a family of lower and higher order transversal linearization techniques in non linear stochastic engineering dynamics sample pathwise numerical integration of noise driven engineering dynamical systems cannot generally be performed beyond a limited level of accuracy especially when the noise processes are modelled using filtered white noises recently a locally transversal linearization ltl strategy has been proposed by the author proc roy soc london a 2001 457 539 566 for direct integration of deterministic and stochastic non linear dynamical systems the present effort is focussed on a host of extensions along with detailed theoretical error analyses of the linearization approach especially as applied to problems in non linear stochastic engineering dynamics thus to begin with estimates of local and global error orders in the basic ltl scheme are obtained separately for the displacement and velocity vectors when the system is driven either by a set of additive noises or by an arbitrary combination of independently evolving additive and multiplicative noises following this a new family of higher order ltl schemes is proposed in order to improve upon the basic ltl method and the associated error orders are established a stepwise implementation of the lower and higher order versions of the ltl method along with certain computational aspects is also outlined the proposed schemes are numerically illustrated to a limited extent for a single degree of freedom sdof and a two degree of freedom tdof non linear engineering systems under additive and or multiplicative white noise excitations

parallel multilevel solution of nonlinear shell structures the analysis of large scale nonlinear shell problems asks for parallel simulation approaches one crucial part of effi cient and well scalable parallel fe simulations is the solver for the system of equations due to the inherent suitability for parallelization one is verymuch directed towards preconditioned iterative solvers however thin walled structures discretized byfinite elements lead to ill conditioned system matrices and therefore performance of iterative solvers is generallypoor this situation further deteriorates when the thickness change of the shell is taken into account a preconditioner for this challenging class of problems is presented combining two approaches in a parallel framework the first approach is a mechanicallymotivated improvement called scaled director conditioning sdc and is able to remove the extra ill conditioning that appears with three dimensional shell formulations as compared to formulations that neglect thickness change of the shell it is introduced at the element level and harmonizes well with the second approach utilizing a multilevel algorithm here a hierarchyof coarse grids is generated in a semi algebraic sense using an aggregation concept therebythe complicated and expensive explicit generation of course triangulations can be avoided the formulation of this combined preconditioning approach is given and the effects on the performance of iterative solvers is demonstrated via numerical examples

a parallel element by element solution scheme a parallel element by element scheme is developed for finite element solution of elliptic boundary value problems it is shown that for a broad class of computational grids the solution algorithm is totally parallelizable moreover the conversion of an existing serial ebe code to a parallel code is seen to be quite simple the method is implemented on the alliant fx 8 and sequent balance parallel computers and speedup performance studies are conducted for a representative elliptic pde in two dimensions the present procedure can be applied quite generally to other finite element applications and the associated programs can be modified in a straightforward way to implement the method

multigrid methods to accelerate convergence of element by element solution algorithms for viscous incompressible flows abstract the use of iterative solvers for large systems of equations results in a slow convergence rate after the small wave length error components are resolved for a fixed convergence tolerance limit the error resolution capability of an iterative solver is a function of the mesh density two iterative solvers gmres and orthomin which utilize the element by element ebe data structure of the finite element mesh are studied to demonstrate this behavior a significant improvement in the accuracy of the solution and the rate of convergence is achieved for these iterative solvers by using a successive mesh refinement scheme like in a multigrid method this approach is found to better resolve both the large and the small scale flow phenomenon for a fine mesh while satisfying the convergence criterion in a fraction of the cpu time required by the standard iterative methods an iterative penalty finite element model is used to solve the governing equations for laminar incompressible isothermal fluid flows the solution accuracy and cpu time savings are demonstrated for two sample problems

on level set regularization for highly ill posed distributed parameter estimation problems the recovery of a distributed parameter function with discontinuities from inverse problems with elliptic forward pdes is fraught with theoretical and practical difficulties better results are obtained for problems where the solution may take on at each point only one of two values thus yielding a shape recovery problem this article considers level set regularization for such problems however rather than explicitly integrating a time embedded pde to steady state which typically requires thousands of iterations methods based on gauss newton are applied more directly one of these can be viewed as damped gauss newton utilized to approximate the steady state equations which in turn are viewed as the necessary conditions of a tikhonov type regularization with a sharpening sub step at each iteration in practice this method is eclipsed however by a special finite time or levenberg marquardt type method which we call dynamic regularization applied to the output least squares formulation our stopping criterion for the iteration does not involve knowledge of the true solution the regularization functional is applied to the smooth level set function rather than to the discontinuous function to be recovered and the second focus of this article is on selecting this functional typical choices may lead to flat level sets that in turn cause ill conditioning we propose a new quartic non local regularization term that penalizes flatness and produces a smooth level set evolution and compare its performance to more usual choices two numerical test cases are considered a potential problem and the classical eit dc resistivity problem

