a consistent finite element formulation for linear buckling analysis of spatial beams a consistent co rotational finite element formulation and numerical procedure for the linear buckling analysis of three dimensional elastic euler beam is presented a mechanism for generating configuration dependent conservative moment is proposed and the corresponding load stiffness matrix is derived it is assumed that the prebuckling displacements and rotations of the structure and the corresponding deformations of the elements are linearly proportional to the external loading the prebuckling rotations of the structure are fixed axis rotations or small rotations and the effect of the prebuckling displacement on transformation matrix for the coordinates transformation can be ignored all coupling among bending twisting and stretching deformations for beam element is considered by consistent linearization of the fully geometrically nonlinear beam theory an inverse power method for the solution of the generalized eigenvalue problem is used to find the buckling load and buckling mode numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method

a relaxation procedure for domain decomposition methods using finite elements we present the convergence analysis of a new domain decomposition technique for finite element approximations this technique was introduced in 11 and is based on an iterative procedure among subdomains in which transmission conditions at interfaces are taken into account partly in one subdomain and partly in its adjacent no global preconditioner is needed in the practice but simply single domain finite element solvers are required an optimal strategy for an automatic selection of a relaxation parameter to be used at interface subdomains is indicated applications are given to both elliptic equations and incompressible stokes equations

shear flexible models for spatial buckling of thin walled curved beams the governing non linear finite element equations for the spatial stability analysis of curved beams using a simple two noded model are derived based on the incremental form of a mixed variational principle with independent discretization for its generalized strain field and the reference line displacements as well as cross sectional warping and bending twisting rotations the formulation is valid for both open and closed type thin walled sections and this is accomplished by the use of a kinematic description based on a generalized beam theory in which shear deformation due to both flexural and warping torsional actions is accounted for the effect of finite rotations in space is included resulting in a second order accurate geometric stiffness matrix and ensuring that all significant instability modes can be predicted finally the results obtained in a number of numerical simulations for lateral torsional bifurcation buckling of circular arches are presented to illustrate the model effectiveness and practical usefulness and to provide explanations for the source of discrepancies noted in the results obtained in previous investigations

the hp local discontinuous galerkin method for low frequency time harmonic maxwell equations the local discontinuous galerkin method for the numerical approximation of the time harmonic maxwell equations in a low frequency regime is introduced and analyzed topologically nontrivial domains and heterogeneous media are considered containing both conducting and insulating materials the presented method involves discontinuous galerkin discretizations of the curl curl and grad div operators derived by introducing suitable auxiliary variables and so called numerical fluxes an hp analysis is carried out and error estimates that are optimal in the meshsize h and slightly suboptimal in the approximation degree p are obtained

an analysis of ne de lec s method for the spatial discretization of maxwell s equations abstract in 1980 nedelec developed a family of curl and divergence conforming finite elements in r 3 he proposed the use of these elements to discretize the time dependent maxwell equations noting that the elements have the advantage that the discrete magnetic displacement can be made exactly divergence free in this paper we shall analyze a slight generalization of nedelec s scheme and prove essentially optimal order convergence estimates in a variety of situations we also demonstrate that the nedelec method can be superconvergent at certain special points and we relate the method to yee s finite difference scheme a by product of our analysis will be a convergence proof for yee s method

parsimonious extreme learning machine using recursive orthogonal least squares novel constructive and destructive parsimonious extreme learning machines cp and dp elm are proposed in this paper by virtue of the proposed elms parsimonious structure and excellent generalization of multiinput multioutput single hidden layer feedforward networks slfns are obtained the proposed elms are developed by innovative decomposition of the recursive orthogonal least squares procedure into sequential partial orthogonalization spo the salient features of the proposed approaches are as follows 1 initial hidden nodes are randomly generated by the elm methodology and recursively orthogonalized into an upper triangular matrix with dramatic reduction in matrix size 2 the constructive spo in the cp elm focuses on the partial matrix with the subcolumn of the selected regressor including nonzeros as the first column while the destructive spo in the dp elm operates on the partial matrix including elements determined by the removed regressor 3 termination criteria for cp and dp elm are simplified by the additional residual error reduction method and 4 the output weights of the slfn need not be solved in the model selection procedure and is derived from the final upper triangular equation by backward substitution both single and multi output real world regression data sets are used to verify the effectiveness and superiority of the cp and dp elm in terms of parsimonious architecture and generalization accuracy innovative applications to nonlinear time series modeling demonstrate superior identification results

