line search acceleration of iterative methods abstract this paper describes and analyzes a simple technique that accelerates the convergence of iterative methods for solving large linear systems the proposed technique can be used with any convergent method however it is especially useful when solving unstructured systems since in this case traditional methods as sor or chebyshev semiiteration have difficulty in obtaining optimal parameters special attention is given to column relaxation and row relaxation it is demonstrated experimentally that an accelerated gauss seidel scheme runs faster than an optimally tuned sor scheme

finite element multiple mode approach to nonlinear free vibrations of shallow shells two finite element fe modal formulations for large amplitude free vibration of isotropic and arbitrary laminated composite shallow shells are presented the system equation of motion is formulated first in the physical structural node degrees of freedom dof then the system is transformed into two distinctly different sets of general duffing type modal equations based on 1 modal amplitudes of coupled linear bending and in plane modes where in plane inertia is included in the formulation and 2 modal amplitudes of linear bending modes only where the in plane inertia is neglected multiple modes and the first order transverse shear deformation are considered in the formulations a shallow shell finite element is developed as an extension from the triangular mindlin min3 plate element with the improved shear correction factor by tessler time numerical integration is employed to determine the nonlinear periodic frequency characteristics the inaccuracy in characterizing a shallow shell response with coupled linear bending and in plane modes is demonstrated and discussed by comparing with the fe solution in structural node dof study cases include isotropic and composite panels of different shallow shell geometries

on a simple triangular reissner mindlin plate element based on incompatible modes and discrete constraints in this paper the formulation of a new triangular element based on the reissner mindlin plate theory is presented the element has three nodes and three d o f per node only it is based on constant bending modes plus incompatible energy orthogonal higher order bending modes the transverse shear effects are represented using the moment equilibrium and the constitutive equations discrete collocation shear constraints are considered on each side to relate the kinematical and the independent shear strains the element has a proper rank is completely locking free passes all constant patch tests exactly the detailed numerical evaluation shows that the element called dst bk is a robust and high performance element for thick and thin plates

p version plate and curved shell element for geometrically non linear analysis this paper presents a p version geometrically non linear formulation based on the total lagrangian approach for a nine node three dimensional curved shell element the element geometry is defined by the coordinates of the nodes located on its middle surface and nodal vectors describing the bottom and top surfaces of the element the element displacement approximation can be of arbitrary and different polynomial orders in the plane of the element and in the transverse direction the element approximation functions and the corresponding nodal variables are derived from the lagrange family of interpolation functions the resulting approximation functions and the nodal variables are hierarchical and the element displacement approximation ensures c continuity the element properties are established using the principle of virtual work and the hierarchical element approximation in formulating the properties of the element complete three dimensional stresses and strains are considered hence the element is equally effective for very thin as well as extremely thick shells and plates incremental equations of equilibrium are derived and solved using the standard newton raphson method the total load is divided into increments and for each increment of load equilibrium iterations are performed until each component of the residuals is within a preset tolerance numerical examples are presented to show the accuracy efficiency and advantages of the present formulation the results obtained from the present formulation are compared with those available in the literature

an adaptive method for homogenization in orthotropic nonlinear elasticity a database methodology is developed in order to characterize the constitutive behavior of macroscopically orthotropic nonlinearly elastic composites this methodology discretizes the material test space in terms of the eigenvalues of the macroscopic strain tensor and the orientation of its eigenvectors with respect to the axes of orthotropy the macroscopic properties of the composite are extracted at points of this test space by subjecting a statistically representative sample of the composite to appropriate boundary conditions and are subsequently employed in an interpolation procedure which creates the so called material map that characterizes the macroscopic behavior the macroscopic tangent required in the finite element calculations are derived either by using the tangent induced by the map for the macroscopic stress or by explicitly computing a map for the tangent the range of deformations over which a material map is applicable to a problem is enhanced by an adaptive scheme where a multi level finite element method is employed at highly deformed regions of a finite element mesh where the map limits are exceeded

convergence studies on iterative algorithms for image reconstruction we introduce a general iterative scheme for image reconstruction based on landweber s method in our configuration a sequential block iterative seqbi version can be readily formulated from a simultaneous block iterative simbi version and vice versa this provides a mechanism to derive new algorithms from known ones it is shown that some widely used iterative algorithms such as the algebraic reconstruction technique art simultaneous art sart cimmino s and the recently designed diagonal weighting and component averaging algorithms are special examples of the general scheme we prove convergence of the general scheme under conditions more general than assumed in earlier studies for its seqbi and simbi versions in the consistent and inconsistent cases respectively our results suggest automatic relaxation strategies for the seqbi and simbi versions and characterize the dependence of the limit image on the initial guess it is found that in all cases the limit is the sum of the minimum norm solution of a weighted least squares problem and an oblique projection of the initial image onto the null space of the system matrix

on stabilized finite element methods for linear systems of convection diffusion reaction equations abstract a stabilized finite element method for solving systems of convection diffusion reaction equations is studied in this paper the method is based on the subgrid scale approach and an algebraic approximation to the subscales after presenting the formulation of the method it is analyzed how it behaves under changes of variables showing that it relies on the law of change of the matrix of stabilization parameters associated to the method an expression for this matrix is proposed for the case of general coupled systems of equations that is an extension of the expression proposed for a one dimensional 1d model problem applications of the stabilization technique to the stokes problem with convection and to the bending of reissner mindlin plates are discussed next the design of the matrix of stabilization parameters is based on the identification of the stability deficiencies of the standard galerkin method applied to these two problems

