finite element formulations for transient dynamic analysis in structural systems with viscoelastic treatments containing fractional derivative models this paper presents finite element formulations for transient dynamic analysis in structural systems with damping treatments in which viscoelastic materials are characterized by means of fractional derivative models in contrast to other formulations such as that of padovan employing the principle of virtual work the proposed formulations begin from the local equation of linear momentum and make use of the weighted residual method providing a matrix equation of motion involving fractional operators the numerical approximations of these are developed through the grunwald letnikov definition which allows to formulate explicit and implicit numerical schemes the principal advantage of the proposed formulations is that the history of the displacements and external forces must be stored but not that of the stress which reduces computational time and storage needs numerical applications are presented for a cantilever beam where a viscoelastic treatment has been applied using damping material modelled by a five parameter fractional derivative model the results of the proposed formulation are compared among them and with those of padovan for different damping values and for different load cases the influence of the truncation of grunwald coefficients and of the integration time step is also investigated copyright 2006 john wiley sons ltd

analytical approximate solution of nonlinear dynamic system containing fractional derivative by modified decomposition method the fractional derivative has been occurring in many physical problems such as frequency dependent damping behavior of materials motion of a large thin plate in a newtonian fluid creep and relaxation functions for viscoelastic materials the pi ld m controller for the control of dynamical systems etc phenomena in electromagnetics acoustics viscoelasticity electrochemistry and material science are also described by differential equations of fractional order the solution of the differential equation containing fractional derivative is much involved instead of application of the existing methods an attempt has been made in the present analysis to obtain the solution of nonlinear dynamic system containing fractional derivative ji zeng wang et al coiflets based method in the solution of nonlinear dynamic system containing fractional derivative in the fourth international conference on nonlinear mechanics icnm iv shanghai august 2002 pp 1304 1308 by the relatively new adomian decomposition method the results obtained by this method are then graphically represented and then compared with the exact solution a good agreement of the results is observed

transient analysis of viscoelastic helical rods subject to time dependent loads abstract the transient analysis of viscoelastic helical rods subject to time dependent loads are examined in the laplace domain the governing equations for naturally twisted and curved spatial rods obtained using the timoshenko beam theory are rewritten for cylindrical helical rods the curvature of the rod axis effect of rotary inertia and shear and axial deformations are considered in the formulation the material of the rod is assumed to be homogeneous isotropic and linear viscoelastic the viscoelastic constitutive equations are written in the boltzmann volterra form ordinary differential equations in canonical form obtained in the laplace domain are solved numerically using the complementary functions method to calculate the dynamic stiffness matrix of the problem the solutions obtained are transformed to the real space using an appropriate numerical inverse laplace transform method numerical results for quasi static and dynamic response of viscoelastic models are presented in the form of graphics

the asymptotic behavior of the composition of two resolvents abstract the asymptotic behavior of the composition of two resolvents in a hilbert space is investigated connections are made between the solutions of associated monotone inclusion problems and their dual versions the applications provided include a study of an alternating minimization procedure and a new proof of von neumann s classical result on the method of alternating projections

power law and fractional calculus model of viscoelasticity mathematical relationships between the power law model and the fractional calculus model of viscoelastic behavior are developed it is demonstrated that the two models have mathematically similar relaxation spectra this similarity is seen to produce an asymptotic equivalence of the models at long relaxation times and correspondingly low frequencies of motion in the lower transition and rubbery regions the divergent behavior of the models at higher frequencies in the transition and glassy regions is presented porposals to take advantage of the similarities between power law and fractional calculus models are discussed

influence of transverse shear on stochastic instability of viscoelastic beam abstract the stochastic instability problem associated with an axially loaded timochenko beam made of viscoelastic material is formulated the beam is treated as voigt kelvin body compressed by time dependent deterministic and stochastic forces by using the direct liapunov method bounds of the almost sure instability of beams as a function of retardation time variance of the stochastic force mode number section shape factor and intensity of the deterministic component of axial loading are obtained calculations are performed for the gaussian process with a zero mean and variance 2 as well as for harmonic process with an amplitude a

iterative methods for large convex quadratic programs a survey in this paper we give a state of the art review of many iterative methods for solving large convex quadratic programs we attempt to classify several of the more basic methods in two categories within each of which a unified iterative scheme will be introduced and its convergence analyzed hybrid iterative methods such as the proximal point algorithm and a diagonalization scheme that make use of the more basic schemes will also be described the results of an extensive computer experimentation which is aimed at comparing the relative performance of the various methods will be reported and discussed finally several important topics which require future research will be highlighted

an approximate numerical method for the complex eigenproblem in systems characterised by a structural damping matrix this paper presents an efficient numerical method that approximates the complex eigenvalues and eigenvectors in structural systems with viscoelastic damping materials characterised by the complex structural damping matrix this new method begins from the solution of the undamped system and approximates the complex eigenpair by finite increments using the eigenvector derivatives and the rayleigh quotient it is implemented in three different approaches single step incremental and iterative schemes the single step technique is presented for systems with low and medium damping from numerical examples it can be verified that the errors committed by the approximate single step technique with respect to the exact solutions obtained by the iram method are less than 0 2 when the loss factor of the material damping is lower than 1 this is a considerable improvement on other approximate methods for higher damped systems an improvement to the previous approach is proposed by an incremental technique that keeps the accuracy without significantly increasing the computational time the complex eigenproblem for materials whose mechanical properties are dependent on frequency is solved by a fast iterative approach whose validity is proved using a four parameter fractional derivative model

cross sectional analysis of composite beams including large initial twist and curvature effects an asymptotically exact methodology based on geometrically nonlinear three dimensional elasticity is presented for cross sectional analysis of initially curved and twisted nonhomogeneous anisotropic beams the analysis is subject only to the restrictions that the strain is small relative to unity and that the maximum dimension of the cross section is small relative to the wavelength of the deformation and to the minimum radius of curvature and or twist the final one dimensional strain energy per unit length exhibits asymptotically correct second order dependence of the initial curvature and twist parameters cross sectional constants of the one dimensional theory are obtained via finite element discretization over the cross sectional plane numerical results obtained for both isotropic and composite beams are compared with published results from special purpose analyses for initially twisted straight beams as well as initially curved untwisted beams the agreement with previously published results is excellent

a modified forward backward splitting method for maximal monotone mappings we consider the forward backward splitting method for finding a zero of the sum of two maximal monotone mappings this method is known to converge when the inverse of the forward mapping is strongly monotone we propose a modification to this method in the spirit of the extragradient method for monotone variational inequalities under which the method converges assuming only the forward mapping is lipschitz continuous on some closed convex subset of its domain the modification entails an additional forward step and a projection step at each iteration applications of the modified method to decomposition in convex programming and monotone variational inequalities are discussed

