finite elements with increased freedom in choosing shape functions starting with a mathematical statement of the convergence requirements for an element stiffness matrix the paper discusses displacement shape functions that may be used in connection with the potential energy principle in short these functions must be force orthogonal and energy orthogonal but they need not be conforming satisfy interelement compatibility it is shown that the requirements to the displacement functions may be greatly relaxed through slight modifications of the coupling stiffness between fundamental and higher order displacement modes several alternative formulations are examined in particular a new free formulation is suggested using this form which is very simple the only requirement to the displacement patterns used is that they should contain the fundamental deformation modes and be linearly independent applications of the theory to triangular and rectangular plate bending elements are shown the simple stiffness matrix for the latter is given explicitly the numerical results compare favourably with other types of finite elements

the nsbeti method an extension of the feti method to non symmetrical bem fem coupled problems summary the finite element tearing and interconnecting feti method is recognized as an effective domain decomposition tool to achieve scalability in the solution of partitioned second order elasticity problems in the boundary element tearing and interconnecting beti method a direct extension of the feti algorithm to the bem the symmetric galerkin bem formulation is used to obtain symmetric system matrices making possible to apply the same feti conjugate gradient solver in this work we propose a new beti variant labeled nsbeti that allows to couple substructures modeled with the fem and or non symmetrical bem formulations the method connects non matching bem and fem subdomains using localized lagrange multipliers and solves the associated non symmetrical flexibility equations with a bi cgstab iterative algorithm scalability issues of nsbeti in bem bem and combined bem fem coupled problems are also investigated copyright 2012 john wiley sons ltd

generalized factorial schur functions biorthogonal rational functions and the rii chain generalized factorial schur functions are introduced through a newton type interpolation they are applied to construct a class of biorthogonal rational functions and a special solution to its spectral transformation chain the rii chain a two parameter deformation of the schur type functions is also discussed

variable node elements for non matching meshes by means of mls moving least square scheme a new class of finite elements is described for dealing with non matching meshes for which the existing finite elements are hardly efficient the approach is to employ the moving least square mls scheme to devise a class of elements with an arbitrary number of nodal points on the parental domain this approach generally leads to elements with the rational shape functions which significantly extends the function space of the conventional finite element method with a special choice of the nodal points and the base functions the method results in useful elements with the polynomial shape functions for which the c 1 continuity breaks down across the boundaries between the subdomains comprising one element the present scheme possesses an extremely high potential for applications which deal with various problems with discontinuities such as material inhomogeneity crack propagation phase transition and contact mechanics the effectiveness of the new elements for handling the discontinuities due to non matching interfaces is demonstrated using appropriate examples

non matching mesh gluing by meshless interpolation an alternative to lagrange multipliers rewards of using non matching meshes are great in many aspects sub meshing a complex structure in a sub structure wise manner separately and or in parallel selective local refinement unlimited scalability guarantee for generating meshes in increasingly large scale finite element simulation etc however when meshes do not match a gluing algorithm is required to enforce inter domain continuity non matching terminologically originates from mesh discretization in nature and the non matching mesh issue is therefore avoidable or does not exist in a node based or meshless discretization in meshless methods motivated by this a gluing algorithm is developed based on meshless interpolation the gluing is accomplished by continuous trial and test functions across non matching meshes constructed using nodes only the developed gluing algorithm is tested in static and wave propagation problems in two and three dimensions it is demonstrated that the gluing algorithm does not deteriorate convergence and accuracy compared with the one piece conforming mesh compared with lagrange multiplier gluing one of the most common approaches the current algorithm has two significant benefits 1 easier implementation in any dimension and 2 positive definite banded system matrices not acting against equation solvers and hence better suited for large scale finite element analysis

reduction of substructural interface degrees of freedom in flexibility based component mode synthesis a flexibility based component mode synthesis cms is proposed for reduced order modelling of dynamic behaviour of large structures the approach employs partitioning via the localized lagrange multiplier method the use of the localized lagrange multipliers leads to unlike the classical lagrange multipliers a linearly independent set of interface forces without any redundancies at multiply connected interface nodes the flexibility based cms method has shown significant advantages over the classical craig bampton method a key feature of the method is its substructural mode selection criterion that is independent of loading conditions unlike the majority of available cms approaches where one retains the full dimension of partition boundary degrees of freedom dofs the flexibility based method allows to reduce significantly the interface dofs the reduction of interface dofs represents the major contribution of the present communication the efficiency of the proposed approach is demonstrated on an analysis of a simple plate partitioned and of a more complex 3d structure both partitioned into several substructures copyright 2006 john wiley sons ltd