component averaged row projections a robust block parallel scheme for sparse linear systems a new method for the parallel solution of large sparse linear systems is introduced it proceeds by dividing the equations into blocks and operating in block parallel iterative mode i e all the blocks are processed in parallel and the partial results are merged to form the next iterate the new scheme performs kaczmarz row projections within the blocks and merges the results by certain component averaging operations hence it is called component averaged row projections or carp the system matrix can be general nonsymmetric and ill conditioned and the division into blocks is unrestricted for partial differential equations pdes if the blocks are domain based then only variables at the boundaries between domains are averaged thereby minimizing data transfer between processors carp is very robust its application to test cases of linear systems derived from pdes shows that it converges in difficult cases where state of the art methods fail it is also very memory efficient and exhibits an almost linear speedup ratio with efficiency greater than unity in some cases a formal proof of convergence is presented it is shown that the component averaging operations are equivalent to row projections in a certain superspace so the convergence properties of carp are identical to those of kaczmarz s algorithm in the superspace carp and its convergence proof also apply to the consistent convex feasibility problem

an efficient hybrid quadrilateral kirchhoff plate bending element this paper discusses the formulation of a hybrid stress quadrilateral kirchhoff plate bending element based on an extended complementary energy functional first proposed by tong with the inclusion of a lagrange multiplier in the functional to enforce a constraint on the assumed moment space the construction of the c1 deflection profile inside the element is no longer necessary the continuity requirement on the deflection across the element interfaces is fulfilled by interpolating the generalized nodal displacements over the element boundary in the usual way special attention is paid to the selection of assumed moment space such that the element stability convergency invariance and nodal point numbering insensitivity are secured while the implementational cost of the element is kept low quadratic serendipity interpolation of the transverse deflection is adopted to discretize the distributed transverse loading numerical examples are presented and the accuracy achieved is found to be satisfactory

convergence studies on block iterative algorithms for image reconstruction the sequential block iterative scheme based on landweber s method is a general iterative one for image reconstruction in this paper we give the finite termination convergence for this scheme which provides an approach to choose relaxation coefficients furthermore sufficient and necessary convergence conditions are also established for the sequential block iterative scheme case

a new hybrid mixed variational approach for reissner mindlin plates the misp model a valuable variational approach for plate problems based on the reissner mindlin theory is presented the new misp mixed shear projected approach is based on the hellinger reissner variational principle with a particular representation of transversal shear forces and transversal shear strains the approximations of the shear forces are derived from those of the bending moments using the corresponding equilibrium relations the shear strains are defined in terms of the edge tangential strains that are projected on the element degrees of freedom two finite elements are developed on the misp approach basis 3 node triangular element misp3 and 4 node quadrilateral element misp4 both elements can be considered as the most simple among the existent mixed elements a modified misp model with a derived 4 node element is also presented numerical experiments are presented which show that the misp elements do not exhibit shear locking and give excellent results for thick and thin plates they also pass the patch test for a general triangle and quadrilateral 1998 john wiley sons ltd

computational homogenization analysis in finite elasticity material and structural instabilities on the micro and macro scales of periodic composites and their interaction the paper investigates instability phenomena in the context of homogenization based micro to macro transitions of heterogeneous materials at finite strains this covers structural instability effects buckling and material instability effects localization which can occur on both the macro as well as the micro scale and may influence each other we develop a general framework for the theoretical and computational treatment of these instability problems for elastic composites with given periodic fine scale micro structures the key methodology is an investigation of the properties and the interaction of two coupled minimization principles which govern a micro heterogeneous material in the context of a classical homogenization procedure the principle of minimum potential energy of the macro structure and the principle of minimum average energy of the micro structure the first variational problem determines the deformation field of the homogenized continuum the latter yields the fine scale fluctuation field on a composite micro structure that is assumed to be attached to each local point of the macro continuum global stability and the existence of solutions are based on weak convexity properties of these variational functionals the convergence of non convex homogenization functionals is based on the limit of periodic heterogeneous micro structures it defines the relevant micro structure as an a priori unknown critical ensemble of periodic cells that catches a possible minimizing buckling mode we summarize these basic results and recast them in a consistent notation suitable for numerical implementation furthermore we in detail discuss the discretization of the coupled minimization problems by means of finite element methods and point out numerical concepts for the detection of material and structural instabilities the treatment provides a comprehensive guide to the classification and computation of instabilities in micro heterogeneous solids focus is put on the interaction of micro and macro instability phenomena such as the loss of macroscopic material stability localization induced by a microscopic structural instability buckling the performance of the proposed computational methods is demonstrated for representative numerical model problems which treat coupled instability phenomena in micro heterogeneous elastic composites

a posteriori error analysis of the linked interpolation technique for plate bending problems we develop a posteriori error estimates for the so called linked interpolation technique to approximate the solution of plate bending problems we show that the proposed residual based estimator is both reliable and efficient

regularization of inverse problems by two point gradient methods in banach spaces in this paper we propose and analyze a two point gradient method for solving inverse problems in banach spaces which is based on the landweber iteration and an extrapolation strategy the method allows to use non smooth penalty terms including the l 1 like and the total variation like penalty functionals which are significant in reconstructing special features of solutions such as sparsity and piecewise constancy in practical applications the design of the method involves the choices of the step sizes and the combination parameters which are carefully discussed numerical simulations are presented to illustrate the effectiveness of the proposed method

graph cut based discrete valued image reconstruction efficient graph cut methods have been used with great success for labeling and denoising problems occurring in computer vision unfortunately the presence of linear image mappings has prevented the use of these techniques in most discrete amplitude image reconstruction problems in this paper we develop a graph cut based framework for the direct solution of discrete amplitude linear image reconstruction problems cast as regularized energy function minimizations we first analyze the structure of discrete linear inverse problem cost functions to show that the obstacle to the application of graph cut methods to their solution is the variable mixing caused by the presence of the linear sensing operator we then propose to use a surrogate energy functional that overcomes the challenges imposed by the sensing operator yet can be utilized efficiently in existing graph cut frameworks we use this surrogate energy functional to devise a monotonic iterative algorithm for the solution of discrete valued inverse problems we first provide experiments using local convolutional operators and show the robustness of the proposed technique to noise and stability to changes in regularization parameter then we focus on nonlocal tomographic examples where we consider limited angle data problems we compare our technique with state of the art discrete and continuous image reconstruction techniques experiments show that the proposed method outperforms state of the art techniques in challenging scenarios involving discrete valued unknowns

