pointwise functional calculi supposeais a possibly unbounded closed linear operator on a banach spacex x x and f is a banach algebra of functions we introduce apointwiseffunctional calculus for a at x this is a bounded linear map from f intox with the properties that one would expect from a mapf f a x ifahad a f functional calculus howeveramay not have such a functional calculus we show that the existence of a pointwise f functional calculus is equivalent to the existence of a continuously embedded banach subspace on whichahas a global f functional calculus we characterize being pointwise generalized scalar atxand give simple sufficient conditions we also discuss the relationship between pointwise functional calculi and the many physical problems that may be modelled as an abstract cauchy problem

analysis of kinematic linked interpolation methods for reissner mindlin plate problems the approximation to the solution of reissner mindlin plate problem is considered in the framework of finite element techniques a general strategy involving a linking operator between rotations and vertical displacements is analyzed an abstract convergence result is provided examples of elements falling into this framework are presented and shown to be stable and locking free numerical tests detail the performances of the elements email lovadina ing unitn it

the patch test for mixed formulations this paper presents a simple extension of the patch test to mixed formulations to provide the necessary and sufficient conditions for convergence the general algebraic conditions of babuska and brezzi are given a simple form and a conceptual application of the patch tests serves to point out the instability of several well known formulations for incompressible problems the test is also applied to mixed displacement strain formulations of elasticity and limiting formulations are noted

eigenvalue bounds versus semidefinite relaxations for the quadratic assignment problem it was recently demonstrated that a well known eigenvalue bound for the quadratic assignment problem qap actually corresponds to a semidefinite programming sdp relaxation however for this bound to be computationally useful the assignment constraints of the qap must first be eliminated and the bound then applied to a lower dimensional problem the resulting projected eigenvalue bound is one of the best available bounds for the qap especially when considering the quality of bounds relative to the complexity of obtaining them in this paper we show that the projected eigenvalue bound is also related to an sdp relaxation of the original qap this implicit sdp relaxation is similar to sdp relaxations of the qap proposed by lin and saigal on solving large scale semidefinite programming problems a case study of quadratic assignment problem department of industrial engineering and operations research university of michigan 1997 and zhao et al j combin optim 2 1998 pp 71 109

a relationship between stabilized finite element methods and the galerkin method with bubble functions abstract a relation between stabilized finite element methods and the galerkin method employing interpolations with bubble functions is established for the advective diffusive model and for the linearized compressible navier stokes equations the bubble functions are shown to help in stabilizing the advective operator without recourse to upwinding or any other numerical strategy in particular for the advective diffusive model the galerkin method employing piecewise linears with bubble functions is shown to be equivalent to the streamline upwind petrov galerkin supg method in the diffusive limit

implementation of a variance reduction based lower bound in a branch and bound algorithm for the quadratic assignment problem the efficient implementation of a branch and bound algorithm for the quadratic assignment problem qap incorporating the lower bound based on variance reduction of li pardalos ramakrishnan and resende 1994 is presented a new data structure for efficient implementation of branch and bound algorithms for the qap is introduced computational experiments with the branch and bound algorithm on different classes of qap test problems are reported the branch and bound algorithm using the new lower bounds is compared with the same algorithm utilizing the commonly applied gilmore lawler lower bound both implementations use a greedy randomized adaptive search procedure for obtaining initial upper bounds the algorithms report all optimal permutations optimal solutions for previously unsolved instances from the literature of dimensions n 16 and n 20 have been found with the new algorithm in addition the new algorithm has been tested on a class of large data variance problems requiring the examination of much fewer nodes of the branch and bound tree than the same algorithm using the gilmore lawler lower bound

linked interpolation for reissner mindlin plate elements part ii a simple triangle the formulation and shape functions given in part i are extended to develop a simple plate bending triangle with good performance in both thin and thick situations indeed its performance is better than that of other nine dof elements and its computer implementation simpler when used with selective reduced integration the element produces identical results as that of xu 1 2 to save space details given in part i are not repeated and some results are also presented in the figures of part i