an algebraically partitioned feti method for parallel structural analysis algorithm description an algebraically partitioned feti method for the solution of structural engineering problems on parallel computers is presented the present algorithm consists of three attributes an explicit generation of the orthogonal null space matrix associated with the interface nodal forces the floating subdomain rigid body modes computed from the subdomain static equilibrium equation of the classical force method and the identification of redundant interface force constraint operator that emanates when the interface force computations are localized comparisons of the present method with the previously developed differentially partitioned feti method are offered in terms of the saddle point formulations at the end of the paper a companion paper reports implementation details and numerical performance of the proposed algorithm 1997 john wiley sons ltd

a variational principle for the formulation of partitioned structural systems a continuum based variational principle is presented for the formulation of the discrete governing equations of partitioned structural systems this application includes coupled substructures as well as subdomains obtained by mesh decomposition the present variational principle is derived by a series of modifications of a hybrid functional originally proposed by atluri for finite element development the interface is treated by a displacement frame and a localized version of the method of lagrange multipliers interior displacements are decomposed into rigid body and deformational components to handle floating subdomains both static and dynamic versions are considered an important application of the present principle is the treatment of nonmatching meshes that arise from various sources such as separate discretization of substructures independent mesh refinement and global local analysis the present principle is compared with that of a globalized version of the multiplier method copyright 2000 john wiley sons ltd

generalized bergman kernels on symplectic manifolds we study the near diagonal asymptotic expansion of the generalized bergman kernel of the renormalized bochner laplacian on high tensor powers of a positive line bundle over a compact symplectic manifold we show how to compute the coefficients of the expansion by recurrence and give a closed formula for the first two of them as a consequence we calculate the density of states function of the bochner laplacian and establish a symplectic version of the convergence of the induced fubini study metric we also discuss generalizations of the asymptotic expansion for non compact or singular manifolds as well as their applications our approach is inspired by the analytic localization techniques of bismut and lebeau

inhomogeneous basis set of symmetric polynomials defined by tableaux abstract a basis set of inhomogeneous symmetric polynomials denoted by tlambda z where z z1 zn and lambda lambda1 lambdan is a partition is defined in terms of young weyl standard tableaux or equivalently in terms of gel fand weyl patterns a number of significant properties of these polynomials are given together with outlines of proofs and compared with properties of the well known basis set of schur functions which are homogeneous polynomials the basis of the ring of symmetric polynomials defined here is shown to be natural for the expansion of inhomogeneous symmetric functions constructed from rising factorials

mls based variable node elements compatible with quadratic interpolation part i formulation and application for non matching meshes two dimensional variable node elements compatible with quadratic interpolation are developed using the moving least square mls approximation the mapping from the parental domain to the physical element domain is implicitly obtained from mls approximation with the shape functions and their derivatives calculated and saved only at the numerical integration points it is shown that the present mls based variable node elements meet the patch test if a sufficiently large number of integration points are employed for numerical integration the cantilever problem with non matching meshes is chosen to check the feasibility of the present mls based variable node elements and the result is compared with that from the lower order case compatible with linear interpolation copyright 2005 john wiley sons ltd

polyhedral elements with strain smoothing for coupling hexahedral meshes at arbitrary nonmatching interfaces abstract managing nonmatching interfaces between dissimilar hexahedral meshes is complicated because the interfaces which are arbitrarily formed by the intersection of element edges are composed of various types of polygons in this paper a simple and efficient scheme is proposed for dealing with nonmatching interfaces using polyhedral elements because polyhedral elements can have arbitrary numbers of polygonal faces and nodes they can be used as transition elements for coupling nonmatching meshes a strain smoothing technique in the cell based smoothed finite element method is introduced to resolve critical difficulties in defining shape functions and in conducting numerical integration for the polyhedral elements as well as to further enhance the accuracy and efficiency of finite element analyses the effectiveness of the proposed scheme is demonstrated through several numerical examples involving nonmatching interfaces the effects of decomposition types of smoothing cells in the strain smoothing technique are also discussed in terms of numerical stability and accuracy

