qualitative and numerical analysis of quasi static problems in elastoplasticity the quasi static problem of elastoplasticity with combined kinematic isotropic hardening is formulated as a time dependent variational inequality vi of the mixed kind that is it is an inequality involving a nondifferentiable functional and is imposed on a subset of a space this vi differs from the standard parabolic vi in that time derivatives of the unknown variable occur in all of its terms the problem is shown to possess a unique solution we consider two types of approximations to the vi corresponding to the quasi static problem of elastoplasticity semidiscrete approximations in which only the spatial domain is discretized by finite elements and fully discrete approximations in which the spatial domain is again discretized by finite elements and the temporal domain is discretized and the time derivative appearing in the vi is approximated in an appropriate way estimates of the errors inherent in the above two types of approximations in suitable sobolev norms are obtained for the quasi static problem of elastoplasticity in particular these estimates express rates of convergence of successive finite element approximations to the solution of the variational inequality in terms of element size h and where appropriate of the time step size k a major difficulty in solving the problems is caused by the presence of the nondifferentiable terms we consider some regularization techniques for overcoming the difficulty besides the usual convergence estimates we also provide a posteriori error estimates which enable us to estimate the error by using only the solution of a regularized problem

adaptive numerical analysis in primal elastoplasticity with hardening the quasi static viscoplastic resp elastoplastic evolution problem with isotropic or kinematic hardening is considered with emphasis on optimal convergence and adapted mesh refining in the spatial discretization within one time step of an implicit time discretization the finite element method leads to a minimisation problem for non smooth convex functions on discrete subspaces for piecewise constant resp affine ansatz functions the stress resp displacement approximations are experimentally and theoretically shown to converge linearly an a posteriori error estimate then justifies an automatic adaptive mesh refining algorithm numerical examples support the superiority of the adapted mesh

invariant properties of the shuffle exchange and a simplified cost effective version of the omega network let denote the set of permutations performable by a pass through the omega network an n stage shuffle exchange network and let denote an arbitrary permutation of n 2n elements in this paper we characterize the sets called left invariants and called right invariants this characterization provides a useful criterion for determining whether or not the composition of two permutations belongs to it also allows a number of known results to be generalized and their derivations simplified

error estimates for the numerical approximation of time dependent flow of bingham fluid in cylindrical pipes by the regularization method the flow of a bingham fluid in a cylindrical pipe can give rise to free boundary problems the fluid behaves like a viscous fluid if the shear stress expressed as a linear function of the shear rate exceeds a yield value and like a rigid body otherwise the surfaces dividing fluid and rigid zones are the free boundaries therefore the solution for such highly nonlinear problems can in general only be obtained by numerical methods considerable progress has been made in the development of numerical algorithms for bingham fluids 2 20 27 29 30 32 however very little research can be found in the literature regarding the rate of convergence of the numerical solution to the true continuous solution that is the error estimate of these numerical methods error estimates are a critically important issue because they tells us how to control the error by appropriately choosing the grid sizes and other related parameters this paper concerns the error estimates of a unsteady bingham fluid modeled as a variational inequality due to duvaut lions 16 and glowinski 30 the difficulty both in the analytical and numerical treatment of the mathematical model is due to the fact that it contains a nondifferentiable term a common technique called the regularization method is to replace the non differentiable term by a perturbed differentiable term which depends on a small regularization parameter the regularization method effectively reduces the variational inequality to an equation a regularized problem which is much easier to cope with this paper has achieved the following 1 error estimates are derived for a continuous time galerkin method in suitable norms 2 we give an estimate of the difference between the true solution and the regularized solution in terms of 3 some regularity properties for both regularized solution and the true solution are proved 4 the error estimates for full discretization of the regularized problem using piecewise linear finite elements in space and backward differencing in time are established for the first time by coupling the regularization parameter and the discretization parameters h and t 5 we are able to improve our estimates in the one dimensional case or under stronger regularity assumptions on the true solution the estimates for the one dimensional case are optimal and confirmed by numerical experiment the estimates from 4 and 5 provide very important information on the measure of the error and give us a powerful mechanism to properly choose the parameters h t and in order to control the error see corollary 4 4 the above estimates extend the error bounds derived in glowinski lions and tremolieres 32 chapter 5 pp 348 404 for the stationary bingham fluid to the time dependent one which is the main contribution of this paper