on effective methods for implicit piecewise smooth surface recovery this paper considers the problem of reconstructing a piecewise smooth model function from given measured data the data are compared to a field which is given as a possibly nonlinear function of the model a regularization functional is added which incorporates the a priori knowledge that the model function is piecewise smooth and may contain jump discontinuities regularization operators related to total variation tv are therefore employed two popular methods are modified tv and huber s function both contain a parameter which must be selected the huber variant provides a more natural approach for selecting its parameter and we use this to propose a scheme for both methods our selected parameter depends both on the resolution and on the model average roughness thus it is determined adaptively its variation from one iteration to the next yields additional information about the progress of the regularization process the modified tv operator has a smoother generating function nonetheless we obtain a huber variant with comparable and occasionally better performance for large problems e g high resolution the resulting reconstruction algorithms can be tediously slow we propose two mechanisms to improve efficiency the first is a multilevel continuation approach aimed mainly at obtaining a cheap yet good estimate for the regularization parameter and the solution the second is a special multigrid preconditioner for the conjugate gradient algorithm used to solve the linearized systems encountered in the procedures for recovering the model function

a new numeric analytical principle for nonlinear deterministic and stochastic dynamical systems a new implicit local linearization method termed as the locally transversal linearization ltl is developed in the present paper for a numeric analytical integration of nonlinear dynamical systems under deterministic and or stochastic excitations the ltl procedure is developed in such a way that at a chosen time instant the ltl solution manifold transversally intersects the nonlinear solution manifold at that particular point or cross section in the state space where the solution vector needs to be obtained in general construction of the ltl equation is non unique and thus it is generally needed to substitute the conditionally linear ltl based solution into the given nonlinear ordinary differential equation ode at a specified time instant to ensure a transversal intersection in the present study however it is demonstrated that a transversal intersection at a given time instant may as well be ensured by just choosing a few specific forms of the ltl equation thereby eliminating the need for substitution this new variant of ltl is particularly suitable for discretization of stochastic differential equations sdes in that one simultaneously avoids dealing with formal derivatives of wiener processes while satisfying the nonlinear sde at discrete time points the stochastic ltl procedure is adaptable for obtaining strong pathwise solutions of a general nonlinear dynamical system with continuous but not necessarily differentiable vector fields under additive and or multiplicative excitations a specific advantage of the ltl method is that for a class of response regime herein referred to as the phase independent regime it can obtain an accurate description of response irrespective of the choice of the time step and without a propagation of local errors presently the method has been numerically illustrated for strong solutions of the hardening duffing oscillator under deterministic sinusoidal or additive stochastic white noise excitations or their combination limited numerical results on periodic solutions chaos with or without noise and stochastic resonance are included in this study the results presented are indicative of the sample path accuracy consistency stochastic numerical stability and a partial insensitivity to time step sizes of the proposed method

numerical errors and uncertainties in finite element modeling of trabecular bone abstract although micromechanical finite element models are being increasingly used to help interpret the results of bio mechanical tests there has not yet been a systematic study of the numerical errors and uncertainties that occur with these methods in this work finite element models of human l1 vertebra have been used to analyze the sensitivity of the calculated elastic moduli to resolution boundary conditions and variations in the poisson s ratio of the tissue material our results indicate that discretization of the bone architecture inherent in the tomography process leads to an underestimate in the calculated elastic moduli of about 20 at 20 m resolution these errors vary roughly linearly with the size of the image voxels however it turns out that there is a cancellation of errors between the softening introduced by the discretization of the bone architecture and the excess bending resistance of eight node hexahedral finite elements our empirical finding is that eight node cubic elements of the same size as the image voxels lead to the most accurate calculation for a given number of elements with errors of less than 5 at 20 m resolution comparisons with mechanical testing are also hindered by uncertainties in the grip conditions our results show that these uncertainties are of comparable magnitude to the systematic differences in mechanical testing methods both discretization errors and uncertainties in grip conditions have a smaller effect on relative moduli used when comparing between different specimens or different load directions than on an absolute modulus the effects of variations in the poisson s ratio of the bone tissue were found to be negligible

