the construction of preconditioners for elliptic problems by substructuring i in earlier parts of this series of papers we constructed preconditioners for the discrete systems of equations arising from the numerical approximation of elliptic boundary value problems the resulting algorithms are well suited for implementation on computers with parallel architecture in this paper we will develop a technique which utilizes these earlier methods to derive even more efficient preconditioners the iterative algorithms using these new preconditioners converge to the solution of the discrete equations with a rate that is independent of the number of unknowns these preconditioners involve an incomplete chebyshev iteration for boundary interface conditions which results in a negligible increase in the amount of computational work theoretical estimates and the results of numerical experiments are given which demonstrate the effectiveness of the methods

h_ infty filtering for nonlinear discrete time systems subject to quantization and packet dropouts this paper investigates the problem of h filtering for a class of nonlinear discrete time systems with measurement quantization and packet dropouts each output is transmitted via an independent communication channel and the phenomenon of packet dropouts in transmission is governed by an individual random binary distribution while the quantization errors are treated as sector bound uncertainties based on a piecewise lyapunov function an approach to the design of h piecewise filter is pro posed such that the filtering error system is stochastically stable with a guaranteed h performance some slack matrices are introduced to facilitate the filter design procedure by eliminating the coupling between the lyapunov matrices and the system matrices the filter parameters can be obtained by solving a set of linear matrix inequalities lmis which are numerically tractable with commercially available software finally two illustrative examples are provided to show the effectiveness of the proposed method

a subspace of the dssy nonconforming quadrilateral finite element space for the stokes equations in this paper we propose a subspace of the dssy nonconforming quadrilateral finite element space the product of this space together with the piecewise constant space can be used for approximating the velocity and pressure variables respectively in solving stokes problems more precisely this space consists of the p 1 nonconforming quadrilateral finite element space augmented by macro bubble functions based on the dssy nonconforming quadrilateral space under a hood taylor type assumption on meshes it is shown that the pair satisfies the discrete inf sup condition using a boundedness estimate of an interpolation operator based on edge integrals numerical results are presented

a multigrid method for the mortar type morley element approximation of a plate bending problem in this paper a multigrid algorithm is presented for the mortar element method for the morley nonconforming plate element based on the multigrid theory developed by bramble pasciak and xu in math comp 56 1991 pp 1 34 we prove that the w cycle multigrid method is optimal i e the convergence rate is independent of the mesh size and mesh level moreover a variable v cycle multigrid preconditioner is constructed which results in a preconditioned system with a uniformly bounded condition number

a unified theory for formulation of hybrid stress membrane elements a theory is proposed in this paper to explain in a unified manner the three rational approaches using the incompatible displacements u in the hybrid element formulation limited to the plane stress case the theory suggests that the introduction of u is to constrain the total value of the invariant i2 x y of the assumed stresses over the element to zero in the plane stress case this is the well known condition for the stress distributions to be independent of the elastic constants of the material the theory proposed is also used to explain the closeness of the performances of the four 4 node hybrid stress membrane elements 5 i 5 ii 5 a and 5 c that have been developed previously the differences among them are shown to be of the second degree in the distortion measures of the element shape when they are compared on the basis of the non vanishing total value of i2 of their respectively adopted assumed stress field several numerical examples are used to verify and to illustrate the proposed theory

t s fuzzy model based piecewise h output feedback controller design for networked nonlinear systems with medium access constraint abstract this paper investigates the problem of h output feedback control for a class of networked nonlinear systems subject to medium access constraint where the nonlinear systems are represented by takagi sugeno t s fuzzy models with norm bounded uncertainties the communication constraint concerned is that only one sensor node and one actuator node can access the shared network which is the case in network environment the accessibility of sensor nodes and or actuator nodes is determined by medium access control with a prescribed probability the attention is focused on the design of a piecewise static output feedback controller such that the closed loop control system is stochastically stable with a guaranteed h performance based on piecewise quadratic lyapunov functions together with some matrix inequality convexifying techniques an approach to the design of h output feedback controller is proposed in terms of linear matrix inequalities finally two simulation examples are provided to illustrate the effectiveness of the proposed methods

fault detection for uncertain fuzzy systems an lmi approach this paper studies the problem of designing a robust fault detection system for uncertain takagi sugeno fuzzy models the worst case fault sensitivity measure is formulated in terms of linear matrix inequalities the existence of a robust fault detection system that guarantees i the l2 gain from a fault signal to a residual signal greater than a prescribed value and ii the l2 gain from an exogenous input to a residual signal less than a prescribed value is given in terms of the solvability of linear matrix inequalities numerical examples are used to illustrate the effectiveness of the proposed design techniques

parallel spectral element solution of the stokes problem abstract in this paper we present a high efficiency medium grained parallel spectral element method for numerical solution of the stokes problem in general domains the method is based upon naturally concurrent uzawa and jacobi preconditioned conjugate gradient iterative methods geometry based data parallel distribution of work amongst processors nearest neighbor sparsity and high order substructuring for minimum communication general locally structured globally unstructured parallel constructs and efficient embedding of vector reduction operations for inner product and norm calculation an analysis is given for the computational complexity of the algorithm on a native medium grained parallel processor and the potential communication superiority of high order discretizations is described lastly the method is implemented on the fast intel vector hypercube and the performance of this algorithm architecture coupling is evaluated in a technical and economic framework that reflects the true advantages of parallel solution of partial differential equations

on micro to macro connections in domain decomposition multiscale methods abstract micro to macro connection techniques constitute a key ingredient in the formulation of multiscale strategies in this contribution several connection methods are explored for the concurrent multiscale analysis of brittle heterogeneous materials particularly these techniques are investigated in a domain decomposition strong coupling multiscale framework the structural component under analysis is partitioned into a number of non overlapping domains and a fine scale resolution is assigned therein in an adaptive manner exploiting a zoom in technique mesh refinement is employed in the domains where crack coalescence and growth take place the original contribution presented in this manuscript consists in the study of different strong and weak locality constraints that connect coarse and fine resolution domains standard collocation and average compatibility are considered and serve as a basis for the development of two new interscale links the influence of different locality constraints is studied in terms of the mechanical response and the error distribution is compared to a full fine scale analysis