a survey of parametrized variational principles and applications to computational mechanics abstract this survey paper describes recent developments in the area of parametrized variational principles pvps and selected applications to finite element computational mechanics a pvp is a variational principle containing free parameters that have no effect on the euler lagrange equations the theory of single field pvps based on gauge functions also known as null lagrangians is a subset of the inverse problem of variational calculus that has limited value on the other hand multifield pvps are more interesting from theoretical and practical standpoints following a tutorial introduction the paper describes the recent construction of multifield pvps in several areas of elasticity and electromagnetics it then discusses three applications to finite element computational mechanics the derivation of high performance finite elements the development of element level error indicators and the construction of finite element templates the paper concludes with an overview of open research areas

clustered generalized finite element methods for mesh unrefinement non matching and invalid meshes in spite of significant advancements in automatic mesh generation during the past decade the construction of quality finite element discretizations on complex three dimensional domains is still a difficult and time demanding task in this paper the partition of unity framework used in the generalized finite element method gfem is exploited to create a very robust and flexible method capable of using meshes that are unacceptable for the finite element method while retaining its accuracy and computational efficiency this is accomplished not by changing the mesh but instead by clustering groups of nodes and elements the clusters define a modified finite element partition of unity that is constant over part of the clusters this so called clustered partition of unity is then enriched to the desired order using the framework of the gfem the proposed generalized finite element method can correctly and efficiently deal with i elements with negative jacobian ii excessively fine meshes created by automatic mesh generators iii meshes consisting of several sub domains with non matching interfaces under such relaxed requirements for an acceptable mesh and for correctly defined geometries today s automated tetrahedral mesh generators can practically guarantee successful volume meshing that can be entirely hidden from the user a detailed technical discussion of the proposed generalized finite element method with clustering along with numerical experiments and some implementation details are presented copyright 2006 john wiley sons ltd

a new three dimensional variable node finite element and its application for fluid solid interaction problems abstract a new three dimensional variable node element is proposed to achieve an efficient connection of non matching interfaces between dissimilar finite element meshes the variable node elements at interfaces are compatible with conventional finite elements and satisfy the interface conditions of continuity and completeness across non matching meshes the present method thereby provides a seamless connection between dissimilar finite element meshes and a correct load transfer across non matching interfaces therefore it leads to an efficient approach for solving a class of problems involving the non matching interfaces such as fluid solid interaction problems numerical examples are presented to show the effectiveness of the present method for solving fluid solid interaction problems with non conforming interfaces and the usefulness and application of the present method are discussed

treatment of acoustic fluid structure interaction by localized lagrange multipliers formulation a new concept is presented for modeling the dynamic interaction between an acoustic fluid and an elastic structure the coupling of this multiphysics system is done by inserting a kinematic interface frame between the fluid and the structure and using node collocated lagrange multipliers to connect the frame to each subsystem the time domain response analysis is performed by a partitioned analysis procedure the main advantages of this localized lagrange multiplier llm primal dual coupling method are complete localization of the structure and fluid subsystems elimination of the conventional predictor in the partitioned time integration method and the ability to accommodate non matching meshes the standard newmark time integrator is used on both the fluid and structure models it is shown that if the integrator is a stable and second order accurate for a monolithic treatment it retains those properties for both mortar and llm partitioned solution procedures infinite and finite piston problems are used to explain and verify the methodology a sequel paper under preparation presents and discusses a set of benchmark and application examples that involve the response of existing dams to seismic excitation

a direct flexibility method we present a direct flexibility method dfm for the solution of finite element equations this method is based on a decomposition of the finite element model into substructures which may reduce to individual elements substructures are preprocessed by the direct stiffness method dsm to generate free free flexibility matrices for floating substructures the interface problem is solved for the interface forces and the solution recovered over substructure interiors the dfm shares with the dsm the advantages of being automatic maintaining locality and sparseness efficiently handling continuum elements and requiring only the availability of element stiffness libraries the new method appears to be advantageous for specific applications these include massively parallel processing inverse problems treatment of rigid members and inclusions and use of underintegrated elements without spurious mode stabilization