a hybrid mixed model for non linear shell analysis and its applications to large rotation problems adopting an updated lagrange approach the general framework for the fully non linear analysis of curved shells is developed using a simple quadrilateral c0 model hmsh5 the governing equations are derived based on a consistent linearization of an incremental mixed variational principle of the modified hellinger reissner type with independent assumptions for displacement and strain fields emphasis is placed on devising effective solution procedures to deal with large rotations in space finite stretches and generalized rate type material models in particular a geometrically exact scheme for configuration update is developed by making use of the so called exponential mapping algorithm and the resulting element was shown to exhibit a quadratic rate of asymptotic convergence in solving practical shell problems with newton raphson type iterative schemes for the purpose of updating the spatial stress field of the element an objective generalized midpoint integration rule is utilized which relies crucially on the concept of polar decomposition for the deformation gradient and is in keeping with the underlying mixed method finally the effectiveness and practical usefulness of the hmsh5 element are demonstrated through a number of test cases involving beams plates and shells undergoing very large displacements and rotations

sirt and cg type methods for the iterative solution of sparse linear least squares problems abstract sirt and cg type methods have been successfully employed for the approximate solution of least squares problems arising in tomography in this paper we study and compare their convergence and regularization properties it is pointed out that sirt methods apply an uncontrollable implicit rescaling which affects the statistical characteristics of the system whereas cg type methods do not for a large class of model problems it is shown that virtually the same solutions as obtained by sirt methods can be obtained by applying a cg type method to a properly rescaled system but with an amount of work proportional to the square root of the amount of work with sirt

uncertainty quantification in computational stochastic multiscale analysis of nonlinear elastic materials abstract this paper is devoted to a computational stochastic multiscale analysis of nonlinear structures made up of heterogeneous hyperelastic materials at the microscale level the nonlinear constitutive equation of the material is characterized by a stochastic potential for which a polynomial chaos representation is used the geometry of the microstructure is random and characterized by a high number of random parameters the method is based on a deterministic non concurrent multiscale approach devoted to micro macro nonlinear mechanics which leads us to characterize the nonlinear constitutive equation with an explicit continuous form of the strain energy density function with respect to the large scale cauchy green strain states to overcome the curse of dimensionality due to the high number of involved random variables the problem is transformed into another one consisting in identifying the potential on a polynomial chaos expansion several strategies based on novel algorithms dedicated to high stochastic dimension are used and adapted for the class of multi modal random variables which may characterize the potential numerical examples at both small and large scales allow analyzing the efficiency of the approach through comparisons with classical methods

noise representation in residuals of lsqr lsmr and craig regularization abstract golub kahan iterative bidiagonalization represents the core algorithm in several regularization methods for solving large linear noise polluted ill posed problems we consider a general noise setting and derive explicit relations between noise contaminated bidiagonalization vectors and the residuals of bidiagonalization based regularization methods lsqr lsmr and craig for lsqr and lsmr residuals we prove that the coefficients of the linear combination of the computed bidiagonalization vectors reflect the amount of propagated noise in each of these vectors for craig the residual is only a multiple of a particular bidiagonalization vector we show how its size indicates the regularization effect in each iteration by expressing the craig solution as the exact solution to a modified compatible problem validity of the results for larger two dimensional problems and influence of the loss of orthogonality is also discussed

assumed strain formulation for triangular c0 plate elements based on a weak form of the kirchhoff constraints application of a weak form of the kirchhoff constraints in the formulation of triangular assumed shear strain c0 plate element is described it is shown that compared to a similar formulation of the quadrilateral elements formulation of the triangles requires some additional considerations which lead to additional terms in the energy expression with those terms performance of the assumed shear strain triangular elements is comparable to that of the quadrilateral elements

a multi level computational model for multi scale damage analysis in composite and porous materials abstract an adaptive multi level methodology is developed in this paper to create a hierarchy of computational sub domains with varying resolution for multiple scale problems it is intended to concurrently predict evolution of variables at the structural and microstructural scales as well as to track the incidence and propagation of microstructural damage in composite and porous materials the microstructural analysis is conducted with the voronoi cell finite element model vcfem while a conventional displacement based fem code executes the macroscopic analysis the model introduces three levels in the computational domain which include macro macro micro and microscopic analysis it differentiates between non critical and critical regions and ranges from macroscopic computations using continuum constitutive relations to zooming in at hotspots for pure microscopic simulations coupling between the scales in regions of periodic microstructure is accomplished through asymptotic homogenization an adaptive process significantly increases the efficiency while retaining appropriate level of accuracy for each region numerical examples are conducted for composite and porous materials with a variety of microscopic architectures to demonstrate the potential of the model

improvements in 3 node triangular shell elements low order triangular finite shell elements are computationally economical and easy to implement but often exhibit very slow convergence two new membrane formulations for triangular shell elements are examined which rectify these drawbacks the first element is based on the marguerre shallow shell theory and a strain projection method that eliminates spurious membrane strain energy resulting expressions are provided in an explicit form for easy implementation of the element the second element is based on a linear membrane field governed by normal rotations and reduced quadrature the difficulties with shell normal rotations are analysed and a method for omitting these rotations while preserving rigid body motion is presented and tested finally a set of test problems are examined which show the importance of mesh patterns and degrees of freedom per node on triangular element performance

determination of the size of the representative volume element for random composites statistical and numerical approach the representative volume element rve plays a central role in the mechanics and physics of random heterogeneous materials with a view to predicting their effective properties a quantitative definition of its size is proposed in this work a rve size can be associated with a given precision of the estimation of the wanted overall property and the number of realizations of a given volume v of microstructure that one is able to consider it is shown to depend on the investigated morphological or physical property the contrast in the properties of the constituents and their volume fractions the methodology is applied to a specific random microstructure namely a two phase three dimensional voronoi mosaic finite element simulations of volumes of different sizes are performed in the case of linear elasticity and thermal conductivity the volumes are subjected to homogeneous strain stress or periodic boundary conditions the effective properties can be determined for large volumes and a small number of realizations conversely smaller volumes can be used providing that a sufficient number of realizations are considered a bias in the estimation of the effective properties is observed for too small volumes for all types of boundary conditions the variance of computed apparent properties for each volume size is used to define the precision of the estimation the key notion of integral range is introduced to relate this error estimation and the definition of the rve size for given wanted precision and number of realizations one is able to provide a minimal volume size for the computation of effective properties the results can also be used to predict the minimal number of realizations that must be considered for a given volume size in order to estimate the effective property for a given precision the rve sizes found for elastic and thermal properties but also for a geometrical property like volume fraction are compared