quasi static and dynamic response of viscoelastic helical rods in this study the dynamic behaviour of cylindrical helical rods made of linear viscoelastic materials are investigated in the laplace domain the governing equations for naturally twisted and curved spatial rods obtained using the timoshenko beam theory are rewritten for cylindrical helical rods the curvature of the rod axis effect of rotary inertia and shear and axial deformations are considered in the formulation the material of the rod is assumed to be homogeneous isotropic and linear viscoelastic in the viscoelastic material case according to the correspondence principle the material constants are replaced with their complex counterparts in the laplace domain ordinary differential equations in scalar form obtained in the laplace domain are solved numerically using the complementary functions method to calculate the dynamic stiffness matrix of the problem in the solutions the kelvin model is employed the solutions obtained are transformed to the real space using the durbin s numerical inverse laplace transform method numerical results for quasi static and dynamic response of viscoelastic models are presented in the form of graphics

fixed points of generalized approximate message passing with arbitrary matrices the estimation of a random vector with independent components passed through a linear transform followed by a componentwise possibly nonlinear output map arises in a range of applications approximate message passing amp methods based on gaussian approximations of loopy belief propagation have recently attracted considerable attention for such problems for large random transforms these methods exhibit fast convergence and admit precise analytic characterizations with testable conditions for optimality even for certain non convex problem instances however the behavior of amp under general transforms is not fully understood in this paper we consider the generalized amp gamp algorithm and relate the method to more common optimization techniques this analysis enables a precise characterization of the gamp algorithm fixed points that applies to arbitrary transforms in particular we show that the fixed points of the so called max sum gamp algorithm for map estimation are critical points of a constrained maximization of the posterior density the fixed points of the sum product gamp algorithm for estimation of the posterior marginals can be interpreted as critical points of a certain free energy

fractional calculus a different approach to the analysis of viscoelastically damped structures fractional calculus is used to construct stress strain relationships for viscoelastic materials these relationships are used in the finite element analysis of viscoelastically damped structures and closed form solutions to the equations of motion are found the attractive feature of this approach is that very few empirical parameters are required to model the viscoelastic material and calculate the response of the structure for general loading conditions

convergence rates in forward backward splitting forward backward splitting methods provide a range of approaches to solving large scale optimization problems and variational inequalities in which structures conducive to decomposition can be utilized apart from special cases where the forward step is absent and a version of the proximal point algorithm comes out efforts at evaluating the convergence potential of such methods have so far relied on lipschitz properties and strong monotonicity or inverse strong monotonicity of the mapping involved in the forward step the perspective mainly being that of projection algorithms here convergence is analyzed by a technique that allows properties of the mapping in the backward step to be brought in as well for the first time in such a general setting global and local contraction rates are derived moreover they are derived in a form which makes it possible to determine the optimal step size relative to certain constants associated with the given problem insights are thereby gained into the effects of shifting strong monotonicity between the forward and backward mappings when a splitting is selected

total variation projection with first order schemes this article proposes a new algorithm to compute the projection on the set of images whose total variation is bounded by a constant the projection is computed through a dual formulation that is solved by first order non smooth optimization methods this yields an iterative algorithm that applies iterative soft thresholding to the dual vector field and for which we establish convergence rate on the primal iterates this projection algorithm can then be used as a building block in a variety of applications such as solving inverse problems under a total variation constraint or for texture synthesis numerical results are reported to illustrate the usefulness and potential applicability of our tv projection algorithm on various examples including denoising texture synthesis inpainting deconvolution and tomography problems we also show that our projection algorithm competes favorably with state of the art tv projection methods in terms of convergence speed

asynchronous block iterative primal dual decomposition methods for monotone inclusions we propose new primal dual decomposition algorithms for solving systems of inclusions involving sums of linearly composed maximally monotone operators the principal innovation in these algorithms is that they are block iterative in the sense that at each iteration only a subset of the monotone operators needs to be processed as opposed to all operators as in established methods flexible strategies are used to select the blocks of operators activated at each iteration in addition we allow lags in operator processing permitting asynchronous implementation the decomposition phase of each iteration of our methods is to generate points in the graphs of the selected monotone operators in order to construct a half space containing the kuhn tucker set associated with the system the coordination phase of each iteration involves a projection onto this half space we present two related methods the first method provides weakly convergent primal and dual sequences under general conditions while the second is a variant in which strong convergence is guaranteed without additional assumptions neither algorithm requires prior knowledge of bounds on the linear operators involved or the inversion of linear operators our algorithmic framework unifies and significantly extends the approaches taken in earlier work on primal dual projective splitting methods

perspective functions proximal calculus and applications in high dimensional statistics abstract perspective functions arise explicitly or implicitly in various forms in applied mathematics and in statistical data analysis to date no systematic strategy is available to solve the associated typically nonsmooth optimization problems in this paper we fill this gap by showing that proximal methods provide an efficient framework to model and solve problems involving perspective functions we study the construction of the proximity operator of a perspective function under general assumptions and present important instances in which the proximity operator can be computed explicitly or via straightforward numerical operations these results constitute central building blocks in the design of proximal optimization algorithms we showcase the versatility of the framework by designing novel proximal algorithms for state of the art regression and variable selection schemes in high dimensional statistics

parameter selection for total variation based image restoration using discrepancy principle there are two key issues in successfully solving the image restoration problem 1 estimation of the regularization parameter that balances data fidelity with the regularity of the solution and 2 development of efficient numerical techniques for computing the solution in this paper we derive a fast algorithm that simultaneously estimates the regularization parameter and restores the image the new approach is based on the total variation tv regularized strategy and morozov s discrepancy principle the tv norm is represented by the dual formulation that changes the minimization problem into a minimax problem a proximal point method is developed to compute the saddle point of the minimax problem by adjusting the regularization parameter adaptively in each iteration the solution is guaranteed to satisfy the discrepancy principle we will give the convergence proof of our algorithm and numerically show that it is better than some state of the art methods in terms of both speed and accuracy