a mixed variational method for linear coupled thermoelastic analysis abstract a variational method for linear coupled quasi static thermoelastic analysis is presented the variational support is a statement in terms of displacement temperature stress and heat flux the statement is based on the hybrid stress formulation for the elastic part and on the mixed flux temperature formulation for the thermal one and includes the rate dependent terms of the energy balance equations and the initial condition a finite element model for the semidiscrete analysis is developed within this variational framework and a guideline for implementing a family of thermoelastic finite elements is given some test cases enlighten the effectiveness and reliability of the approach proposed

on the modelling of incompressibility in linear and non linear elasticity with the master slave approach this is the pre peer reviewed version of the following article munoz jose j on the modelling of incompressibility in linear and non linear elasticity with the master slave approach international journal for numerical methods in engineering abril 2008 vol 74 num 2 p 269 293 which has been published in final form at http www3 interscience wiley com journal 116323442 abstract

non fragile h filtering for delayed takagisugeno fuzzy systems with randomly occurring gain variations in this study we consider a non fragile h filter design for a class of continuous time delayed takagisugeno ts fuzzy systems the filter design is assumed to include randomly occurring gain variations according to the filter s implementation two independent bernoulli distributions are employed to describe these random phenomena we focus mainly on the design of a non fragile filter so the filtering error system is asymptotically mean square stable with the prescribed h performance in the presence of both randomly occurring gain variations and a time delay a sufficient condition is developed by employing the lyapunov functional approach based on this condition an improved h filter for delayed ts fuzzy system is described which is free of randomly occurring gain variations the filter parameters are obtained by solving a set of linear matrix inequalities the effectiveness and the advantages of the proposed techniques are demonstrated by two numerical examples

a new paradigm for parallel adaptive meshing algorithms we present a new approach to the use of parallel computers with adaptive finite element methods this approach addresses the load balancing problem in a new way requiring far less communication than current approaches it also allows existing sequential adaptive pde codes such as pltmg and mc to run in a parallel environment without a large investment in recoding in this new approach the load balancing problem is reduced to the numerical solution of a small elliptic problem on a single processor using a sequential adaptive solver without requiring any modifications to the sequential solver the small elliptic problem is used to produce a posteriori error estimates to predict future element densities in the mesh which are then used in a weighted recursive spectral bisection of the initial mesh the bulk of the calculation then takes place independently on each processor with no communication using possibly the same sequential adaptive solver each processor adapts its region of the mesh independently and a nearly load balanced mesh distribution is usually obtained as a result of the initial weighted spectral bisection only the initial fan out of the mesh decomposition to the processors requires communication two additional steps requiring boundary exchange communication may be employed after the individual processors reach an adapted solution namely the construction of a global conforming mesh from the independent subproblems followed by a final smoothing phase using the subdomain solutions as an initial guess we present a series of convincing numerical experiments which illustrate the effectiveness of this approach the justification of the initial refinement prediction step as well as the justification of skipping the two communication intensive steps is supported by some recent j xu and a zhou math comp to appear and not so recent j a nitsche and a h schatz math comp 28 1974 pp 937 958 a h schatz and l b wahlbin math comp 31 1977 pp 414 442 a h schatz and l b wahlbin math comp 64 1995 pp 907 928 results on local a priori and a posteriori error estimation

fixed point theorems for set valued maps and existence principles for integral inclusions new fixed point theorems of monch type are presented for set valued maps these theorems are then used to establish general existence principles for hammerstein integral inclusions in banach spaces

stabilized low order finite elements for failure and localization problems in undrained soils and foundations abstract geomaterials in general and soils in particular are highly nonlinear materials presenting a very strong coupling between solid skeleton and intersticial water in the limit of zero compressibility of water and soil grains and zero permeability which correspond to the classical undrained assumption of soil mechanics the functions used to interpolate displacements and pressures must fulfill either the babuska brezzi conditions or the much simpler patch test proposed by zienkiewicz and taylor these requirements exclude the use of elements with equal order interpolation for pressures and displacements for which spurious oscillations may appear the simplest elements with continuous pressures which can be used in 2d are the quadratic triangle and quadrilateral with linear and bilinear pressures respectively the purpose of this paper is to present a stabilization technique allowing the use of both linear triangles for displacements and pressures t3p3 and bilinear quadrilaterals q4p4 the proposed element will be applied to obtain limit loads and failure surfaces in simple boundary value problems for which analytical solutions exist

superconvergence of mixed finite element methods for parabolic problems with nonsmooth initial data a semidiscrete mixed finite element approximation to parabolic initial boundary value problems is introduced and analyzed superconvergence estimates for both pressure and velocity are obtained the estimates for the errors in pressure and velocity depend on the smoothness of the initial data including the limiting cases of data in l 2 and data in h r for r sufficiently large because of the smoothing properties of the parabolic operator these estimates for large time levels essentially coincide with the estimates obtained earlier for smooth solutions however for small time intervals we obtain the correct convergence orders for nonsmooth data

model approximation for discrete time state delay systems in the t s fuzzy framework this paper is concerned with the problem of h model approximation for discrete time takagi sugeno t s fuzzy time delay systems for a given stable t s fuzzy system our attention is focused on the construction of a reduced order model which not only approximates the original system well in an h performance but is also translated into a linear lower dimensional system by applying the delay partitioning approach a delay dependent sufficient condition is proposed for the asymptotic stability with an h error performance for the error system then the h model approximation problem is solved by using the projection approach which casts the model approximation into a sequential minimization problem subject to linear matrix inequality lmi constraints by employing the cone complementary linearization algorithm moreover by further extending the results h model approximation with special structures is obtained i e delay free model and zero order model finally two numerical examples are provided to illustrate the effectiveness of the proposed methods

