optimal procedure for the identification of constitutive parameters from experimentally measured displacement fields abstract measured displacement fields constitute a rich database for the identification of mechanical behavior a variety of methods are available today to address this problem a formalism is proposed showing that they all revert to the minimization of a quadratic norm or semi norm between measured and computed displacement fields however they differ in the chosen metric transporting image noise through digital image correlation and identification procedures the uncertainty in the measured displacement fields i e their full covariance and the resulting uncertainty in the estimated constitutive parameters is assessed consequently an optimal choice of metric with respect to image noise is proposed so that the resulting identification uncertainty is minimized

direct error in constitutive equation formulation for plane stress inverse elasticity problem we present a new computational formulation for inverse problems in elasticity with full field data the formulation is a variant of an error in the constitutive equation formulation but allows direct solution for the modulus field and accommodates discontinuous strain fields the development of the formulation is motivated by the relatively poor performance of current direct formulations reported so far in literature in dealing with discontinuities in the strain and material property distribution the formulation relies on minimizing the error in the constitutive equation and a momentum equation constraint numerical results on model problems show that the formulation is capable handling discontinuous and noisy strain fields and also converging with mesh refinement for continuous and discontinuous material property distributions the application to reconstruct the elastic modulus distribution in solid breast tumors is shown

deformed quantum calogero moser problems and lie superalgebras the deformed quantum calogero moser sutherland problems related to the root systems of the contragredient lie superalgebras are introduced the construction is based on the notion of the generalized root systems suggested by v serganova for the classical series a recurrent formula for the quantum integrals is found which implies the integrability of these problems the corresponding algebras of the quantum integrals are investigated the explicit formulas for their poincare series for generic values of the deformation parameter are presented

analysis of the equilibrated residual method for a posteriori error estimation on meshes with hanging nodes the equilibrated residual method is now accepted as the best residual type a posteriori error estimator nevertheless there remains a gap in the theory and practice of the method the present work tackles the problem of existence construction and stability of equilibrated fluxes for hp finite element approximation on hybrid meshes consisting of quadrilateral and triangular elements with hanging nodes a practical algorithm for post processing the finite element approximation is presented and shown to produce equilibrated fluxes for a general one irregular partition the resulting fluxes are shown to be stable in the sense that the associated error estimator provides a lower bound on the local error which does not degenerate with the mesh size numerical examples are included to illustrate the theoretical results

new integrable generalizations of calogero moser quantum problem a one parameter deformation of calogero moser quantum problem is introduced it is shown that corresponding schrodinger operator is integrable for any value of the parameter and algebraically integrable in case of integer value

a domain decomposition method for bodies with heterogeneous microstructure basedon material regularization abstract a domain decomposition methodis developed to reduce the computational complexity of boundary value problems associated withthe structural analysis of bodies with arbitrary external geometry loading and linearly elasticmicrostructure the purpose of the method is to augment existing numerical discretizationmethods of analysis such as the finite element method the approach is to partition and decouplethe heterogeneous body into more computationally tractable nonoverlapping subdomains whoseunion forms the entire domain under analysis this is achieved by approximating the subdomainboundary conditions the approximate boundary conditions of displacement or traction type aresupplied from the solution to a relatively computationally inexpensive auxiliary boundary valueproblem characterized by a simple regularized microstructure since the decoupled subdomainsmay then be analyzed separately the memory requirements are reduced and computingprocedures are trivially parallelizable a posteriori error bounds are developed for solutionsgenerated by this process it is shown that in the special case of uniform exterior loading theerror bounds collapse into forms which imply results pertaining to effective property orderingcoinciding with those published by huet 1990

a non intrusive method for the calculation of strict and efficient bounds of calculated outputs of interest in linear viscoelasticity problems this paper presents a non intrusive method which yields strict and high quality error bounds of calculated quantities of interest in structural problems solved by the finite element method the focus is on linear viscoelasticity problems described through internal variables in order to solve the adjoint problem in a non intrusive way we use handbook techniques involving enrichment functions introduced through the partition of unity method pum then the mesh and operators used to calculate the reference problem can be reused such a procedure also enables one to address error estimation on pointwise quantities of interest although this implies dealing with infinite energy green functions