convergence rate analysis of primal dual splitting schemes primal dual splitting schemes are a class of powerful algorithms that solve complicated monotone inclusions and convex optimization problems that are built from many simpler pieces they decompose problems that are built from sums linear compositions and infimal convolutions of simple functions so that each simple term is processed individually via proximal mappings gradient mappings and multiplications by the linear maps this leads to easily implementable and highly parallelizable or distributed algorithms which often obtain nearly state of the art performance in this paper we analyze a monotone inclusion problem that captures a large class of primal dual splittings as a special case we introduce a unifying scheme and use some abstract analysis of the algorithm to prove convergence rates of the proximal point algorithm forward backward splitting peaceman rachford splitting and forward backward forward splitting applied to the model problem our ergodic convergence rates are deduced under var

complex modal analysis of rods with viscous damping devices abstract the complex modal analysis of rods equipped with an arbitrary number of viscous damping devices is addressed the following types of damping devices are considered external grounded spring damper attached mass spring damper and internal spring damper within a standard 1d formulation of the vibration problem the theory of generalized functions is used to model axial stress and displacement discontinuities at the locations of the damping devices by using the separate variable approach a simple solution procedure of the motion equation leads to exact closed form expressions of the characteristic equation and eigenfunctions which inherently fulfill the required matching conditions at the locations of the damping devices based on the characteristic equation a closed form sensitivity analysis of the eigensolution is implemented the displacement eigenfunctions exhibit orthogonality conditions they can be used with the complex mode superposition principle to tackle forced vibration problems and in conjunction with the stress eigenfunctions to build the exact dynamic stiffness matrix of the rod for complex modal analysis of truss structures numerical results are discussed for a variety of parameters

generalized functions on infinite dimensional spaces and its application to white noise calculus in this paper a theory of generalized functions is established on an arbitrary abstract wiener space it is shown that it provides a nice framework for reformulating white noise calculus initiated by t hida unlike hida s approach the generalized brownian functionals are defined and studied through the generalized function test function pairing instead of employing the u functionals besides the fourier transform is extended to infinite dimensions and a new definition of the composition of a tempered distribution with the brownian motion is given at the end of the paper the ito formula for generalized brownian functionals and the kubo takenaka s theorem for stochastic integration are verified by our approach

dynamic stiffness formulation free vibration and wave motion of helical springs a coil spring can only be treated as a simple massless force element at low frequencies the effects of internal resonances leading to significant dynamic stiffening for an automotive suspension spring this occurs at frequencies as low as about 40 hz this paper presents an efficient method for calculating the dynamic stiffness of a helical coil spring the partial differential equations of motion are used to derive the relation between wavenumber and frequency along with the associated wave shapes by expressing the response in terms of these waves the dynamic stiffness matrix is assembled natural frequencies are obtained from the reduced stiffness matrix allowing for different boundary conditions making use of the wittrick williams algorithm the results of the dynamic stiffness method are compared with those of the transfer matrix method and the finite element method the nature of the wave propagation is also investigated although at low frequencies four wave types propagate above a particular frequency only two propagating waves remain these are composite waves which are excited by both axial and transverse motion for lower values of helix angle an intermediate frequency range exists where six propagating waves can occur

dynamic analysis of linear viscoelastic cylindrical and conical helicoidal rods using the mixed fem abstract the objective of this study is to investigate the influence of the rotary inertia on dynamic behavior of linear viscoelastic cylindrical and conical helixes by means of the laplace transform mixed finite element formulation and solution the element matrix is based on the timoshenko beam theory the influence of rotary inertias is considered in the dynamic analysis which is original in the literature rectangular sine and step type of impulsive loads are applied on helices having rectangular cross sections with various aspect ratios the kelvin and standard models are used for defining the linear viscoelastic material behavior and by means of the correspondence principle the elastic viscoelastic analogy the material parameters are replaced with their complex counterparts in the laplace domain the analysis is carried out in the laplace domain and the results are transformed back to time space numerically by modified durbin s algorithm first the solution algorithm is verified using the existing open sources in the literature and afterwards some benchmark examples such as conical viscoelastic rods are handled

a class of dantzig wolfe type decomposition methods for variational inequality problems we consider a class of decomposition methods for variational inequalities which is related to the classical dantzig wolfe decomposition of linear programs our approach is rather general in that it can be used with certain types of set valued or nonmonotone operators as well as with various kinds of approximations in the subproblems of the functions and derivatives in the single valued case also subproblems may be solved approximately convergence is established under reasonable assumptions we also report numerical experiments for computing variational equilibria of the game theoretic models of electricity markets our numerical results illustrate that the decomposition approach allows to solve large scale problem instances otherwise intractable if the widely used path solver is applied directly without decomposition

methods of interconversion between linear viscoelastic material functions part ii an approximate analytical method abstract a new very simple approximate interconversion method is proposed and verified by examples this technique employing the slope of the source function on logarithmic scales is found to substantially enhance the accuracy compared to existing approximate methods the new method is based on the characteristic mathematical properties of the narrow band weight functions involved in the interrelationships between broad band material functions with the material functions represented locally by a power law they are interrelated in terms of adjustment factors expressed through the local log log slope of the given source function a number of existing approximate interconversion methods are also tested and compared with the new method in part i park and schapery 1998 an efficient numerical interconversion method based on a prony exponential series representation of both the source and target functions was presented such a series representation is not needed here the new method when applied to the prediction of broad band time dependent functions from laplace or fourier transforms is an approximate method of transform inversion that is applicable to functions which are not necessarily viscoelastic material functions

convergence rates with inexact non expansive operators in this paper we present a convergence rate analysis for the inexact krasnosel ski mann iteration built from non expansive operators the presented results include two main parts we first establish the global pointwise and ergodic iteration complexity bounds then under a metric sub regularity assumption we establish a local linear convergence for the distance of the iterates to the set of fixed points the obtained results can be applied to analyze the convergence rate of various monotone operator splitting methods in the literature including the forward backward splitting the generalized forward backward the douglas rachford splitting alternating direction method of multipliers and primal dual splitting methods for these methods we also develop easily verifiable termination criteria for finding an approximate solution which can be seen as a generalization of the termination criterion for the classical gradient descent method we finally develop a parallel analysis for the non stationary krasnosel ski mann iteration

on timoshenko like modeling of initially curved and twisted composite beams abstract a generalized finite element based cross sectional analysis for nonhomogenous initially curved and twisted anistropic beams is formulated from geometrically nonlinear three dimensional 3 d elasticity the 3 d strain field is formulated based on the concept of decomposition of the rotation tensor and is given in terms of one dimensional 1 d generalized strains and a 3 d warping displacement that is obtained from the formulation not assumed the warping is found in terms of the 1 d strains via the variational asymptotic method vam in this paper a timoshenko like model is presupposed for a beam with cross sectional characteristic length h wavelength of deformation given by l and the magnitude of the radius of initial curvature and or twist is taken to be of the order r first a solution for the asymptotically correct refinement of classical anisotropic beam theory for initially curved and twisted beams through o h2 r2 is obtained next the o h2 l2 correction is computed it is known that timoshenko like theory is not capable of capturing all the o h2 l2 corrections for generally anisotropic beams however if all the o h2 l2 terms are known then the corresponding timoshenko like theory is uniquely defined numerical results are presented to illustrate the trends of the various classical extension twist bending twist and extension bending and nonclassical couplings extension shear bending shear and shear torsion as the initial twist and curvatures are varied