solution algorithms for nonlinear transient heat conduction analysis employing element by element iterative strategies abstract despite continuing advancements in computer technology there are many problems of engineering interest that exceed the combined capabilities of today s numerical algorithms and computational hardware the resources required by traditional finite element algorithms tend to grow geometrically as the problem size is increased thus for the forseeable future there will be problems of interest which cannot be adequately modeled using currently available algorithms for this reason we have undertaken the development of algorithms whose resource needs grow only linearly with problem size in addition these new algorithms will fully exploit the parallel processing capability available in the new generation of multi processor computers the approach taken in the element by element solution procedures is to approximate the global implicit operator by a product of lower order operators this type of product approximation originated with adi techniques and was further refined into the method of fraction steps the current effort involves the use of a more natural operator split for finite element analysis based on element operators this choice of operator splitting based on element operators has several advantages first it fits easily within the architecture of current finite element programs second it allows the development of parallel algorithms finally the computational expense varies only linearly with the number of elements the particular problems considered arise from nonlinear transient heat conduction the nonlinearity enters through both material temperature dependence and radiation boundary conditions the latter condition typically introduces a stiff component in the resultant matrix odes which precludes effective use of explicit solution techniques on the other hand typical implicit techniques involving direct equation solving can be prohibitively expensive instead the matrix equations are solved by combining a modified newton raphson iteration scheme for the nonlinear algebraic problem with an element by element preconditioned conjugate gradient procedure for the linear problems an adaptive intercommunicative strategy is developed for setting termination criteria for the nonlinear and linear equation solving algorithms errors and computational efficiency in the transient solution are controlled by an automatic time step selection strategy the resultant procedure has proven to be both accurate and reliable in the solution of medium size test problems

imf an incomplete multifrontal lu factorization for element structured sparse linear systems we propose an incomplete multifrontal lu factorization imf preconditioner that extends supernodal multifrontal methods to incomplete factorizations it can be used as a preconditioner in a krylov subspace method to solve large scale sparse linear systems with an element structure e g those arising from a finite element discretization of a partial differential equation the fact that the element matrices are dense is exploited to increase the computational performance and the robustness of the factorization through efficient partial pivoting imf is compared with the multilevel arms2 the level of fill in ilu and the threshold based ilutp preconditioners our experiments indicate that imf is competitive with arms2 on saddle point problems arising in the solution of the steady state navier stokes equation experiments with element structured matrices arising from structural engineering applications found in the university of florida sparse matrix collection illustrate the robustness of imf final

natural finite element techniques for viscous fluid motion abstract the paper surveys recent work on fluid dynamics performed at the isd university of stuttgart it is in particular directed to a natural description of the flow phenomena and includes also a consideration of thermally coupled problems the derivation of the relevant finite element equations when referred to natural quantities is outlined and examples of application are given also presented is a discussion on the associated modern developments in numerical solutions techniques

a monolithic approach for interaction of incompressible viscous fluid and an elastic body based on fluid pressure poisson equation this paper describes a new monolithic approach based on the fluid pressure poisson equation ppe to solve an interaction problem of incompressible viscous fluid and an elastic body the ppe is derived so as to be consistent with the coupled equation system for the fluid structure interaction fsi based on this approach we develop two kinds of efficient monolithic methods in both methods the fluid pressure is derived implicitly so as to satisfy the incompressibility constraint and all other unknown variables are derived fully explicitly or partially explicitly the coefficient matrix of the ppe for the fsi becomes symmetric and positive definite and its condition is insensitive to inhomogeneity of material properties the arbitrary lagrangian eulerian ale method is employed for the fluid part in order to take into account the deformable fluid structure interface to demonstrate fundamental performances of the proposed approach the developed two monolithic methods are applied to evaluate the added mass and the added damping of a circular cylinder as well as to simulate the vibration of a rectangular cylinder induced by vortex shedding copyright 2005 john wiley sons ltd

parallel preconditioning based on h hierarchical finite elements with application to acoustics abstract in this paper we consider the hierarchical basis preconditioning approach which is closely related to the h version of the hierarchical finite element method in general finite element formulations that employ hierarchical shape functions yield better conditioned matrix problems than those based on the lagrange nodal basis these matrix problems are also better suited to a faster rate of convergence with krylov subspace iterative methods we consider a purely algebraic approach to describe projections between the nodal and the h hierarchical bases functions which are then used to construct the preconditioning operator implementation details of the preconditioner are provided for solving finite element problems on unstructured grids we employ the preconditioning approach in the iterative solution of linear systems that arise from finite element discretization of the exterior helmholtz problem numerical results are presented to examine convergence rates for practical discretizations in acoustics and to illustrate the computational performance of the preconditioning algorithm on serial and data parallel computers