fast orthogonal least squares algorithm for efficient subset model selection an efficient implementation of the orthogonal least squares algorithm for subset model selection is derived computational complexity of the algorithm is examined and the result shows that this new fast orthogonal least squares algorithm significantly reduces computational requirements

a co rotational formulation for thin walled beams with monosymmetric open section abstract a consistent co rotational total lagrangian finite element formulation and numerical procedure for the geometric nonlinear buckling and postbuckling analysis of thin walled beams with monosymmetric open section is presented the element developed here has two nodes with seven degrees of freedom per node the element nodes are chosen to be located at the shear centers of the end cross sections of the beam element and the shear center axis is chosen to be the reference axis the deformations of the beam element are described in the current element coordinate system which is constructed at the current configuration of the beam element in element nodal forces all coupling among bending twisting and stretching deformations of the beam element is considered by consistent second order linearization of the fully geometrically nonlinear beam theory however the third order term of the twist rate of the beam axis is considered in element nodal forces an incremental iterative method based on the newton raphson method combined with constant arc length of incremental displacement vector is employed for the solution of nonlinear equilibrium equations the zero value of the tangent stiffness matrix determinant of the structure is used as the criterion of the buckling state a parabolic interpolation method of the arc length is used to find the buckling load numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method

numerical solution of eddy current problems in bounded domains using realistic boundary conditions abstract the aim of this paper is to analyze a finite element method to solve the low frequency harmonic maxwell equations in a bounded domain containing conductors and dielectrics and using realistic boundary conditions in that they can be easily measured these equations provide a model for the so called eddy currents the problem is formulated in terms of the magnetic field this formulation is discretized by using nedelec edge finite elements on a tetrahedral mesh error estimates are easily obtained when the curl free condition is imposed explicitly on the elements in the dielectric domain a multivalued magnetic scalar potential is introduced then to impose this curl free condition the discrete counterpart of this formulation leads to an important saving in computational effort problems related to the topology are also considered more precisely the possibility of having a non simply connected dielectric domain is taken into account finally the method is applied to solve two three dimensional model problems a test with a known analytical solution and the computation of the electromagnetic field in a metallurgical arc furnace

a finite element method with lagrange multipliers for low frequency harmonic maxwell equations the aim of this paper is to analyze a finite element method to solve the low frequency harmonic maxwell equations in a bounded domain containing conductors and dielectrics this system of partial differential equations is a model for the so called eddy currents problem after writing this problem in terms of the magnetic field it is discretized by nedelec edge finite elements on a tetrahedral mesh error estimates are easily obtained if the curl free condition is imposed on the elements in the dielectric domain then the curl free condition is imposed at a discrete level by introducing a piecewise linear multivalued potential the resulting problem is shown to be a discrete version of other continuous formulation in which the magnetic field in the dielectric part of the domain has been replaced by a magnetic potential moreover this approach leads to an important saving in computational effort problems related to the topology are also considered in that the possibility of having a nonsimply connected dielectric domain is taken into account implementation issues are discussed including an amenable procedure to impose the boundary conditions by means of a lagrange multiplier finally the method is applied to solve a three dimensional model problem a cylindrical electrode surrounded by dielectric

co rotational finite element formulation for thin walled beams with generic open section a consistent co rotational total lagrangian finite element formulation for the geometric nonlinear buckling and postbuckling analysis of thin walled beams with generic open section is presented the element developed here has two nodes with seven degrees of freedom per node the element nodes are chosen to be located at the shear centers of the end cross sections of the beam element and the shear center axis is chosen to be the reference axis the deformations of the beam element are described in the current element coordinate system constructed at the current configuration of the beam element the element nodal forces are derived using the virtual work principle the virtual rigid body motion corresponding to the virtual nodal displacements is excluded in the derivation of the element nodal forces a procedure is proposed to determine the virtual rigid body motion the way used to determine the element coordinate system and element nodal deformations corresponding to the virtual nodal displacements and that corresponding to the incremental nodal displacement are consistent in element nodal forces all coupling among bending twisting and stretching deformations of the beam element is considered by consistent second order linearization of the fully geometrically nonlinear beam theory in the derivation of the element tangent stiffness matrix the change of element nodal forces induced by the element rigid body rotations should be considered for the present method thus a stability matrix is included in the element tangent stiffness matrix an incremental iterative method based on the newton raphson method combined with constant arc length of incremental displacement vector is employed for the solution of nonlinear equilibrium equations the zero value of the tangent stiffness matrix determinant of the structure is used as the criterion of the buckling state numerical examples are presented to investigate the accuracy and efficiency of the proposed method the effect of the terms in the element nodal force and tangent stiffness matrix which will converge to zero with the decrease of element size on the convergence rate of solution and accuracy for the buckling load and nonlinear behavior of three dimensional beam structures are also investigated through numerical examples 2005 elsevier b v all rights reserved

