nonlinear boundary value problems for first order impulsive functional differential equations this paper is concerned with solutions of nonlinear boundary value problems for a class of first order functional differential equations we introduce new concept of lower and upper solutions and present that the method of lower and upper solutions coupled with monotone iterative technique is still valid obviously we extend previous results

simultaneous adaptive control and identification via the weighted least square algorithm in this note we prove the almost sure convergence of the proposed adaptive control and identification algorithms involving a weighted least square parameter estimator the analysis presented here strengthens the previous results achieved in this context the proposed algorithm and the analysis achieve the convergence of the tracking error in a strong sense at an asymptotically arithmetic rate the stronger result is obtained under a regularity and persistency condition introduced in this note which also ensures that with probability one the algorithm affords equal weighting to all the measurements after a finite number of iterations under these conditions it is also shown that the parameter estimation error also converges to zero in the context of siso armax models it is proved that the regularity and persistency conditions are satisfied under mild mixing conditions on the noise and no pole zero cancellation in the plant input output transfer function by a random perturbation of the reference trajectory

fft based homogenization for microstructures discretized by linear hexahedral elements summary the fft based homogenization method of moulinec suquet has recently emerged as a powerful tool for computing the macroscopic response of complex microstructures for elastic and inelastic problems in this work we generalize the method to problems discretized by trilinear hexahedral elements on cartesian grids and physically nonlinear elasticity problems we present an implementation of the basic scheme that reduces the memory requirements by a factor of four and of the conjugate gradient scheme that reduces the storage necessary by a factor of nine compared with a naive implementation for benchmark problems in linear elasticity the solver exhibits mesh and contrast independent convergence behavior and enables the computational homogenization of complex structures for instance arising from computed tomography computed tomography ct imaging techniques there exist 3d microstructures involving pores and defects for which the original fft based homogenization scheme does not converge in contrast for the proposed scheme convergence is ensured also the solution fields are devoid of the spurious oscillations and checkerboarding artifacts associated to conventional schemes we demonstrate the power of the approach by computing the elasto plastic response of a long fiber reinforced thermoplastic material with 172 106 displacement degrees of freedom copyright 2016 john wiley sons ltd

global attractivity of positive periodic solutions for nonlinear impulsive systems abstract in this paper the existence uniqueness and global attractivity of positive periodic solutions for nonlinear impulsive systems are studied firstly existence conditions are established by the method of lower and upper solutions then uniqueness and global attractivity are obtained by developing the theories of monotone and concave operators and lastly the method and the results are applied to the impulsive n species cooperative lotka volterra system and a model of a single species dispersal among n patches

effective properties of composite materials with periodic microstructure a computational approach abstract this study reviews several problems which are specific of composites with periodic microstructure composed of linear or nonlinear constituents the theoretical background of the method is recalled first two different families of numerical methods are considered to solve the problem the first is based on the finite element method the concept of macroscopic degrees of freedom is presented the implementation of periodicity conditions is discussed a general framework permitting either a strain or stress control is proposed the second numerical method is based on fast fourier transforms it considers first the problem of a homogeneous linear reference material undergoing a nonhomogeneous periodic eigenstrain the solution of this problem is based on the explicit form of the periodic green s function of the reference medium the relative merits of the two methods are compared and several examples are discussed both methods give very comparable results on test examples and their domains of applications appear to be complementary

periodic boundary value problems for a class of functional differential equations in this paper we show that the method of upper and lower solutions coupled with the monotone iterative technique is valid to obtain constructive proofs of existence of solutions for nonlinear periodic boundary value problems of functional differential equations without assuming properties of monotonicity in the nonlinear part

reduced order modeling strategies for computational multiscale fracture the paper proposes some new computational strategies for affordably solving multiscale fracture problems through a fe2 approach to take into account the mechanical effects induced by fracture at the microstructure level the representative volume element rve assumed constituted by an elastic matrix and inclusions is endowed with a large set of cohesive softening bands providing a good representation of the possible microstructure crack paths the rve response is then homogenized in accordance with a model previously developed by the authors and upscaled to the macro scale level as a continuum stress strain constitutive equation which is then used in a conventional framework of a finite element modeling of propagating fracture for reduced order modeling rom purposes the rve boundary value problem is first formulated in displacement fluctuations and used via the proper orthogonal decomposition pod to find a low dimension space for solving the reduced problem a domain separation strategy is proposed as a first technique for model order reduction unconventionally the low dimension space is spanned by a basis in terms of fluctuating strains as primitive kinematic variables instead of the conventional formulation in terms of displacement fluctuations the rve spatial domain is then decomposed into a regular domain made of the matrix and the inclusions and a singular domain constituted by cohesive bands the required rve boundary conditions are rephrased in terms of strains and imposed via lagrange multipliers in the corresponding variational problem specific low dimensional strain basis is then derived independently for each domain via the pod of the corresponding strain snapshots next step consists of developing a hyper reduced model hprom it is based on a second proposed technique the reduced optimal quadrature roq which again unconventionally is determined through optimization of the numerical integration of the primitive saddle point problem arising from the rve problem rather than its derived variational equations and substitutes the conventional gauss quadrature the roq utilizes a very reduced number of optimally placed sampling points the corresponding weights and placements being evaluated through a greedy algorithm the resulting low dimensional and reduced quadrature variational problem translates into very relevant savings on the computational cost and high computational speed ups particular attention is additionally given to numerical tests and performance evaluations of the new hyper reduced methodology by a priori and a posteriori error assessments moreover for the purposes of validation of the present techniques a real structural problem exhibiting propagating fracture at two scales is modeled on the basis of the strain injection based multiscale approach previously developed by the authors the performance of the proposed strategy in terms of speed up vs error is deeply analyzed and reported