reconstructing displacements from the solution to the periodic lippmann schwinger equation discretized on a uniform grid uniform grid solvers of the periodic lippmann schwinger equation have been introduced by moulinec and suquet for the numerical homogenization of heterogeneous materials based on the fast fourier transform these methods use the strain as main unknown and usually do not produce displacement fields while this is generally not perceived as a restriction for homogenization purposes some tasks might require kinematically admissible displacement fields in this paper we show how the numerical solution to the periodic lippmann schwinger equation can be post processed to reconstruct a displacement field our procedure is general it applies to any variant of the moulinec suquet solver the reconstruction is formulated as an auxiliary elastic equilibrium problem of a homogeneous material which is solved with displacement based finite elements taking advantage of the periodicity the uniformity of the grid and the homogeneity of the material the resulting linear system is formulated and solved efficiently in fourier space the cost of our procedure is lower than that of one iteration of the lippmann schwinger solver an application of this post processing procedure is proposed in which the reconstructed displacement field is used to compute a rigorous upper bound on the effective shear modulus of some model microstructure this is the pre peer reviewed version of the following article reconstructing displacements from the solution to the periodic lippmann schwinger equation discretized on a uniform grid which has been published in final form at 10 1002 nme 5263 this article may be used for non commercial purposes in accordance with wiley terms and conditions for self archiving sections 1 introduction and 5 numerical results have been significantly reworked in the published final version of this article the remainder of this article including sections 3 and 4 where the method itself is presented is essentially unchanged

a strict error bound with separated contributions of the discretization and of the iterative solver in non overlapping domain decomposition methods this paper deals with the estimation of the distance between the solution of a static linear mechanic problem and its approximation by the finite element method solved with a non overlapping domain decomposition method feti or bdd we propose a new strict upper bound of the error which separates the contribution of the iterative solver and the contribution of the discretization numerical assessments show that the bound is sharp and enables us to define an objective stopping criterion for the iterative solver

fast estimation of discretization error for fe problems solved by domain decomposition this paper presents a strategy for a posteriori error estimation for substructured problems solved by non overlapping domain decomposition methods we focus on global estimates of the discretization error obtained through the error in constitutive relation for linear mechanical problems our method allows to compute error estimate in a fully parallel way for both primal bdd and dual feti approaches of non overlapping domain decomposition whatever the state converged or not of the associated iterative solver results obtained on an academic problem show that the strategy we propose is efficient in the sense that correct estimation is obtained with fully parallel computations they also indicate that the estimation of the discretization error reaches sufficient precision in very few iterations of the domain decomposition solver which enables to consider highly effective adaptive computational strategies

a simple error estimator and adaptive procedure for practical engineerng analysis a new error estimator is presented which is not only reasonably accurate but whose evaluation is computationally so simple that it can be readily implemented in existing finite element codes the estimator allows the global energy norm error to be well estmated and alos gives a good evaluation of local errors it can thus be combined with a full adaptive process of refinement or more simply provide guidance for mesh redesign which allows the user to obtain a desired accuracy with one or two trials when combined with an automatic mesh generator a very efficient guidance process to analysis is avaiable estimates other than the energy norm have successfully been applied giving for instance a predetermined accuracy of stresses

recovery of equilibrium on star patches using a partition of unity technique a technique for recovering equilibrated element stresses is developed for finite element models of structural mechanics problems the data for the method consist of the prescribed loading and the stress and displacement fields resulting from a conventional compatible finite element model local problems are defined for each star of elements via the introduction of fictitious body forces and strains these problems can be solved independently for equilibrium in a process that can be easily parallelized the quality of the solutions is assessed for two dimensional linear elastic problems by using them to compute bounds of the error of the finite element solutions in terms of both global and local quantities of interest copyright 2009 john wiley sons ltd

dual analysis with general boundary conditions abstract the dual analysis concept was introduced by fraeijs de veubeke 1 as a consequence of upper and lower bounds of the energy as such bounds exist only in those cases where one type of condition is homogeneous it is commonly admitted that a dual error measure does not exist with general boundary conditions this paper presents a re examination of the dual error measure by a way which avoids any use of upper and lower bounds of the energy it is found that such an error measure holds whatever the boundary conditions be furthermore it is not necessary to obtain the approximate solutions by a rayleigh ritz process so that the second analysis which seemed necessary in the original dual analysis concept may be replaced by any admissible approximation this implies the possibility of a dual error measure at a simple post processor level