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

on the regularizing behavior of the sda and sdc gradient methods in the solution of linear ill posed problems we analyze the regularization properties of two recently proposed gradient methods sda and sdc applied to discrete linear inverse problems by studying their filter factors we show that the tendency of these methods to eliminate first the eigencomponents of the gradient corresponding to large singular values allows to reconstruct the most significant part of the solution thus yielding a useful filtering effect this behavior is confirmed by numerical experiments performed on some image restoration problems furthermore the experiments show that for severely ill conditioned problems and high noise levels the sda and sdc methods can be competitive with the conjugate gradient cg method since they are slightly slower than cg but exhibit a better semiconvergence behavior

finite element stabilization matrices a unification approach abstract in this paper we show that the stabilization vector can be obtained naturally by taking the partial derivatives with respect to the natural coordinates hence the components of the strains and stresses can be expressed in terms of a set of orthogonal coordinates with these definitions of stresses and strains a general form of the finite element stabilization matrices is then constructed for underintegrated irregular shape and anisotropic elements the explicit expressions of the stabilization matrices for the 4 9 and 8 node laplace and continuum elements and the 4 node plate element are then derived from the general form these are sufficiently general for the developments herein the generalization of the stabilization matrices concept to nonlinear problems which usually require the numerical integration of a fairly general class of nonlinear finite deformation constitutive equations is also presented the computer implementation aspects and numerical evaluation of these stabilized elements are also considered numerical tests confirm the stability and accuracy characteristics of the resulting elements in particular the numerical experiments reported here also show that the rates of convergence in the l2 norm and in the energy norm agree well with the expected convergence rates

notes on flexible sequential block iterative methods abstract we consider a flexible sequential block iterative method for the solution of consistent linear systems of equations and give its convergence analysis the method is able to use weight matrices and relaxation parameters which can be updated in each iteration whereas the most of previous studies on sequential block iterative methods considered a finite number of weight matrices furthermore we consider the constraint version of the method and give its convergence analysis for the special case of relaxation parameters and weight matrices we report on some numerical tests with examples taken from the field of image reconstruction from projections our numerical results show considerable improvement specially on noisy data compared to the other methods which use finite number of weight matrices

a unified 3d based technique for plate bending analysis using scaled boundary finite element method summary this paper presents a unified technique for solving the plate bending problems by extending the scaled boundary finite element method the formulation is based on the three dimensional governing equation without enforcing the kinematics of plate theory only the in plane dimensions are discretised into finite elements any two dimensional displacement based elements can be employed the solution along the thickness is expressed analytically by using a matrix function the proposed technique is consistent with the three dimensional theory and applicable to both thick and thin plates without exhibiting the numerical locking phenomenon moreover the use of higher order spectral elements allows the proposed technique to better represent curved boundaries and to achieve high accuracy and fast convergence numerical examples of various plate structures with different thickness to length ratios demonstrate the applicability and accuracy of the proposed technique copyright 2012 john wiley sons ltd

functional approximation and projection of stored energy functions in computational homogenization of hyperelastic materials a probabilistic perspective abstract this work is concerned with the construction of a surrogate model for the homogenized stored energy functions defining the effective behavior of nonlinear elastic microstructures here a probabilistic standpoint is adopted and allows for the definition of a nonlinear mapping between the macroscopic deformations and the homogenized potential this functional approximation is specifically obtained by means of a polynomial chaos expansion the coefficients of which are computed through a gauss legendre quadrature rule by invoking well known results related to projections in hilbert spaces closest approximations of arbitrary potentials to standard e g ogden type models are subsequently defined and characterized by appropriate residuals numerical illustrations on various microstructures are finally provided in order to discuss the relevance of the proposed framework in particular it is shown that the surrogate model compares very well with reference results at both the macroscale and the structural scale even for moderate order expansions and that the aforementioned closest approximations constitute very accurate approximation provided that the subset onto which the homogenized response is projected is properly chosen this result readily allows for nonconcurrent coupling using standard constitutive models available in commercial codes and therefore makes the approach very attractive for engineering applications

a three node mindlin plate element with improved transverse shear abstract a displacement methodology for mindlin elements recently employed in the development of an efficient four node quadrilateral min4 is the basis for a three node explicitly integrated triangular element min3 the approach herein referred to as anisoparametric is founded upon two kinematic requirements that are auxiliary to the standard convergence criteria the initial complete quadratic deflection field is constrained by continuous shear edge constraints to achieve an isoparametric like three node configuration much success of the element is due to an innovative shear correction factor concept several numerical experiments are performed in the linear elasto static regime to ascertain the element performance

a parallel subgradient projections method for the convex feasibility problem abstract an iterative method to solve the convex feasibility problem for a finite family of convex sets is presented the algorithm consists in the application of a generalization of an acceleration procedure introduced by de pierro in a parallel version of the subgradient projections method proposed by censor and lent the generated sequence is shown to converge for any starting point some numerical results are presented