on the compactification of hyperconcave ends and the theorems of siu yau and nadel we show that the pseudoconcave holes of some naturally arising class of manifolds called hyperconcave ends can be filled in including the case of complex dimension two as a consequence we obtain a stronger version of the compactification theorem of siu yau and extend nadel s theorems to dimension two

factorial type schur functions and the discrete kp equation a class of factorial type schur functions is introduced from a viewpoint of a newton type interpolation their basic properties are presented it is shown that the factorial type schur functions can be used to describe a particular solution to a nonautonomous version of the discrete kp equation

review of coupling methods for non matching meshes abstract domain decomposition is nowadays a common way to speed up complex computations however the discrete meshes used in the different domains do not have to match at their common interface especially when different physical fields are involved such as in fluid structure interaction computations exchange of information over this interface is therefore no longer trivial in this paper six methods that can deal with the information transfer between non matching meshes in fluid structure interaction computations are compared for different criteria this is done for analytical test cases as well as a quasi 1d fluid structure interaction problem two methods based on radial basis functions one with compact support and one using thin plate splines are favoured over the other methods because of their high accuracy and efficiency

compactification of complete kahler manifolds of negative ricci curvature soit m une variete de kahler complete de dimension m et soit la forme de kahler on suppose 1 ric 0 2 m est tres fortement m 2 pseudoconcave 3 le recouvrement universel de m est de stein alors m est biholomorphe a une variete quasiprojective

a formulation based on localized lagrange multipliers for bem fem coupling in contact problems this paper presents a unified formulation for the combination of the finite element method fem and the boundary element method bem in 3d frictional contact problems that is based on the use of localized lagrange multipliers llms resolution methods for the contact problem between non matching meshes have traditionally been based on a direct coupling of the contacting solids using classical lagrange multipliers these methods tend to generate strongly coupled systems that require a deep knowledge of the discretization characteristics on each side of the contact zone complicating the process of mixing different numerical techniques in this work a displacement contact frame is inserted between the fe and be interface meshes discretized and finally connected to the contacting substructures using llms collocated at the mesh interface nodes this methodology will provide a partitioned formulation which preserves software modularity and facilitates the connection of non matching fe and be meshes

equivariant littlewood richardson skew tableaux we give a positive equivariant littlewood richardson rule also discovered independently by molev our proof generalizes a proof by stembridge of the classical littlewood richardson rule we describe a weight preserving bijection between our indexing tableaux and trapezoid puzzles which restricts to a bijection between positive indexing tableaux and knutson tao puzzles

a modified node to segment algorithm passing the contact patch test summary several investigations have shown that the classical one pass node to segment nts algorithms for the enforcement of contact constraints fail the contact patch test this implies that the algorithms may introduce solution errors at the contacting surfaces and these errors do not necessarily decrease with mesh refinement the previous research has mainly focused on the lagrange multiplier method to exactly enforce the contact geometry conditions the situation is even worse with the penalty method due to its inherent approximation that yields a solution affected by a non zero penetration the aim of this study is to analyze and improve the contact patch test behavior of the one pass nts algorithm used in conjunction with the penalty method for 2d frictionless contact the paper deals with the case of linear elements for this purpose several sequential modifications of the basic formulation have been considered which yield incremental improvements in results of the contact patch test the final proposed formulation is a modified one pass nts algorithm which is able to pass the contact patch test also if used in conjunction with the penalty method in other words this algorithm is able to correctly reproduce the transfer of a constant contact pressure with a constant proportional penetration copyright q 2009 john wiley sons ltd

the method weak lefschetz theorems and the topology of kahler manifolds in no nori studied the fundamental group of complements of nodal curves with ample normal bundle in smooth projective surfaces the main tool was the following weak lefschetz theorem theorem nori suppose u x is a local biholomorphism from a connected complex manifold u into a connected smooth projective variety x of dimension at least 2 and u contains a connected effective divisor y with compact support and ample normal bundle then for every zariski open subset z of x the image of 1 1 z in 1 z is of finite index