confluent hypergeometric orthogonal polynomials related to the rational quantum calogero system with harmonic confinement two families type a and type b of confluent hypergeometric polynomials in several variables are studied we describe the orthogonality properties differential equations and pieri type recurrence formulas for these families in the one variable case the polynomials in question reduce to the hermite polynomials type a and the laguerre polynomials type b respectively the multivariable confluent hypergeometric families considered here may be used to diagonalize the rational quantum calogero models with harmonic confinement for the classical root systems and are closely connected to the symmetric generalized spherical harmonics investigated by dunkl

error estimate procedure in the finite element method and applications statically and kinematically admissible fields are explicitly derived from the finite element solution of the primal form of linear models the error on constitutive law for these fields yields an expression of the finite element error moreover the contribution of each element to this error allows to implement an automatic mesh refinement procedure leading to a uniform distribution of a given accuracy

on generalizations of the calogero moser sutherland quantum problem and wdvv equations it is proved that if the schrodinger equation l of calogero moser sutherland type with l a m m 1 sin2 x has a solution of the product form 0 a sin m x then the function f x a m x 2 log x 2 satisfies the generalized wdvv equations this explains the relation between these equations and the deformed cms quantum problems observed in an earlier work phys lett a 261 297 1999

on the techniques for constructing admissible stress fields in model verification performances on engineering examples robust global goal oriented error estimation is used nowadays to control the approximate finite element solutions obtained from simulation in the context of computational mechanics the construction of admissible stress fields ie stress tensors which verify the equilibrium equations is required to set up strict and guaranteed error bounds using residual based error estimators and plays an important role in the quality of the error estimates this work focuses on the different procedures used in the calculation of admissible stress fields which is a crucial and technically complicated point the three main techniques that currently exist called the element equilibration technique eet the star patch equilibration technique spet and the element equilibration star patch technique eespt are investigated and compared with respect to three different criteria namely the quality of associated error estimators computational cost and easiness of practical implementation into commercial finite element codes the numerical results which are presented focus on industrial problems they highlight the main advantages and drawbacks of the different methods and show that the behavior of the three estimators which have the same convergence rate as the exact global error is consistent two and three dimensional experiments have been carried out in order to compare the performance and the computational cost of the three different approaches the analysis of the results reveals that the spet is more accurate than eet and eespt methods but the corresponding computational cost is higher overall the numerical tests prove the interest of the hybrid method eespt and show that it is a correct compromise between quality of the error estimate practical implementation and computational cost furthermore the influence of the cost function involved in the eet and the eespt is studied in order to optimize the estimators

commuting toeplitz operators on bounded symmetric domains and multiplicity free restrictions of holomorphic discrete series abstract for any given bounded symmetric domain we prove the existence of commutative c algebras generated by toeplitz operators acting on any weighted bergman space the symbols of the toeplitz operators that generate such algebras are defined by essentially bounded functions invariant under suitable subgroups of the group of biholomorphisms of the domain these subgroups include the maximal compact groups of biholomorphisms we prove the commutativity of the toeplitz operators by considering the bergman spaces as the underlying space of the holomorphic discrete series and then applying known multiplicity free results for restrictions to certain subgroups of the holomorphic discrete series in the compact case we completely characterize the subgroups that define invariant symbols that yield commuting toeplitz operators in terms of the multiplicity free property

feti and neumann neumann iterative substructuring methods connections and new results the feti and neumann neumann families of algorithms are among the best know and most severely tested domain decomposition methods for elliptic partial differential equations they are iterative substructuring methods and have many algorithmic components in common but there are also differences the purpose of this paper is to further unify the theory for these two families of methods and to introduce a new family of feti algorithms bounds on the rate of convergence which are uniform with respect to the coefficients of a family of elliptic problems with heterogeneous coefficients are established for these new algorithms the theory for a variant of the neumann neumann algorithm is also redeveloped stressing similarities to that for the feti methods