element based preconditioners for elasto plastic problems in geotechnical engineering iterative solvers are widely regarded as the most efficient way to solve the very large linear systems arising from finite element models their memory requirements are small compared to those for direct solvers consequently there is a major interest in iterative methods and particularly the preconditioning necessary to achieve rapid convergence in this paper we present new element based preconditioners specifically designed for linear elasticity and elasto plastic problems the study presented here is restricted to simple associated plasticity but should find wide application in other plasticity models used in geotechnics

spectral problems for the weyl ordered form of operators 1pnqn in this paper we consider quantization of powers of the ratio between the hamiltonian coordinates for position and momentum in one dimensional systems the domain of the operators consists of square integrable functions over a finite real interval to ensure boundedness and self adjointness the spectral problems for the operators that result from using weyl ordering are discussed by introducing fredholm integral operator forms in position representation and the symmetry of the actions of the parity and time reversal operators on the kernels is discussed finally the general structures and properties of the eigenfunctions and eigenvalues are also derived and analyzed

higher order weak linearizations of stochastically driven nonlinear oscillators we present derivative free weak and strong solutions of stochastically driven nonlinear oscillators of engineering interest using higher order forms of the locally transversal linearization ltl method unlike strong solutions weak stochastic solutions attempt to predict only mathematical expectations of functions of the true solution and are obtainable with much less computational effort the linearized equations corresponding to the higher order implicit ltl schemes are arrived at using backward euler maruyama and newmark expansions in order to conditionally replace nonlinear drift and multiplicative diffusion vector fields we also briefly describe alterations through which explicit forms of such higher order linearizations are obtained in the weak forms the gaussian stochastic integrals appearing in the linearized solutions are replaced by random variables with simpler and discrete probability distributions the resulting local approximations to the true solution are of significantly higher formal order of accuracy as reflected through local error estimates numerical illustrations are presently provided for the duffing and van der pol oscillators driven by additive and multiplicative noises which are indicative of the numerical accuracy computational speed and algorithmic simplicity

a pseudo dynamical systems approach to a class of inverse problems in engineering a pseudo dynamical approach for a class of inverse problems involving static measurements is proposed and explored following linearization of the minimizing functional associated with the underlying optimization problem the new strategy results in a system of linearized ordinary differential equations odes whose steady state solutions yield the desired reconstruction we consider some explicit and implicit schemes for integrating the odes and thus establish a deterministic reconstruction strategy without an explicit use of regularization a stochastic reconstruction strategy is then developed making use of an ensemble kalman filter wherein these odes serve as the measurement model finally we assess the numerical efficacy of the developed tools against a few linear and nonlinear inverse problems of engineering interest

a sequential importance sampling filter with a new proposal distribution for state and parameter estimation of nonlinear dynamical systems the problem of estimating parameters of nonlinear dynamical systems based on incomplete noisy measurements is considered within the framework of bayesian filtering using monte carlo simulations the measurement noise and unmodelled dynamics are represented through additive and or multiplicative gaussian white noise processes truncated ito taylor expansions are used to discretize these equations leading to discrete maps containing a set of multiple stochastic integrals these integrals in general constitute a set of non gaussian random variables the system parameters to be determined are declared as additional state variables the parameter identification problem is solved through a new sequential importance sampling filter this involves ito taylor expansions of nonlinear terms in the measurement equation and the development of an ideal proposal density function while accounting for the non gaussian terms appearing in the governing equations numerical illustrations on parameter identification of a few nonlinear oscillators and a geometrically nonlinear euler bernoulli beam reveal a remarkably improved performance of the proposed methods over one of the best known algorithms i e the unscented particle filter

parallel transient algorithm with multistep substructure computation the computation is parallelized on the basis of a division of the structure into substructures with each processor computing the response of a substructure independently independently computed substructure responses are reconciled directly reconciliation of substructure responses can be postponed until after the responses have been computed independently for multiple time steps

new computational approaches for wrinkled and slack membranes the static response of thin wrinkled membranes is studied using both a tension field approximation based on plane stress conditions and a 3d nonlinear elasticity formulation discretized through 8 noded cosserat point elements while the tension field approach only obtains the wrinkled slack regions and at best a measure of the extent of wrinkliness the 3d elasticity solution provides in principle the deformed shape of a wrinkled slack membrane however since membranes barely resist compression the discretized and linearized system equations via both the approaches are ill conditioned and solutions could thus be sensitive to discretizations errors as well as other sources of noises imperfections we propose a regularized pseudo dynamical recursion scheme that provides a sequence of updates which are almost insensitive to the regularizing term as well as the time step size used for integrating the pseudo dynamical form this is borne out through several numerical examples wherein the relative performance of the proposed recursion scheme vis a vis a regularized newton strategy is compared the pseudo time marching strategy when implemented using 3d cosserat point elements also provides a computationally cheaper numerically accurate and simpler alternative to that using geometrically exact shell theories for computing large deformations of membranes in the presence of wrinkles