non linear finite element modal approach for the large amplitude free vibration of symmetric and unsymmetric composite plates a theoretical analysis is presented for the large amplitude vibration of symmetric and unsymmetric composite plates using the non linear finite element modal reduction method the problem is first reduced to a set of duffing type modal equations using the finite element modal reduction method the main advantage of the proposed approach is that no updating of the non linear stiffness matrices is needed without loss of generality accurate frequency ratios for the fundamental mode and the higher modes of a composite plate at various values of maximum deflection are then determined by using the runge kutta numerical integration scheme the procedure for obtaining proper initial conditions for the periodic plate motions is very time consuming thus an alternative scheme the harmonic balance method is adopted and assessed as it was employed to formulate the large amplitude free vibration of beams in a previous study and the results agreed well with the elliptic solution the numerical results that are obtained with the harmonic balance method agree reasonably well with those obtained with the runge kutta method the contribution of each linear mode to the maximum deflection of a plate can also be obtained the frequency ratios for isotropic and composite plates at various maximum deflections are presented and convergence of frequencies with the number of finite elements number of linear modes and number of harmonic terms is also studied copyright 2005 john wiley sons ltd

necessary and sufficient convergence conditions for algebraic image reconstruction algorithms the landweber scheme is an algebraic reconstruction method and includes several important algorithms as its special cases the convergence of the landweber scheme is of both theoretical and practical importance using the singular value decomposition svd we derive an iterative representation formula for the landweber scheme and consequently establish the necessary and sufficient conditions for its convergence in addition to verifying the necessity and sufficiency of known convergent conditions we find new convergence conditions allowing relaxation coefficients in an interval not covered by known results moreover it is found that the landweber scheme can converge within finite iterations when the relaxation coefficients are chosen to be the inverses of squares of the nonzero singular values furthermore the limits of the landweber scheme in all convergence cases are shown to be the sum of the minimum norm solution of a weighted least squares problem and an oblique projection of the initial image onto the null space of the system matrix

convergence of the simultaneous algebraic reconstruction technique sart computed tomography ct has been extensively studied for years and widely used in the modern society although the filtered back projection algorithm is the method of choice by manufacturers efforts are being made to revisit iterative methods due to their unique advantages such as superior performance with incomplete noisy data in 1984 the simultaneous algebraic reconstruction technique sart was developed as a major refinement of the algebraic reconstruction technique art however the convergence of the sart has never been established since then in this paper the convergence is proved under the condition that coefficients of the linear imaging system are nonnegative it is shown that from any initial guess the sequence generated by the sart converges to a weighted least square solution

projected randomized kaczmarz methods abstract for a constrained linear ill posed problems the projected algebra reconstruction technique part usually has a faster convergence rate than the projected simultaneous iterative reconstruction technique psirt but can not be applied to the inconsistent case in this work we propose the projected randomized kaczmarz method prk to further accelerate the convergence of part and analyze its convergence with the noise free right hand side we show that the prk method can converge exponentially in expectation to the solution for the consistent system with the noisy right hand side we present some insights into the semiconvergence property of the prk method and propose an extended version of prk prek method to seek the least squares solution we prove that the prek method can converge exponentially in expectation to the least squares solution for the inconsistent systems

formulation and implementation of stress driven and or strain driven computational homogenization for finite strain in this paper we present a homogenization approach that can be used in the geometrically nonlinear regime for stress driven and strain driven homogenization and even a combination of both special

multiscale structural topology optimization with an approximate constitutive model for local material microstructure abstract this paper builds on our recent work xia and breitkopf 2014 on multiscale structural topology optimization where at the microscopic scale local materials are optimized concurrently according to current loading status the former design framework requires intensive computational cost due to large number of repetitive local material optimizations to circumvent this limitation in the present work we construct a reduced database model viewing the local material optimization process as a generalized constitutive behavior using separated representations in this model the database is built from a set of numerical experiments of local material optimizations in the macroscopic strain tensor space each value in the database corresponds to the strain energy density evaluated on a material microstructure optimized according to the imposed macroscopic strain by tensor decomposition a continuous representation of the strain energy density is built as a sum of products of one dimensional interpolation functions as a result of this a priori off line step the effective strain energy and stress strain relations required for macroscopic structural evaluation and optimization are provided in a numerically explicit manner the results given by the reduced database model are compared with full scale results it is also shown that this explicit constitutive behavior representation can well serve multiscale structural design at a significantly reduced computational cost

a kirchhoff mode method for c0 bilinear and serendipity plate elements abstract a new formulation for the c0 quadrilateral and serendipity plate elements is presented it is an extension of the mode decomposition approach that has been successfully applied in evaluating the c0 triangular linear plate element in contrast to the triangular element the concept of an equivalent discrete kirchhoff configuration is utilized the elements are applied to several examples and the performance of these elements is shown to be quite good

a general methodology for deriving shear constrained reissner mindlin plate elements in this paper the necessary requirements for the good behaviour of shear constrained reissner mindlin plate elements for thick and thin plate situations are re interpreted and a simple explicit form of the substitute shear strain matrix is obtained this extends the previous work of the authors presented in references 18 and 31 the general methodology is applied to the re formulation of some well known quadrilateral plate elements and some new triangular and quadrilateral plate elements which show promising features some examples of the good behaviour of these elements are given

a two node beam element including transverse shear and transverse normal deformations a variational higher order theory for bending and stretching of linearly elastic orthotropic beams including the deformations due to transverse shearing and stretching of the transverse normal fibre is presented the theory assumes a linear distribution for the longitudinal displacement and a parabolic variation of the transverse displacement across the thickness additionally independent expansions are introduced for the through thickness displacement gradients with the requirement of a least square compatibility for the transverse strains and the satisfaction of exact stress boundary conditions at the top bottom beam surfaces the theory is shown to be well suited for finite element development requiring simple c0 and c 1 continuous displacement interpolation fields to demonstrate the computational utility of the theory a simple two node stretching bending finite element is formulated the analytic and finite element results are obtained for a simple bending problem for which an exact elasticity solution is available it is shown that the inclusion of the transverse normal deformation in the present theory enables improved displacement strain and stress predictions particularly in the analysis of deep beams