a posteriori error estimator and error control for contact problems in this paper we consider two error estimators for one body contact problems the first error estimator is defined in terms of h div conforming stress approximations and equilibrated fluxes while the second is a standard edge based residual error estimator without any modification with respect to the contact we show reliability and efficiency for both estimators more over the error is bounded by the first estimator with a constant one plus a higher order data oscillation term plus a term arising from the contact that is shown numerically to be of higher order the second estimator is used in a control based afem refinement strategy and the decay of the error in the energy is shown several numerical tests demonstrate the performance of both estimators

laguerre functions on symmetric cones and recursion relations in the real case in this article we derive differential recursion relations for the laguerre functions on the cone of positive definite real matrices the highest weight representations of the group sp n r play a fundamental role each such representation acts on a hilbert space of holomorphic functions on the tube domain isym n r we then use the laplace transform to carry the lie algebra action over to l2 d v the differential recursion relations result by restricting to a distinguished three dimensional subalgebra which is isomorphic to s 2 r

a new non intrusive technique for the construction of admissible stress fields in model verification in this paper we investigate a new procedure for constructing admissible stress tensors that are needed in some methods for robust global goal oriented error estimation this procedure is based on properties of the approximate finite element solution which are applied through prolongation conditions it involves the calculation of equilibrated tractions along element boundaries leading to the determination of admissible stress tensors at the element level the main idea of the proposed approach is to use the partition of unity method for the calculation of the equilibrated tractions thus defining local problems on patches of elements which can be solved in an automatic and non intrusive manner therefore this hybrid procedure leads to reasonable computational costs and can be easily implemented into existing finite element codes two dimensional experiments illustrate the capabilities of the method as compared to alternative approaches

new advances on a posteriori error on constitutive relation in f e analysis this paper deals with error estimators based on residuals on the constitutive relation which have been developed for the past 20 years at cachan especially in the case of elasticity these error estimators can become poor in situations where the material and the mesh are strongly anisotropic the crucial point herein is the construction of equilibrated stress fields from the computed finite element solution therefore in this paper the approach and in particular this last point are re examined several important modifications are introduced in the concepts and basic techniques hence a new generation of error estimators which seem to be extremely robust upon initial applications has been generated

the calogero sutherland model and generalized classical polynomials multivariable generalizations of the classical hermite laguerre and jacobi polynomials occur as the polynomial part of the eigenfunctions of certain schrodinger operators for calogero sutherland type quantum systems for the generalized hermite and laguerre polynomials the multidimensional analogues of many classical results regarding generating functions differentiation and integration formulas recurrence relations and summation theorems are obtained we use this and related theory to evaluate the global limit of the ground state density obtaining in the hermite case the wigner semi circle law and to give an explicit solution for an initial value problem in the hermite and laguerre case

strict bounding of quantities of interest in computations based on domain decomposition abstract this paper deals with bounding the error on the estimation of quantities of interest obtained by finite element and domain decomposition methods the proposed bounds are written in order to separate the two errors involved in the resolution of reference and adjoint problems on the one hand the discretization error due to the finite element method and on the other hand the algebraic error due to the use of the iterative solver beside practical considerations on the parallel computation of the bounds it is shown that the interface conformity can be slightly relaxed so that local enrichment or refinement are possible in the subdomains bearing singularities or quantities of interest which simplifies the improvement of the estimation academic assessments are given on 2d static linear mechanic problems

a simple and efficient extension of a class of substructure based preconditioners to heterogeneous structural mechanics problems several domain decomposition methods with lagrange multipliers have been recently designed for solving iteratively large scale systems of finite element equations while these methods differ typically by implementational details they share in most cases the same substructure based preconditioners that were originally developed for the feti method the success of these preconditioners is due to the fact that for homogeneous structural mechanics problems they ensure a computational performance that scales with the problem size in this paper we address the suboptimal behaviour of these preconditioners in the presence of material and or discretization heterogeneities we propose a simple and virtually no cost extension of these preconditioners that exhibits scalability even for highly heterogeneous systems of equations we consider several intricate structural analysis problems and demonstrate numerically the optimal performance delivered by the new preconditioners for problems with discontinuities copyright 1999 john wiley sons ltd