new stress assumption for hybrid stress elements and refined four node plane and eight node brick elements a new stress assumption for hybrid stress elements is presented generalized incompatible modes are proposed and incorporated into the constraint equations for assumed stresses the physical meaning of the resulting constraint equations is discussed the present stress assumption which can consider the mesh distortion more rigorously is based on the physical interpretation of the role of the generalized incompatible modes and substantiated with simple mesh distortion measures defined in this paper the stress assumption is adapted to the previous four node hybrid stress element 5 i and the eight node hybrid stress brick element 18 which results in a new four node plane element m5 and an new eight node brick element m18 numerical results show that the refined elements are noticeable in low sensitivity to mesh distortion and in high accuracy of stresses 1997 john wiley sons ltd

coupled fe be method for eigenvalue analysis of elastic structures submerged in an infinite fluid domain summary for thin elastic structures submerged in heavy fluid e g water a strong interaction between the structural domain and the fluid domain occurs and significantly alters the eigenfrequencies therefore the eigenanalysis of the fluid structure interaction system is necessary in this paper a coupled finite element and boundary element fe be method is developed for the numerical eigenanalysis of the fluid structure interaction problems the structure is modeled by the finite element method the compressibility of the fluid is taken into consideration and hence the helmholtz equation is employed as the governing equation and solved by the boundary element method bem the resulting nonlinear eigenvalue problem is converted into a small linear one by applying a contour integral method adequate modifications are suggested to improve the efficiency of the contour integral method and avoid missing the eigenvalues of interest the burton miller formulation is applied to tackle the fictitious eigenfrequency problem of the bem and the optimal choice of its coupling parameter is investigated for the coupled fe be method numerical examples are given and discussed to demonstrate the effectiveness and accuracy of the developed fe be method copyright 2016 john wiley sons ltd

fast bem fem mortar coupling for acoustic structure interaction a coupling algorithm based on lagrange multipliers is proposed for the simulation of structure acoustic field interaction finite plate elements are coupled to a galerkin boundary element formulation of the acoustic domain the interface pressure is interpolated as a lagrange multiplier thus allowing the coupling of non matching grids the resulting saddle point problem is solved by an approximate uzawa type scheme in which the matrix vector products of the boundary element operators are evaluated efficiently by the fast multipole boundary element method the algorithm is demonstrated on the example of a cavity backed elastic panel

fault detection and control co design for discrete time delayed fuzzy networked control systems subject to quantization and multiple packet dropouts abstract this paper investigates the problem of fault detection fd for discrete time delayed fuzzy networked control systems with quantization and packet dropouts different from existing results for fd the proposed ones are toward closed loop design problem that is the controller gain and the fault detection filter fdf gains are designed simultaneously the missing phenomenon is assumed to occur in the communication links for quantizer to fdf and controller to physical plant where the missing probability of packet dropouts is governed by an individual random binary distribution while the quantization errors are treated as sector bound uncertainties the discrete time fuzzy networked system is first transformed into the form of interconnection of two subsystems by applying an input output method and a two term approximation approach which is employed to approximate the time varying delay our attention is focused on the design of fuzzy fault detection filter ffdf such that for all data missing conditions and measurement quantization the residual system is stochastically stable with a guaranteed h performance sufficient conditions are first established via introducing some slack matrices to facilitate the fdf design procedure by eliminating the coupling between the lyapunov matrices and the system matrices numerical examples are provided to demonstrate the effectiveness and applicability of the proposed method

bv estimates for mortar methods in linear elasticity this paper is concerned with the convergence of mortar methods applied to linear elasticity we prove that the conventional mesh dependent norms used in the analysis of mortar methods are bounded below by the bv norm when combined with standard results this bound establishes a decomposition independent and mesh independent proof of the convergence of mortar methods in linear elasticity

primal dual weak galerkin finite element methods for elliptic cauchy problems abstract the authors propose and analyze a well posed numerical scheme for a type of ill posed elliptic cauchy problem by using a constrained minimization approach combined with the weak galerkin finite element method the resulting euler lagrange formulation yields a system of equations involving the original equation for the primal variable and its adjoint for the dual variable and is thus an example of the primal dual weak galerkin finite element method this new primal dual weak galerkin algorithm is consistent in the sense that the system is symmetric well posed and is satisfied by the exact solution a certain stability and error estimates were derived in discrete sobolev norms including one in a weak l 2 topology some numerical results are reported to illustrate and validate the theory developed in the paper

observer design of discrete time t s fuzzy systems via multi instant homogenous matrix polynomials this paper is concerned with the design of observer for discrete time nonlinear systems in the takagi sugeno t s fuzzy form under the framework of multi instant homogenous matrix polynomials a novel fuzzy observer and a new lyapunov function which are homogenous polynomially parameter dependent on both the current time normalized fuzzy weighting functions and the m steps past time normalized fuzzy weighting functions are proposed for conceiving less conservative observer design conditions since the algebraic properties of both the current time normalized fuzzy weighting functions and the m steps past time normal ized fuzzy weighting functions are fully considered the relaxation quality of the fuzzy observer design of discrete time t s fuzzy systems is significantly improved in particular some existing fuzzy lyapunov functions and fuzzy observers are special cases of the lyapunov function and the fuzzy observer given in this paper respectively finally a numerical example is provided to illustrate the effectiveness of the proposed approach index terms discrete time system homogenous matrix polynomials multi instant observer design takagi sugeno t s fuzzy model

substructuring preconditioners for the q_1 mortar element method the q 1 mortar element method is a non conforming finite element method with q 1 elements based on domain decomposition for the laplace equation it yields an ill conditioned linear system for solving the linear system the so called preconditioned conjugate gradient method in a subspace is used preconditioners are proposed and estimates on condition numbers and arithmetical complexity are given finally numerical experiments are presented

consistency and recovery in electroelasticity part i standard finite elements developing finite elements for electroelastic analysis requires a special care as the coupling in the discrete equations depends on the matching between the approximations assumed for mechanical and electrical variables to provide a formal basis to this intuitive remark a notion of consistency is established and a rigorous consistency analysis is presented for the standard finite element model based on assumed displacement and electric potential in this way specific analytical requirements are obtained which serve as a guide to select the interpolation functions for primary variables moreover the analysis shows that violating consistency can be reflected as spurious outcomes upsetting the local distributions of secondary variables indeed this undesirable effect is shown to be typical of the standard approach if stress and electric flux density are computed via the constitutive equations to cure the trouble an alternative recovery procedure is devised based on the consistency analysis the procedure is variationally correct and reconstitutes in a consistent manner the distributions of stress and electric flux density