systems of structured monotone inclusions duality algorithms and applications a general primal dual splitting algorithm for solving systems of structured coupled monotone inclusions in hilbert spaces is introduced and its asymptotic behavior is analyzed each inclusion in the primal system features compositions with linear operators parallel sums and lipschitzian operators all the operators involved in this structured model are used separately in the proposed algorithm most steps of which can be executed in parallel this provides a flexible solution method applicable to a variety of problems beyond the reach of the state of the art several applications are discussed to illustrate this point

comparison of numerical methods for identification of viscoelastic line spectra from static test data viscoelastic line spectra are identified from creep or relaxation data of static experiments with different numerical methods which may or may not depend on additional informations to be provided by the user about the unknown parameters if the least square method is applied a non linear optimization problem with non negative constraints on the parameters has to be solved its solution can be achieved directly by using a gradient based optimization algorithm like the projected newton method of bertsekas however appropriate starting values for the unknown parameters must be chosen the problem can be alleviated by dividing the identification task into three successive steps based on the tschebyscheff approximation and the quadratic optimization method by wolfe alternatively the identification task can be reduced to a quadratic optimization problem if the user provides additional informations about the distribution of the respondance times of the spectra the windowing method of emri and tschoegl is based on this assumption if the line spectrum is assumed to have equally distributed spectrum lines on the logarithmic axis the identification problem can also be solved by standard regularization techniques like the truncated singular value decomposition or the tikhonov regularization the choice of qualified respondance times as additional information requires some experience with the identification task at hand its results may be improved after several reruns of the algorithms various applications of the methods to test and experimental data are given and a comparison of their performance is discussed copyright 2005 john wiley sons ltd

power law damping parameter identification abstract the parameter estimation of a nonlinear power damping system is studied the parameter identification method used here assumes a priori the equation of motion describing the system dynamics the method which is based on the measured data acceleration was applied to the free and forced vibrations the identification procedure was found to be robust on the guessed value of parameters at the numerical experimentation the parameter values were estimated with a good accuracy for both modes of system operation free and forced if only the measured time history was sampled at a high enough rate for the noise level contained within it was shown that the steady state of the harmonically excited system is not the best region for the parameter identification with this method during the experimentation the method was applied to the free vibrations in different media air and water the results obtained by the parameter identification method were compared to the ones obtained by separate tests and good agreement was found the identification procedure was found to work fine for all models under consideration and the models responses correspond well to the measured acceleration time histories

steady state response of axially moving viscoelastic beams with pulsating speed comparison of two nonlinear models abstract principal parametric resonance in transverse vibration is investigated for viscoelastic beams moving with axial pulsating speed a nonlinear partial differential equation governing the transverse vibration is derived from the dynamical constitutive and geometrical relations under certain assumption the partial differential reduces to an integro partial differential equation for transverse vibration of axially accelerating viscoelastic nonlinear beams the method of multiple scales is applied to two equations to calculate the steady state response closed form solutions for the amplitude of the vibration are derived from the solvability condition of eliminating secular terms the stability of straight equilibrium and nontrivial steady state response are analyzed by use of the lyapunov linearized stability theory numerical examples are presented to highlight the effects of speed pulsation viscoelascity and nonlinearity and to compare results obtained from two equations

a generalization of the riesz representation theorem to infinite dimensions lethbe a real separable hilbert space and lete hbe a nuclear space with the chain of hilbert spaces ep p 1 2 3 such thate p 1 ep lete ande pdenote the dual spaces ofeandep respectively let cpbe the collection of real valued functionsfdefined one psuch thatfis uniformly continuous on bounded subsets ofe pand such that f p supx e p f x exp 12 x 2 p is finite set c p 1 cp thenc is a complete countably normed space equipped with the family p p 1 2 3 of norms in this paper it is shown that to every bounded linear functionalfin c there corresponds a signed measure fsuch thatf e x f dx for c it is also shown that there exists somepsuch that the measurable support of is contained ine pand e p exp 12 x 2 p f dx this result extends the riesz representation theorem to infinite dimensions in the course of the proof an infinite dimensional analogue of the weierstrass approximation theorem is also established one

a family of single step houbolt time integration algorithms for structural dynamics a new family of implicit single step time integration methods is presented for solving structural dynamics problems the proposed method is unconditionally stable second order accurate and asymptotically annihilating it is spectrally equivalent to houbolt s method but is cast in single step form rather than multi step form thus the new algorithm computationally is more convenient an explicit predictor correcter algorithm is presented based upon the new implicit scheme the explicit algorithm is spectraily equivalent to the central difference method the two new algorithms are merged into an implicit explicit method resulting in an improved algorithm for solving structural dynamics problems composed of soft and stiff domains numerical results are presented demonstrating the improved performance of the new implicit explicit method compared to previously developed implicit explicit schemes for structural dynamics

a new class of alternating proximal minimization algorithms with costs to move given two objective functions f mathcal x mapsto r cup infty and g mathcal y mapsto r cup infty on abstract spaces mathcal x and mathcal y and a coupling function c mathcal x times mathcal y mapsto r we introduce and study alternative minimization algorithms of the following type x 0 y 0 in mathcal x times mathcal y mbox given x n y n rightarrow x n 1 y n rightarrow x n 1 y n 1 mbox as follows left begin array l x n 1 in mbox argmin f xi beta n c xi y n alpha n h x n xi xi in mathcal x y n 1 in mbox argmin g eta mu n c x n 1 eta nu n k y n eta eta in mathcal y end array right their most original feature is the introduction of the terms h mathcal x times mathcal x mapsto r and k mathcal y times mathcal y mapsto r which are costs to change or to move distance like functions relative entropies accounting for various inertial friction or anchoring effects these algorithms are studied in a general abstract framework the introduction of the costs to change h and k leads to proximal minimizations with corresponding dissipative effects as a result the algorithms enjoy nice convergent properties coefficients alpha n beta n mu n nu n are nonnegative parameters when taking alpha n nu n 0 and quadratic costs on a hilbert space one recovers the classical alternating minimization algorithm which itself is a natural extension of the alternating projection algorithm of von neumann a number of new significant results hold in general metric spaces we pay particular attention to the following cases 1 mathcal x d mathcal x and mathcal y d mathcal y are complete metric spaces and h geq d mathcal x k geq d mathcal y high local costs to move the algorithms then provide sequences that converge to nash equilibria 2 mathcal x mathcal y mathcal h is a hilbert space the costs to change are quadratic low local costs to move and the functions f g mathcal h mapsto r cup infty are closed convex proper then some of the classical convergence theorems for alternating convex minimization algorithms including those of acker and prestel are properly extended with original proofs