first order shear deformation p version finite element for laminated plate nonlinear vibrations a p version hierarchical finite element for moderately thick composite laminated plates is presented where the effects of the rotary inertia transverse shear and geometrical nonlinearity are taken into account the time domain free vibration equations of motion are obtained by applying the principle of virtual work those equations are mapped into the frequency domain by the harmonic balance method and solved by a predictor corrector procedure the linear natural frequencies of vibration of several plates are determined and the convergence properties of the element are investigated it is shown that the element is not prone to shear locking and that a moderate number of degrees of freedom is sufficient for accuracy the influences of the plate s thickness of the width to length ratio and of the fiber orientation on nonlinear free vibrations are investigated

adaptive projection selection for computed tomography the number of projections is a critical factor in tomographic imaging the larger the number the better the quality of the reconstructed image however it increases the radiation dose delivered to the patient therefore it is important to keep the number of projections as small as possible traditionally the projections are taken by moving the x ray source around the patient at uniform angular steps taking projections at nonuniform steps may result in better images as compared with that obtained using uniform projections this paper describes two different approaches that adjust the step size to adaptively select the angle of projections the first one is based on the spectral richness of the acquired projections and the second relies on the amount of new information added by successive projections the superior performance of the two proposed methods over the uniform projection scheme is demonstrated through simulation results using both phantom and real images

acceleration of material dominated calculations via phase space simplicial subdivision and interpolation we develop an acceleration method for material dominated calculations based on phase space simplicial interpolation of the relevant material response functions this process of interpolation constitutes an approximation scheme by which an exact material response function is replaced by a sequence of approximating response functions the terms in the sequence are increasingly accurate thus ensuring the convergence of the overall solution the acceleration ratio depends on the dimensionality the complexity of the deformation the time step size and the fineness of the phase space interpolation we ascertain these trade offs analytically and by recourse to selected numerical tests the numerical examples with piecewise quadratic interpolation in phase space confirm the analytical estimates

on diagonally relaxed orthogonal projection methods we propose and study a block iterative projection method for solving linear equations and or inequalities the method allows diagonal componentwise relaxation in conjunction with orthogonal projections onto the individual hyperplanes of the system and is thus called diagonally relaxed orthogonal projections drop diagonal relaxation has proven useful in accelerating the initial convergence of simultaneous and block iterative projection algorithms but until now it was available only in conjunction with generalized oblique projections in which there is a special relation between the weighting and the oblique projections drop has been used by practitioners and in this paper a contribution to its convergence theory is provided the mathematical analysis is complemented by some experiments in image reconstruction from projections which illustrate the performance of drop

an adaptive multiscale resolution strategy for the finite deformation analysis of microheterogeneous structures abstract standard homogenized formulations of problems posed on microheterogeneous domains provide a lower order of accuracy in regions where highly localized variations are observed in the solution fields in order to account for this loss of accuracy for the finite deformation analysis of generally inelastic macrostructures a scale adaptation strategy is developed where a transition from a homogenized description to an explicit microstructural resolution is pursued in designated zones of interest motivated by higher order homogenization techniques the adaptation zones are identified based on a post processing step on the homogenized solution and correspond to regions with high strain gradients in order to avoid modeling errors emanating from the use of approximate explicit macroscale constitutive formulations an exact homogenization procedure based on databased and direct multilevel finite element computations is employed the overall methodology is investigated in a two dimensional setting where special attention is paid to the underlying multiscale mesh resolution and additionally demonstrated with a three dimensional problem numerical observations suggest the concept of a representative adaptation zone within which scale adaptation effects can be assessed

nonlinear flutter of composite panels under yawed supersonic flow using finite elements a finite element formulation is presented for the effects of arbitrary flow direction on the large amplitude supersonic flutter of composite panels the von karman large deflection plate theory is used to account for large amplitude limit cyde oscillations quasisteady first order piston theory aerodynamics is employed for aerodynamic loading and first order shear deformation theory is used for laminated composite panels an efficient solution procedure is presented by using the modal transformation to reduce the number of nonlinear panel flutter equations and then applying the linearized updated mode with nonlinear time function approximation to the reduced nonlinear panel flutter modal equations a modal participation is defined and the minimum number of linear modes for accurate and converged limit cycle response can be ensured examples are given for isotropic and composite panels at yawed supersonic flow

iterative algorithms for large partitioned linear systems with applications to image reconstruction abstract we present a unifying framework for a wide class of iterative methods in numerical linear algebra in particular the class of algorithms contains kaczmarz s and richardson s methods for the regularized weighted least squares problem with weighted norm the convergence theory for this class of algorithms yields as corollaries the usual convergence conditions for kaczmarz s and richardson s methods the algorithms in the class may be characterized as being group iterative and incorporate relaxation matrices as opposed to a single relaxation parameter we show that some well known iterative methods of image reconstruction fall into the class of algorithms under consideration and are thus covered by the convergence theory we also describe a novel application to truly three dimensional image reconstruction

c0 finite element discretization of kirchhoff s equations of thin plate bending an alternative formulation of kirchhoff s equations is given which is amenable to a standard c 0 finite element discretization in this formulation the potential energy of the plate is formulated entirely in terms of rotations whereas the deflections are the outcome of a subsidiary problem the nature of the resulting equations is such that c 0 interpolation can be used on both rotations and deflections in particular general classes of triangular and quadrilateral isoparametric elements can be used in conjunction with the method unlike other finite element methods which are based on three dimensional or mindlin formulations the present approach deals directly with kirchhoff s equations of thin plate bending excellent accuracy is observed in standard numerical tests using both distorted and undistorted mesh patterns

computational homogenization of nonlinear elastic materials using neural networks in this work a decoupled computational homogenization method for nonlinear elastic materials is proposed using neural networks nn in this method the effective potential is represented as a response surface parameterized by the macroscopic strains and some microstructural parameters the discrete values of the effective potential are computed by fem through random sampling in the parameter space and nn are used to approximate the surface response and to derive the macroscopic stress and tangent tensor components we show through several numerical convergence analyses that smooth functions can be efficiently evaluated in parameter spaces with dimension up to 10 allowing to consider 3d representative volume elements rve and an explicit dependence of the effective behavior on microstructural parameters like volume fraction we present several applications of this technique to the homogenization of nonlinear elastic composites involving a two scale example of heterogeneous structure with graded nonlinear properties