boundary value problem for second order impulsive functional differential equations this paper is concerned with the existence of minimal and maximal solutions of boundary value problem for second order impulsive functional differential equations the method of upper and lower solutions and the monotone iterative technique are used

green s operator for a periodic medium with traction free boundary conditions and computation of the effective properties of thin plates this paper presents a new green s operator gamma operator for mixed periodic and stress free boundary conditions the solution is split into a classical periodic solution and a complementary solution to account for stress free boundary conditions this operator is used to obtain the effective properties of thin heterogeneous plates made of periodic cells using the fast fourier transform the periodic thin plate theory and the computation of the strain energy within the cell numerical applications are provided including comparisons with closed form solutions and finite element solutions

filtering material properties to improve fft based methods for numerical homogenization fft based solvers introduced in the 1990s for the numerical homogenization of heterogeneous elastic materials have been extended to a wide range of physical properties in parallel alternative algorithms and modified discrete green operators have been proposed to accelerate the method and or improve the description of the local fields in this short note filtering material properties is proposed as a third complementary way to improve fft based methods it is evidenced from numerical experiments that the grid refinement and consequently the computation time and or the spurious oscillations observed on local fields can be significantly reduced in addition if the two filters based on voigt or reuss homogenization rules can improve or deteriorate the method depending on the microstructure a stiff inclusion within a compliant matrix or the reverse the proposed 2 layer filter is efficient in both situations the study is proposed in the context of linear elasticity but similar results are expected in a different physical context thermal electrical

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

a series solution for the effective properties of incompressible viscoelastic media this paper presents a series solution for the homogenization problem of a linear viscoelastic periodic incompressible composite the method uses the laplace transform and the correspondence principle which are combined with the classical expansion along neumann series of the solution of the periodic elasticity problem in fourier space the terms of the neumann series appear as decoupled containing geometry dependent terms and viscoelastic properties dependent terms which are polynomial fractions whose inverse laplace transforms are provided explicitly

overall elastic properties of composites from optimal strong contrast expansion abstract in this paper we propose a new systematic procedure of estimating elastic properties of composites constituted of two phases matrix and inclusions a class of integral equations based on eigenstrain or eigenstress with the matrix as reference material is constructed with an explicit form in fourier space each integral equation belonging to this class can yield estimates of the overall elastic tensor via neumann series expansion the best estimates and series are selected based on the convergence rate criteria of the series i e the spectral radius must be minimized the optimized series is convergent for any finite contrast between inclusions and matrix applying the optimized series and the associated estimates to different microstructures yields very satisfying results when compared with the related full solution for the case of a random distribution of spherical inclusions exact relations between the elastic tensor and nth order structure factors are demonstrated

an accelerated fft algorithm for thermoelastic and non linear composites a fast numerical algorithm to compute the local and overall responses of non linear composite materials is developed this alternative formulation allows us to improve the convergence of the existing method of moulinec and suquet e g comput meth appl mech eng 1998 157 1 2 69 94 in the present method a non linear elastic or conducting material is replaced by infinitely many locally linear thermoelastic materials with moduli that depend on the values of the local fields this makes it possible to use the advantages of an algorithm developed by eyre and milton eur phys j appl phys 1999 6 1 41 47 which has faster convergence the method is applied to compute the local fields as well as the effective response of non linear conducting and elastic periodic composites copyright 2008 john wiley sons ltd

on nonlinear two point boundary value problems for impulsive differential algebraic problems in this paper we investigate boundary value problems for first order impulsive differential algebraic problems with causal operators note that a corresponding boundary condition is given by a nonlinear function using a monotone iterative method we formulate general sufficient conditions under which such problems have solutions extremal or a unique an example shows that corresponding assumptions are satisfied the results are new