the factorial schur function the application of the divided difference of a function to the inhomogeneous symmetric functions factorial schur functions of biedenharn and louck is shown to lead to new relations and simplified proofs of their properties these results include determinantal definitions and the factorial jacobi trudi identities with extensions to skew versions similar properties of a second class of symmetric functions depending on an arbitrary parameter and of importance for generalized hypergeometric functions and series are shown also to be derivable from the divided difference notion slightly extended

a formulation of conserving impact system based on localized lagrange multipliers this paper proposes a new finite element method of frictional impact of elastic bodies the formulation introduces a contact frame that is placed in between contacting bodies and represents the contact surface the nonpenetration condition and the slip stick condition are defined between the contacting body and the contact frame with the aid of the independent localized lagrange multipliers representing the contact forces the position of the contact frame and the local coordinate of the contacting node along the contact frame are also treated as the independent variable which enables the exact satisfaction of the constraint conditions without the deficiency or redundant constraint the energy and momentum conservation algorithm is applied to the proposed impact system for the case of frictional impact the linear momentum is exactly conserved and the angular momentum is approximately conserved with negligible error copyright 2006 john wiley sons ltd

asynchronous multi domain variational integrators for non linear problems we develop an asynchronous time integration and coupling method with domain decomposition for linear and non linear problems in mechanics to ensure stability in the time integration and in coupling between domains we use variational integrators with local lagrange multipliers to enforce continuity at the domain interfaces the asynchronous integrator lets each domain step with its own time step using a smaller time step where required by stability and accuracy constraints and a larger time step where allowed we show that in practice the time step is limited by accuracy requirements rather than by stability requirements copyright 2008 john wiley sons ltd

a geometry constraint handling technique for stiffener layout optimization problem abstract beam stiffeners have frequently been used for raising natural frequencies of base structures in stiffener layout optimization problems most of the previous researches considering the position and or the length of the stiffener as design variables dealt with structures having just simple convex shapes such as a square or rectangle the reason was because concave shape structures have difficulties in formulating geometry constraints in this paper a new geometry constraint handling technique which can define both convex and concave feasible regions and measure a degree of geometry constraint violation was proposed evolution strategies ess was utilized as an optimization tool in addition the constraint handling technique of evoslinoc evolution strategies for scalar optimization with linear and nonlinear constraints was utilized to solve constrained optimization problems from numerical examples the proposed geometry constraint handling technique was verified and proved that the technique can easily be applied to structures in not only convex but also concave shapes even with a protrusion or interior holes

factorial type schur functions orthogonal rational functions and discrete dressing chains a relationship between orthogonal rational functions and discrete integrable systems is studied by an approach based on schur type symmetric functions a system of orthogonal rational functions is constructed using a multiparameter deformation of the schur functions spectral equations for the orthogonal rational functions are derived by using properties of the schur type symmetric functions the compatibility condition of the spectral equations induces a discrete dressing chain which is a toda type discrete integrable system describing dressing transformations for orthogonal rational functions

a new dual mortar method for curved interfaces 2d elasticity dual mortar method formulations have shown to be a very effective and efficient way for interfacing e g tying contacting dissimilar meshes on the other hand we have recently found that they can sometimes perform quite poorly when applied to curved surfaces in some solid mechanics applications a new modified two dimensional dual mortar method for piecewise linear finite elements is developed that overcomes this deficiency and is demonstrated on a model problem furthermore mathematical analysis is provided to demonstrate the optimal convergence and stability of the new method copyright 2005 john wiley sons ltd

littlewood richardson polynomials abstract we introduce a family of rings of symmetric functions depending on an infinite sequence of parameters a distinguished basis of such a ring is comprised by analogues of the schur functions the corresponding structure coefficients are polynomials in the parameters which we call the littlewood richardson polynomials we give a combinatorial rule for their calculation by modifying an earlier result of b sagan and the author the new rule provides a formula for these polynomials which is positive in the sense of w graham we apply this formula for the calculation of the product of equivariant schubert classes on grassmannians which implies a stability property of the structure coefficients the first manifestly positive formula for such an expansion was given by a knutson and t tao by using combinatorics of puzzles while the stability property was not apparent from that formula we also use the littlewood richardson polynomials to describe the multiplication rule in the algebra of the casimir elements for the general linear lie algebra in the basis of the quantum immanants constructed by a okounkov and g olshanski