an edge based smoothed finite element method es fem with stabilized discrete shear gap technique for analysis of reissner mindlin plates abstract an edge based smoothed finite element method es fem for static free vibration and buckling analyses of reissner mindlin plates using 3 node triangular elements is studied in this paper the calculation of the system stiffness matrix is performed by using the strain smoothing technique over the smoothing domains associated with edges of elements in order to avoid the transverse shear locking and to improve the accuracy of the present formulation the es fem is incorporated with the discrete shear gap dsg method together with a stabilization technique to give a so called edge based smoothed stabilized discrete shear gap method es dsg the numerical examples demonstrated that the present es dsg method is free of shear locking and achieves the high accuracy compared to the exact solutions and others existing elements in the literature

a new bound for the quadratic assignment problem based on convex quadratic programming we describe a new convex quadratic programming bound for the quadratic assignment problem qap the construction of the bound uses a semidefinite programming representation of a basic eigenvalue bound for qap the new bound dominates the well known projected eigenvalue bound and appears to be competitive with existing bounds in the trade off between bound quality and computational effort

spectral representations for unbounded operators with real spectrum soit t un operateur agissant dans un espace de banach reflexif x avec domaine d t et spectre reel alors il existe une mesure spectrale e sur z la variete de semisimplicite pour t telle que 1 pour chaque b r e commute avec chaque u b x qui commute avec t 2 d t z x z r se ds x existe et appartient a z et 3 tx r se ds x pour tout x d t z

an isostatic assumed stress triangular element for the reissner mindlin plate bending problem the paper describes a new assumed stress triangular element for reissner mindlin plates called tip3 with three nodes and three degrees of freedom per node the kinematics is constructed by means of the so called linked interpolation ruled by technically significant degrees of freedom i e one transversal displacement and two rotations per node without using additional bubble modes the static representation starts from a moment shear uncoupled polynomial approximation and is constrained to satisfy some equilibrium conditions in order to reduce the stress parameters to a minimum number the resulting element is locking free presents correct rank and passes the bending patch test even for very thin plates the good performances of the element are demonstrated by several comparisons with other triangular plate elements available in the literature copyright 2007 john wiley sons ltd

linked interpolation for reissner mindlin plate elements part i a simple quadrilateral in most plate elements using the reissner mindlin assumptions the interpolations used for the lateral displacements w and the rotation involve the independent representation of each variable by its nodal values usually with identical interpolations to ensure a higher order of expansion for displacement w its representation is linked in the present paper with both sets of nodal variables conditions necessary for the use of such expansions are established here and the paper shows the development of a linear quadrilateral element q4bl whose performance and robustness are good although it possesses one singularity if only three degrees of freedom are prescribed in part ii we apply the identical formulation to develop a triangular element t3bl which performs equally well and is fully robust

a branch and bound algorithm for the quadratic assignment problem based on the hungarian method this paper presents a new branch and bound algorithm for solving the quadratic assignment problem qap the algorithm is based on a dual procedure dp similar to the hungarian method for solving the linear assignment problem our dp solves the qap in certain cases i e for some small problems n 7 and for numerous larger problems 7 n 16 that arise as sub problems of a larger qap such as the nugent 20 the dp however does not guarantee a solution it is used in our algorithm to calculate lower bounds on solutions to the qap as a result of a number of recently developed improvements the dp produces lower bounds that are as tight as any which might be useful in a branch and bound algorithm these are produced relatively cheaply especially on larger problems experimental results show that the computational complexity of our algorithm is lower than known methods and that its actual runtime is significantly shorter than the best known algorithms for qaplib test instances of size 16 through 22 our method has the potential for being improved and therefore can be expected to aid in solving even larger problems

a low order nonconforming finite element for reissner mindlin plates we propose a locking free element for plate bending problems based on the use of nonconforming piecewise linear functions for both rotations and deflections we prove optimal error estimates with respect to both the meshsize and the analytical solution regularity

finite element methods for a modified reissner mindlin free plate model the solution of the reissner mindlin plate problem with free boundary conditions presents a strong layer effect near the free edges as a consequence the solution is not even uniformly bounded even in h3 2 which implies that at most an o h1 2 uniform convergence rate can be reached by finite element methods in the h1 norm following instead the modified free boundary model presented by beirao da veiga and brezzi which gives more regular solutions better error estimates can be obtained in principle in this paper we present and analyze the extension of different families of well known optimal plate methods to this new model all the modified methods presented are proved to be optimal and free of locking