combining galerkin approximation techniques with the principle of hashin and shtrikman to derive a new fft based numerical method for the homogenization of composites we report on the mathematical analysis of two different fft based numerical schemes for the homogenization of composite media within the framework of linear elasticity the basic scheme of moulinec and suquet 1994 1998 9 and 10 and the energy based scheme of brisard and dormieux 2010 13 casting these two schemes as galerkin approximations of the same variational problem allows us to assert their well posedness and convergence more importantly we extend in this work their domains of application by relieving some stringent conditions on the reference material which were previously thought necessary the origins of the flaws of each scheme are identified and a third scheme is proposed which seems to combine the strengths of the basic and energy based schemes while leaving out their weaknesses finally a rule is proposed for handling heterogeneous pixels voxels a situation frequently met when images of real materials are used as input to these schemes

discrete time stochastic adaptive control this paper establishes global convergence of a stochastic adaptive control algorithm for discrete time linear systems it is shown that with probability one the algorithm will ensure the system inputs and outputs are sample mean square bounded and the conditional mean square output tracking error achieves its global minimum possible value for linear feedback control thus asymptotically the adaptive control algorithm achieves the same performance as could be achieved if the system parameters were known

periodic boundary value problem for first order impulsive functional differential equations this paper discusses the periodic boundary value problem for a class of first order impulsive functional differential equations we establish several existence results under weaker hypotheses by using the leray schauder alternative the lower and upper solution method and the monotone iterative technique the corresponding results in the literature are improved or extended some examples are also given to illustrate the advantage of the results

a computational scheme for linear and non linear composites with arbitrary phase contrast a numerical method making use of fast fourier transforms has been proposed in moulinec and suquet 1994 1998 to investigate the effective properties of linear and non linear composites this method is based on an iterative scheme the rate of convergence of which is proportional to the contrast between the phases composites with high contrast typically above 104 or infinite contrast those containing voids or rigid inclusions or highly non linear materials cannot be handled by the method this paper presents two modified schemes the first one is an accelerated scheme for composites with high contrast which extends to elasticity a scheme initially proposed in eyre and milton 1999 its rate of convergence varies as the square root of the contrast the second scheme adequate for composites with infinite contrast is based on an augmented lagrangian method the resulting saddle point problem involves three steps the first step consists of solving a linear elastic problem using the fast fourier transform method in the second step a non linear problem is solved at each individual point in the volume element the third step consists of updating the lagrange multiplier applications of this scheme to rigidly reinforced and to voided composites are shown copyright 2001 john wiley sons ltd

nonlinear boundary value problem for first order impulsive integro differential equations of mixed type this paper discusses nonlinear boundary value problem for first order impulsive integro differential equations of mixed type the lower and upper solutions and monotone iterative techniques are used to achieve the existence results two examples are provided to illustrate the efficiency of the obtained results

a comparative study on low memory iterative solvers for fft based homogenization of periodic media in this paper we assess the performance of four iterative algorithms for solving non symmetric rank deficient linear systems arising in the fft based homogenization of heterogeneous materials defined by digital images our framework is based on the fourier galerkin method with exact and approximate integrations that has recently been shown to generalize the lippmann schwinger setting of the original work by moulinec and suquet from 1994 it follows from this variational format that the ensuing system of linear equations can be solved by general purpose iterative algorithms for symmetric positive definite systems such as the richardson the conjugate gradient and the chebyshev algorithms that are compared here to the eyre milton scheme the most efficient specialized method currently available our numerical experiments carried out for two dimensional elliptic problems reveal that the conjugate gradient algorithm is the most efficient option while the eyre milton method performs comparably to the chebyshev semi iteration the richardson algorithm equivalent to the still widely used original moulinec suquet solver exhibits the slowest convergence besides this we hope that our study highlights the potential of the well established techniques of numerical linear algebra to further increase the efficiency of fft based homogenization methods

the existence of solutions for impulsive neutral functional differential equations this work deals with the existence of mild solutions for a class of impulsive functional differential equations of the neutral type associated with the family of linear closed not necessarily bounded operators a t email protected i

positive solutions of three point boundary value problems for second order impulsive differential equations with advanced arguments in this paper we discuss three point boundary value problems for second order impulsive differential equations with advanced arguments we establish sufficient conditions under which such problems have positive solutions to obtain the results we use the fixed point index

periodic boundary value problems for impulsive integro differential equations of mixed type by developing a comparison result and using the monotone iterative technique we are able to obtain existence of minimal and maximal solutions of periodic boundary value problems for first order nonlinear impulsive integro differential equations of mixed type

