the eulerian frame is accounted for by a conservative cut cell immersed boundary method the present approach enables sub cell resolution by considering individual cut elements within a single fluid cell which guarantees an accurate representation of the time varying solid interface the cut cell procedure inevitably leads to non matching interfaces demanding for a special treatment a mortar method is chosen in order to obtain a conservative and consistent load transfer we validate our method by investigating two dimensional test cases comprising a shock loaded rigid cylinder and a deformable panel moreover the aeroelastic instability of a thin plate structure is studied with a focus on the prediction of flutter onset finally we propose a three dimensional fluid structure interaction test case of a flexible inflated thin shell interacting with a shock wave involving large and complex structural deformations

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

generalization as search abstract the problem of concept learning or forming a general description of a class of objects given a set of examples and non examples is viewed here as a search problem existing programs that generalize from examples are characterized in terms of the classes of search strategies that they employ several classes of search strategies are then analyzed and compared in terms of their relative capabilities and computational complexities

feature selection for support vector machines using generalized benders decomposition abstract we propose an exact method based on generalized benders decomposition to select the best m features during induction we provide details of the method and highlight some interesting parallels between the technique proposed here and some of those published in the literature we also propose a relaxation of the problem where selecting too many features is penalized the original method performs well on a variety of data sets the relaxation though competitive is sensitive to the penalty parameter

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

a mortar based frictional contact formulation for large deformations using lagrange multipliers abstract in this work a lagrange multiplier method is proposed to solve 2d coulomb frictional contact problems in the context of large deformations as the proposed formulation is based on the mortar method the constraints are imposed in a weak integral sense along the contact surface in order to compute the contact integrals we use a numerical integration based on the definition of the kinematical variables gap slip and their variations at the quadrature points the linearization of non linear equations virtual work and contact constraints is developed in order to apply a newton s method the examples show that the numerical integration still preserves the optimal rate of convergence of the finite element solution

correntropy based feature selection using binary projection most feature selection algorithms based on information theoretic learning itl adopt ranking process or greedy search as their searching strategies the former selects features individually so that it ignores feature interaction and dependencies the latter heavily relies on the search paths as only one path will be explored with no possible back track in addition both strategies typically lead to heuristic algorithms to cope with these problems this article proposes a novel feature selection framework based on correntropy in itl namely correntropy based feature selection using binary projection bpfs our framework selects features by projecting the original high dimensional data to a low dimensional space through a special binary projection matrix the formulated objective function aims at maximizing the correntropy between selected features and class labels and this function can be efficiently optimized via standard mathematical tools we apply the half quadratic method to optimize the objective function in an iterative manner where each iteration reduces to an assignment subproblem which can be highly efficiently solved with some off the shelf toolboxes comparative experiments on six real world datasets indicate that our framework is effective and efficient

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

biorthogonal splines for optimal weak patch coupling in isogeometric analysis with applications to finite deformation elasticity abstract a new construction of biorthogonal splines for isogeometric mortar methods is proposed the biorthogonal basis has a local support and at the same time optimal approximation properties which yield optimal results with mortar methods we first present the univariate construction which has an inherent crosspoint modification the multivariate construction is then based on a tensor product for weighted integrals whereby the important properties are inherited from the univariate case numerical results including large deformations confirm the optimality of the newly constructed biorthogonal basis

using simulated annealing to optimize the feature selection problem in marketing applications the feature selection also specification problem is concerned with finding the most influential subset of predictors in predictive modeling from a much larger set of potential predictors that can contain hundreds of predictors the problem belongs to the realm of combinatorial optimization where the objective is to find the subset of variables that optimize the value of some goodness of fit function due to the dimensionality of the problem the feature selection problem belongs to the group of np hard problems most of the available predictors are noisy or redundant and add very little if any to the prediction power of the model using all the predictors in the model often results in strong over fitting and very poor predictions constructing a prediction model by checking out all possible subsets is impractical due to computational volume looking on the contribution of each predictor separately is not accurate because it ignores the inter correlations between predictors as a result no analytic solution is available for the feature selection problem requiring that one resorts to heuristics in this paper we employ the simulated annealing sa approach which is one of the leading stochastic search methods for specifying a large scale linear regression model the sa results are compared to the results of the more common stepwise regression swr approach for model specification the models are applied on realistic data sets in database marketing we also use simulated data sets to investigate what data characteristics make the swr approach equivalent to the supposedly more superior sa approach