efficient solvers for saddle point problems arising from domain decompositions with lagrange multipliers in this paper we are concerned with the domain decomposition method with lagrange multipliers for solving three dimensional elliptic problems with variable coefficients we shall first introduce a weighted saddle point problem resulting from this domain decomposition which can be solved by existing iterative methods then we will construct two simple preconditioners one for the system associated with the displacement variable and the other for the schur complement system associated with the multiplier variable that are applicable to various discretization schemes the new preconditioners possess such local properties that they can be implemented cheaply we will show that the condition number of the global preconditioned system grows only as the logarithm of the dimension of the local problem associated with an individual substructure and is independent of the large variations of the coefficients across the local interfaces

an efficient approach for reducing the conservatism of lmi based stability conditions for continuous time t s fuzzy systems this paper deals with reducing the conservatism of stability conditions for continuous time t s fuzzy systems previous stability conditions are relaxed by further exploring the properties of the time derivatives of normalized fuzzy weighting functions and by introducing more slack matrix variables by relying on analysis of the positive and negative characteristics of the time derivatives of normalized fuzzy weighting functions some redundant terms are removed from the problem formulation furthermore more slack matrix variables are introduced to enlarge the design space consequently less conservative stability conditions are obtained finally a well known numerical example is provided to illustrate the effectiveness of the proposed result

network based output tracking control for t s fuzzy systems using an event triggered communication scheme this paper is concerned with network based output tracking control for a t s fuzzy system an event triggered communication scheme under which the threshold depends on the latest successfully transmitted sampled data is introduced to reduce network resource utilization taking the event triggered communication scheme and the asynchronous operation between the fuzzy system and the fuzzy controller the resulting system is modeled as an asynchronous threshold error dependent system with an interval time varying delay a new delay dependent criterion for l 2 gain tracking performance of the asynchronous system is derived by applying the deviation bounds of asynchronous normalized membership functions based on this performance criterion some criteria on the existence of the fuzzy tracking controller are established a co design algorithm is presented to obtain the control gains and the event triggering parameters simultaneously an example is given to illustrate the effectiveness of the proposed method

a stabilized explicit lagrange multiplier based domain decomposition method for parabolic problems a fully explicit stabilized domain decomposition method for solving moderately stiff parabolic partial differential equations pdes is presented writing the semi discretized equations as a differential algebraic equation dae system where the interface continuity constraints between subdomains are enforced by lagrange multipliers the method uses the runge kutta chebyshev projection scheme to integrate the dae explicitly and to enforce the constraints by a projection with mass lumping techniques and node to node matching grids the method is fully explicit without solving any linear system a stability analysis is presented to show the extended stability property of the method the method is straightforward to implement and to parallelize numerical results demonstrate that it has excellent performance

the schwarz alternating method in solid mechanics abstract we advance the schwarz alternating method as a means for concurrent multiscale coupling in finite deformation solid mechanics we prove that the schwarz alternating method converges to the solution of the problem on the entire domain and that the convergence rate is geometric provided that each of the subdomain problems is well posed i e their corresponding energy density functions are quasi convex it is shown that the use of a newton type method for the solution of the resultant nonlinear system leads to two kinds of block linearized systems depending on the treatment of the dirichlet boundary conditions the first kind is a symmetric block diagonal linear system in which each diagonal block is the tangent stiffness of each subdomain i e the off diagonal blocks are all zero and the coupling terms appear only on the right hand side the second kind is a nonsymmetric block system with off diagonal coupling terms several variants of the schwarz alternating method are proposed for the first kind of linear system including one in which the schwarz alternating iterations and the newton iterations are combined into a single scheme this version of the method is particularly attractive as it lends itself to a minimally intrusive implementation into existing finite element codes finally we demonstrate the performance of the proposed variants of the schwarz alternating method on several one dimensional and three dimensional examples

brief paper robust filtering with stochastic nonlinearities and multiple missing measurements this paper is concerned with the filtering problem for a class of discrete time uncertain stochastic nonlinear time delay systems with both the probabilistic missing measurements and external stochastic disturbances the measurement missing phenomenon is assumed to occur in a random way and the missing probability for each sensor is governed by an individual random variable satisfying a certain probabilistic distribution over the interval 01 such a probabilistic distribution could be any commonly used discrete distribution over the interval 01 the multiplicative stochastic disturbances are in the form of a scalar gaussian white noise with unit variance the purpose of the addressed filtering problem is to design a filter such that for the admissible random measurement missing stochastic disturbances norm bounded uncertainties as well as stochastic nonlinearities the error dynamics of the filtering process is exponentially mean square stable by using the linear matrix inequality lmi method sufficient conditions are established that ensure the exponential mean square stability of the filtering error and then the filter parameters are characterized by the solution to a set of lmis illustrative examples are exploited to show the effectiveness of the proposed design procedures

fault detection for fuzzy systems with intermittent measurements this paper investigates the problem of fault detection for takagi sugeno t s fuzzy systems with intermittent measurements the communication links between the plant and the fault detection filter are assumed to be imperfect i e data packet dropouts occur intermittently which appear typically in a network environment and a stochastic variable satisfying the bernoulli random binary distribution is utilized to model the unreliable communication links the aim is to design a fuzzy fault detection filter such that for all data missing conditions the residual system is stochastically stable and preserves a guaranteed performance the problem is solved through a basis dependent lyapunov function method which is less conservative than the quadratic approach the results are also extended to t s fuzzy systems with time varying parameter uncertainties all the results are formulated in the form of linear matrix inequalities which can be readily solved via standard numerical software two examples are provided to illustrate the usefulness and applicability of the developed theoretical results