elements finis mixtes incompressibles pour l equation de stokes dans ℝ3 we introduce some new families of finite element approximation for the stationary stokes and navier stokes equations in a bounded domain in 3 these elements can used tetahedrons or cubes the approximation satisfie exactly the incompressibility condition

a co rotational finite element formulation for buckling and postbuckling analyses of spatial beams abstract a consistent co rotational finite element formulation and numerical procedure for the buckling and postbuckling analyses of three dimensional elastic euler beam is presented all coupling among bending twisting and stretching deformations for a beam element is considered by consistent second order linearization of the fully geometrically nonlinear beam theory however the third order terms which are relevant to the twist rate and curvature of the beam axis are also considered an incremental iterative method based on the newton raphson method combined with constant arc length of incremental displacement vector is employed for the solution of nonlinear equilibrium equations the zero value of the tangent stiffness matrix determinant of the structure is used as the criterion of the buckling state a bisection method of the arc length is proposed to find the buckling load numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method and to investigate the effect of third order terms on the buckling load and postbuckling behavior of three dimensional beams

generalized mixed finite element model for pre and post quasistatic buckling response of thin walled framed structures adopting an updated lagrangian approach the general framework for the fully non linear analysis of thin walled framed structures is developed using a simple two node c0 model hmb2 the governing equations are derived based on a consistent linearization of an incremental mixed variational principle of modified hellinger reissner type with independent assumptions for displacement and strain fields all coupled significant modes of deformations i e stretching bending shear torsion and warping are accounted for in the generalized beam theory employed emphasis is placed on devising effective solution procedures to deal with finite rotations in space particularly with regard to their effect on the derivations of load correction matrices corresponding to configuration dependent externally applied forces moments the effectiveness and practical usefulness of present model are demonstrated through a number of test problems involving beam assemblages undergoing large displacements and rotations in space

a new result on h_ infty state estimation of delayed static neural networks this brief presents a new guaranteed h infty performance state estimation criterion for delayed static neural networks to facilitate the use of the slope information about activation function the estimation error of activation function is separated into two parts for the first time then a novel lyapunov krasovskii functional lkf is constructed which has fully captured the slope information of the activation based on the new lkf a less conservative design criterion of estimator is derived to ensure the asymptotic stability of estimation error system with h infty performance the desired estimator gain matrices and the performance index are obtained by solving a convex optimization problem the simulation results show that the proposed method has much better performance than the most recent results

coupling of viscous and inviscid stokes equations via a domain decomposition method for finite elements a generalized stokes problem is addressed in the framework of a domain decomposition method in which the physical computational domain is partitioned into two subdomains 1 and 2 three different situations are covered in the former the viscous terms are kept in both subdomains then we consider the case in which viscosity is dropped out everywhere in finally a hybrid situation in which viscosity is dropped out only in 1 is addressed the latter is motivated by physical applications in all cases correct transmission conditions across the interface between 1 and 2 are devised and an iterative procedure involving the successive resolution of two subproblems is proposed the numerical discretization is based upon appropriate finite elements and stability and convergence analysis is carried out we also prove that the iteration by subdomain algorithms which are associated with the various domain decomposition approaches converge with a rate independent of the finite element mesh size

numerical analysis of electric field formulations of the eddy current model this paper deals with finite element methods for the numerical solution of the eddy current problem in a bounded conducting domain crossed by an electric current subjected to boundary conditions involving only data easily available in applications two different cases are considered depending on the boundary data input current intensities or differences of potential weak formulations in terms of the electric field are given in both cases in the first one the input current intensities are imposed by means of integrals on curves lying on the boundary of the domain and joining current entrances and exit in the second one the electric potentials are imposed by means of lagrange multipliers which are proved to represent the input current intensities optimal error estimates are proved in both cases and implementation issues are discussed finally numerical tests confirming the theoretical results are reported