parallel frictional contact algorithms and industrial applications in this paper various parallel strategies to solve frictional contact problems are introduced in the frame of hybrid formulations the discussion is focussed on element by element factorizations and domain decomposition methods two industrial applications are presented

unconditionally stable element by element algorithms for dynamic problems a collection of results is presented regarding the consistency stability and accuracy of operator split methods and product formula algorithms for general nonlinear equations of evolution these results are then applied to the structural dynamics problem the basic idea is to exploit an element by element additive decomposition of a particular form of the discrete dynamic equations resulting from a finite element discretization it is shown that such a particular form of the discrete dynamic equations is obtained when velocity and stress are taken as unknowns by applying the general product formula technique to the element by element decomposition unconditionally stable algorithms are obtained that involve only element coefficient matrices the storage requirements and operation counts are comparable to those of explicit methods the method places no restriction on the topology of the finite element mesh

parallel finite element simulations of incompressible viscous fluid flow by domain decomposition with lagrange multipliers a parallel approach to solve three dimensional viscous incompressible fluid flow problems using discontinuous pressure finite elements and a lagrange multiplier technique is presented the strategy is based on non overlapping domain decomposition methods and lagrange multipliers are used to enforce continuity at the boundaries between subdomains the novelty of the work is the coupled approach for solving the velocity pressure lagrange multiplier algebraic system of the discrete navier stokes equations by a distributed memory parallel ilu 0 preconditioned krylov method a penalty function on the interface constraints equations is introduced to avoid the failure of the ilu factorization algorithm to ensure portability of the code a message based memory distributed model with mpi is employed the method has been tested over different benchmark cases such as the lid driven cavity and pipe flow with unstructured tetrahedral grids it is found that the partition algorithm and the order of the physical variables are central to parallelization performance a speed up in the range of 5 13 is obtained with 16 processors finally the algorithm is tested over an industrial case using up to 128 processors in considering the literature the obtained speed ups on distributed and shared memory computers are found very competitive

a study of the efficiency of iterative methods for linear problems in structural mechanics the efficiency of iterative methods in linear structural mechanics is studied the efficiency concerns the calculation time the numerical accuracy and the core storage needed we state that iterative methods are effective in connection with hierarchical improvement of a primary approximation three iterative methods are studied the conjugate gradient method preconditioned by a modified incomplete factorization matrix the same method preconditioned by a matrix obtained from natural factors on elemental level and a jacobi integration preconditioned by viscous relaxation split in an element by element way we make comparisons with direct methods gaussian elimination and factorization by use of natural factors

structural optimization based on preconditioned conjugate gradient analysis methods an efficient method for structural optimization is presented instead of classical direct decomposition methods preconditioned conjugate gradient pcg methods in conjunction with two proposed starting vector generation schemes are used to solve the systems of linear equations associated with the finite element analysis and behaviour sensitivity analysis problems these inherently iterative analysis procedures are then used to carry out the analyses needed at the beginning of each stage in an approximation concepts approach to structural optimization this technique has been implemented in a research program and used to solve a collection of minimum weight truss sizing design problems subject to static deflection and stress constraints the effectiveness of the pcg methods of analysis in structural optimization is demonstrated comparison among different preconditioners is made the effect of the proposed starting vector generation schemes is shown the comparative merits of analytical sensitivity analysis and finite difference sensitivity analysis when using pcg methods of analysis are assessed the parallel computation potential of pcg methods is discussed because of the iterative nature of pcg analysis methods and the prospects they offer for parallel computation it is found that pcg analysis methods show promise in the context of structural optimization

an efficient diagonal preconditioner for finite element solution of biot s consolidation equations finite element simulations of very large scale soil structure interaction problems e g excavations tunnelling pile rafts etc typically involve the solution of a very large ill conditioned and indefinite biot system of equations the traditional preconditioned conjugate gradient solver coupled with the standard jacobi sj preconditioner can be very inefficient for this class of problems this paper presents a robust generalized jacobi gj preconditioner that is extremely effective for solving very large scale biot s finite element equations using the symmetric quasi minimal residual method the gj preconditioner can be formed inverted and implemented within an element by element framework as readily as the sj preconditioner it was derived as a diagonal approximation to a theoretical form which can be proven mathematically to possess an attractive eigenvalue clustering property the effectiveness of the gj preconditioner over a wide range of soil stiffness and permeability was demonstrated numerically using a simple three dimensional footing problem this paper casts a new perspective on the potentialities of the simple diagonal preconditioner which has been commonly perceived as being useful only in situations where it can serve as an approximate inverse to a diagonally dominant coefficient matrix copyright 2002 john wiley sons ltd