locking free curved beam element based on curvature the formulation of a curved beam element with 3 nodes for curvature to eliminate the shear membrane locking phenomenon is presented the element is based on curvature so that it may represent the bending energy fully and the shear membrane strain energy is incorporated into the formulation by the equilibrium equations to deal with general boundary conditions a transformation matrix between nodal curvature and nodal displacement vector is introduced several examples are presented in order to verify the element formulation and its analytical capability the solutions obtained reveal that the element describes the curved beam behaviour quite correctly and efficiently showing no locking phenomena and that it is also applicable to the analysis of both thin and thick curved beams

air tools a matlab package of algebraic iterative reconstruction methods we present a matlab package with implementations of several algebraic iterative reconstruction methods for discretizations of inverse problems these so called row action methods rely on semi convergence for achieving the necessary regularization of the problem two classes of methods are implemented algebraic reconstruction techniques art and simultaneous iterative reconstruction techniques sirt in addition we provide a few simplified test problems from medical and seismic tomography for each iterative method a number of strategies are available for choosing the relaxation parameter and the stopping rule the relaxation parameter can be fixed or chosen adaptively in each iteration in the former case we provide a new training algorithm that finds the optimal parameter for a given test problem the stopping rules provided are the discrepancy principle the monotone error rule and the ncp criterion for the first two methods training can be used to find the optimal discrepancy parameter

on the computation of the macroscopic tangent for multiscale volumetric homogenization problems in this contribution methods of computing the macroscopic tangent that is required in multiscale volumetric homogenization problems are investigated a condensation procedure that employs the tangent information from the microscale finite element analysis is derived within a special framework where deformation controlled boundary conditions in micromechanical testing are enforced via the penalty method the developed methodology is demonstrated by sample macroscale problems in the context of the multilevel finite element strategy due to the high memory allocation costs that the condensation procedure induces a perturbation procedure is developed based on a minimal number of micromechanical tests results from the condensation and perturbation procedures are compared for sample infinitesimal and finite deformation inelasticity problems and the algorithmic consistency of the macroscopic tangent with the evolution of the macroscopic stress is discussed it is shown that the ability to compute the macroscopic tangent can also be employed to construct a stress controlled micromechanical testing procedure

a mixed formulation of c0 linear triangular plate shell element the role of edge shear constraints a simple and effective linear c0 triangular element for plates and shells is developed on the basis of the hellinger reissner mixed variational principle with independently assumed stress and displacement fields two main features are emphasized in this development concerning the assumed transverse shear stress field firstly this assumption results in edge type penalty constraints in the thin plate shell regimes secondly the element is used in the form of a four triangle cross diagonal macroelement mesh as a result the element is shown to be free from shear locking in thin plate shell applications and it satisfied all the appropriate patch tests required for kirchhoff plate models in addition the element exhibits good overall convergence properties in a variety of test problems for plates and shells finally from the computational standpoint the element is very efficient since all stiffness component matrices are derived in explicit forms

semiconvergence and relaxation parameters for projected sirt algorithms we give a detailed study of the semiconvergence behavior of projected nonstationary simultaneous iterative reconstruction technique sirt algorithms including the projected landweber algorithm we also consider the use of a relaxation parameter strategy proposed recently for the standard algorithms for controlling the semiconvergence of the projected algorithms we demonstrate the semiconvergence and the performance of our strategies by examples taken from tomographic imaging

tomographic image reconstruction using training images abstract we describe and examine an algorithm for tomographic image reconstruction where prior knowledge about the solution is available in the form of training images we first construct a non negative dictionary based on prototype elements from the training images this problem is formulated within the framework of sparse learning as a regularized non negative matrix factorization incorporating the dictionary as a prior in a convex reconstruction problem we then find an approximate solution with a sparse representation in the dictionary the dictionary is applied to non overlapping patches of the image which reduces the computational complexity compared to previous formulations computational experiments clarify the choice and interplay of the model parameters and the regularization parameters and we show that in few projection low dose settings our algorithm is competitive with total variation regularization and tends to include more texture and more correct edges

an excursion into large rotations the present discourse develops an enlarged exploration of the matrix formulation of finite rotations in space initiated in 1 it is shown how a consistent but subtle matrix calculus inevitably leads to a number of elegant expressions for the transformation or rotation matrix t appertaining to a rotation about an arbitrary axis also analysed is the case of multiple rotations about fixed or follower axes particular attention is paid to an explicit derivation of a single compound rotation vector equivalent to two consecutive arbitrary rotations this theme is discussed in some detail for a number of cases semitangential rotations for which commutativity holds first proposed in 2 3 are also considered furthermore an elementary geometrical analysis of large rotations is also given finally we deduce in an appendix using a judicious reformulation of quarternions the compound pseudovector representing the combined effect of n rotations in the author s opinion the present approach appears preferable to a pure vectorial scheme and even more so to an indicial formulation and is computationally more convenient

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

schultz matrix iteration based method for stable solution of discrete ill posed problems abstract in this paper we propose an iterative method for solving discrete ill posed problems based on matrix iterations generated by schultz method and known to converge to the moore penrose pseudoinverse of a matrix practically letting the schultz matrix iteration be x k we construct the vector x k x k b where b is a data vector hence by construction the iterates converge to the minimum 2 norm solution of a least squares problem with coefficient matrix a and data vector b we derive theoretical properties of the sequence x k and show that it is quadratically convergent in the case of corrupted data we analyze the semi convergence behavior of the iterates and conclude that the iteration must be truncated to control the propagation of the noise error as a result we derive an error estimate for the case where the truncation parameter is chosen by the discrepancy principle in addition combining a projected approach with the new method we propose variants of the method that are well suited for large scale problems several numerical results are presented to illustrate the effectiveness of the method on well known test problems