mixed discontinuous galerkin approximation of the maxwell operator we introduce and analyze a discontinuous galerkin discretization of the maxwell operator in mixed form here all the unknowns of the underlying system of partial differential equations are approximated by discontinuous finite element spaces of the same order for piecewise constant coefficients the method is shown to be stable and optimally convergent with respect to the mesh size numerical experiments highlighting the performance of the proposed method for problems with both smooth and singular analytical solutions are presented

a constructive hybrid structure optimization methodology for radial basis probabilistic neural networks in this paper a novel heuristic structure optimization methodology for radial basis probabilistic neural networks rbpnns is proposed first a minimum volume covering hyperspheres mvch algorithm is proposed to select the initial hidden layer centers of the rbpnn and then the recursive orthogonal least square algorithm rolsa combined with the particle swarm optimization pso algorithm is adopted to further optimize the initial structure of the rbpnn the proposed algorithms are evaluated through eight benchmark classification problems and two real world application problems a plant species identification task involving 50 plant species and a palmprint recognition task experimental results show that our proposed algorithm is feasible and efficient for the structure optimization of the rbpnn the rbpnn achieves higher recognition rates and better classification efficiency than multilayer perceptron networks mlpns and radial basis function neural networks rbfnns in both tasks moreover the experimental results illustrated that the generalization performance of the optimized rbpnn in the plant species identification task was markedly better than that of the optimized rbfnn

a hybrid constructive algorithm for single layer feedforward networks learning single layer feedforward networks slfns have been proven to be a universal approximator when all the parameters are allowed to be adjustable it is widely used in classification and regression problems the slfn learning involves two tasks determining network size and training the parameters most current algorithms could not be satisfactory to both sides some algorithms focused on construction and only tuned part of the parameters which may not be able to achieve a compact network other gradient based optimization algorithms focused on parameters tuning while the network size has to be preset by the user therefore trial and error approach has to be used to search the optimal network size because results of each trial cannot be reused in another trial it costs much computation in this paper a hybrid constructive hc algorithm is proposed for slfn learning which can train all the parameters and determine the network size simultaneously at first by combining levenberg marquardt algorithm and least square method a hybrid algorithm is presented for training slfn with fixed network size then with the hybrid algorithm an incremental constructive scheme is proposed a new randomly initialized neuron is added each time when the training entrapped into local minima because the training continued on previous results after adding new neurons the proposed hc algorithm works efficiently several practical problems were given for comparison with other popular algorithms the experimental results demonstrated that the hc algorithm worked more efficiently than those optimization methods with trial and error and could achieve much more compact slfn than those construction algorithms

the coulomb gauged vector potential formulation for the eddy current problem in general geometry well posedness and numerical approximation in this paper we prove that in a general geometric situation the coulomb gauged vector potential formulation of the eddy current problem for the time harmonic maxwell equations is well posed i e its solution exists and is unique moreover a quasi optimal error estimate for its finite element approximation with nodal elements is proved to illustrate the performances of the finite element algorithm some numerical results are also presented

adaptive approximation based regulation control for a class of uncertain nonlinear systems without feedback linearizability in this paper for a general class of uncertain nonlinear cascade systems including unknown dynamics which are not feedback linearizable and cannot be solved by existing approaches an innovative adaptive approximation based regulation control aarc scheme is developed within the framework of adding a power integrator api by deriving adaptive laws for output weights and prediction error compensation pertaining to single hidden layer feedforward network slfn from the lyapunov synthesis a series of slfn based approximators are explicitly constructed to exactly dominate completely unknown dynamics by the virtue of significant advancements on the api technique an adaptive api methodology is eventually established in combination with slfn based adaptive approximators and it contributes to a recursive mechanism for the aarc scheme as a consequence the output regulation error can asymptotically converge to the origin and all other signals of the closed loop system are uniformly ultimately bounded simulation studies and comprehensive comparisons with backstepping and api based approaches demonstrate that the proposed aarc scheme achieves remarkable performance and superiority in dealing with unknown dynamics