finite element preconditioning of g ni spectral methods several old and new finite element preconditioners for nodal based spectral discretizations of delta u f in the domain omega 1 1 d d 2 or 3 with dirichlet or neumann boundary conditions are considered and compared in terms of both condition number and computational efficiency the computational domain covers the case of classical single domain spectral approximations see c canuto et al spectral methods fundamentals in single domains springer heidelberg 2006 as well as that of more general spectral element methods in which the preconditioners are expressed in terms of local upon every element algebraic solvers the primal spectral approximation is based on the galerkin approach with numerical integration g ni at the legendre gauss lobatto lgl nodes in the domain the preconditioning matrices rely on either mathbb p 1 mathbb q 1 or mathbb q 1 ni i e with numerical integration finite elements on meshes whose vertices coincide with the lgl nodes used for the spectral approximation the analysis highlights certain preconditioners which yield the solution at an overall cost proportional to n d 1 where n denotes the polynomial degree in each direction

anisotropic linear elastic parameter estimation using error in the constitutive equation functional a modified error in the constitutive equation based approach for identification of heterogeneous and linear anisotropic elastic parameters involving static measurements is proposed and explored following an alternating minimization procedure associated with the underlying optimization problem the new strategy results in an explicit material parameter update formula for general anisotropic material this immediately allows us to derive the necessary constraints on measured data and thus restrictions on physical experimentation to achieve the desired reconstruction we consider a few common materials to derive such conditions then we exploit the invariant relationships of the anisotropic constitutive tensor to propose an identification procedure for space dependent material orientations finally we assess the numerical efficacy of the developed tools against a few parameter identification problems of engineering interest

a differential geometric approach to nonlinear filtering the projection filter this paper presents a new and systematic method of approximating exact nonlinear filters with finite dimensional filters using the differential geometric approach to statistics the projection filter is defined rigorously in the case of exponential families a convenient exponential family is proposed which allows one to simplify the projection filter equation and to define an a posteriori measure of the local error of the projection filter approximation finally simulation results are discussed for the cubic sensor problem

nineteen dubious ways to compute the exponential of a matrix twenty five years later in principle the exponential of a matrix could be computed in many ways methods involving approximation theory differential equations the matrix eigenvalues and the matrix characteristic polyn

an iterative algorithm for finite element analysis in this paper we state in a new form the algebraic problem arising from the one field displacement finite element method fem the displacement approach in this discrete form can be considered as the dual approach force or equilibrium with subsidiary constraints this approach dissociates the nonlinear operator to the linear ones and their sizes are linear functions of integration rule which is of interest in the case of reduced integration this new form of the problem leads to an inexpensive improvement of fem computations which acts at local elementary and global levels we demonstrate the numerical performances of this approach which is independent of the mesh structure using the gmres algorithm we build for nonsymmetric problems a new algorithm based upon the discretized field of strain the new algorithms proposed are more closer to the mechanical problem than the classical ones because all fields appear during the resolution process the sizes of the different operators arising in these new forms are linear functions of integration rule which is of great interest in the case of reduced integration

high performance computational kernels for selected segments of a p finite element code a high performance implementation is presented for three kernel routines commonly found in element byelement preconditioned conjugate gradient finite element codes these routines include forming the element stiffness matrices and loading vectors or in the case of a non linear problem element residual vectors and routines for applying element matrix vector products the present study considers tensor product elements of arbitrary mapping in 2 d although the generalization to triangular elements and serendipity elements is straightforward the implementation presented is most appropriate for high p type finite element methods where the element matrices are relatively large and dense this results in a set of high performance kernels for superscalar architectures which otherwise may be memory bandwidth limited performance studies are presented for a representative superscalar microprocessor the intel i860 as these types of microprocessors are at the heart of modern workstations as well as several parallel supercomputing systems this work is relevant across a variety of platforms the resulting kernels yield both high performance on a variety of sequential architectures as well as a high degree of code portability through the basic linear algebra subprograms mechanism