an h adaptive mortar finite element method for finite deformation contact with higher order p extension in this work we present a generalization of the mortar segment to segment method for finite deformations contact to an h adaptive version with possible p extension i e using higher order approximation we recall the main ideas of the mortar algorithm and present the key aspects of adaptivity error estimation and an h adaptive strategy the p extension exploits the feature of the hp adaptive code in which the contact solver is implemented to handle meshes with nodes of nonuniform orders we use it to set interior nodes to higher order while leaving linear boundary contact nodes which can be processed by the standard mortar algorithm accuracy of elements with low order nodes is restored by adequate subdividing of these elements adaptivity and p extension are illustrated with a few numerical tests

a mortar based approach for the enforcement of periodic boundary conditions on arbitrarily generated meshes a new approach for the enforcement of periodic boundary conditions on representative volume element rve problems is presented the strategy is based on a mortar formulation and considers two and three dimensional problems in the finite deformation frame the mortar discretization is combined with the lagrange multiplier method for the enforcement of periodicity constraints at each pair of corresponding boundaries of the rve in a weak integral sense the interpolation of the lagrange multipliers is undertaken with dual shape functions which can be locally eliminated from the rve system of equations by static condensation avoiding an increase on the system size the numerical treatment within a newton based finite element solution procedure for the rve equilibrium problem is discussed in detail the resulting method is able to efficiently enforce periodic configurations over complex rves at finite strains with arbitrarily generated finite element meshes several numerical examples are presented to demonstrate the robustness of the method and the quality of results

formulation and comparison of algorithms for frictional contact problems this paper presents two algorithms for solving the discrete quasi static small displacement linear elastic contact problem with coulomb friction the algorithms are adoptions of a newton method for solving b differentiable equations and an interior point method for solving smooth constrained equations for the application of the former method the contact problem is formulated as a system of b differentiable equations involving the projection operator onto sets with simple structure for the application of the latter method the contact problem is formulated as a system of smooth equations involving complementarity conditions and with the non negativity of variables treated as constraints the two algorithms are numerically tested for two dimensional problems containing up to 100 contact nodes and up to 100 time increments results show that at the present stage of development the newton method is superior both in robustness and speed additional comparison is made with a commercial finite element code

spl alpha complete information in factor space in daily life we normally describe our concepts and problems in linguistic terms due to the vagueness of our natural languages the classical approach is unable to fully capture the properties factors of such concepts and problems and hence cannot provide decision makers complete information for making an appropriate decision therefore in this paper we first classify general fuzzy data of a problem which are presented by human linguistic terms into different categories and based on their properties each of them is described by an appropriate fuzzy set then by investigating the properties of a problem as factors of a system a fuzzy multiobjective linear programming fmolp model is proposed from the viewpoint of evidence theory and information theory to measure the uncertainty of a fuzzy problem a learning procedure is also designed to inquire the complete information according to the required level of sufficiency spl alpha finally an example of mobile phone service mps is presented to show that the proposed model can aid decision makers to identify representative significant factors and obtain complete information of the mps within a few steps

asymptotic imaging of perfectly conducting cracks in this paper we consider cracks with dirichlet boundary conditions we first derive an asymptotic expansion of the boundary perturbations that are due to the presence of a small crack based on this formula we design a noniterative approach for locating a collection of small cracks in order to do so we construct a response matrix from the boundary measurements the location and the length of the crack are estimated respectively from the projection onto the noise space and the first significant singular value of the response matrix indeed the direction of the crack is estimated from the second singular vector we then consider an extended crack with dirichlet boundary conditions we rigorously derive an asymptotic expansion for the boundary perturbations that are due to a shape deformation of the crack to reconstruct an extended crack from many boundary measurements we develop two methods for obtaining a good guess several numerical experiments show how the proposed techniques for imaging small cracks as well as those for obtaining good initial guesses toward reconstructing an extended crack behave

on some aspects for contact with rigid surfaces surface to rigid surface and curves to rigid surface algorithms abstract special algorithms allowing a simplified description of contact between deformable body and rigid surfaces are developed based on the geometrically exact covariant description of contact a special attention is given to various geometric combinations where the contact can be represented as a contact between surfaces and b contact between a curve and a surface for contact between surfaces leading to the segment to analytical surface stas approach two algorithms can be distinguished based on the selection of a coordinate system for the closest point projection cpp procedure a rigid surface is a slave surface and b rigid surface is a master surface a special combination of both contact kinematics for the surface to surface and for the curve to curve approaches is employed for the contact between a curve and a surface leading to the curve to rigid surface ctrs approach the last algorithm is verified with the well known euler formula for the rope cylinder interaction as well as with a new derived generalization into a 3d spiral rope on a cylinder the developed algorithms can be straightforwardly implemented within an iso geometric approach as well as within the conventional finite elements where rigid surfaces are given by cad patches any type of elements can be employed for the contacting deformable surface curve because the algorithms are formulated in a covariant form