co rotational formulation for geometric nonlinear analysis of doubly symmetric thin walled beams abstract a doubly symmetric thin walled beam element with open section is derived using co rotational cr total lagrangian tl formulation the effects of deformation dependent third order terms of element nodal forces on the buckling load and post buckling behavior are investigated all coupling among bending twisting and stretching deformations for beam element is considered by consistent second order linearization of the fully geometrically nonlinear beam theory however all third order terms of nodal forces which are relevant to the twist rate rate of twist rate and curvature of the beam axis are also considered an incremental iterative method based on the newton raphson method combined with constant arc length of incremental displacement vector is employed for the solution of nonlinear equilibrium equations the zero value of the tangent stiffness matrix determinant of the structure is used as the criterion of the buckling state a parabolic interpolation method of the arc length is used to find the buckling load numerical examples are presented to demonstrate the accuracy and efficiency of the proposed element and to investigate the effect of third order terms of element nodal forces on the buckling load and post buckling behavior of doubly symmetric thin walled beams

an iterative method for elliptic problems on regions partitioned into substructures some new preconditioners for discretizations of elliptic boundary problems are studied with these preconditioners the domain under consideration is broken into subdomains and preconditioners are defined which only require the solution of matrix problems on the subdomains analytic estimates are given which guarantee that under appropriate hypotheses the preconditioned iterative procedure converges to the solution of the discrete equations with a rate per iteration that is independent of the number of unknowns numerical examples are presented which illustrate the theoretically predicted iterative convergence rates

homogeneous and heterogeneous domain decomposition methods for plate bending problems we consider the approximation of fourth order problems derived e g by the kirchoff plate model and the heterogeneous coupling between a fourth order problem and a reduced second order one describing e g a plate membrane model this paper is devoted to the analysis of an iteration by subdomain method the so called dirichlet neumann method which is used to solve both homogeneous and heterogeneous couplings numerical results obtained by the spectral element method are shown

a variational approach for the vector potential formulation of the stokes and navier stokes problems in three dimensional domains abstract a few well posed variational problems are constructed whose solutions are vector potentials of the velocity field of the three dimensional stokes problem a choice of the adequate boundary conditions to be imposed is performed in a systematic manner even in the case of not simply connected domains the test functions do not have to be divergence free in the formulations given here it is then seen that a similar approach is well suited to the treatment of the non linear navier stokes problem

nonlinear finite element analysis of elastic systems under nonconservative loading natural formulation part ii dynamic problems abstract the paper presents a nonlinear finite element analysis of elastic structures subject to nonconservative forces attention is focused on the stability behaviour of such systems this leads mathematically to non self adjoint boundary value problems which are of great theoretical and practical interest in particular in connection with alternative modes of instability like divergence of flutter only quasistatic effects are however considered in the present part the methodology of our theory is general but the specific thrust of the present research is directed towards the analysis of structures acted upon by displacement dependent nonconservative follower forces in a finite element formulation the analysis of geometrically nonlinear elastic systems subject to such forces gives in general rise to a contributory nonsymmetric stiffness matrix known as the load correction matrix as a result the total tangent stiffness matrix becomes unsymmetric an indication of the non self adjoint character of the problem our theory is based on the natural mode technique 1 2 3 and permits i a a simple but elegant derivation of the load correction matrix the application of the general theory as evolved in this paper is demonstrated on the beam element in space a number of numerical examples are considered including divergence and flutter types of instability for which exact analytic solutions are known the problems demonstrate the efficiency of the present finite element formulation the paper furnishes also a novel and concise formulation of finite rotations in space which may be considered as a conceptual generalization of the theory presented in 2 3

a mixed formulation for 3d magnetostatic problems theoretical analysis and face edge finite element approximation a mixed field based variational formulation for the solution of threedimensional magnetostatic problems is presented and analyzed this method is based upon the minimization of a functional related to the error in the constitutive magnetic relationship while constraints represented by maxwell s equations are imposed by means of lagrange multipliers in this way both the magnetic field and the magnetic induction field can be approximated by using the most appropriate family of vector finite elements and boundary conditions can be imposed in a natural way moreover this method is more suitable than classical approaches for the approximation of problems featuring strong discontinuities of the magnetic permeability as is usually the case a finite element discretization involving face and edge elements is also proposed performing stability analysis and giving error estimates

analysis of finite element approximation for time dependent maxwell problems we provide an error analysis of finite element methods for solving time dependent maxwell problem using nedelec and thomas raviart elements we study the regularity of the solution and develop some new error estimates of nedelec finite elements as a result the optimal l 2 error bound for the semidiscrete scheme is obtained