a new numerical scheme for discrete constrained total variation flows and its convergence in this paper we propose a new numerical scheme for a spatially discrete model of total variation flows whose values are constrained to a riemannian manifold the difficulty of this problem is that the underlying function space is not convex hence it is hard to calculate a minimizer of the functional with the manifold constraint even if it exists we overcome this difficulty by localization technique using the exponential map and prove a finite time error estimate finally we show a few numerical results for the target manifolds s 2 and so 3

a convergence analysis of a p version finite element method for one dimensional elastoplasticity problem with constitutive laws based on the gauge function method in this paper we will give a p version finite element method for the one dimensional nonlinear elastoplasticity problem a family of admissible constitutive laws based on the so called gauge function method is introduced first and then a p version semi discretization scheme is presented we show that the existence and uniqueness of the solution for the semi discrete problem can be guaranteed by using some special properties of the constitutive law finally we show that as the polynomial degree of the elements bf p to infty oo the solution of the semi discrete problem will converge to the solution of the continuous problem the p version convergence analysis given here is only for one dimensional problems with a linear hardening constitutive law hypothesis however it also gives us a very useful idea for the study of the hp version finite element method for the one dimensional problem with more general constitutive laws or even two dimensional problems

learning boolean concepts in the presence of many irrelevant features abstract in many domains an appropriate inductive bias is the min features bias which prefers consistent hypotheses definable over as few features as possible this paper defines and studies this bias in boolean domains first it is shown that any learning algorithm implementing the min features bias requires ln l 2 p p ln n e training examples to guarantee pac learning a concept having p relevant features out of n available features this bound is only logarithmic in the number of irrelevant features for implementing the min features bias the paper presents five algorithms that identify a subset of features sufficient to construct a hypothesis consistent with the training examples focus 1 is a straightforward algorithm that returns a minimal and sufficient subset of features in quasi polynomial time focus 2 does the same task as focus 1 but is empirically shown to be substantially faster than focus 1 finally the simple greedy mutual information greedy and weighted greedy algorithms are three greedy heuristics that trade optimality for computational efficiency experimental studies are presented that compare these exact and approximate algorithms to two well known algorithms id3 and fringe in learning situations where many irrelevant features are present these experiments show that contrary to expectations the id3 and fringe algorithms do not implement good approximations of min features the sample complexity and generalization performance of the focus algorithms is substantially better than either id3 or fringe on learning problems where the min features bias is appropriate these experiments also show that among our three heuristics the weighted greedy algorithm provides an excellent approximation to the focus algorithms

reliable and efficient equilibrated a posteriori finite element error control in elastoplasticity and elastoviscoplasticity with hardening this paper establishes the reliability and efficiency of equilibrated a posteriori estimates for l 2 stress error control of conforming displacement finite element approximations of incremental plasticity and viscoplasticity with hardening explicit expressions for upper bounds of the reliability constant that enters the guaranteed upper error bound illustrate its crucial dependence on the hardening material constants numerical experiments show that adaptive finite element solutions with marking strategy based on the max refinement rule and local equilibrated error estimators lead to optimal empirical convergence rates 2005 elsevier b v all rights reserved

error estimation and adaptive meshing in strongly nonlinear dynamic problems we present work aimed at developing a general framework for mesh adaption in strongly nonlinear possibly dynamic problems we begin by showing that the solutions of the incremental boundary value problem for a wide class of materials including nonlinear elastic materials compressible newtonian fluids and viscoplastic solids obey a minimum principle provided that the constitutive updates are formulated appropriately this minimum principle can be taken as a basis for asymptotic error estimation in particular we chose to monitor the error of a lower order projection of the finite element solution the optimal mesh size distribution then follows from a posteriori error indicators which are purely local i e can be computed element by element we demonstrate the robustness and versatility of the computational framework with the aid of convergence studies and selected examples of application