periodic boundary value problem for the second order impulsive functional differential equations this paper considers the existence of extreme solutions of the periodic boundary value problem for second order functional differential equations by using the method of lower and upper solutions coupled with monotone iterative technique

first order impulsive ordinary differential equations with advanced arguments this paper deals with impulsive advanced ordinary differential equations with boundary conditions we investigate the existence of solutions and quasisolutions for advanced impulsive differential equations to obtain such results we apply schauder s fixed point theorem corresponding results are also formulated for differential inequalities

combining fft methods and standard variational principles to compute bounds and estimates for the properties of elastic composites abstract in this paper we develop a computational approach based on variational principles combined with fft technique to determine the effective elastic properties of composite materials the unit cell problem of the composite is recast in a weak and integral form by making use of classic variational approaches based on the strain and the stress potential and the hashin shtrikman variational principles the problem is discretized with fourier series and the stationary point is computed numerically by means of an iterative scheme these algorithms use a representation of the local elastic tensor on the double grid twice the size of the discretization which is introduced by the integral formulation it advantageously accounts for the exact geometry of the microstructure and allows the derivation of rigorous bounds of the effective elasticity coefficients in the second part of the paper we establish a hierarchy between the different fft solutions the strain the stress based solutions coming from the classic variational formulations and the polarization based solution derived from the hashin shtrikman principle which depends on the choice of the elastic moduli of the reference material it is proved that the strain and the stress based solutions deliver optimal bounds since they are always better than those obtained from the hashin shtrikman variational principle when the same discretization is used alternatively when the elastic moduli of the reference material is negative the polarization based solution provides an estimate of the effective properties which is comprised between the strain based upper bound and the stress based lower bound

periodic boundary value problem for the second order impulsive functional differential equations this paper considers the existence of extreme solutions of the periodic boundary value problems for the second order functional differential equations the novelty is that we introduce a new concept for lower and upper solutions and present that the method of lower and upper solutions coupled with monotone iterative technique is still valid meanwhile we extend previous results

periodic boundary value problems for second order impulsive integro differential equations by developing a new comparison result and using the monotone iterative technique we are able to obtain existence of minimal and maximal solutions of periodic boundary value problems for second order nonlinear impulsive integro differential equations of mixed type

a finite element perspective on non linear fft based micromechanical simulations fourier solvers have become efficient tools to establish structure property relations in heterogeneous materials introduced as an alternative to the finite element fe method they are based on fixed point solutions of the lippmann schwinger type integral equation their computational efficiency results from handling the kernel of this equation by the fast fourier transform fft however the kernel is derived from an auxiliary homogeneous linear problem which renders the extension of fft based schemes to nonlinear problems conceptually difficult this paper aims to establish a link between fe based and fft based methods in order to develop a solver applicable to general history dependent and time dependent material models for this purpose we follow the standard steps of the fe method starting from the weak form proceeding to the galerkin discretization and the numerical quadrature up to the solution of nonlinear equilibrium equations by an iterative newton krylov solver no auxiliary linear problem is thus needed by analyzing a two phase laminate with nonlinear elastic elastoplastic and viscoplastic phases and by elastoplastic simulations of a dual phase steel microstructure we demonstrate that the solver exhibits robust convergence these results are achieved by re using the nonlinear fe technology with the potential of further extensions beyond small strain inelasticity considered in this paper

nonlinear boundary problem of first order impulsive integro differential equations this paper focuses on first order impulsive integro differential equations with nonlinear boundary the lower and upper solutions combined with monotone iterative techniques are used to obtain the existence of extremal solutions of the problem numerical examples are given to prove its validity

boundary value problems for a class of impulsive functional equations this paper is related to the existence and approximation of solutions for impulsive functional differential equations with periodic boundary conditions we study the existence and approximation of extremal solutions to different types of functional differential equations with impulses at fixed times by the use of the monotone method some of the options included in this formulation are differential equations with maximum and integro differential equations in this paper we also prove that the lipschitzian character of the function which introduces the functional dependence in a differential equation is not a necessary condition for the development of the monotone iterative technique to obtain a solution and to approximate the extremal solutions to the equation in a given functional interval the corresponding results are established for the impulsive case the general formulation includes several types of functional dependence delay equations equations with maxima integro differential equations finally we consider the case of functional dependence which is given by nonincreasing and bounded functions

periodic boundary value problem for first order impulsive functional differential equations in this paper by means of the method of upper and lower solutions and the monotone iterative technique the existence of minimal and maximal solutions of the periodic boundary value problem for first order impulsive functional differential equations is considered

remarks on periodic boundary value problems for functional differential equations we extend some results on existence and approximation of solution for a class of first order functional differential equations with periodic boundary conditions we show the validity of the monotone iterative technique under weaker hypotheses and present some examples