stabilized discontinuous finite element approximations for stokes equations in this paper we derive two stabilized discontinuous finite element formulations symmetric and nonsymmetric for the stokes equations and the equations of the linear elasticity for almost incompressible materials these methods are derived via stabilization of a saddle point system where the continuity of the normal and tangential components of the velocity displacements are imposed in a weak sense via lagrange multipliers for both methods almost all reasonable pair of discontinuous finite element spaces can be used to approximate the velocity and the pressure optimal error estimate for the approximation of both the velocity of the symmetric formulation and pressure in l2 norm are obtained as well as one in a mesh dependent norm for the velocity in both symmetric and nonsymmetric formulations

skew symmetric nitsche s formulation in isogeometric analysis dirichlet and symmetry conditions patch coupling and frictionless contact abstract a simple skew symmetric nitsche s formulation is introduced into the framework of isogeometric analysis iga to deal with various problems in small strain elasticity essential boundary conditions symmetry conditions for kirchhoff plates patch coupling in statics and in modal analysis as well as signorini contact conditions for linear boundary or interface conditions the skew symmetric formulation is parameter free for contact conditions it remains stable and accurate for a wide range of the stabilization parameter several numerical tests are performed to illustrate its accuracy stability and convergence performance we investigate particularly the effects introduced by nitsche s coupling including the convergence performance and condition numbers in statics as well as the extra outlier frequencies and corresponding eigenmodes in structural dynamics we present the hertz test the block test and a 3d self contact example showing that the skew symmetric nitsche s formulation is a suitable approach to simulate contact problems in iga

domain decomposition for linear elasticity with dg jumps and mortars in this article we present a domain decomposition method for solving a linear elasticity system data are transmitted by jumps as in a discontinuous galerkin method and mortars are introduced at the interfaces to dissociate the computation between neighboring subdomains a decoupling algorithm condenses the unknowns on the interface the matrix of the system is constructed by parallel computation numerical experiments confirming the theory are presented

wavelet stabilization of the lagrange multiplier method we propose here a stabilization strategy for the lagrange multiplier formulation of dirichlet problems the stabilization is based on the use of equivalent scalar products for the spaces h 1 2 partial omega and h 1 2 partial omega which are realized by means of wavelet functions the resulting stabilized bilinear form is coercive with respect to the natural norm associated to the problem a uniformly coercive approximation of the stabilized bilinear form is constructed for a wide class of approximation spaces for which an optimal error estimate is provided finally a formulation is presented which is obtained by eliminating the multiplier by static condensation this formulation is closely related to the nitsche s method for solving dirichlet boundary value problems

mortar based frictional contact formulation for higher order interpolations using the moving friction cone abstract finite element discretizations including contact usually apply the standard nts node to segment element thus a coupling with higher order solid elements leads to inconsistencies in the transmission of contact stresses one can circumvent this using the mortar method which includes a weak projection of the contact constraints in this paper we present a penalty formulation based on the mortar concept for two dimensional large deformation frictional contact the discretization of the contact surfaces contains quadratic approximations which can be used within a quadratic approximation of the solid elements to obtain a simple and efficient matrix formulation the moving friction cone algorithm is applied

flow rate boundary problems for an incompressible fluid in deformable domains formulations and solution methods in this paper we consider the numerical solution of the interaction of an incompressible fluid and an elastic structure in a truncated computational domain as well known in this case there is the problem of prescribing realistic boundary data on the artificial sections when only partial data are available this problem has been investigated extensively for the rigid case in this work we start considering the compliant case by focusing on the flow rate conditions for the fluid we propose three formulations of this problem different algorithms for its numerical solution and carry out several 2d numerical simulations with the aim of comparing the performances of the different algorithms

an essential map approach for multivalued a proper weakly inward dkt and weakly closed maps abstract we introduce the notion of an essential map for dkt p 1 compact weakly dkt and weakly closed maps the ideas involved are elementary and rely on urysohn s lemma and the appropriate schauder fixed point theorem for the maps involved

a preconditioner for the feti dp formulation with mortar methods in two dimensions in this paper we consider a dual primal feti feti dp method for elliptic problems on nonmatching grids the feti dp method is a domain decomposition method that uses lagrange multipliers to match solutions continuously across subdomain boundaries in the sense of dual primal variables we use the mortar matching condition as the continuity constraints for the feti dp formulation we construct a preconditioner for the feti dp operator and show that the condition number of the preconditioned feti dp operator is bounded by c max i 1 ldots n left 1 log left h i h i right right 2 where h i and h i are sizes of domain and mesh for each subdomain respectively and c is a constant independent of h i s and h i s we allow jumps of coefficients of elliptic problems across subdomain boundaries numerical results are included

alternative ways for formulation of hybrid stress elements an element stiffness matrix can be derived by the conventional potential energy principle and indirectly also by generalized variational principles such as the hu washizu principle and the hellinger reissner principle the present investigation has the objective to show an approach which is concerned with the formulation of incompatible elements for solid continuum and for plate bending problems by the hellinger reissner principle it is found that the resulting scheme is equivalent to that considered by tong 1982 for the construction of hybrid stress elements in tong s scheme the inversion of a large flexibility matrix can be avoided it is concluded that the introduction of additional internal displacement modes in mixed finite element formulations by the hellinger reissner principle and the hu washizu principle can lead to element stiffness matrices which are equivalent to the assumed stress hybrid method