a new a posteriori error estimation for nonlinear time dependent finite element analysis abstract in this paper an error on the constitutive law labeled the dissipation error is used to measure the quality of finite element computations of plastic and viscoplastic structures whose behavior is described by internal variables this measure takes into account all the classical sources of error involved in the computation the space discretization the mesh the time discretization and the iterative technique used to solve the nonlinear discrete problem more specifically to quantify the quality of the space and time discretizations two quantities called indicators are introduced the efficiency of both the error and the indicators is shown for several examples

a posteriori error analysis for higher order dissipative methods for evolution problems we prove a posteriori error estimates for time discretizations by the discontinuous galerkin method dg q and the corresponding implicit runge kutta radau method irk r q of arbitrary order q 0 for both linear and nonlinear evolution problems of the form u prime mathfrak f u f with 2 angle bounded operator mathfrak f the key ingredient is a novel higher order reconstruction widehat u of the discrete solution u which restores continuity and leads to the differential equation widehat u prime pi mathfrak f u f for a suitable interpolation operator and piecewise polynomial approximation f of f we discuss applications to linear pde such as the convection diffusion equation 1 2 and the wave equation formally and nonlinear pde corresponding to subgradient operators 1 such as the p laplacian as well as lipschitz operators 1 2 we also derive conditional a posteriori error estimates for the time dependent minimal surface problem

error estimates for space time discretizations of a rate independent variational inequality this paper deals with error estimates for space time discretizations in the context of evolutionary variational inequalities of rate independent type after introducing a general abstract evolution problem we address a fully discrete approximation and provide a priori error estimates the application of the abstract theory to a semilinear case is detailed in particular we provide explicit space time convergence rates for classical strain gradient plasticity and the isothermal souza auricchio model for shape memory alloys

notes on shuffle exchange type permutation sets properties of some shuffle exchange type permutation sets are studied from operational points of view the permutation sets studied are omega omega sup 1 psi l and u omega and omega sup 1 are respectively the omega and inverse omega permutation sets omega identical to omega intersection omega sup 1 and l and u are respectively the admissible lower and upper triangular permutation sets several intuitive operations are introduced based on these operations important known results relating to these sets are readdressed the recursive nature of the sets is also discussed

convergence analysis for splitting of the abstract differential riccati equation we consider a splitting based approximation of the abstract differential riccati equation in the setting of hilbert schmidt operators the riccati equation arises in many different areas and is important within the field of optimal control in this paper we conduct a temporal error analysis and prove that the splitting method converges with the same order as the implicit euler scheme under the same low regularity requirements on the initial values for a subsequent spatial discretization the abstract setting also yields uniform temporal error bounds with respect to the spatial discretization parameter the spatial discretizations commonly lead to large scale problems where the use of structural properties of the solution is essential we therefore conclude by proving that the splitting method preserves low rank structure in the matrix valued case numerical results demonstrate the validity of the convergence analysis less

error estimates for the finite volume discretization for the porous medium equation we analyze the convergence of a numerical scheme for a class of degenerate parabolic problems modelling reactions in porous media and involving a nonlinear possibly vanishing diffusion the scheme involves the kirchhoff transformation of the regularized nonlinearity as well as an euler implicit time stepping and triangle based finite volumes we prove the convergence of the approach by giving error estimates in terms of the discretization and regularization parameter

an efficient routing algorithm for realizing linear permutations on p sup t shuffle exchange networks the authors present an efficient routing algorithm for realizing any permutation in lin linear permutation class on single stage shuffle exchange networks with k k switching elements where k p is a prime number for any positive integer number n there are n k sup n processors connected by the network the proposed algorithm can realize lin in 2n 1 passes it can be implemented by using nn processors in o n time it can also be extended to the shuffle exchange networks with p sup t p sup t switching elements where t is a positive integer number in addition the routing of any arbitrary permutations on the networks with any integer k 2 is discussed further by using the techniques developed here the authors present an optimal o log n parallel algorithm for solving a set of linear equations with a nonsingular coefficient matrix when the arithmetic is over the finite field gf p sup t

convergence of the implicit explicit euler scheme applied to perturbed dissipative evolution equations we present a convergence analysis for the implicit explicit imex euler discretization of nonlinear evolution equations the governing vector field of such an equation is assumed to be the sum of an unbounded dissipative operator and a lipschitz continuous perturbation by employing the theory of dissipative operators on banach spaces we prove that the imex euler and the implicit euler schemes have the same convergence order i e between one half and one depending on the initial values and the vector fields concrete applications include the discretization of diffusion reaction systems with fully nonlinear and degenerate diffusion terms the convergence and efficiency of the imex euler scheme are also illustrated by a set of numerical experiments less