anti periodic boundary value problems for first order impulsive functional differential equations this paper considers existence of solutions for a class of first order functional differential equation with anti periodic boundary value conditions we introduce new concept of lower and upper solutions which is quite different from the former one and we present that monotone iterative technique coupled with lower and upper solutions is still valid

periodic boundary value problems for delay differential equations with impulses existence and approximation of solutions for an impulsive delay differential equation with periodic boundary value conditions are presented we use comparison principles and monotone iterative techniques

a numerical spectral approach for solving elasto static field dislocation and g disclination mechanics a spectral approach is developed to solve the elasto static equations of field dislocation and g disclination mechanics in periodic media given the spatial distribution of nye s dislocation density and or g disclination density tensors in heterogeneous or homogenous linear elastic media the incompatible and compatible elastic distortions are respectively obtained from the solutions of poisson and navier type equations in the fourier space intrinsic discrete fourier transforms solved by the fast fourier transform fft method which are consistent with the pixel grid for the calculation of first and second order spatial derivatives are preferred and compared to the classical discrete approximation of continuous fourier transforms when deriving elastic fields of defects numerical examples are provided for homogeneous linear elastic isotropic solids for various defects a regularized defect density in the core is considered and smooth elastic fields without gibbs oscillations are obtained when using intrinsic discrete fourier transforms the results include the elastic fields of single screw and edge dislocations standard wedge disclinations and associated dipoles as well as twinning g disclinations in order to validate the present spectral approach comparisons are made with analytical solutions using the riemann graves integral operator and with numerical simulations using the finite element approximation

a full field image conversion method for the inverse conductivity problem with internal measurements this article investigates a fourier based algorithm for computing heterogeneous material parameter distributions from internal measurements of physical fields within the framework of the periodic scalar conductivity model a pair of dual lippmann schwinger integral equations is derived for the sought constitutive parameters based on full intensity or current density field measurements a numerical method based on the fast fourier transform and fixed point iterations is proposed convergence stability and approximation quality of the method are analysed for materials with small contrast a first order born like approximation is also obtained overall the proposed reconstruction approach enables a direct conversion of full field measurement images possibly noisy into maps of material conductivity a set of numerical results is presented to illustrate the performance of the method

fourier based schemes with modified green operator for computing the electrical response of heterogeneous media with accurate local fields a modified green operator is proposed as an improvement of fou rier based numerical schemes commonly used for computing the electrical or thermal response of heterogeneous media contrary to other methods the number of iterations necessary to achieve convergence tends to a finite value when the contrast of properties between the phases becomes infinite furtherm ore it is shown that the method produces much more accurate local field s inside highly conducting and quasi insulating phases as well as in the vicinity of the phases interfaces these good propert ies stem from the discretization of green s function which is consistent with the pixel grid while retaining the local nature of the op erator that acts on the polarization field finally a fast im plementation of the direct scheme of moulinec et al 1994 that allows for parcimonious memory use is proposed

positive solutions for nonlinear first order periodic boundary value problems of impulsive dynamic equations on time scales in this paper existence criteria of positive solutions to a class of nonlinear first order periodic boundary value problems of impulsive dynamic equations on time scales are obtained the main tool used in this paper is the well known guo krasnoselskii fixed point theorem

existence of solutions for second order impulsive differential equations with deviating arguments abstract this paper deals with impulsive second order differential equations with deviating arguments we investigate the existence of solutions of such problems with nonlinear boundary conditions to obtain corresponding results we discuss also second order impulsive differential inequalities with deviating arguments

monotone iterative techniques of v lakshmikantham for a boundary value problem for systems of impulsive differential difference equations by means of the monotone iterative techniques of v lakshmikantham a couple of minimal and maximal quasisolutions of a two point boundary value problem for a system of impulsive differential difference equations are constructed

periodic boundary value problem for non lipschitzian impulsive functional differential equations we consider a class of first order impulsive functional differential equations where the functional dependence is not necessarily a lipschitzian function the new maximum principle improves and extends previous results and uniqueness of solution between a lower and an upper solution for a particular nonlinear problem is presented we give conditions for existence of extremal solutions in an interval delimited by a lower and an upper solution

impulsive anti periodic boundary value problem of first order integro differential equations this paper is concerned with the anti periodic boundary value problem of first order nonlinear impulsive integro differential equations we first establish a new comparison principle and then obtain the existence of extremal solutions by upper lower solution and monotone iterative techniques some examples are presented to illustrate the main results

exponential convergence of adaptive identification and control algorithms output and equation error adaptive identification algorithms are shown to be exponentially convergent under a deterministic or stochastic persistently exciting or spanning condition on the system inputs together with several other standard conditions an adaptive control algorithm is shown to be exponentially convergent under a deterministic or stochastic persistently exciting condition on the reference trajectory together with some standard conditions