generalized single hidden layer feedforward networks for regression problems in this paper traditional single hidden layer feedforward network slfn is extended to novel generalized slfn gslfn by employing polynomial functions of inputs as output weights connecting randomly generated hidden units with corresponding output nodes the significant contributions of this paper are as follows 1 a primal gslfn p gslfn is implemented using randomly generated hidden nodes and polynomial output weights whereby the regression matrix is augmented by full or partial input variables and only polynomial coefficients are to be estimated 2 a simplified gslfn s gslfn is realized by decomposing the polynomial output weights of the p gslfn into randomly generated polynomial nodes and tunable output weights 3 both p and s gslfn are able to achieve universal approximation if the output weights are tuned by ridge regression estimators and 4 by virtue of the developed batch and online sequential ridge elm br elm and osr elm learning algorithms high performance of the proposed gslfns in terms of generalization and learning speed is guaranteed comprehensive simulation studies and comparisons with standard slfns are carried out on real world regression benchmark data sets simulation results demonstrate that the innovative gslfns using br elm and osr elm are superior to standard slfns in terms of accuracy training speed and structure compactness

finite element analysis of two and three dimensional elasto plastic frames the natural approach abstract the paper presents a finite element analysis of large deformations in elasto plastic frames attention is focused on the step by step analysis of the nonlinear behaviour of such structures advantage is taken of the so called natural formulation in terms of the generalised cross sectional forces limit state functions applying to different loading conditions and frame geometries are implemented into a computer program a number of test examples illustrate practical applications

orthogonal least squares methods and their application to non linear system identification abstract identification algorithms based on the well known linear least squares methods of gaussian elimination cholesky decomposition classical gram schmidt modified gram schmidt householder transformation givens method and singular value decomposition are reviewed the classical gram schmidt modified gram schmidt and householder transformation algorithms are then extended to combine structure determination or which terms to include in the model and parameter estimation in a very simple and efficient manner for a class of multivariate discrete time non linear stochastic systems which are linear in the parameters

numerical treatment of realistic boundary conditions for the eddy current problem in an electrode via lagrange multipliers this paper deals with the finite element solution of the eddy current problem in a bounded conducting domain crossed by an electric current and subject to boundary conditions appropriate from a physical point of view two different cases are considered depending on the boundary data input current density flux or input current intensities the analysis of the former is an intermediate step for the latter which is more realistic in actual applications weak formulations in terms of the magnetic field are studied the boundary conditions being imposed by means of appropriate lagrange multipliers the resulting mixed formulations are analyzed depending on the regularity of the boundary data finite element methods are introduced in each case and error estimates are proved finally some numerical results to assess the effectiveness of the methods are reported

universal approximation using incremental constructive feedforward networks with random hidden nodes according to conventional neural network theories single hidden layer feedforward networks slfns with additive or radial basis function rbf hidden nodes are universal approximators when all the parameters of the networks are allowed adjustable however as observed in most neural network implementations tuning all the parameters of the networks may cause learning complicated and inefficient and it may be difficult to train networks with nondifferential activation functions such as threshold networks unlike conventional neural network theories this paper proves in an incremental constructive method that in order to let slfns work as universal approximators one may simply randomly choose hidden nodes and then only need to adjust the output weights linking the hidden layer and the output layer in such slfns implementations the activation functions for additive nodes can be any bounded nonconstant piecewise continuous functions g r r and the activation functions for rbf nodes can be any integrable piecewise continuous functions g r r and rg x dx 0 the proposed incremental method is efficient not only for sflns with continuous including nondifferentiable activation functions but also for slfns with piecewise continuous such as threshold activation functions compared to other popular methods such a new network is fully automatic and users need not intervene the learning process by manually tuning control parameters

approximation of the thermally coupled mhd problem using a stabilized finite element method a numerical formulation to solve the mhd problem with thermal coupling is presented in full detail the distinctive feature of the method is the design of the stabilization terms which serve several purposes first convective dominated flows in the navier stokes and the heat equation can be dealt with second there is no restriction in the choice of the interpolation spaces of all the variables and finally flows highly coupled with the magnetic field can be accounted for different aspects related to the design of the final fully discrete and linearized algorithm are also discussed