laplace and segal bargmann transforms on hermitian symmetric spaces and orthogonal polynomials let d g k be a complex bounded symmetric domain of tube type in a complex jordan algebra v and let dr j d d be its real form in a formally real euclidean jordan algebra j v dr h l is a bounded realization of the symmetric cone in j we consider representations of h that are gotten by the generalized segal bargmann transform from a unitary g space of holomorphic functions on d to an l2 space on dr we prove that in the unbounded realization the inverse of the unitary part of the restriction map is actually the laplace transform we find the extension to d of the spherical functions on dr and find their expansion in terms of the l spherical polynomials on d which are jack symmetric polynomials we prove that the coefficients are orthogonal polynomials in an l2 space the measure being the harish chandra plancherel measure multiplied by the symbol of the berezin transform we prove the difference equation and recurrence relation for those polynomials by considering the action of the lie algebra and the cayley transform on the polynomials on d finally we use the laplace transform to study generalized laguerre functions on symmetric cones

adaptive hpq finite element methods for the analysis of 3d based models of complex structures part 2 a posteriori error estimation abstract this is the second paper out of a series of papers devoted to model and hpq adaptive finite element methods assigned for the modeling and analysis of elastic structures of complex mechanical description in our previous publication we investigated the issue of hierarchical models and approximations of such structures we applied 3d or 3d based mechanical models hierarchical modeling and hierarchical approximations within the proposed finite element formulation furthermore we assumed that the mechanical model and discretization parameters such as the size h of the element and the longitudinal and transverse approximation orders p and q could vary locally i e they could be different in each finite element the a posteriori error estimation discussed in the present paper is based on the generalization of the residual equilibration method on the models with internal constraints the generalized method is applied to the assessment of the total and approximation errors while the modeling error is calculated as the difference between the former two errors the corresponding error controlled adaptive procedures are based on a three step strategy with possible iterations of h and p steps

multidimensional baker akhiezer functions and huygens principle a notion of the rational baker akhiezer ba function related to a configuration of hyperplanes in c n is introduced it is proved that the ba function exists only for very special configurations locus configurations which satisfy a certain overdetermined algebraic system the ba functions satisfy some algebraically integrable schrodinger equations so any locus configuration determines such an equation some results towards the classification of all locus configurations are presented this theory is applied to the famous hadamard problem of description of all hyperbolic equations satisfying huygens principle we show that in a certain class all such equations are related to locus configurations and the corresponding fundamental solutions can be constructed explicitly from the ba functions

validation of a posteriori error estimators by numerical approach abstract a numerical methodology which determines the quality or robustness of a posteriori error estimators is described the methodology accounts precisely for the factors which affect the quality of error estimators for finite element solutions of linear elliptic problems namely the local geometry of the grid and the structure of the solution the methodology can be employed to check the robustness of any estimator for the complex grids which are used in engineering computations

a posteriori error estimation and adaptivity for linear elasticity using the reciprocal theorem the reciprocal theorem of betti and rayleigh or in other notions duality arguments are used to derive error estimators for the finite element approximation of various quantities including local variables like single displacements and stresses the proposed error estimator is evaluated solving the set of equations for an additional right hand side simply applying the energy norm error estimators two times furthermore a general h adaptive algorithm is introduced which allows us to optimize meshes with respect to different user specified variables the efficiency of the current approach is demonstrated for plate and shell examples

generalized hermite polynomials and the heat equation for dunkl operators based on the theory of dunkl operators this paper presents a general concept of multivariable hermite polynomials and hermite functions which are associated with finite reflection groups on n the definition and properties of these generalized hermite systems extend naturally those of their classical counterparts partial derivatives and the usual exponential kernel are here replaced by dunkl operators and the generalized exponential kernel k of the dunkl transform in the case of the symmetric group s n our setting includes the polynomial eigenfunctions of certain calogero sutherland type operators the second part of this paper is devoted to the heat equation associated with dunkl s laplacian as in the classical case the corresponding cauchy problem is governed by a positive one parameter semigroup this is assured by a maximum principle for the generalized laplacian the explicit solution to the cauchy problem involves again the kernel k which is on the way proven to be nonnegative for real arguments

subdomain based flux free a posteriori error estimators a new residual type flux free error estimator is presented it estimates upper and lower bounds of the error in energy norm the proposed approach precludes the main drawbacks of standard residual type estimators circumvents the need of flux equilibration and results in a simple implementation that uses standard resources available in finite element codes this is specially interesting for 3d applications where the implementation of this technique is as simple as in 2d recall that on the contrary the complexity of the flux equilibration techniques increases drastically in the 3d case the bounds for the energy norm of the error are used to produce upper and lower bounds of linear functional outputs representing quantities of engineering interest the presented estimators demonstrate their efficiency in numerical tests producing sharp estimates both for the energy and the quantities of interest