convergence of adaptive minimum variance algorithms via weighting coefficient selection weighted least squares and related stochastic approximation algorithms are studied for parameter estimation adaptive state estimation adaptive n step ahead prediction and adaptive control in both white and colored noise environments for the fundamental algorithm which is the basis for the various applications the step size in the stochastic approximation versions and the weighting coefficient in the weighted least squares schemes are selected according to a readily calculated stability measure associated with the estimator the selection is guided by the convergence theory in this way strong global convergence of the parameter estimates state estimates and prediction or tracking errors is not only guaranteed under the appropriate noise passivity and stability or minimum phase conditions but the convergence is also as fast as it appears reasonable to achieve given the simplicity of the adaptive scheme

on the convergence of the self tuning algorithms based on nonmodified least squares self tuning servo control based on a nonmodified least squares algorithm is considered the fundamental result of the analysis is that the passivity of the two time varying operators depending on the noise process dynamics regression vector and the ponderation matrix sequence of the algorithm is essential for the global stability of the self tuning regulator the methodology can be applied to problems of adaptive prediction based on a nonmodified least squares algorithm and system parameter identification by a least squares algorithm with a priori prediction

use of composite voxels in fft based homogenization abstract fft based homogenization methods operate on regular voxel grids in general such grids cannot resolve interfaces exactly in this article we assign voxels containing an interface a stiffness different from the constituent materials in a systematic fashion more precisely we characterize the class of these so called composite voxels leading to convergence of the discretizations considering the interface in the composite voxel as linear we furnish the voxel with the corresponding laminate stiffness these laminate voxels are shown to increase both the accuracy of the calculated effective properties and the local quality of the strain and stress fields dramatically

computational analysis of nonlinear composite structures using the nonuniform transformation field analysis abstract a reduced model for the effective behavior of nonlinear composites such as metal matrix composite materials has been recently proposed by the authors 1 it extends and improves on the transformation field analysis of dvorak 2 by considering nonuniform transformation strains also called plastic modes and is referred to as the nonuniform transformation field analysis the present study is devoted to the implementation of this new homogenized model into a structural computation a brief account on the reduction procedure is given first then the time integration of the model which is required at each integration point of the structural problem is performed by means of an implicit scheme two examples are discussed the response of the homogenized structure is compared to the exact response of the actual heterogeneous structure computed with a very fine mesh it is seen that not only the structural response is accurately captured by the ntfa model but also the local stress field is correctly approximated

fea in elasticity of random structure composites reinforced by heterogeneities of non canonical shape abstract one considers linearly elastic composite media which consist of a homogeneous matrix containing a statistically homogeneous random set of aligned homogeneous heterogeneities of non canonical shape effective elastic moduli as well as the first statistical moments of stresses in the phases are estimated the explicit new representations of the effective moduli and stress concentration factors are expressed through some building block described by numerical solution for one heterogeneity inside the infinite medium subjected to homogeneous remote loading the method uses as a background a new general integral equation proposed in buryachenko 2010a buryachenko 2010b which incorporates influence of stress inhomogeneity inside the inclusion on the effective field and makes it possible to reconsider basic concepts of micromechanics such as effective field hypothesis quasi crystalline approximation and the hypothesis of ellipsoidal symmetry the results of this reconsideration are quantitatively estimated for some modeled composite reinforced by aligned homogeneous heterogeneities of non canonical shape some new effects are detected that are impossible in the framework of a classical background of micromechanics

existence of solutions of boundary value problems for differential equations with delayed arguments we study the existence and approximation of solution of boundary value problems for differential equations with delayed arguments sufficient conditions are established for the existence of a unique solution or extremal ones of the given problem a monotone iterative technique is applied

persistence of excitation in extended least squares in least squares parameter estimation schemes persistency of excitation conditions on the plant states are required for consistent estimation in the case of extended least squares the persistency conditions are on the state estimates here these persistency of excitation conditions are translated into sufficiently rich conditions on the plant noise and inputs in the case of adaptive minimum variance control schemes the sufficiently rich conditions are on the noise and specified output trajectory with sufficiently rich input signals guaranteed convergence rates of prediction errors improve and it is conjectured that the algorithms are consequently more robust