a survey for the quadratic assignment problem the quadratic assignment problem qap one of the most difficult problems in the np hard class models many real life problems in several areas such as facilities location parallel and distributed computing and combinatorial data analysis combinatorial optimization problems such as the traveling salesman problem maximal clique and graph partitioning can be formulated as a qap in this paper we present some of the most important qap formulations and classify them according to their mathematical sources we also present a discussion on the theoretical resources used to define lower bounds for exact and heuristic algorithms we then give a detailed discussion of the progress made in both exact and heuristic solution methods including those formulated according to metaheuristic strategies finally we analyze the contributions brought about by the study of different approaches

a low dimensional semidefinite relaxation for the quadratic assignment problem the quadratic assignment problem qap is arguably one of the hardest np hard discrete optimization problems problems of dimension greater than 25 are still considered to be large scale current successful solution techniques use branch and bound methods which rely on obtaining strong and inexpensive bounds in this paper we introduce a new semidefinite programming sdp relaxation for generating bounds for the qap in the trace formulation we apply majorization to obtain a relaxation of the orthogonal similarity set of the quadratic part of the objective function this exploits the matrix structure of qap and results in a relaxation with much smaller dimension than other current sdp relaxations we compare the resulting bounds with several other computationally inexpensive bounds such as the convex quadratic programming relaxation qpb we find that our method provides stronger bounds on average and is adaptable for branch and bound methods

virtual bubbles and galerkin least squares type methods ga l s abstract the equivalence between stabilized finite element methods or galerkin least squares tyoe methods ga l s and the standard galerkin method with bubble functions is established in an abstract framework the results are applicable to various finite element spaces including high order elements and applications to the advective diffusive model and to the stokes problem are presented illustrating the potential of the abstract theory introduced here

distortion immune nine node displacement based quadrilateral thick plate finite elements that satisfy constant bending patch test we employ the linked interpolation concept to develop a higher order 9 node quadrilateral plate finite element with curved sides which passes the constant bending patch test for arbitrary node positions the linked interpolation for the plate displacements is expanded with three bubble parameters to get polynomial completeness necessary to satisfy the patch test in contrast to some other techniques the elements developed in this way retain a symmetric stiffness matrix at a marginal computational expense at the element level two new elements are generated using this concept and tested on several examples with curved sides or some kind of geometric distortion

a shear deformable plate element with an exact thin limit abstract we present a quadrilateral finite element developed within the framework of a shear deformable plate theory the interpolation for the rotation takes advantage of internal rotational degrees of freedom through the use of bubble functions while the interpolation for the transverse displacement is linked to the nodal rotations a careful study of the element behavior is performed using an extensive set of mixed patch tests results from several numerical examples are also presented the element has proper rank and excellent interpolating capacity moreover without using any ad hoc assumption e g energy balancing schemes the element presents no locking effects at all in fact the shear energy may be set identically equal to zero without introducing any ill conditioning in the problem thus recovering a proper thin plate limit

unbounded holomorphic functional calculus and abstract cauchy problems for operators with polynomially bounded resolvents abstract we consider linear unbounded operators b on a banach space x whose spectrum is contained in an open set v such that the resolvent w b 1 exists and is o 1 w for w v for some 1 we will call this an operator of type v for such operators we construct a functional calculus b defined for functions holomorphic on v whose real part is bounded above such that b generates an exponentially bounded b m semigroup where m 2 v this map is a continuous algebra homomorphism in a sense that is made precise later we give best possible spectral mapping theorems applications of this construction include the following we characterize subsets v of the complex plane with the property that whenever a is densely defined and of type v then the abstract cauchy problem has a solution for all initial data in a dense set we show that when b is of a type v then there exists a ranach subspace y such that d b m y x and there exists an h v functional calculus for b y on this interpolating space the imaginary powers of b form a c 0 group and we have spectral decompositions of b when v is disconnected our construction produces solutions for all initial data in dense sets of wide classes of first and second order cauchy problems including the schrodinger equation the backwards heat equation and the laplace equation on l p r n or l p i p where is a region in r n with smooth boundary we also consider incomplete cauchy problems of arbitrarily high order we emphasize that in our construction of b we do not assume that is meromorphic at this allows us to define exponentials cosines and logarithms of b directly for large classes of operators b for example we may define the exponential e 5 of an operator b with real spectrum