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

multi frequency subspace migration for imaging of perfectly conducting arc like cracks in full and limited view inverse scattering problems multi frequency subspace migration imaging techniques are usually adopted for the non iterative imaging of unknown electromagnetic targets such as cracks in concrete walls or bridges and anti personnel mines in the ground in the inverse scattering problems it is confirmed that this technique is very fast effective robust and can not only be applied to full but also to limited view inverse problems if a suitable number of incidents and corresponding scattered fields are applied and collected however in many works the application of such techniques is heuristic with the motivation of such heuristic application this study analyzes the structure of the imaging functional employed in the subspace migration imaging technique in two dimensional full and limited view inverse scattering problems when the unknown targets are arbitrary shaped arc like perfectly conducting cracks located in the two dimensional homogeneous space in contrast to the statistical approach based on statistical hypothesis testing our approach is based on the fact that the subspace migration imaging functional can be expressed by a linear combination of the bessel functions of integer order of the first kind this is based on the structure of the multi static response msr matrix collected in the far field at nonzero frequency in either transverse magnetic tm mode dirichlet boundary condition or transverse electric te mode neumann boundary condition the investigation of the expression of imaging functionals gives us certain properties of subspace migration and explains why multi frequency enhances imaging resolution in particular we carefully analyze the subspace migration and confirm some properties of imaging when a small number of incident fields are applied consequently we introduce a weighted multi frequency imaging functional and confirm that it is an improved version of subspace migration in tm mode various results of numerical simulations performed on the far field data affected by large amounts of random noise are similar to the analytical results derived in this study and they provide a direction for future studies

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

a finite deformation mortar contact formulation using a primal dual active set strategy in recent years nonconforming domain decomposition techniques and in particular the mortar method have become popular in developing new contact algorithms here we present an approach for two dimensional frictionless multibody contact based on a mortar formulation and using a primal dual active set strategy for contact constraint enforcement we consider linear and higher order quadratic interpolations throughout this work so called dual lagrange multipliers are introduced for the contact pressure but can be eliminated from the global system of equations by static condensation thus avoiding an increase in system size for this type of contact formulation we provide a full linearization of both contact forces and normal non penetration and tangential frictionless sliding contact constraints in the finite deformation frame the necessity of such a linearization in order to obtain a consistent newton scheme is demonstrated by further interpreting the active set search as a semi smooth newton method contact nonlinearity and geometrical and material nonlinearity can be resolved within one single iterative scheme this yields a robust and highly efficient algorithm for frictionless finite deformation contact problems numerical examples illustrate the efficiency of our method and the high quality of results

on the topological derivative in shape optimization in this paper the topological derivative for an arbitrary shape functional is defined examples are provided for elliptic equations and the elasticity system in the plane the topological derivative can be used for solving shape optimization problems in structural mechanics

fuzzy criteria for feature selection the presence of less relevant or highly correlated features often decrease classification accuracy feature selection in which most informative variables are selected for model generation is an important step in data driven modeling in feature selection one often tries to satisfy multiple criteria such as feature discriminating power model performance or subset cardinality therefore a multi objective formulation of the feature selection problem is more appropriate in this paper we propose to use fuzzy criteria in feature selection by using a fuzzy decision making framework this formulation allows for a more flexible definition of the goals in feature selection and avoids the problem of weighting different goals is classical multi objective optimization the optimization problem is solved using an ant colony optimization algorithm proposed in our previous work we illustrate the added value of the approach by applying our proposed fuzzy feature selection algorithm to eight benchmark problems

analysis of multi frequency subspace migration weighted by natural logarithmic function for fast imaging of two dimensional thin arc like electromagnetic inhomogeneities the present study seeks to investigate mathematical structures of a multi frequency subspace migration weighted by the natural logarithmic function for imaging of thin electromagnetic inhomogeneities from measured far field pattern to this end we designed the algorithm and calculated the indefinite integration of square of bessel function of order zero of the first kind multiplied by the natural logarithmic function this is needed for mathematical analysis of improved algorithm to demonstrate the reason why proposed multi frequency subspace migration contributes to yielding better imaging performance compared to previously suggested subspace migration algorithm this analysis is based on the fact that the singular vectors of the collected multi static response msr matrix whose elements are the measured far field pattern can be represented as an asymptotic expansion formula in the presence of such inhomogeneities to support the main research results several numerical experiments with noisy data are illustrated