adaptive wavelet enriched hierarchical finite element model for polycrystalline microstructures abstract this paper proposes an adaptive wavelet enriched hierarchical finite element model fem to enhance computational efficiency and solution accuracy for heterogeneous domains of anisotropic elastic materials it is motivated by the need to overcome shortcomings of conventional methods like the standard fem or fast fourier transformation fft based method for analyzing deformation in large polycrystalline microstructures the multi resolution wavelet functions are advantageous for selection of an optimal set of functions that can adaptively enrich the solution space with a prescribed level of accuracy the proposed method introduces a discretization space that conforms to the profile of the solution sought the method engages a second generation family of wavelets with a lifting scheme to generate hierarchical interpolation functions an iterative algorithm efficiently calculates estimates of the solution from the previous iterate using a modified jacobi method the adaptive fe method performs significantly better than uniformly refined fem in validation tests with focus on the convergence rate and error mitigation a polycrystalline microstructure with elastically anisotropic grains is simulated by the adaptive wavelet enriched hierarchical method showing high convergence rates

an fft based galerkin method for homogenization of periodic media in 1994 moulinec and suquet introduced an efficient technique for the numerical resolution of the cell problem arising in homogenization of periodic media the scheme is based on a fixed point iterative solution to an integral equation of the lippmann schwinger type with action of its kernel efficiently evaluated by the fast fourier transform techniques the aim of this work is to demonstrate that the moulinec suquet setting is actually equivalent to a galerkin discretization of the cell problem based on approximation spaces spanned by trigonometric polynomials and a suitable numerical integration scheme for the latter framework and scalar elliptic problems we prove convergence of the approximate solution to the weak solution including a priori estimates for the rate of convergence for sufficiently regular data and the effects of numerical integration moreover we also show that the variational structure implies that the resulting non symmetric system of linear equations can be solved by the conjugate gradient method apart from providing a theoretical support to fast fourier transform based methods for numerical homogenization these findings significantly improve on the performance of the original solver and pave the way to similar developments for its many generalizations proposed in the literature

a stochastic computational method for evaluation of global and local behavior of random elastic media a stochastic computational method is developed to evaluate global effective properties and local probabilistic behavior of random elastic media the elasticity solution for random media is addressed with a method that combines a fast iterative numerical method with stochastic decomposition techniques stochastic homogenization problems are mathematically formulated with an ensemble average approximation scheme based on a concept of stochastic representative volume element srve probabilistic descriptors of local strain are generated based on convolution equations derived from the equilibrium equations of elasticity with the application of the galerkin formulation in probability space and the fourier transform of the convolution equations an efficient numerical scheme is implemented using an iterative algorithm that takes advantage of fast fourier transform two algorithms are provided for gaussian and non gaussian random media respectively with corresponding sufficient conditions for convergence derived finally numerical experiments are conducted for a gaussian and a non gaussian random medium respectively with verifications obtained from monte carlo simulation

convergence and rate of convergence of a recursive identification and adaptive control method which uses truncated estimators a stochastic approximation like method is used for the recursive identification of the coefficients in y n sum min 1 max l 1 a i y n i sum min 0 max l 2 b i u n i sum min 1 max l 3 c i w n i w n where w n is a sequence of mutually independent and bounded random variables and is independent of the bounded u n such methods normally require the recursive estimation of the residuals or the w n and the algorithms for doing this can be unstable if the parameter estimates are not close enough to their true values the problem is solved here by use of a simple truncated estimator which is probably what would be used in implementation in any case then under a stability and strict positive real type condition with probability 1 w p 1 convergence is proved and the rate of convergence is obtained an associated adaptive control problem is also treated

a multiscale approach for modeling progressive damage of composite materials using fast fourier transforms abstract composite materials possess a highly complex material behavior and thus advanced simulation techniques are necessary to compute their mechanical response in this regard especially modeling failure and progressive damage presents a challenging task conventional macro mechanical methods and even closed form estimates are in many cases not sufficient to predict the appropriate mechanical material response full field simulations must be resorted to but these are known to be very expensive from the computational point of view in this contribution we propose a more efficient multiscale approach similar to fe2 nonlinear material effects caused by progressive damage behavior are captured directly on the discretized material level using simple isotropic continuum damage laws in contrast to conventional fe2 methods which use the finite element method fem to solve both scales numerically the fine scale problem material level is rewritten in an integral form of lippmann schwinger type and solved efficiently using the fast fourier transformation fft the calculation is carried out on a regular voxel grid that can be obtained from 3d images like tomographies the fine scale problem is integrated in a standard finite element framework which is used to solve the macroscopic bvp component level in the work at hand the scale coupling technique and the computation of the macroscopic tangent are described and in some numerical examples the convergence behavior of the macroscopic newton algorithm is investigated thereby the simulations were considered until localization and softening on the material scale occurred it is shown that the proposed method presents an effective way to determine the exact physical macroscopic response considering arbitrary microstructures and loading conditions