analytic version of test functionals fourier transform and a characterization of measures in white noise calculus it is shown that the space j of test white noise functionals has an analytic version a which is an algebra as well as a topological linear space topologized by the projective limit of a sequence ap p n of banach spaces with respective norm given by ap supz cj p z exp 2 1 z p2 where sj p denotes the complexification of j p furthermore it is shown that the a topology and the j topology are equivalent in the course of the proof it is also shown that the space jp is isometrically isomorphic to the bargmann segal analytic functions on bj p under s transform employing this new version we are able to define the fourier transform of a generalized white noise functional as the adjoint of fourier wiener transform t1 i with parameter 1 i and moreover we show that every measure in j always satisfies a certain growth condition

applications of splitting algorithm to decomposition in convex programming and variational inequalities recently han and lou proposed a highly parallelizable decomposition algorithm for minimizing a strongly convex cost over the intersection of closed convex sets it is shown that their algorithm is in fact a special case of a splitting algorithm analyzed by gabay for finding a zero of the sum of two maximal monotone operators gabay s convergence analysis for the splitting algorithm is sharpened and new applications of this algorithm to variational inequalities convex programming and the solution of linear complementarily problems are proposed for convex programs with a certain separable structure a multiplier method that is closely related to the alternating direction method of multipliers of gabay mercier and of glowinski marrocco but which uses both ordinary and augmented lagrangians is obtained

stability and performance verification of optimization based controllers this paper presents a method to verify closed loop properties of optimization based controllers for deterministic and stochastic constrained polynomial discrete time dynamical systems the closed loop properties amenable to the proposed technique include global and local stability performance with respect to a given cost function both in a deterministic and stochastic setting and the mathcal l 2 gain the method applies to a wide range of practical control problems for instance a dynamical controller e g a pid plus input saturation model predictive control with state estimation inexact model and soft constraints or a general optimization based controller where the underlying problem is solved with a fixed number of iterations of a first order method are all amenable to the proposed approach the approach is based on the observation that the control input generated by an optimization based controller satisfies the associated karush kuhn tucker kkt conditions which provided all data is polynomial are a system of polynomial equalities and inequalities the closed loop properties can then be analyzed using sum of squares sos programming

parallel scalable adjoint based adaptive solution of variable viscosity stokes flow problems we present a framework for parallel adaptive solution of variable viscosity stokes flow problems we focus on data structures algorithms and solvers that can scale to thousands of processor cores the problem is discretized by octree based finite elements with explicit enforcement of continuity constraints at hanging nodes the parallel octree structure allows for fast neighbor finding and facilitates local coarsening and refinement of the mesh mesh adaptivity is driven by a posteriori error indicators including adjoint based goal oriented techniques dynamic load balancing is achieved by dynamically partitioning a morton ordered space filling curve the stokes system is solved iteratively using the minimum residual method minres preconditioned by a schur complement based approximate inverse that employs algebraic multigrid v cycle approximations of the inverses of the poisson like operators we demonstrate the effectiveness of this framework on several testbed problems with up to 6 orders of magnitude variation in viscosity and up to 1 7 billion unknowns on up to 4096 cores the results indicate that the overhead due to all amr components is less than 3 of the overall solve time the solver exhibits very good algorithmic and parallel implementation scalability the solver is insensitive to the magnitude of viscosity variation and adjoint based adaptivity results in over two orders of magnitude reduction in number of unknowns and up to an order of magnitude improvement in runtime relative to a uniform mesh for the same level of error

eliminating the modal truncation problem encountered in frequency responses of viscoelastic systems increasing the number of degrees of freedom used in finite element analysis for mechanical and structural systems with viscoelastic damping the need to consider the modal truncation problem of viscoelastic systems is more than ever before the higher modes may be unnecessary to obtain in dynamic analysis for engineering applications for viscoelastic systems the modal truncation problem may be more frequently encountered since the nonviscous modes are difficult or even impossible to be found accurately even if a small scaled problem is considered for some eigensolution methods this study aims at eliminating the influence of the higher modes on the frequency responses of viscoelastically damped systems a method is presented by making the equilibrium equations of motion into a subspace equation spanned in terms of the columns of a projection basis obtained by considering the use of the contribution of the lower modes and the first two terms of the neumann expansion of the contribution of the unavailable modes finally three example studies are provided to illustrate the effectiveness of the derived results it is shown that the proposed method can reduce the modal truncation error significantly

convergence rate analysis for the alternating direction method of multipliers with a substitution procedure for separable convex programming recently in he et al he bs tao m yuan xm 2012 alternating direction method with gaussian back substitution for separable convex programming siam j optim 22 2 313 340 we have showed the first possibility of combining the douglas rachford alternating direction method of multipliers admm with a gaussian back substitution procedure for solving a convex minimization model with a general separable structure this paper is a further study on this theme we first derive a general algorithmic framework to combine admm with either a forward or backward substitution procedure then we show that convergence of this framework can be easily proved from the contraction perspective and its local linear convergence rate is provable if certain error bound condition is assumed without such an error bound assumption we can estimate its worst case convergence rate measured by the iteration complexity

warped proximal iterations for monotone inclusions abstract resolvents of set valued operators play a central role in various branches of mathematics and in particular in the design and the analysis of splitting algorithms for solving monotone inclusions we propose a generalization of this notion called warped resolvent which is constructed with the help of an auxiliary operator the properties of warped resolvents are investigated and connections are made with existing notions abstract weak and strong convergence principles based on warped resolvents are proposed and shown to not only provide a synthetic view of splitting algorithms but to also constitute an effective device to produce new solution methods for challenging inclusion problems