an improved interface element with variable nodes for non matching finite element meshes extensive improvements of the interface element method iem are proposed for the efficient treatment of non matching finite element meshes our approach enables us to establish the master element via the moving least square mls approximation and so to remove the cumbersome process of constructing interface elements the values of shape functions and their derivatives are therefore mapped from the master element as in the conventional finite element method for the assurance of convergence and compatibility condition a patch test is demonstrated through several examples of 2d linear elasticity the convergence rate is compared between the present interface element and the previous version

embeddability of some strongly pseudoconvex cr manifolds we obtain an embedding theorem for compact strongly pseudoconvex cr manifolds which are boundaries of some complete hermitian manifolds we use this to compactify some negatively curved kahler manifolds with compact strongly pseudoconvex boundary an embedding theorem for sasakian manifolds is also derived

a contact formulation based on localized lagrange multipliers formulation and application to two dimensional problems the non penetration condition in contact problems is traditionally based on the classical lagrange multiplier method this method makes extensive use of modelling details of the contacting bodies for contact enforcement as the contact surface meshes are in general non matching to deal with this problem we introduce a novel element in the lagrange multiplier approach of contact modelling namely a contact frame placed in between contacting bodies it acts as a medium through which contact forces are transferred without violating equilibrium in the contact domain for discrete contact models only nodal information of the contacting bodies is required which makes the proposed contact enforcement generic the contact frame has its own independent freedoms which allows the formulation to pass contact patch tests by design copyright 2002 john wiley sons ltd

stanley s zrank conjecture on skew partitions we present an affirmative answer to stanley s zrank conjecture namely the zrank and the rank are equal for any skew partition we show that certain classes of restricted cauchy matrices are nonsingular and furthermore the signs are determined by the number of zero entries we also give a characterization of the rank in terms of the giambelli type matrices of the corresponding skew schur functions our approach also applies to the factorial cauchy matrices and the inverse binomial coefficient matrices

asynchronous multi domain variational integrators for nonlinear hyperelastic solids we present the asynchronous multi domain variational time integrators with a dual domain decomposition method for the initial hyperbolic boundary value problem in hyperelasticity variational time integration schemes based on the principle of minimal action within the lagrangian framework are constructed for the equation of motion and implemented into a variational finite element framework which is systematically derived from the three field de veubeke hu washizu variational principle to accommodate the incompressibility constraint present in an analysis of nearly incompressible materials for efficient parallel computing we use the dual domain decomposition method with local lagrange multipliers to ensure the continuity of the displacement field at the interface between subdomains the method for time discretization and the multi domain spatial decomposition enable us to use different types of integrators explicit vs implicit and different time steps on different parts of a computational domain and thus efficiently capture the underlying physics with less computational effort the energy conservation of our nonlinear midpoint asynchronous integration scheme is investigated using the energy method and both local and the global energy error estimates are derived we illustrate the performance of proposed variational multi domain time integrators by means of three examples first the method of manufactured solutions is used to examine the consistency of the formulation in the second example we investigate energy conservation and stability finally we apply the method to the motion of a heterogeneous plane domain where different integrators and time discretization steps are used accordingly with disparate material data of individual parts

a monotonicity formula on complete kahler manifolds with nonnegative bisectional curvature in y yau proposed to study the uniformization of complete kahler manifolds with nonnegative curvature in particular one wishes to determine whether or not a complete kahler manifold m with positive bisectional curvature is biholomorphic to cm see also gw si for this sake it was further asked in y whether or not the ring of the holomorphic functions with polynomial growth which we denote by op m is finitely generated and whether or not the dimension of the spaces of holomorphic functions of polynomial growth is bounded from above by the dimension of the corresponding spaces of polynomials on cm this paper addresses the latter questions we denote by 0 m the space of holomorphic functions of polynomial growth with degree d see section 3 for the precise definition then op m jd 0 od m in this paper we show that