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

a priori l r error estimates for galerkin approximations to porous medium and fast diffusion equations galerkin approximations to solutions of a cauchy dirichlet problem governed by the generalized porous medium equation formulamath on bounded convex domains are considered the range of the parameter includes the fast diffusion case 1 2 using an euler finite difference approximation in time the semi discrete solution is shown to converge to the exact solution in l 0 t l norm with an error controlled by o t1 4 for 1 2 and o t1 2 for 2 for the fully discrete problem a global convergence rate of o t1 4 in l 2 0 t l norm is shown for the range 2n n 1 2 for 2 a rate of o t1 2 is shown in l 0 t l norm

constitutive relation error estimators for visco plastic finite element analysis with softening a posteriori error estimators based on constitutive relation residuals have been developed for 20 years in particular at cachan this approach has a strong physical meaning and is quite general here we introduce an extended constitutive relation error estimators family able to measure the quality of finite element computations of structures which exhibit plastic viscoplastic behavior with softening these measures take into account over the studied time interval all the classical error sources involved in the computation the space discretization the mesh the time discretization and the iterative technique used to solve the nonlinear discrete problem

adaptive mesh refinement in strain localization problems an adaptive meshing method tailored to problems of strain localization is given the adaption strategy consists of equi distributing the variation of the velocity field over the elements of the mesh a heuristic justification for the use of variations as indicators is advanced and possible connections with interpolation error bounds are discussed meshes are constructed by delaunay triangulation it is shown how the hu washizu principle determines a consistent transfer operator for the state variables examples of application are given which demonstrate the versatility of the method

a posteriori error estimation and adaptivity for elastoplasticity using the reciprocal theorem we present a posteriori error estimators and adaptive methods for the finite element approximation of nonlinear problems and especially elastoplasticity the main characteristic of the proposed method is the introduction of duality techniques or in other notions the reciprocal theorem for error estimation at an equilibrium point the nonlinear boundary value problem and an additional linearized dual problem are considered the loading of the dual problem is specifically designed for capturing the influence of the errors of the entire domain to the considered variable our approach leads to easy computable refinement indicators for locally or integrally defined variables for instationary problems as elastoplasticity in a first step we neglect the errors due to time discretization and evaluate the error indicators within each time step for a stationary problem the versatility of the presented framework is demonstrated with numerical examples

adaptive finite element procedures for linear and non linear dynamics this paper discusses implementation and adaptivity of the discontinuous galerkin dg finite element method as applied to linear and non linear structural dynamic problems by the dg method both displacements and velocities are approximated as piecewise bilinear functions in space and time and may be discontinuous at the discrete time levels both implicit and explicit iterative algorithms for solving the resulted system of coupled equations are derived they are third order accurate and while the implicit procedure is unconditionally stable the explicit one is conditionally stable an h adaptive procedure based on the zienkiewicz zhu error estimate using the spr technique is applied numerical examples are presented to show the suitability of the dg method for both linear and non linear structural dynamic analysis copyright 1999 john wiley sons ltd

numerical analysis of time depending primal elastoplasticity with hardening the quasi static elastoplastic evolution problem with combined isotropic and kinematic hardening is considered with emphasis on optimal convergence of the lowest order scheme in each time step of a generalized midpoint scheme such as the implicit euler or the crank nicolson scheme the spatial discretization consists of minimizing a convex but nonsmooth function on a subspace of continuous piecewise linear resp piecewise constant trial functions an a priori error estimate is established for the fully discrete method which for smooth data and a smooth exact solution proves linear convergence as the mesh size tends to zero strong convergence of the time derivatives is established under mild conditions on the mesh and time step sizes numerical experiments confirm our theoretical predictions on the improved spatial convergence and indicate that the crank nicolson scheme is not always superior over the implicit euler scheme in practice