linearized proximal alternating minimization algorithm for motion deblurring by nonlocal regularization abstract non blind motion deblurring problems are highly ill posed and so it is quite difficult to find the original sharp and clean image to handle ill posedness of the motion deblurring problem we use nonlocal total variation abbreviated as tv regularization approaches nonlocal tv can restore periodic textures and local geometric information better than local tv but since nonlocal tv requires weighted difference between pixels in the whole image it demands much more computational resources than local tv by using the linearization of the fidelity term and the proximal function our proposed algorithm does not require any inversion of blurring operator and nonlocal operator therefore the proposed algorithm is very efficient for motion deblurring problems we compare the numerical performance of our proposed algorithm with that of several state of the art algorithms for deblurring problems our numerical results show that the proposed method is faster and more robust than state of the art algorithms on motion deblurring problems

solving coupled composite monotone inclusions by successive fejer approximations of their kuhn tucker set we propose a new class of primal dual fejer monotone algorithms for solving systems of composite monotone inclusions our construction is inspired by a framework used by eckstein and svaiter for the basic problem of finding a zero of the sum of two monotone operators at each iteration points in the graph of the monotone operators present in the model are used to construct a half space containing the kuhn tucker set associated with the system the primal dual update is then obtained via a relaxed projection of the current iterate onto this half space an important feature that distinguishes the resulting splitting algorithms from existing ones is that they do not require prior knowledge of bounds on the linear operators involved or the inversion of linear operators

a combined approach of the laplace transform and pade approximation solving viscoelasticity problems in this paper the laplace transform method is combined with pade approximations to solve linear viscoelastic problems this approach allows to avoid the usual difficulties of original function determination an algorithm is given to find solution with arbitrary precision as an example the solution for problem of viscoelastic orthotropic half plane stress state under concentrated normal force is given

sharp inequalities and regularity of heat semigroup on infinite dimensional spaces abstract this paper discusses the regularity of the heat semigroup p t generated from the abstract wiener measure p t on an abstract wiener space h b it is shown that if f l x p t x dy for some 1 then p t f x is infinitely h differentiable and d n p t f x is a symmetric n linear hilbert schmidt operator in l n h a compact formula of d n p t f x and the estimation of d n p t f x hs are also given in the course of proving the above results we obtain some sharp integral inequalities

on positive generalized functionals abstract a class of spaces of test and generalized functionals over gaussian spaces is constructed and two theorems of bochner s type are proved

on the convergence of alternating minimization for convex programming with applications to iteratively reweighted least squares and decomposition schemes this paper is concerned with the alternating minimization am method for solving convex minimization problems where the decision variables vector is split into two blocks the objective function is a sum of a differentiable convex function and a separable possibly nonsmooth extended real valued convex function and consequently constraints can be incorporated we analyze the convergence rate of the method and establish a nonasymptotic sublinear rate of convergence where the multiplicative constant depends on the minimal block lipschitz constant we then analyze the iteratively reweighted least squares irls method for solving convex problems involving sums of norms based on the results derived for the am method we establish a nonasymptotic sublinear rate of convergence of the irls method in addition we show an asymptotic rate of convergence whose efficiency estimate does not depend on the data of the problem finally we study the convergence properties of a decomposition based approach designed t

alternating proximal algorithms for linearly constrained variational inequalities application to domain decomposition for pde s abstract let x y z be real hilbert spaces let f x r g y r be closed convex functions and let a x z b y z be linear continuous operators let us consider the constrained minimization problem p min f x g y a x b y given a sequence n which tends toward 0 as n we study the following alternating proximal algorithm a x n 1 argmin n 1 f 1 2 a b y n z 2 2 x n x 2 x y n 1 argmin n 1 g 1 2 a x n 1 b z 2 2 y n y 2 y where and are positive parameters it is shown that if the sequence n tends moderately slowly toward 0 then the iterates of a weakly converge toward a solution of p the study is extended to the setting of maximal monotone operators for which a general ergodic convergence result is obtained applications are given in the area of domain decomposition for pde s

full waveform inversion in three dimensional pml truncated elastic media abstract we are concerned with high fidelity subsurface imaging of the soil which commonly arises in geotechnical site characterization and geophysical explorations specifically we attempt to image the spatial distribution of the lame parameters in semi infinite three dimensional arbitrarily heterogeneous formations using surficial measurements of the soil s response to probing elastic waves we use the complete waveform response of the medium to drive the inverse problem by using a partial differential equation pde constrained optimization approach directly in the time domain to minimize the misfit between the observed response of the medium at select measurement locations and a computed response corresponding to a trial distribution of the lame parameters we discuss strategies that lend algorithmic robustness to our proposed inversion scheme to limit the computational domain to the size of interest we employ perfectly matched layers pmls in order to resolve the forward problem we use a recently developed hybrid finite element approach where a displacement stress formulation for the pml is coupled to a standard displacement only formulation for the interior domain thus leading to a computationally cost efficient scheme time integration is accomplished by using an explicit runge kutta scheme which is well suited for large scale problems on parallel computers we verify the accuracy of the material gradients obtained via our proposed scheme and report numerical results demonstrating successful reconstruction of the two lame parameters for both smooth and sharp profiles

measurement of viscoelastic properties of homogeneous soft solid using transient elastography an inverse problem approach two main questions are at the center of this paper the first one concerns the choice of a rheological model in the frequency range of transient elastography sonoelasticity or nmr elastography for soft solids 20 1000 hz transient elastography experiments based on plane shear waves that propagate in an agar gelatin phantom or in bovine muscles enable one to quantify their viscoelastic properties the comparison of these experimental results to the prediction of the two simplest rheological models indicate clearly that voigt s model is the better the second question studied in the paper deals with the feasibility of quantitative viscosity mapping using inverse problem algorithm in the ideal situation where plane shear waves propagate in a sample a simple inverse problem based on the helmholtz equation correctly retrieves both elasticity and viscosity in a more realistic situation with nonplane shear waves this simple approach fails nevertheless it is shown that quantitative viscosity mapping is s

spectral element technique for efficient parameter identification of layered media part iii viscoelastic aspects this article addresses the issues of wave propagation in elastic viscoelastic layered systems and viscous parameter identification from non destructive dynamic tests a methodology that combines the spectral element technique for the simulation of wave propagation with the differential operator technique for stress strain relationship in viscoelastic materials is adopted the compatibility between the two techniques stems from the fact that both can be treated in the frequency domain which enables naturally the adoption of fourier superposition the mathematical formulation of spectral elements for burger s viscoelastic material model is highlighted also an inverse procedure for the identification of the material s young s moduli and complex moduli for layer systems is described it is shown that the proposed methodology enables the substitution of an expensive laboratory testing procedure for the determination of material complex moduli with non destructive dynamic testing 2002 elsevier science ltd all rights reserved