partitioned formulation of internal and gravity waves interacting with flexible structures abstract this paper presents a partitioned modeling of internal and gravity fluid waves that interact with flexible structures the governing interaction model consists of three completely partitioned entities fluid model structural model and interface model that acts as an internal constraint on the fluid structure interface boundary thus the proposed partitioned multi physics modeling can employ two completely modular fluid and structure software modules plus an interface solver hence amenable to partitioned solution algorithms the interface discretization can exploit the nonmatching interface algorithm previously developed via the method of localized lagrange multipliers also noted is that the present fluid model can make use of widely available finite element software for standard poisson type problems

exponential estimate for the asymptotics of bergman kernels we prove an exponential estimate for the asymptotics of bergman kernels of a positive line bundle under hypotheses of bounded geometry further we give bergman kernel proofs of complex geometry results such as separation of points existence of local coordinates and holomorphic convexity by sections of positive line bundles

mls moving least square based finite elements for three dimensional nonmatching meshes and adaptive mesh refinement abstract with the aid of moving least square mls approximation a new class of three dimensional finite elements are proposed for treating nonmatching meshes and adaptive mesh refinement for which the existing finite elements are hardly efficient with a special choice of the weight function supports and the base functions the method results in useful elements with the polynomial shape function for which the c 1 continuity breaks down on the boundaries between the neighboring subdomains comprising one element the effectiveness of the new elements in handling the discontinuities due to nonmatching interfaces and automatic mesh refinement is demonstrated via three dimensional examples

ample subvarieties and q ample divisors abstract we introduce a notion of ampleness for subschemes of any codimension using the theory of q ample line bundles we also investigate certain geometric properties satisfied by ample subvarieties e g the lefschetz hyperplane theorems and numerical positivity using these properties we also construct a counterexample to the converse of the andreotti grauert vanishing theorem

a perturbed lagrangian formulation for the finite element solution of contact problems making use of a perturbed lagrangian formulation a finite element procedure for contact problems is developed for the general case in which node to node contact no longer holds the proposed procedure leads naturally to a discretization of the contact interface into contact segments within the context of a bilinear interpolation for the displacement field a mixed finite element approximation is introduced by assuming discont naous contact pressure constant on the contact segment because of this piece wise constant approximation the gap function enters into the formulation in an average sense instead of through a point wise definition numerical examples are presented that illustrate the performance of the proposed procedure current finite element formulations for contact problems based on either the classical lagrange parameter procedure l 3 12 203 or the penalty function method 4 6 11 are characterized by a point wise enforcement of the contact constraint condition in the sense that penetration of the bodies is established on a nodal basis moreover in this methods the recovery of the contact pressure over the element from the contact nodal forces generally requires an additional procedure within the framework of classical lagrange multiplier methods the contact condition is exactly satisfied by transforming the constrained problem into an unconstrained one with the introduction of additional variables lagrange multipliers these extra variables add computational effort to the solution process which often requires special procedures to handle the presence of zero diagonal terms penalty methods on the other hand enable one to transform the constrained problem into an unconstrained one without introducing additional variables the constraint condition is now satisfied only approximately for finite values of the penalty parameter the main difhculty associated with these methods however lies in the poor conditioning of the problem as the penalty is increased to more accurately enforce the constraint condition this is a well understood phenomenon particularly in the context of the incompressible and nearly incompressible problem in solid and fluid mechanics e g see l 22 25 for a review recently augmented lagrangian procedures have been proposed as a promising way to partially overcome these difficulties and regularize the penalty formulation e g see the survey in 7 8 within the framework of zinearited e u c it is possible to restrict the finite element formulation of contact problems by assuming that node to node contact occurs this is in fact the case often considered in the literature l 2 4 6 12 20 211 in the general context of fully

an eulerian lagrangian method for fluid structure interaction based on level sets abstract we describe a method for fluid structure interaction with the interface and free surfaces defined by level sets the fluid is treated by an eulerian mesh whereas the solid or structure by a lagrangian mesh the level set method provides a compact framework for writing the weak form and for developing and computing the discretized equations lagrange multiplier methods and penalty methods are used to couple the fluid and structure results are presented for a few compressible fluid problems representative of high pressure waves