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

fixed point theory for set valued mappings between topological vector spaces having sufficiently many linear functions abstract we present new fixed point theorems for multivalued maps on hausdorff topological spaces having sufficiently many linear functionals in addition a continuation theory is presented for the maps discussed

plane isoparametric hybrid stress elements invariance and optimal sampling formulation and applications of the hybrid stress finite element model to plane elasticity problems are examined conditions for invariance of the element stiffness are established for two dimensional problems the results of which are easily extended to three dimensional cases next the hybrid stress functional for a 3 d continuum is manipulated into a more convenient form in which the location of optimal stress strain sampling points can be identified to illustrate these concepts 4 and 8 node plane isoparametric hybrid stress elements which are invariant and of correct rank are developed and compared with existing hybrid stress elements for a 4 node element lack of invariance is shown to lead to spurious zero energy modes under appropriate element rotation alternative 8 node elements are considered and the best invariant element is shown to be one in which the stress compatibility equations are invoked results are also presented which demonstrate the validity of the optimal sampling points the effects of reduced orders of numerical integration and the behaviour of the elements for nearly incompressible materials

stability and convergence of nonconforming hp finite element methods the stability and convergence of nonconforming hp finite element methods in par ticular the mortar finite element method and its variants are established based on a new stability measure for these methods using a generalized eigenvalue analysis estimates for this measure are computed numerically our numerical results demonstrate that these nonconforming methods prove to be good candidates for hp implementation and also behave ss well as conforming finite element methods the discussion here ls primarily in two dimensions but some extensions to three dimensions

a rational approach for choosing stress terms for hybrid finite element formulations a new approach for choosing the stress terms for hybrid stress elements is based on the condition of vanishing of the virtual work along the element boundary due to the stress terms higher than constant and the additional incompatible displacements examples using 4 node plane stress elements have shown that when the incompatible displacements also satisfy the constant strain patch test the resulting element will provide the most accurate solutions

on the incompressible constraint of the 4 node quadrilateral element the standard plane 4 node element is written as the summation of a constant gradient matrix usually obtained from underintegration and a stabilization matrix the split is based on a taylor series expansion of element basis functions in the incompressible limit the locking effect of the quadrilateral is traced back to the stabilization matrix which reflects the incomplete higher order term in the taylor series the incompressibility condition is formulated in a weak sense so that the element displacement field is divergence free when integrated over the element volume the resulting algebraic constraint is shown to coincide with a particular eigenvector of the constant gradient matrix which is obtained from the first order terms of the taylor series the corresponding eigenvalue enforces incompressibility implicitly by means of a penalty constraint analytical expressions for that constant dilatation eigenpair are derived for arbitrary element geometries it is shown how the incompressible constraint carries over to the element stiffness matrix if the element stabilization is performed in a particular manner for several classical and recent elements the eigensystems are analysed numerically it is shown that most of the formulations reflect the incompressible constraint identically in the incompressible limit the numerical accuracies of the elements are compared

development and testing of stable invariant isoparametric curvilinear 2 and 3 d hybrid stress elements abstract linear and quadratic serendipity hybrid stress elements are examined in respect of stability coordinate invariance and optimality a formulation based upon symmetry group theory successfully addresses these issues in undistorted geometries and is fully detailed for plane elements the resulting least order stable invariant stress polynomials can be applied as astute approximations in distorted cases through a variety of tensor components and variational principles a distortion sensitivity study for two and three dimensional elements provides favourable numerical comparisons with the assumed displacement method

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

extension of field consistence approach into developing plane stress elements in this research paper the possibilities for extending the field consistence approach l yunhua on shear locking in finite elements licentiate thesis stockholm 1997 l yunhua explanation and elimination of shear locking and membrane locking with field consistence approach comput methods appl mech engrg in press starting from different variational principles to plane stress elements are investigated in the extension two main difficulties are explicitly solving a set of coupled partial differential equations and satisfying inter element compatibility the first one is alleviated by constructing element interpolations from a set of quasi general solutions rather than the real general solutions to the euler lagrangian equations the second one is solved by combining the field consistence approach with the iso parametric interpolation technique the traditional assumed stress method is improved and an efficient plane stress element is obtained it seems that the relations between the three commonly used variational principles can be more reasonably established in the framework of the field consistence approach

coupling finite element and spectral methods first results a poisson equation on a rectangular domain is solved by coupling two methods the domain is divided in two squares a finite element approximation is used on the first square and a spectral discretization is used on the second one two kinds of matching conditions on the interface are presented and compared in both cases error estimates are proved

static output feedback mathscr h _ bm infty control of continuous time t s fuzzy affine systems via piecewise lyapunov functions this paper investigates the problem of robust h output feedback control for a class of continuous time takagi sugeno t s fuzzy affine dynamic systems with parametric uncertainties and input constraints the objective is to design a suitable constrained piecewise affine static output feedback controller guaranteeing the asymptotic stability of the resulting closed loop fuzzy control system with a prescribed h disturbance attenuation level based on a smooth piecewise quadratic lyapunov function combined with s procedure and some matrix inequality convexification techniques some new results are developed for static output feedback controller synthesis of the underlying continuous time t s fuzzy affine systems it is shown that the controller gains can be obtained by solving a set of linear matrix inequalities lmis finally three examples are provided to illustrate the effectiveness of the proposed methods

superconvergence of least squares methods for a coupled system of elliptic equations abstract we present a numerical method for solving a coupled system of elliptic partial differential equations pdes our method is based on the least squares ls approach we develop ellipticity estimates and error bounds for the method the main idea of the error estimates is the establishment of supercloseness of the ls solutions and solutions of the mixed finite element methods and ritz projections using the supercloseness property we obtain l 2 norm error estimates and the error estimates for each quantity of interest show different convergence behaviors depending on the choice of the approximation spaces moreover we present maximum norm error estimates and construct asymptotically exact a posteriori error estimators under mild conditions application to optimal control problems is briefly considered

a novel approach to filter design for t s fuzzy discrete time systems with time varying delay in this paper the problem of l2 l filtering for a class of discrete time takagi sugeno t s fuzzy time varying delay systems is studied our attention is focused on the design of full and reduced order filters that guarantee the filtering error system to be asymptotically stable with a prescribed h performance sufficient conditions for the obtained filtering error system are proposed by applying an input output approach and a two term approximation method which is employed to approximate the time varying delay the corresponding full and reduced order filter design is cast into a convex optimization problem which can be efficiently solved by standard numerical algorithms finally simulation examples are provided to illustrate the effectiveness of the proposed approaches