comparison between element edge and compressed storage schemes for iterative solutions in finite element analyses this paper is concerned with optimization techniques for the iterative solution of sparse linear systems arising from finite element discretization of partial differential equations three different data structures are used to store the coefficient matrices the usual element based data structure the compressed storage row format and the edge based approach a comparison between these storage schemes is performed quantifying for most common linear elements the number of floating points operations indirect addressing and memory requirements necessary to perform matrix vector products the overall performance of the preconditioned conjugate gradient method is measured for different situations involving 2d and 3d diffusion and elasticity problems highlighting the pros and cons of each storage scheme

iterative method for constrained and mixed approximation an inexpensive improvement of f e m performance a general iterative procedure for solving mixed lagrangian finite element equations is introduced the method allows a dramatic improvement in accuracy of simple irreducible formulations to be achieved in a few resolutions applications to incompressible flow stress analysis and metal forming problems are given the procedures can be easily implemented into standard programs

an analysis of element by element preconditioners for nonsymmetric problems abstract a group of preconditioners for systems of linear equations arising from finite element discretization which is of increasing interest is the class of element by element preconditioners these preconditioners allow the solution of a system without the need to assemble the global stiffness matrix the success of a preconditioner depends on how much it reduces the condition number of the global stiffness matrix in this paper a bound on the condition number of the preconditioned stiffness matrix is derived in terms of norms of the element stiffness matrices the element preconditioning matrices and the flexibility matrix ideas are proposed how to improve the element by element preconditioner

self regularized pseudo time marching schemes for structural system identification with static measurements we explore the application of pseudo time marching schemes involving either deterministic integration or stochastic filtering to solve the inverse problem of parameter identification of large dimensional structural systems from partial and noisy measurements of strictly static response solutions of such non linear inverse problems could provide useful local stiffness variations and do not have to confront modeling uncertainties in damping an important yet inadequately understood aspect in dynamic system identification problems the usual method of least square solution is through a regularized gauss newton method gnm whose results are known to be sensitively dependent on the regularization parameter and data noise intensity finite time recursive integration of the pseudo dynamical gnm pd gnm update equation addresses the major numerical difficulty associated with the near zero singular values of the linearized operator and gives results that are not sensitive to the time step of integration therefore we also propose a pseudo dynamic stochastic filtering approach for the same problem using a parsimonious representation of states and specifically solve the linearized filtering equations through a pseudo dynamic ensemble kalman filter pd enkf for multiple sets of measurements involving various load cases we expedite the speed of thepd enkf by proposing an inner iteration within every time step results using the pseudo dynamic strategy obtained through pd enkf and recursive integration are compared with those from the conventional gnm which prove that the pd enkf is the best performer showing little sensitivity to process noise covariance and yielding reconstructions with less artifacts even when the ensemble size is small

an element by element solution algorithm for problems of structural and solid mechanics abstract it is proposed to solve large scale finite element equation systems arising in structural and solid mechanics by way of an element by element approximate factorization technique which obviates the need for a global coefficient matrix the procedure has considerable operation count and i o advantages over direct elimination schemes and it is easily implemented numerical results demonstrate the effectiveness of the method and suggest its potential for the analysis of large scale systems

finite element methods for first order hyperbolic systems with particular emphasis on the compressible euler equations a petrov galerkin finite element formulation is presented for first order hyperbolic systems of conservation laws with particular emphasis on the compressible euler equations applications of the methodology are made to one and two dimensional steady and unsteady flows with shocks results obtained suggest the potential of the type of methods developed

integrated structural analysis and design using three dimensional finite elements a design approach that combines iterative structural analysis with a traditional iterative optimization algorithm is applied to the optimum design of the shape of a hole in a plate in tension the plate is modeled by threedimensional finite elements and an element by el ement preconditioned conjugate gradient iterative algorithm is used for solving the equations of equilibrium several parameterizations of the optimum shape are considered and it is shown that a sine series can describe the optimum shape with only three design variables whereas other series require seven variables for similar results the optimum shape compares well with an experimental optimum obtained by a j durelli an investigation is performed to determine the best way of obtaining finite difference derivatives of the stresses with respect to design variables it is shown that a method based on modifying the equations of equilibrium for the perturbed problem performs best the benefit of the integrated approach is determined by comparing convergence with different initial iterates for the displacement field it is shown that using the final iterate of the previous solution can reduce the number of analysis iterations by about 40 compared to starting with a zero initial iterate