partitioned analysis of flexible multibody systems using filtered linear finite element deformational modes summary this work presents a partitioned finite element formulation for flexible multibody systems based on the floating frame ff approach under the assumption of small deformations but arbitrarily large rotations of the bodies in classical ff of reference methods deformational modes are normally computed by modal analysis in this approach free floating modes are eliminated from the linear model using projection techniques and substituted by a complete set of non linear finite rotations in this way all deformational modes are retained and no modal selection is needed the main difference between this work and a classical ff of reference formulation is an algebraic separation of pure deformational modes from rigid body motions the proposed methodology presents the following advantages first the position and orientation of the ff has no restriction and can be freely located in the body with identical results second the formulation uses only the linear finite element matrices of a classical vibration problem hence they can be easily obtained from linear fem packages third no selection of modes is needed all deformational modes are retained through the filtering process and finally thanks to the use of localized lagrangian multipliers llm a partitioned system is obtained that can be solved iteratively and in a distributed manner by available scalable solvers copyright 2014 john wiley sons ltd

a simple algorithm for localized construction of non matching structural interfaces a simple and effective algorithm for the modular construction of non matched interfaces is presented for the partitioned solution of large scale structural problems the formulation is based on a recently developed four field variational principle which introduces a connection frame between the interfaced partitions a key result of the present study is a frame nodal placement criterion that uniquely determines the frame discretization into piecewise linear elements so that the interface patch test condition is satisfied a priori the method is demonstrated with several 2d and 3d example problems

the d alembert lagrange principal equations and applications to floating flexible systems this paper addresses the dynamics and quasi statics of floating flexible structures as well as extensions to unconstrained substructures and partitions of coupled mechanical systems the principal solution is defined as the state of self equilibrated forces obtained as the particular solution of the rigid motion and interface equilibrium equations this solution is independent of the stress strain constitutive properties as well as of the compatibility equations for statically determinate systems the principal solution is the final force solution for statically indeterminate systems the correction due to flexibility and compatibility is orthogonal to the principal solution the formulation is done in the context of d alembert s principle which supplies the d alembert lagrange principal equations for floating bodies these are obtained by summation of virtually working forces and moments acting on the floating systems applications of this approach are demonstrated on a set of dynamic and quasi static example problems of increasing generality linkage to variational principles with an interface potential is eventually discussed as providing the theoretical foundation for handling interacting semi discrete subsystems linked by node collocated lagrange multipliers copyright 2008 john wiley sons ltd

analysis and applications of a generalized finite element method with global local enrichment functions abstract this paper presents a procedure to build enrichment functions for partition of unity methods like the generalized finite element method and the hp cloud method the procedure combines classical global local finite element method concepts with the partition of unity approach it involves the solution of local boundary value problems using boundary conditions from a global problem defined on a coarse discretization the local solutions are in turn used to enrich the global space using the partition of unity framework the computations at local problems can be parallelized without difficulty allowing the solution of large problems very efficiently the effectiveness of the approach in terms of convergence rates and computational cost is investigated in this paper we also analyze the effect of inexact boundary conditions applied to local problems and the size of the local domains on the accuracy of the enriched global solution key aspects of the computational implementation in particular the numerical integration of generalized fem approximations built with global local enrichment functions are presented the method is applied to fracture mechanics problems with multiple cracks in the domain our numerical experiments show that even on a serial computer the method is very effective and allows the solution of complex problems our analysis also demonstrates that the accuracy of a global problem defined on a coarse mesh can be controlled using a fixed number of global degrees of freedom and the proposed global local enrichment functions

fem and bem coupling in elastostatics using localized lagrange multipliers the equations produced by the finite and boundary element methods in structural mechanics are expressed in different variables and cannot be linked without modifications conventional coupling methods of these numerical techniques have traditionally been based on the use of classical lagrange multipliers making a direct connection of the two solids through their common interfaces using matching meshes and altering the formulation of one of the methods to make it compatible with the other in this work a discrete surface called frame is interposed between the connected subdomains to approximate their common interface displacements it is treated using a finite element discretization and connected to each substructure using localized lagrange multipliers collocated at the interface nodes this methodology facilitates the connection of non matching finite and boundary element meshes avoiding modifications to the numerical methods used and providing a partitioned formulation which preserves software modularity