an iterative stabilized fractional step algorithm for finite element analysis in saturated soil dynamics abstract the discretization of the u p model for saturated porous media results in the semi discrete system of mixed type in displacements and pressures the babuska brezzi condition or the simpler patch test proposed by zienkiewicz and taylor precludes the use of elements with the equal low order of interpolation for u and p unless special stabilization techniques such as the fractional step algorithms are used the purpose of this paper is to present a modified version of the fractional step algorithm which allows much larger time step sizes than those for the existing ones the method is based on introducing an iteration algorithm the numerical experiments demonstrate the effectiveness and improved performance of the proposed modified version of the fractional step algorithm

two level finite element discretization of viscoelastic fluid flow abstract we propose and analyze a two level method of discretizing the equations of steady state flow of a viscoelastic fluid obeying an oldroyd type constitutive equation with no slip boundary condition the two level algorithm consists of solving a small non linear system of equations on the coarse mesh and then using that solution to solve a larger linear system on the fine mesh specifically following najib and sandri numer math 72 1995 223 we linearize the oldroyd type constitutive equation about the coarse mesh solution thus nullifying the difficulties brought by the advection term our theoretical error estimates show that it has optimal order accuracy provided the true solution is smooth and its norm is sufficiently small in addition our computational error estimates exhibit the validity of our analysis

a novel control design on discrete time takagi sugeno fuzzy systems with time varying delays this paper focuses on analyzing a new model transformation of discrete time takagi sugeno t s fuzzy systems with time varying delays and applying it to dynamic output feedback dof controller design a new comparison model is proposed by employing a new approximation for time varying delay state and then a delay partitioning method is used to analyze the scaled small gain of this comparison model a sufficient condition on discrete time t s fuzzy systems with time varying delays which guarantees the corresponding closed loop system to be asymptotically stable and has an induced l2 disturbance attenuation performance is derived by employing the scaled small gain theorem then the solvability condition for the induced l2 dof control is also established by which the dof controller can be solved as linear matrix inequality optimization problems finally examples are provided to illustrate the effectiveness of the proposed approaches

effects of element distortions on the performance of isoparametric elements we discuss the effects of element distortions on the performance of displacement based isoparametric quadrilateral finite elements suitable example problems for both the lagrangian and the serendipity types of elements are used to show numerically the effects of element distortions the effects of angular and curved edge distortions are evaluated analytically in terms of the abilities of the elements to represent exactly various polynomial displacement fields we then solve a plane stress problem adaptively to demonstrate the effect of element distortions on the accuracy of the stress distribution the conclusion is that the lagrangian elements are not affected by angular distortions and are therefore the more reliable elements for general use

two scale dirichlet neumann preconditioners for elastic problems with boundary refinements abstract the present work deals with the efficient resolution of elastostatics problems on domains with boundary refinements the proposed approach separates the boundary refinements from the interior of the domain by the mortar method and uses dirichlet neumann preconditioners to solve the corresponding algebraic system we prove that the simplest dirichlet neumann algorithm achieves independence of the condition number of the preconditioned system with respect to the number and the size of the small details nevertheless the situation no longer prevails when the refined boundary is clamped an enhanced preconditioner is then designed by the introduction of a coarse space to mitigate the aforementioned sensitivity some numerical tests are performed to confirm the analysis and the tools are extended by the proposition of a quasi newton method in the case of nonlinear elasticity this paper is an extended version of a work presented at the dd16 conference with proofs and complete numerical results

hp submeshing via non conforming finite element methods abstract non conformity in the hp version can involve incompatibility in both the degrees and the meshes between adjoining subdomains in this paper we show how the mortar finite element method m0 and two new variants m1 m2 can be used to join together such incompatible hp sub discretizations our results show optimality of the resulting non conforming method for various h p and hp discretizations including the case of exponential hp convergence over geometric meshes we also present numerical results for the lagrange multiplier when the method is implemented via a mixed method three dimensional considerations suggest that our methods m1 m2 are easier to generalize to arbitrary meshes than m0

input output approach to stability and l2 gain analysis of systems with time varying delays abstract stability and l 2 l 2 gain of linear continuous time and discrete time systems with uncertain bounded time varying delays are analyzed under the assumption that the nominal delay values are not equal to zero the delay derivatives in the continuous time are not assumed to be less than q 1 an input output approach is applied by introducing a new input output model which leads to effective frequency domain and time domain criteria the new method significantly improves the existing results for delays with derivatives not greater than 1 which were treated in the past as fast varying delays without any constraints on the delay derivatives new bounded real lemmas brls are derived for systems with state and objective vector delays and norm bounded uncertainties numerical examples illustrate the efficiency of the new method

fuzzy model based reliable static output feedback mathscr h _ infty control of nonlinear hyperbolic pde systems this paper investigates the problem of output feedback robust mathscr h infty control for a class of nonlinear spatially distributed systems described by first order hyperbolic partial differential equations pdes with markovian jumping actuator faults the nonlinear hyperbolic pde systems are first expressed by takagi sugeno fuzzy models with parameter uncertainties and then the objective is to design a reliable distributed fuzzy static output feedback controller guaranteeing the stochastic exponential stability of the resulting closed loop system with certain mathscr h infty disturbance attenuation performance based on a markovian lyapunov functional combined with some matrix inequality convexification techniques two approaches are developed for reliable fuzzy static output feedback controller design of the underlying fuzzy pde systems it is shown that the controller gains can be obtained by solving a set of finite linear matrix inequalities based on the finite difference method in space finally two examples are presented to demonstrate the effectiveness of the proposed methods

adaptive finite time control of stochastic nonlinear systems with actuator failures abstract this paper investigates a finite time tracking control of stochastic nonlinear systems with actuator failures as the nonlinearities and actuator failures are completely unknown the existing control methods are unavailable by applying an approximation property of fuzzy logic systems an adaptive finite time control strategy is presented since the existing finite time stability criterion can not deal with the finite time control under the effect of approximation error lemma 5 is first established under the proposed scheme the actuator failures are compensated successfully and the finite time tracking performance and stability of stochastic nonlinear system are assured based on lemma 5 and jessen s inequality the finite time stability of stochastic nonlinear systems is proved