a consistent control of spurious singular modes in the 9 node lagrange element for the laplace and mindlin plate equations abstract when 2 2 quadrature is used with the 9 node lagrange element which is essential in c 0 plate elements to avoid locking spurious singular modes appear on the element level which can lead to singularity or near singularity of the global equations here these modes are controlled by a procedure that introduces additional generalized stresses and strains so that the spurious modes are eliminated and the consistency of the resulting finite difference equations is not impaired hence the procedure passes the patch test applications to the diffusion and mindlin plate equations are presented results show that h 3 convergence in the l 2 norm is almost retained

mixed finite element methods reduced and selective integration techniques a unification of concepts the equivalence of certain classes of mixed finite element methods with displacement methods which employ reduced and selective integration techniques is established this enables one to obtain the accuracy of the mixed formulation without incurring the additional computational expense engendered by the auxiliary field of the mixed method applications and numerical examples are presented for problems with constraints which can be difficult to enforce in finite element approximations and have often dictated the use of mixed principles these include thin beams and plates and linear and nonlinear incompressible and nearly incompressible continuum problems in solid and fluid mechanics

numerical homogenization of periodic composite materials with non linear material components in this paper a numerically developed homogenized constitutive relation for the global behaviour of periodic composite materials with elasto plastic components is derived the algorithm presented is general and can be applied to any kind of non linear material behaviour respecting the complementarity rule the method different from those presented in the literature is currently restricted to small strains plane problems and monotonic proportional loading conditions copyright 1999 john wiley sons ltd

a nonlinear manifold based reduced order model for multiscale analysis of heterogeneous hyperelastic materials a new manifold based reduced order model for nonlinear problems in multiscale modeling of heterogeneous hyperelastic materials is presented the model relies on a global geometric framework for nonlinear dimensionality reduction isomap and the macroscopic loading parameters are linked to the reduced space using a neural network the proposed model provides both homogenization and localization of the multiscale solution in the context of computational homogenization to construct the manifold we perform a number of large three dimensional simulations of a statistically representative unit cell using a parallel finite strain finite element solver the manifold based reduced order model is verified using common principles from the machine learning community both homogenization and localization of the multiscale solution are demonstrated on a large three dimensional example and the local microscopic fields as well as the homogenized macroscopic potential are obtained with acceptable engineering accuracy

a c0 triangular plate element with one point quadrature on developpe un element de plaque triangulaire du type de mindlin qui utilise des champs lineaires pour les rotations et les deflexions transversales l element ne necessite qu un seul point de quadrature ce qui est tres interessant pour l analyse non lineaire

image reconstruction and restoration using the simplified topological e algorithm in order to compute meaningful approximations of the solutions of large scale linear inverse ill posed problems some form of regularization should be employed cimmino and landweber methods are well known iterative regularization methods that can be quite successfully applied for tomographic reconstruction and image restoration problems despite their usually slow convergence the goal of this paper is to explore the performance of a recent extrapolation algorithm when applied to accelerate the convergence of these iterative regularization methods in particular we provide insight and algorithmic details about the simplified topological e algorithm applied to slow converging iterative regularization methods the results of many numerical experiments and comparisons with other methods are also displayed

acceleration and filtering in the generalized landweber iteration using a variable shaping matrix the generalized landweber iteration with a variable shaping matrix is used to solve the large linear system of equations arising in the image reconstruction problem of emission tomography the method is based on the property that once a spatial frequency image component is almost recovered within in in the generalized landweber iteration this component will still stay within in during subsequent iterations with a different shaping matrix as long as this shaping matrix satisfies the convergence criterion for the component two different shaping matrices are used the first recovers low frequency image components and the second may be used either to accelerate the reconstruction of high frequency image components or to attenuate these components to filter the image the variable shaping matrix gives results similar to truncated inverse filtering but requires much less computation and memory since it does not rely on the singular value decomposition

computational nonlinear stochastic homogenization using a nonconcurrent multiscale approach for hyperelastic heterogeneous microstructures analysis this paper is devoted to the computational nonlinear stochastic homogenization of a hyperelastic heterogeneous microstructure using a non concurrent multiscale approach the geometry of the microstructure is random since the non concurrent multiscale approach is based on the use of a tensorial decomposition which is then submitted to the curse of dimensionality we perform an analysis with respect to the stochastic dimension the technique uses a database describing the strain energy density function potential in both the macroscopic cauchy green strain space and the geometrical random parameters domain each value of the potential is numerically computed by means of the finit element method on an elementary cell an interpolation scheme is finall introduced to obtain a continuous explicit form of the potential which by derivation allows to evaluate the macroscopic stress and elastic tangent tensors during the macroscopic structural computations two numerical examples are presented

a new triangular discrete kirchhoff plate shell element we present a new 6 node triangular bending element called dktp based on a discrete kirchhoff model a corresponding new flat shell element dltp having quadratic variation of in plane displacement is also presented this element has 6 degrees of freedom u v w x y z at each corner node and 3 degrees of freedom u v w at each mid side node detailed numerical experimentation is presented to demonstrate the efficiency and reliability of these elements

appropriate number of unit cells in a representative volume element for micro structural bifurcation encountered in a multi scale modeling the paper proposes a method to determine the number of unit cells basic structural elements to be employed for a representative volume element rve of the multi scale modeling for a solid with periodic micro structures undergoing bifurcation main difficulties for the multi scale modeling implementing instability are twofold loss of convexity of the total potential energy that should be homogenized and determination of a pertinent rve that contains multiple unit cells in order to resolve these difficulties variational formulation is achieved with the help of convergence theory within the framework of non convex homogenization method while the number of unit cells in an rve is determined by the block diagonalization method of group theoretic bifurcation theory the latter method enables us to identify the most critical bifurcation mode among possible bifurcation patterns for an assembly of arbitrary number of periodic micro structures thus the appropriate number of unit cells to be employed in the rve can be determined in a systematic manner representative numerical examples for a cellular solid show the feasibility of the proposed method and illustrate material instability at a macroscopic point due to geometrical instability in a micro scale