formulation of geometrically non linear problems in the spatial reference frame this paper presents a new formulation for geometrically non linear problems and their numerical treatment by the p version of the finite element method the formulation is characterized by a weak form based on the spatial representation of the equilibrium equations a deformed geometry mapped by the displacement field a natural description for non conservative loads that keeps the symmetry of the equations and a direct non incremental iterative algorithm to solve the equations the paper is concerned only with problems for which the solution is unique i e the load displacement curves are single valued and the strains are small examples are presented 1997 by john wiley sons ltd

effective modelling of spatial buckling of beam assemblages accounting for warping constraints and rotation dependency of moments a simple two noded finite element model for the three dimensional buckling analysis of beam assemblages is developed the underlying generalized beam theory employed accounts for all coupled significant modes of deformations including stretching bending shear and torsion as well as warping its mixed formulation is of the two field type utilizing linear and constant interpolants for displacements and strain fields due considerations are given to the effect off inite rotations in space on the non linear kinematic descriptions as well as the configuration dependent behaviour of externally applied moment vectors of the conservative and non conservative types the performance of the model and particularly the accuracy of its geometric and load correction stiffnesses is assessed in a fairly complete set of numerical simulations

generalized finite element systems for smooth differential forms and stokes problem we provide both a general framework for discretizing de rham sequences of differential forms of high regularity and some examples of finite element spaces that fit in the framework the general framework is an extension of the previously introduced notion of finite element systems and the examples include conforming mixed finite elements for stokes equation in dimension 2 we detail four low order finite element complexes and one infinite family of highorder finite element complexes in dimension 3 we define one low order complex which may be branched into whitney forms at a chosen index stokes pairs with continuous or discontinuous pressure are provided in arbitrary dimension the finite element spaces all consist of composite polynomials the framework guarantees some nice properties of the spaces in particular the existence of commuting interpolators it also shows that some of the examples are minimal spaces

a new family of mixed finite elements in ir 3 we introduce two families of mixed finite element on conforming inh div and one conforming inh curl these finite elements can be used to approximate the stokes system

a preconditioning technique for indefinite systems resulting from mixed approximations of elliptic problems this paper provides a preconditioned iterative technique for the solution of saddle point problems these problems typically arise in the numerical approximation of partial differential equations by lagrange multiplier techniques and or mixed methods the saddle point problem is reformulated as a symmetric positive definite system which is then solved by conjugate gradient iteration applications to the equations of elasticity and stokes are discussed and the results of numerical experiments are given

orthogonal least squares learning algorithm for radial basis function networks the radial basis function network offers a viable alternative to the two layer neural network in many applications of signal processing a common learning algorithm for radial basis function networks is based on first choosing randomly some data points as radial basis function centers and then using singular value decomposition to solve for the weights of the network such a procedure has several drawbacks and in particular an arbitrary selection of centers is clearly unsatisfactory the authors propose an alternative learning procedure based on the orthogonal least squares method the procedure chooses radial basis function centers one by one in a rational way until an adequate network has been constructed in the algorithm each selected center maximizes the increment to the explained variance or energy of the desired output and does not suffer numerical ill conditioning problems the orthogonal least squares learning strategy provides a simple and efficient means for fitting radial basis function networks this is illustrated using examples taken from two different signal processing applications

an excursion into large rotations the present discourse develops an enlarged exploration of the matrix formulation of finite rotations in space initiated in 1 it is shown how a consistent but subtle matrix calculus inevitably leads to a number of elegant expressions for the transformation or rotation matrix t appertaining to a rotation about an arbitrary axis also analysed is the case of multiple rotations about fixed or follower axes particular attention is paid to an explicit derivation of a single compound rotation vector equivalent to two consecutive arbitrary rotations this theme is discussed in some detail for a number of cases semitangential rotations for which commutativity holds first proposed in 2 3 are also considered furthermore an elementary geometrical analysis of large rotations is also given finally we deduce in an appendix using a judicious reformulation of quarternions the compound pseudovector representing the combined effect of n rotations in the author s opinion the present approach appears preferable to a pure vectorial scheme and even more so to an indicial formulation and is computationally more convenient

an optimal domain decomposition preconditioner for low frequency time harmonic maxwell equations the time harmonic maxwell equations are considered in the low frequency case a finite element domain decomposition approach is proposed for the numerical approximation of the exact solution this leads to an iteration by subdomain procedure which is proven to converge the rate of convergence turns out to be independent of the mesh size showing that the preconditioner implicitly defined by the iterative procedure is optimal for obtaining this convergence result it has been necessary to prove a regularity theorem for dirichlet and neumann harmonic fields