a monotone skew splitting model for composite monotone inclusions in duality the principle underlying this paper is the basic observation that the problem of simultaneously solving a large class of composite monotone inclusions and their duals can be reduced to that of finding a zero of the sum of a maximally monotone operator and a linear skew adjoint operator an algorithmic framework is developed for solving this generic problem in a hilbert space setting new primal dual splitting algorithms are derived from this framework for inclusions involving composite monotone operators and convergence results are established these algorithms draw their simplicity and efficacy from the fact that they operate in a fully decomposed fashion in the sense that the monotone operators and the linear transformations involved are activated separately at each iteration comparisons with existing methods are made and applications to composite variational problems are demonstrated

operator splittings bregman methods and frame shrinkage in image processing we examine the underlying structure of popular algorithms for variational methods used in image processing we focus here on operator splittings and bregman methods based on a unified approach via fixed point iterations and averaged operators in particular the recently proposed alternating split bregman method can be interpreted from different points of view as a bregman as an augmented lagrangian and as a douglas rachford splitting algorithm which is a classical operator splitting method we also study similarities between this method and the forward backward splitting method when applied to two frequently used models for image denoising which employ a besov norm and a total variation regularization term respectively in the first setting we show that for a discretization based on parseval frames the gradient descent reprojection and the alternating split bregman algorithm are equivalent and turn out to be a frame shrinkage method for the total variation regularizer we also present a numerical comparison with multistep methods

numerical inversion of the laplace transform from the real axis a numerical method for inversion of the laplace transform f p given for p 0 only is proposed recommendations for the choice of the abscissa of convergence and parameters of numerical integration are given the results of the numerical tests are discussed

the hybrid laplace transform finite element method applied to the quasi static and dynamic analysis of viscoelastic timoshenko beams the quasi static and dynamic responses of a linear viscoelastic beam are solved numerically by using the hybrid laplace transform finite element method in the analysis the timoshenko beam theory which includes the transverse shear and rotatory inertia effect and conventional beam theory are used to solve this problem the temperature field is assumed to be constant and homogeneous and that the relaxation modulus has the form of the prony series in the hybrid method the laplace transform with respect to time is applied to the coupled equations and the finite element model is developed by applying hamilton s variational principle without any integral transformation the numerical results of quasi static and dynamic responses for the models of maxwell fluid and three parameter solid types are presented and discussed

hard constrained inconsistent signal feasibility problems we consider the problem of synthesizing feasible signals in a hilbert space in the presence of inconsistent convex constraints some of which must imperatively be satisfied this problem is formalized as that of minimizing a convex objective measuring the amount of violation of the soft constraints over the intersection of the sets associated with the hard ones the resulting convex optimization problem is analyzed and numerical solution schemes are presented along with convergence results the proposed formalism and its algorithmic framework unify and extend existing approaches to inconsistent signal feasibility problems an application to signal synthesis is demonstrated

a parallel splitting method for coupled monotone inclusions a parallel splitting method is proposed for solving systems of coupled monotone inclusions in hilbert spaces and its convergence is established under the assumption that solutions exist unlike existing alternating algorithms which are limited to two variables and linear coupling our parallel method can handle an arbitrary number of variables as well as nonlinear coupling schemes the breadth and flexibility of the proposed framework is illustrated through applications in the areas of evolution inclusions variational problems best approximation and network flows

dynamic stability in parametric resonance of axially accelerating viscoelastic timoshenko beams abstract this paper investigates dynamic stability of an axially accelerating viscoelastic beam undergoing parametric resonance the effects of shear deformation and rotary inertia are taken into account by the timoshenko thick beam theory the beam material obeys the kelvin model in which the material time derivative is used the axial speed is characterized as a simple harmonic variation about the constant mean speed the governing partial differential equations are derived from newton s second law euler s angular momentum principle and the constitutive relation the method of multiple scales is applied to the equations to establish the solvability conditions in summation and principal parametric resonances the sufficient and necessary condition of the stability is derived from the routh hurvitz criterion some numerical examples are presented to demonstrate the effects of related parameters on the stability boundaries

the green s matrix and the boundary integral equations for analysis of time harmonic dynamics of elastic helical springs helical springs serve as vibration isolators in virtually any suspension system various exact and approximate methods may be employed to determine the eigenfrequencies of vibrations of these structural elements and their dynamic transfer functions the method of boundary integral equations is a meaningful alternative to obtain exact solutions of problems of the time harmonic dynamics of elastic springs in the framework of bernoulli euler beam theory in this paper the derivations of the green s matrix of the somigliana s identities and of the boundary integral equations are presented the vibrational power transmission in an infinitely long spring is analyzed by means of the green s matrix the eigenfrequencies and the dynamic transfer functions are found by solving the boundary integral equations in the course of analysis the essential features and advantages of the method of boundary integral equations are highlighted the reported analytical results may be used to study the time harmonic motion i

an inverse model and mathematical solution for inferring viscoelastic properties and dynamic deformations of heterogeneous structures abstract we proposed an adjoint based inverse method and mathematical solutions using lagrange multiplier theorem for inferring dynamic viscoelastic properties of heterogeneous structures with displacement observations to improve computation reliability and efficiency existing methods such as the one using finite difference approximated gradient may not be efficient and accurate enough for considering complex situations of the coupled effects of dynamic loading material deformation memory and structural heterogeneity the proposed method derives both gradient and hessian mathematically to satisfy the first order necessary and second order sufficient optimal conditions which has great advantages compared to other approaches we also proposed robust numerical algorithms for accurate and fast computations including a regularization to control reasonable parameter ranges a newton s method with hessian function to determine search direction for fast convenience and a modified armijo rule to find a stable step length we developed a galerkin time domain finite element method for numerical solutions of resulting partial differential equations and validated the model for a layered structure under dynamic loading tests results indicate that the proposed method has greatly improved computation accuracy and speed as compared to existing approaches it may be applied to a broad range of heterogeneous materials and structures at different length and time scales

dynamic analysis of frames with viscoelastic dampers modelled by rheological models with fractionalderivatives frame structures with viscoelastic dampers mounted on them are considered in this paper viscoelastic ve dampers are modelled using two three parameter fractional rheological models the structures are treated as elastic linear systems the equation of motion of the whole system structure with dampers is written in terms of state space variables the resulting matrix equation of motion is the fractional differential equation the proposed state space formulation is new and does not require matrices with huge dimensions the paper is devoted to determine the dynamic properties of the considered structures the nonlinear eigenvalue problem is formulated from which the dynamic parameters of the system can be determined the continuation method is used to solve the nonlinear eigenvalue problem moreover results of typical calculations are presented