a four node plate bending element based on mindlin reissner plate theory and a mixed interpolation this communication discusses a 4 node plate bending element for linear elastic analysis which is obtained as a special case from a general nonlinear continuum mechanics based 4 node shell element formulation the formulation of the plate element is presented and the results of various example solutions are given that yield insight into the predictive capability of the plate and shell element

an improved treatment of transverse shear in the mindlin type four node quadrilateral element abstract an improved displacement methodology based on mindlin theory is developed and applied to a four node twelve degrees of freedom quadrilateral element special attention is directed toward enhancement of the transverse shear energy representation particularly a non uniform order kinematic interpolation scheme is accompanied by what is termed element appropriate shear correction factors the element matrices are consistently derived from hamilton s variational principle using exact numerical integration throughout the element stiffness matrix possesses correct rank and is well conditioned over the entire mindlin theory range of thickness to length ratios exceptionally good element performance is demonstrated by solutions to a set of static and vibrational problems

recent advances in the solution of quadratic assignment problems the quadratic assignment problem qap is notoriously difficult for exact solution methods in the past few years a number of long open qaps including those posed by steinberg 1961 nugent et al 1968 and krarup 1972 were solved to optimality for the first time the solution of these problems has utilized both new algorithms and novel computing structures we describe these developments as well as recent work which is likely to result in the solution of even more difficult instances

the patch test a condition for assessing fem convergence this paper discusses various forms of the irons patch test and shows again that its satisfaction is a necessary convergence condition being equivalent to consistency further it is shown that the test can be applied for verification of stability requirements thus providing also a sufficient condition of convergence the patch test is useful in testing the order of asymptotic convergence and the satisfaction of the test gives a guide for development of certain incompatible element forms

a class of mixed assumed strain methods and the method of incompatible modes a three field mixed formulation in terms of displacements stresses and an enhanced strain field is presented which encompasses as a particular case the classical method of incompatible modes within this frame work incompatible elements arise as particular compatible mixed approximations of the enhanced strain field the conditions that the stress interpolation contain piece wise constant functions and be l2 ortho gonal to the enhanced strain interpolation ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation the preceding conditions are formulated in a form particularly convenient for element design as an illustration of the methodology three new elements are developed and shown to exhibit good performance a plane 3d elastic plastic quad an axisymmetric element and a thick plate bending quad the formulation described herein is suitable for non linear analysis

the finite element patch test revisited a computer test for convergence validation and error estimates abstract the patch test was introduced in the mid 1960s first as a check of satisfactory performance for elements violating continuity requirements and later simply as a necessary condition which all elements had to satisfy and which frequently checked simple programming errors in its original form the patch test simply verified that the minimum local consistency error was achievable and that the programming was correct later it was established that the test could also be used to find the convergence order of any finite element type while consistency is one of the necessary requirements for convergence the second is of course that of stability in the original early work only displacement type structural elements were involved and thus stability was ensured by rejecting elements which could form mechanisms in a 1986 reformulation of the patch test this stability or solvability requirement was formalized to all element assemblies and the patch test extended to become a generally applicable sufficient and necessary condition for convergence of all element forms 1 2 although some misinterpretation of the patch test has occurred in literature 3 4 the authors believe that with certain restrictions on regularity of the problem dealt with the satisfaction of the patch test is equivalent to the satisfaction of the more mathematical babuska brezzi criteria 5 6 in recent years another important use of the patch test has been found by babuska and his coworkers 7 9 this work tests the asymptotic effectivity of various error estimating procedures used with various element patterns

linked interpolation for reissner mindlin plate elements part iii an alternative quadrilateral an alternative quadrilateral element for reissner mindlin plates which extends the mixed formulation described in part 1 using linked interpolations is presented differently from element q4bl presented in part i this element q4bla employs four internal rotation nodes and a linear approximation for transverse shear forces it is shown that the element passes various patch tests it does not possess any zero energy mode and its performance is good for both thick and thin plates

a triangular element based on reissner mindlin plate theory a new triangular plate blending element based on the reissner mindlin theory is developed through a mixed formulation emanating from the hu washizu variational principle a main feature of the formulation is the use of a linear transverse shear interpolation scheme with discrete constraint conditions on the edges