information transfer between incompatible finite element meshes application to coupled thermo viscoelasticity this article is concerned with information transfer between non matching finite element meshes such a feature is not new in the literature but we focus herein on a geometric approach to transfer solution fields in order to be as application independent as possible moreover the dedicated case concerns the transfer of finite element fields defined at integration points of the meshes and allows iterative exchange of fields in both directions to do so we propose an extension to the mortar technique that fulfills these goals and that does not suffer from a high computational cost the application is the simulation of a strongly coupled thermo viscoelastic problem with phase transition solved with a partitioning technique

the mortar finite element method for 3d maxwell equations first results in the framework of domain decomposition methods we extend the main ideas of the mortar element method to the numerical solution of maxwell s equations in wave form by h curl conforming finite elements the method we propose turns out to be a new nonconforming nonoverlapping domain decomposition method where nonmatching grids are allowed at the interfaces between subdomains a model problem is considered the convergence of the discrete approximation is analyzed and an error estimate is provided the method is proven to be slightly suboptimal with a loss of a factor scriptstyle sqrt rm ln h with respect to the degree of polynomials in order to achieve this convergence result we nevertheless need extra regularity assumptions on the solution of the continuous problem

mortar boundary elements we establish a mortar boundary element scheme for hypersingular boundary integral equations representing elliptic boundary value problems in three dimensions we prove almost quasi optimal convergence of the scheme in broken sobolev norms of order 1 2 subdomain decompositions can be geometrically nonconforming and meshes must be quasi uniform only on subdomains numerical results confirm the theory

multigrid methods for saddle point problems optimality systems abstract we develop multigrid methods for an elliptic distributed optimal control problem on convex domains that are robust with respect to a regularization parameter we prove the uniform convergence of the w cycle algorithm and demonstrate the performance of v cycle and w cycle algorithms through numerical experiments

on the accuracy of the mortar finite volume element method with lagrange multipliers abstract in this paper the mortar finite volume element mfve method with lagrange multipliers is considered for second order elliptic boundary value problems we prove l 2 error estimates which are affected by regularities in both the exact solution and the source term meanwhile the uniform convergence of the solution is obtained for the mfve method under minimal regularity assumption

co design of event generator and filtering for a class of t s fuzzy systems with stochastic sensor faults this paper is firstly concerned with reliable h filter design for a class of t s fuzzy systems with stochastic sensor faults under an event triggered scheme 1 a t s fuzzy model is used to approximate the nonlinear dynamics of the plant a set of stochastic variables are used to describe the sensor failure 2 an event triggered scheme which has some advantages over some existing ones is introduced to the networked control systems under the event triggered scheme the sensor data are transmitted only when the sampled measurements of the plant violate the specified event condition then an event based filter design model for t s fuzzy systems is constructed by taking the effect of event triggered scheme and the sensor faults into consideration sufficient conditions for the existence of the desired filter are established in terms of linear matrix inequalities and the explicit expression is given for the designed filter parameters a numerical example is provided to illustrate the design method

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

on the consistency of finite element models in thermoelastic analysis in thermoelastic analysis compatible finite elements may predict oscillating stresses if the temperature distribution is not coherent with the element strain coming from the assumed displacement approximation modelling the stress field as an independent variable could be a viable alternative to avoid these spurious outcomes to this purpose the behavior of mixed hybrid stress and equilibrium finite element models in the presence of initial strains due to temperature is investigated and compared with the usually employed displacement approach the consistency requirement for each model is established and the spurious outcomes due to inconsistent temperature fields are discussed examining also the effects of element geometry distortions the analysis illustrated through some numerical tests shows that a direct approximation for the stress field can eliminate or at least reduce the generation of spurious stress modes although this is not a priori guaranteed by a mixed approach

rational approach for assumed stress finite elements a new method for the formulation of hybrid elements by the hellinger reissner principle is established by expanding the essential terms of the assumed stresses as complete polynomials in the natural coordinates of the element the equilibrium conditions are imposed in a variational sense through the internal displacements which are also expanded in the natural co ordinates the resulting element possesses all the ideal qualities i e it is invariant it is less sensitive to geometric distortion it contains a minimum number of stress parameters and it provides accurate stress calculations for the formulation of a 4 node plane stress element a small perturbation method is used to determine the equilibrium constraint equations the element has been proved to be always rank sufficient

new strategy for assumed stresses for 4 node hybrid stress membrane element an oblique skew co ordinate system defined at the origin of the isoparametric co ordinates is introduced as the reference co ordinate system for assumed stresses in the formulation of a 4 node hybrid membrane element the initially uncoupled stresses in these reference co ordinates can be constrained to satisfy the equilibrium conditions pointwise by using the procedure of pian and wu7 when suitable incompatible displacements are introduced such strategy allows the element stiffness to be formulated by using either the hellinger reissner or the complementary energy functional numerical results show that the performances of three elements constructed by using different sets of incompatible displacements in this paper are practically identical and are all of slightly higher accuracy than that of the pian sumihara element6

relations between incompatible displacement model and hybrid stress model an examination of the variational formulations confirms the similarity between the incompatible displacement model and the assumed stress hybrid model that was pointed out by irons in 1972 but the basic differences between the two are also identified for 8 node solid elements the assumed stress terms obtained through a rational procedure also agree with those deduced by irons purely from his physical insight

brief an lmi approach to design robust fault detection filter for uncertain lti systems in this paper the robust fault detection filter design problem for uncertain linear time invariant lti systems with both unknown inputs and modelling errors is studied the basic idea of our study is to use an optimal residual generator assuming no modelling errors as the reference residual model of the robust fault detection filter design for uncertain lti systems with modelling errors and based on it to formulate the robust fault detection filter design as an h model matching problem by using some recent results of h optimization a solution of the optimization problem is then presented via a linear matrix inequality lmi formulation the main results include the development of an optimal reference residual model the formulation of robust fault detection filter design problem the derivation of a sufficient condition for the existence of a robust fault detection filter and a construction of it based on the lmi solution parameters the determination of adaptive threshold for fault detection an illustrative design example is employed to demonstrate the effectiveness of the proposed approach