linear dynamics of elastic helical springs asymptotic analysis of wave propagation helical springs serve as vibration isolators in virtually any suspension system a variety of theories to describe the dynamic behaviour of these structural elements which involves interaction of flexural torsion and longitudinal waves can be found in the literature alongside this various approximate methods are employed to determine the eigenfrequencies of vibrations of springs in this paper the validity ranges of alternative theories are assessed by comparison of the location of the dispersion curves this paper also contains a rigorous asymptotic analysis of the exact dispersion equation with two small parameters being employed it allows for the identification of significant regimes of linear wave motion in a helical spring in each of these regimes simple formulae for wavenumbers are obtained by the dominant balance method and their validity ranges are checked against direct numerical solution mode shapes associated with each wavenumber are also analysed

determination of mechanical spectra from experimental responses abstract a recursive computer algorithm was developed which generates line spectra from experimental response functions the method allows storing information on the mechanical properties of polymeric materials in a convenient way the algorithm also interconverts between relaxation and retardation spectra from the spectra any desired response function can then be recovered the algorithm essentially utilizes the fact that the kernel functions resemble step functions slightly different codes are used for each kernel function the appearance of negative relaxation or retardation lines is obviated mathematically such lines would be acceptable and they do not seriously affect reconstruction of responses within relaxation or retardation behavior however they would seriously interfere with interconversion between the two types of behavior and they would also pose problems in the interpretation of the spectra

methods of interconversion between linear viscoelastic material functions part i a numerical method based on prony series abstract an efficient and accurate numerical method of interconversion between linear viscoelastic material functions based on a prony series representation is presented and tested using experimental data from selected polymeric materials the method is straightforward and applicable to interconversion between modulus and compliance functions in time frequency and laplace transform domains good agreement is shown between solutions obtained from the method in different domains a detailed computational procedure and selection of values for parameters involved in the method are presented and illustrated in particular the effects of different choices of relaxation and retardation times on the accuracy of the method are discussed the mathematical efficiency associated with prony series representations of both source and target transient material functions is fully utilized the method is general enough to cover both viscoelastic solids and liquids the tensile relaxation data from polymethyl methacrylate pmma and the shear storage compliance data from polyisobutylene are used in illustrating the method in a companion paper schapery and park 1998 an extended approximate analytical interconversion method is presented

a proximal based decomposition method for convex minimization problems this paper presents a decomposition method for solving convex minimization problems at each iteration the algorithm computes two proximal steps in the dual variables and one proximal step in the primal variables we derive this algorithm from rockafellar s proximal method of multipliers which involves an augmented lagrangian with an additional quadratic proximal term the algorithm preserves the good features of the proximal method of multipliers with the additional advantage that it leads to a decoupling of the constraints and is thus suitable for parallel implementation we allow for computing approximately the proximal minimization steps and we prove that under mild assumptions on the problem s data the method is globally convergent and at a linear rate the method is compared with alternating direction type methods and applied to the particular case of minimizing a convex function over a finite intersection of closed convex sets

mechanism of complicated volume deformation in polymers and its fractional time based description abstract in tension and compression of polymers some abnormal phenomena of volume changes were often observed and its mechanism is still unclear in this paper based on the thermodynamics principle it is shown that the combined effects of internal energy and entropy are the basic reason of causing the anomaly in polymers moreover to describe the complicated deformation through a simple model and have a correct modelization of mechanical behaviors a volume strain model is presented in which the variation of volume strain resulted from the combined effects is characterized through a fractional integral expression comparison between fitting results and experimental results reveals the proposed model can describe the volume deformation of polymers

nonlinear vibration of viscoelastic beams described using fractional order derivatives abstract the problem of non linear steady state vibration of beams harmonically excited by harmonic forces is investigated in the paper the viscoelastic material of the beams is described using the zener rheological model with fractional derivatives the constitutive equation which contains derivatives of both stress and strain significantly complicates the solution to the problem the von karman theory is applied to take into account geometric nonlinearities amplitude equations are obtained using the finite element method together with the harmonic balance method and solved using the continuation method the tangent matrix of the amplitude equations is determined in an explicit form the stability of the steady state solution is also examined a parametric study is carried out to determine the influence of viscoelastic properties of the material on the beam s responses

analytical modeling of viscoelastic dampers for structural and vibration control different approaches to the mathematical modeling of viscoelastic dampers are addressed and their theoretical basis and performance are compared the standard mechanical model smm comprising linear springs and dashpots is shown to accurately describe the broad band rheological behavior of common viscoelastic dampers and be more efficient than other models such as the fractional derivative model and the modified power law the smm renders a prony series expression for the modulus and compliance functions in the time domain and the remarkable mathematical efficiency associated with the exponential basis functions of a prony series greatly facilitates model calibration and interconversion while cumbersome nonlinear regression is usually required for other models a simple collocation or least squares method can be used to fit the smm to available experimental data the model allows viscoelastic material functions to be readily determined either directly from the experimental data or through interconversion from a function established in another domain numerical examples on two common viscoelastic dampers demonstrate the advantages of the smm over fractional derivative and power law models detailed computational procedures for fitting and interconversion are discussed and illustrated published experimental data from a viscoelastic liquid damper and a viscoelastic solid damper are used in the examples

a parallel algorithm for a class of convex programs a parallel algorithm is proposed in this paper for solving the problem min q x x in c 1 cap cdots cap c m where q is an uniformly convex function and c i are closed convex sets in r n in each iteration of the method we solve in parallel m independent subproblems each minimizing a definite quadratic function over an individual set c i the method has attractive convergence properties and can be implemented as parallel algorithms for tackling definite quadratic programs linear programs systems of linear equations and systems of generalized nonlinear inequalities

formulation and integration of the standard linear viscoelastic solid with fractional order rate laws abstract a physically sound three dimensional anisotropic formulation of the standard linear viscoelastic solid with integer or fractional order rate laws for a finite set of the pertinent internal variables is presented it is shown that the internal variables can be expressed in terms of the strain as convolution integrals with kernels of mittag leffler function type a time integration scheme based on the generalized midpoint rule together with the grunwald algorithm for numerical fractional differentiation for integration of the constitutive response is developed the predictive capability of the viscoelastic model for describing creep relaxation and damped dynamic responses is investigated both analytically and numerically the algorithm and the present general linear viscoelastic model are implemented into the general purpose finite element code abaqus the algorithm is then used together with an explicit difference scheme for integration of structural responses in numerical examples the quasi static and damped responses of a viscoelastic ballast material that is subjected to loads simulating the overrolling of a train are investigated