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

membershipmap data transformation based on granulation and fuzzy membership aggregation we propose a new data driven transformation that facilitates many data mining interpretation and analysis tasks our approach called membershipmap strives to granulate and extract the underlying subconcepts of each raw attribute the orthogonal union of these subconcepts are then used to define a new membership space the subconcept soft labels of each point in the original space determine the position of that point in the new space since subconcept labels are prone to uncertainty inherent in the original data and in the initial extraction process a combination of labeling schemes that are based on different measures of uncertainty will be presented in particular we introduce the crispmap the fuzzymap and the possibilisticmap we outline the advantages and disadvantages of each mapping scheme and we show that the three transformed spaces are complementary we also show that in addition to improving the performance of clustering by taking advantage of the richer information content the membershipmap can be used as a flexible preprocessing tool to support such tasks as sampling data cleaning and outlier detection

optimal solid shells for non linear analyses of multilayer composites ii dynamics abstract we are presenting a simple low order solid shell element formulation having only displacement degrees of freedom dofs i e without rotational dofs that has an optimal number of parameters to pass the patch tests and thus allows for efficient and accurate analyses of large deformable multilayer shell structures using elements at extremely high aspect ratio with the dynamics referred to a fixed inertial frame the elements can be used to analyze multilayer shell structures undergoing large overall motion the formulation of this element is based on the mixed hu washizu variational principle leading to a novel enhancing strain tensor enhanced assumed strain eas method that renders the computation particularly efficient with improved in plane and out of plane bending behavior poisson thickness locking especially in refined analyses of composite structures involving a large number of high aspect ratio layers the energy momentum conserving algorithm in the context of current solid shell element is presented we discuss the eas formulation based on the displacement gradient and its complexity compared to formulation on the green lagrange strain shear locking and curvature thickness locking are treated using the assumed natural strain ans method the element has an optimal combination of the ans method and the minimal number of eas parameters required to pass the plate bending patch test numerical examples involving dynamic analyses with conservation of energy and momentum of multilayer shell structures having a large range of element aspect ratios are presented several implicit direct integration methods with without numerical dissipation are used and compared in terms of the accuracy stability and cost in multilayer shell structure finally we note that the topic in this paper is a fitting dedication to professor ekkehard ramm who has made important pioneering contributions in this research direction

an augmented lagrangian technique combined with a mortar algorithm for modelling mechanical contact problems summary a finite element formulation for three dimensional 3d contact mechanics using a mortar algorithm combined with a mixed penalty duality formulation from an augmented lagrangian approach is presented in this method no penalty parameter is introduced for the regularisation of the contact problem the contact approach based on the mortar method gives a smooth representation of the contact forces across the bodies interface and can be used in arbitrarily curved 3d configurations the projection surface used for integrating the equations is built using a local cartesian basis defined in each contact element a unit normal to the contact surface is defined locally at each element simplifying the implementation and linearisation of the equations the displayed examples show that the algorithm verifies the contact patch tests exactly and is applicable to large displacements problems with large sliding motions copyright 2012 john wiley sons ltd

music type imaging of perfectly conducting cracks in limited view inverse scattering problems abstract although standard multiple signal classification music algorithm has been considered a promising non iterative imaging technique for cracks its application is restricted to the full view inverse scattering problems many experimental results revealed that music can be applied to the imaging of perfectly conducting cracks with small length in limited view inverse scattering problem on the other hand music is not applicable for imaging of extended cracks in limited view problems but the reason behind this restricted application has not been theoretically investigated this gave an impetus for this study to attempt to identify the structure of music type algorithm that appears in the limited view inverse scattering problems by establishing a relationship between music and bessel functions of integer order of the first kind some numerical experiments are illustrated to support the identified structure of music

a dual mortar approach for 3d finite deformation contact with consistent linearization in this paper an approach for three dimensional frictionless contact based on a dual mortar formulation and using a primal dual active set strategy for direct constraint enforcement is presented we focus on linear shape functions but briefly address higher order interpolation as well the study builds on previous work by the authors for two dimensional problems first and foremost the ideas of a consistently linearized dual mortar scheme and of an interpretation of the active set search as a semi smooth newton method are extended to the 3d case this allows for solving all types of nonlinearities i e geometrical material and contact within one single newton scheme owing to the dual lagrange multiplier approach employed this advantage is not accompanied by an undesirable increase in system size as the lagrange multipliers can be condensed from the global system of equations moreover it is pointed out that the presented method does not make use of any regularization of contact constraints numerical examples illustrate the efficiency of our method and the high quality of results in 3d finite deformation contact analysis