coercive domain decomposition algorithms for advection diffusion equations and systems abstract two families of non overlapping coercive domain decomposition methods are proposed for the numerical approximation of advection dominated advection diffusion equations and systems convergence is proven for both the continuous and the discrete problem the rate of convergence of the first method is shown to be independent of the total number of degrees of freedom several numerical results are presented showing the efficiency and robustness of the proposed interative algorithms

an algorithm for rls identification parameters that vary quickly with time an alternative to the standard recursive least squares rls algorithm for fixed order systems with exponential data weighting is presented the approach uses givens orthogonal transformations to update the cholesky factor of the information matrix without ever needing to form it the resulting algorithm gives higher precision control and is less sensitive to ill conditioning when compared to other reported approaches it is demonstrated by an example that ill conditioned problems with parameters that vary quickly can be modified to stabilize erratic parameter fluctuations

a domain decomposition approach for heterogeneous time harmonic maxwell equations the time harmonic maxwell equations for a composite medium which behaves like a conductor in one part and like a perfect insulator in the other one are considered an existence and uniqueness theorem is proven for this degenerate problem in the case of dirichlet boundary conditions a finite element domain decomposition approach is then proposed for the numerical approximation of the exact solution this leads to an iteration by subdomain procedure where at each step a non degenerate boundary value problem has to be solved in each subdomain the convergence of these iterations is proven and the rate of convergence turns out to be independent of the mesh size h showing that the preconditioner implicitly defined by the iteration procedure is optimal

incompressible finite elements via hybridization part ii the stokes system in three space dimensions in this paper we introduce a new and efficient way to compute exactly divergence free velocity approximations for the stokes equations in two space dimensions we begin by considering a mixed method that provides an exactly divergence free approximation of the velocity and a continuous approximation of the vorticity we then rewrite this method solely in terms of the tangential fluid velocity and the pressure on mesh edges by means of a new hybridization technique this novel formulation bypasses the difficult task of constructing an exactly divergence free basis for velocity approximations moreover the discrete system resulting from our method has fewer degrees of freedom than the original mixed method since the pressure and the tangential velocity variables are defined just on the mesh edges once these variables are computed the velocity approximation satisfying the incompressibility condition exactly as well as the continuous numerical approximation of the vorticity can at once be obtained locally moreover a discontinuous numerical approximation of the pressure within elements can also be obtained locally we show how to compute the matrix system for our tangential velocity pressure formulation on general meshes and present in full detail such computations for the lowest order case of our method

greedy sparse rls starting from the orthogonal greedy least squares method we build an adaptive algorithm for finding online sparse solutions to linear systems the algorithm belongs to the exponentially windowed recursive least squares rls family and maintains a partial orthogonal factorization with pivoting of the system matrix for complexity reasons the permutations that bring the relevant columns into the first positions are restrained mainly to interchanges between neighbors at each time moment the storage scheme allows the computation of the exact factorization implicitly working on indefinitely long vectors the sparsity level of the solution i e the number of nonzero elements is estimated using information theoretic criteria in particular bayesian information criterion bic and predictive least squares we present simulations showing that for identifying sparse time varying fir channels our algorithm is consistently better than previous sparse rls methods based on the norm regularization of the rls criterion we also use our sparse greedy rls algorithm for computing linear predictions in a lossless audio coding scheme and obtain better compression than mpeg4 als using an rls lms cascade

nonlinear analysis and elastic plastic load carrying behaviour of thin walled spatial beam structures with warping constraints an analysis of the elastic plastic load carrying behaviour of thin walled spatial beam structures is presented it is based on a beam theory valid for large displacements and rotations which admits arbitrary cross sections curved axes initial imperfections a general material description and which fully accounts for the influence of warping constraints as well as the stress history dependence of the elastic plastic shear moduli an incremental updated lagrangian viewpoint is adopted in the derivation of the basic beam equations from a generalized variational principle and in the numerical solution procedure the displacement finite element approach is followed the associated tangential stiffness matrices are obtained by direct numerical integration of the governing incremental differential equations rather than through the use of shape functions in connection with a virtual work principle applications of the theory are given in which the influence of the loading configuration material parameters geometric nonlinearities and warping constraints on the load carrying behaviour and on the bifurcation and ultimate loads of thin walled beam structures is explored