finite strain fft based non linear solvers made simple computational micromechanics and homogenization require the solution of the mechanical equilibrium of a periodic cell that comprises a generally complex microstructure techniques that apply the fast fourier transform have attracted much attention as they outperform other methods in terms of speed and memory footprint moreover the fast fourier transform is a natural companion of pixel based digital images which often serve as input in its original form one of the biggest challenges for the method is the treatment of geometrically non linear problems partially due to the need for a uniform linear reference problem in a geometrically linear setting the problem has recently been treated in a variational form resulting in an unconditionally stable scheme that combines newton iterations with an iterative linear solver and therefore exhibits robust and quadratic convergence behavior through this approach well known key ingredients were recovered in terms of discretization numerical quadrature consistent linearization of the material model and the iterative solution of the resulting linear system as a result the extension to finite strains using arbitrary constitutive models is at hand because of the application of the fast fourier transform the implementation is substantially easier than that of other finite element methods both claims are demonstrated in this paper and substantiated with a simple code in python of just 59 lines without comments the aim is to render the method transparent and accessible whereby researchers that are new to this method should be able to implement it efficiently the potential of this method is demonstrated using two examples each with a different material model

on differential algebraic problems in this paper the existence of extremal or quasi solutions for differential algebraic problems with causal operators is investigated the case when such problems have a unique solution is also discussed to obtain existence results a monotone iterative technique is applied

existence results for an impulsive abstract partial differential equation with state dependent delay in this paper we establish the existence of mild solutions for a class of impulsive abstract partial functional differential equation with state dependent delay

existence and multiplicity of positive periodic solutions to functional differential equations with impulse effects abstract this paper deals with a new existence theory for single and multiple positive periodic solutions to a kind of nonautonomous functional differential equations with impulse actions at fixed moments by employing a fixed point theorem in cones easily verifiable sufficient criteria are established the paper extends some previous results and reports some new results about impulsive functional differential equations

convergence of iterative methods based on neumann series for composite materials theory and practice iterative fast fourier transform methods are useful for calculating the fields in composite materials and their macroscopic response by iterating back and forth until convergence the differential constraints are satisfied in fourier space and the constitutive law in real space the methods correspond to series expansions of appropriate operators and to series expansions for the effective tensor as a function of the component moduli it is shown that the singularity structure of this function can shed much light on the convergence properties of the iterative fast fourier transform methods we look at a model example of a square array of conducting square inclusions for which there is an exact formula for the effective conductivity obnosov theoretically some of the methods converge when the inclusions have zero or even negative conductivity however the numerics do not always confirm this extended range of convergence and show that accuracy is lost after relatively few iterations there is little point in iterating beyond this accuracy improves when the grid size is reduced showing that the discrepancy is linked to the discretization finally it is shown that none of the three iterative schemes investigated over performs the others for all possible microstructures and all contrasts

periodic boundary value problems for first order functional differential equations with impulse by applying the well known fixed point theorem of cone expansion and compression this paper investigates the existence of multiple positive solutions of periodic boundary value problems for first order functional differential equations with impulse meanwhile four examples are worked out to demonstrate the main results

new comparison results for impulsive integro differential equations and applications we prove some new maximum principles for ordinary integro differential equations this allows us to introduce a new definition of lower and upper solutions which leads to the development of the monotone iterative technique for a periodic boundary value problem related to a nonlinear first order impulsive integro differential equation

periodic boundary value problems for the first order impulsive functional differential equations this paper is concerned with the existence of extreme solutions of the periodic boundary value problems for a class of first order functional differential equations we introduce new concept of lower and upper solutions and present that the method of lower and upper solutions coupled with monotone iterative technique is still valid meanwhile we extend previous results

computational homogenization of elasticity on a staggered grid summary in this article we propose to discretize the problem of linear elastic homogenization by finite differences on a staggered grid and introduce fast and robust solvers our method shares some properties with the fft based homogenization technique of moulinec and suquet which has received widespread attention recently because of its robustness and computational speed these similarities include the use of fft and the resulting performing solvers the staggered grid discretization however offers three crucial improvements firstly solutions obtained by our method are completely devoid of the spurious oscillations characterizing solutions obtained by moulinec suquet s discretization secondly the iteration numbers of our solvers are bounded independently of the grid size and the contrast in particular our solvers converge for three dimensional porous structures which cannot be handled by moulinec suquet s method thirdly the finite difference discretization allows for algorithmic variants with lower memory consumption more precisely it is possible to reduce the memory consumption of the moulinec suquet algorithms by 50 we underline the effectiveness and the applicability of our methods by several numerical experiments of industrial scale copyright 2015 john wiley sons ltd

periodic boundary value problem for the first order impulsive functional differential equations this paper is concerned with the existence of extreme solutions of the periodic boundary value problem for a class of first order impulsive functional differential equations we introduce new concept of lower and upper solutions and present that the method of lower and upper solutions coupled with monotone iterative technique is still valid meanwhile we extend previous results