bounds on the eigenvalue range and on the field of values of non hermitian and indefinite finite element matrices in the early seventies fried formulated bounds on the spectrum of assembled hermitian positive semi definite finite element matrices using the extreme eigenvalues of the element matrices in this paper we will generalise these results by presenting bounds on the field of values the numerical radius and on the spectrum of general possibly complex matrices for both the standard and the generalised problem the bounds are cheap to compute involving operations with element matrices only we illustrate our results with an example from acoustics involving a complex non hermitian matrix as an application we show how our estimates can be used to derive an upper bound on the number of iterations needed to achieve a given residual reduction in the gmres algorithm for solving linear systems

multiadaptive galerkin methods for odes iii a priori error estimates the multiadaptive continuous discontinuous galerkin methods mcgq and mdgq for the numerical solution of initial value problems for ordinary differential equations are based on piecewise polynomial approximation of degree q on partitions in time with time steps which may vary for different components of the computed solution in this paper we prove general order a priori error estimates for the mcgq and mdgq methods to prove the error estimates we represent the error in terms of a discrete dual solution and the residual of an interpolant of the exact solution the estimates then follow from interpolation estimates together with stability estimates for the discrete dual solution

phase space linearization for non linear oscillators deterministic and stochastic systems abstract a new and efficient semi analytical phase space linearization psl scheme for a class of non linear oscillators is developed in this paper the method is based on replacement of the non linear vector field by a set of linear ones each valid over a short segment of the evolving trajectory or over sufficiently small interval of time based on this concept a few explicit and implicit integration schemes are first proposed and applied to a class of low dimensional non linear dynamical systems to accurately determine their response trajectories this approach of local linearization is further extended to non linear oscillators excited by formal derivatives of one or a combination of gauss markov processes since the present methodology reduces the non linear operator by a set of linear operators it is also demonstrated that the principles of linear random vibration may be suitable exploited to arrive at a faster and semi analytical monte carlo scheme for computing the response statistics both in stationary and non stationary regimes limited examples are presented and compared with exact solutions whenever available to illustrate the efficiency and versatility of the proposed schemes

element by element preconditioners for large partially separable optimization problems we study the solution of large scale nonlinear optimization problems by methods which aim to exploit their inherent structure in particular we consider the property of partial separability first studied by griewank and toint nonlinear optimization 1981 pp 301 312 a typical minimization method for nonlinear optimization problems approximately solves a sequence of simplified linearized subproblems in this paper we explore how partial separability may be exploited by iterative methods for solving these subproblems we particularly address the issue of computing effective preconditioners for such iterative methods we concentrate on element by element preconditioners which reflect the structure of the problem we find that the performance of these methods can be considerably improved by amalgamating elements before applying the preconditioners we report the results of numerical experiments which demonstrate the effectiveness of this approach

a homogenization sampling procedure for calculating trabecular bone effective stiffness and tissue level stress a homogenization sampling procedure is introduced which allows computation of effective trabecular bone stiffness and individual trabecula level stress based on precise models of trabecular bone architecture three dimensional digitized images of 53 trabecular bone specimens with a resolution of 50 f per voxel were directly converted into three dimensional finite element meshes by making each voxel an 8 node isoparametric brick element owing to the large mesh of 8ooo elements an element by element pre conditioned conjugate gradient ebepcg program was written to solve the local homogenization finite element equations predicted effective stiffness measures correlated well with experimental results r2 z 0 73 the predicted effective stiffnesses tended to under estimate the experimental values average absolute errors in effective stiffness estimates ranged between 31 and 38 for the sampling procedure compared to a range 49 150 for a regression fit to volume fraction squared trabecula level stress ranged between 200 and 300 times that predicted by analyzing trabecular bone as a continuum both tensile and compressive tissue stresses were engendered by a continuum compressive stress trabecula level strain energy density sed ranged between 0 and 100 times the continuum sed value for two trabecular specimens in conclusion the homogenization sampling procedure consistently predicted the influence of trabecular bone architecture on effective stiffness it can also provide trabecular tissue stress and strain estimates for arbitrary global loading of whole bones tissue stresses and strains showed large variations compared to corresponding continuum level quantities

accuracy of a class of concurrent algorithms for transient finite element analysis the accuracy of a new class of concurrent procedures for transient finite element analysis is examined a phase error analysis is carried out which shows that wave retardation leading to unacceptable loss of accuracy may occur if a courant condition based on the dimensions of the subdomains is violated numerical tests suggest that this courant condition is conservative for typical structural applications and may lead to a marked increase in accuracy as the number of subdomains is increased theoretical speed up ratios are derived which suggest that the algorithms under consideration can be expected to exhibit a performance superior to that of globally implicit methods when implemented on parallel machines