volumetric coupling approaches for multiphysics simulations on non matching meshes summary in finite element analysis of volume coupled multiphysics different meshes for the involved physical fields are often highly desirable in terms of solution accuracy and computational costs we present a general methodology for volumetric coupling of different meshes within a monolithic solution scheme a straightforward collocation approach is compared to a mortar based method for nodal information transfer for the latter dual shape functions based on the biorthogonality concept are used to build the projection matrices thus further reducing the evaluation costs we give a detailed explanation of the integration scheme and the construction of dual shape functions for general first order and second order langrangian finite elements within the mortar method as well as an analysis of the conservation properties of the projection operators moreover possible incompatibilities due to different geometric approximations of curved boundaries are discussed numerical examples demonstrate the flexibility of the presented mortar approach for arbitrary finite element combinations in two and three dimensions and its applicability to different multiphysics coupling scenarios copyright 2016 john wiley sons ltd

development of a systematic methodology of fuzzy logic modeling this paper proposes a systematic methodology of fuzzy logic modeling for complex system modeling it has a unified parameterized reasoning formulation an improved fuzzy clustering algorithm and an efficient strategy of selecting significant system inputs and their membership functions the reasoning mechanism introduces 4 parameters whose variation provides a continuous range of inference operation as a result we are no longer restricted to standard extremes in any step of reasoning the fuzzy model itself can then adjust the reasoning process by optimizing the inference parameters based on input output data the fuzzy rules are generated through fuzzy c means fcm clustering major bottlenecks are addressed and analytical solutions are suggested we also address the classification process to extend the derived fuzzy partition to the entire output space in order to select suitable input variables among a finite number of candidates unlike traditional approaches we suggest a new strategy through which dominant input parameters are assigned in one step and no iteration process is required furthermore a clustering technique called fuzzy fine clustering is introduced to assign the input membership functions in order to evaluate the proposed methodology two examples a nonlinear function and a gas furnace dynamic procedure are investigated in detail the significant improvement of the model is concluded compared to other fuzzy modeling approaches

a nonsmooth version of newton s method newton s method for solving a nonlinear equation of several variables is extended to a nonsmooth case by using the generalized jacobian instead of the derivative this extension includes the b derivative version of newton s method as a special case convergence theorems are proved under the condition of semismoothness it is shown that the gradient function of the augmented lagrangian forc2 nonlinear programming is semismooth thus the extended newton s method can be used in the augmented lagrangian method for solving nonlinear programs

fuzzy rough sets assisted attribute selection attribute selection as refers to the problem of selecting those input attributes or features that are most predictive of a given outcome a problem encountered in many areas such as machine learning pattern recognition and signal processing unlike other dimensionality reduction methods attribute selectors preserve the original meaning of the attributes after reduction this has found application in tasks that involve datasets containing huge numbers of attributes in the order of tens of thousands which for some learning algorithms might be impossible to process further recent examples include text processing and web content classification as techniques have also been applied to small and medium sized datasets in order to locate the most informative attributes for later use one of the many successful applications of rough set theory has been to this area the rough set ideology of using only the supplied data and no other information has many benefits in as where most other methods require supplementary knowledge however the main limitation of rough set based attribute selection in the literature is the restrictive requirement that all data is discrete in classical rough set theory it is not possible to consider real valued or noisy data this paper investigates a novel approach based on fuzzy rough sets fuzzy rough feature selection frfs that addresses these problems and retains dataset semantics frfs is applied to two challenging domains where a feature reducing step is important namely web content classification and complex systems monitoring the utility of this approach is demonstrated and is compared empirically with several dimensionality reducers in the experimental studies frfs is shown to equal or improve classification accuracy when compared to the results from unreduced data classifiers that use a lower dimensional set of attributes which are retained by fuzzy rough reduction outperform those that employ more attributes returned by the existing crisp rough reduction method in addition it is shown that frfs is more powerful than the other as techniques in the comparative study

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

a phase and space coherent direct imaging method a direct imaging algorithm for point and extended targets is presented the algorithm is based on a physical factorization of the response matrix of a transducer array the factorization is used to transform a passive target problem to an active source problem and to extract principal components tones in a phase consistent way the multitone imaging function can superpose multiple tones spatial diversity aperture of the array and frequencies bandwidth of the probing signal based on phase coherence the method is a direct imaging algorithm that is simple and efficient since no forward solver or iteration is needed robustness of the algorithm with respect to noise is demonstrated via numerical examples