a posteriori error estimation for elasto plastic problems based on duality theory abstract in this paper we introduce a new approach to a posteriori error estimation for elasto plastic problems based on the duality theory of the calculus of variations we show that in spite of the prevailing view duality methods provide a viable way for obtaining computable a posteriori error estimates for nonlinear boundary value problems without directly solving the dual problem rigorous mathematical analysis leads to what we call duality error estimators consisting of two parts the error in the constitutive law and the error in the equilibrium equations this representation is both physically meaningful and computationally important the duality error estimators hold for any conforming approximation of the exact solution regardless of whether or not they satisfy the galerkin orthogonality condition in particular they encompass the familiar smoothening or gradient averaging techniques commonly used in practice we prove that the duality error estimators are equivalent to the error when the approximate solution is the exact solution of the discretised problem moreover in the case of linear elasticity the known residual type error estimators can be obtained from the duality error estimators numerical results for a model elasto plastic problem show the accuracy of the duality error estimators

a constitutive relation error estimator based on traction free recovery of the equilibrated stress a new methodology for recovering equilibrated stress fields is presented which is based on traction free subdomains computations it allows a rather simple implementation in a standard finite element code compared with the standard technique for recovering equilibrated tractions these equilibrated stresses are used to compute a constitutive relation error estimator for a finite element model in 2d linear elasticity a lower bound and an upper bound for the discretization error are derived from the error in the constitutive relation these bounds in the discretization error are used to build lower and upper bounds for local quantities of interest copyright 2008 john wiley sons ltd

fock model and segal bargmann transform for minimal representations of hermitian lie groups abstract for any hermitian lie group g of tube type we construct a fock model of its minimal representation the fock space is defined on the minimal nilpotent k c orbit x in p c and the l 2 inner product involves a k bessel function as density here k g is a maximal compact subgroup and g c k c p c is a complexified cartan decomposition in this realization the space of k finite vectors consists of holomorphic polynomials on x the reproducing kernel of the fock space is calculated explicitly in terms of an i bessel function we further find an explicit formula of a generalized segal bargmann transform which intertwines the schrodinger and fock model its kernel involves the same i bessel function using the segal bargmann transform we also determine the integral kernel of the unitary inversion operator in the schrodinger model which is given by a j bessel function

asymptotic exactness of an a posteriori error estimator based on the equilibrated residual method in this paper we analyze an a posteriori error estimator based on the equilibrated residual method we prove that this estimator is asymptotically exact in the energy norm for regular solutions and o h 1 alpha alpha 0 meshes numerical examples are included to illustrate the theoretical results

study of the strong prolongation equation for the construction of statically admissible stress fields implementation and optimization this paper focuses on the construction of statically admissible stress fields sa fields for a posteriori error estimation in the context of verification the recovery of such fields enables to provide strict upper bounds of the energy norm of the discretization error between the known finite element solution and the unavailable exact solution the reconstruction is a difficult and decisive step insofar as the effectiveness of the estimator strongly depends on the quality of the sa fields this paper examines the strong prolongation hypothesis which is the starting point of the element equilibration technique eet we manage to characterize the full space of sa fields satisfying the prolongation equation so that optimizing inside this space is possible the computation exploits topological properties of the mesh so that implementation is easy and costs remain controlled in this paper we describe the new technique in details and compare it to the classical eet and to the flux free technique for different 2d mechanical problems the method is explained on first degree triangular elements but we show how extensions to different elements and to 3d are straightforward

the holomorphic discrete series for affine symmetric spaces i abstract let x g h be an affine symmetric space we study part of the discrete spectrum of l2 x for x of hermitian type a notion we define in analogy with the group case in particular we find intertwining operators from the scalar holomorphic discrete series of g which is automatically of hermitian type into l2 x the multiplicity of this series is then shown to be one by a uniqueness result for the intertwining operators finally we investigate the complexification x c of x and show that the discrete series in question admits holomorphic continuation into a certain domain in x c