adaptive finite element methods for parabolic problems i a linear model problem this paper is the first part in a series of papers on adaptive finite element methods for parabolic problems in this paper an adaptive algorithm is presented and analyzed for choosing the space a

high degree efficient symmetrical gaussian quadrature rules for the triangle gaussian quadrature is required for the computation of matrices based on the isoparametric formulztion of the finite element method a brief review of existing quadrature rules for the triangle is given and the method for the determination of high degree efficient symmetrical rules for the triangle is discussed new quadrature rules of degree 12 20 are presented and a short fortran program is included

rate of convergence of regularization procedures and finite element approximations for the total variation flow we derive rates of convergence for regularization procedures characterized by a parameter and finite element approximations of the total variation flow which arises from image processing geometric analysis and materials sciences practically useful error estimates which depend on open image in new window only in low polynomial orders are established for the proposed fully discrete finite element approximations as a result scaling laws which relate mesh parameters to the regularization parameter are also obtained numerical experiments are provided to validate the theoretical results and show efficiency of the proposed numerical methods

evolution of phase transitions in methane hydrate abstract we consider a simplified model of methane hydrates which we cast as a nonlinear evolution problem for its well posedness we extend the existing theory to cover the case in which the problem involves a measurable family of graphs we represent the nonlinearity as a subgradient and prove a useful comparison principle thus optimal regularity results follow for the numerical solution we apply a fully implicit scheme without regularization and use the semismooth newton algorithm for a solver and the graph is realized as a complementarity constraint cc the algorithm is very robust and we extend it to define an easy and superlinearly convergent fully implicit scheme for the stefan problem and other multivalued examples

error analysis for implicit approximations to solutions to cauchy problems exact error analyses for two implicit approximation schemes to the cauchy problem du t dt mathcal a u t mathrel backepsilon 0 u 0 u 0 in d mathcal a are presented the operator mathcal a is required to be maximal monotone on a hilbert space mathcal h the approximations considered are u h kh i h mathcal a k u 0 and solutions u lambda to the approximating problems du lambda t dt mathcal a lambda u lambda 0 u lambda 0 u 0 where a lambda is the yosida approximation of mathcal a the special case of a being a subgradient is considered and tight estimates of the convergence of both u h and mathcal a h u h or u h and a h u h are given the new results in this case are the linear rates of convergence of u h in l infty 0 infty mathcal h and in the energy norm and the sublinear rate of convergence of a h u h in l 2 0 infty mathcal h applications to both linear and

self routing technique in perfect shuffle networks using control tags the self routing technique using control tags on multiple pass perfect shuffle networks is generalized in particular they show that bit permute complement permutations can be realized and unscrambled in 2n 1 passes or less where n log sub 2 n n being the number of terminals on either side they also show that most of the frequently used permutations are in the intersection of omega realizing and inverse omega realizing sets and can be realized and unscrambled in n passes

a self routing benes network and parallel permutation algorithms a benes permutation network capable of setting its own switches dynamically is presented the total switch setting and delay time for the n input utput self routing network is o log n it is shown that the network is capable of performing a rich class of permutations the self routing scheme leads to efficient o log n parallel algorithms to perform the same class of permutations on cube connected and perfect shuffle computers

conforming and discontinuous galerkin fem in space for solving parabolic obstacle problem abstract in this article we propose and analyze conforming and discontinuous galerkin dg finite element methods for numerical approximation of the solution of the parabolic variational inequality associated with a general obstacle in r d d 2 3 for fully discrete conforming method we use globally continuous and piecewise linear finite element space whereas for the fully discrete dg scheme we employ piecewise linear finite element space for spatial discretization the time discretization has been done by using the implicit backward euler method we present the error analysis for the conforming and the dg fully discrete schemes and derive an error estimate of optimal order o h t in a certain energy norm defined precisely in the article the analysis is performed without any assumptions on the speed of propagation of the free boundary but only assumes the pragmatic regularity that u t l 2 0 t l 2 the obstacle constraints are incorporated at the lagrange nodes of the triangular mesh and the analysis exploits the lagrange interpolation we present some numerical experiment to illustrate the performance of the proposed methods

a convergent adaptive finite element method for the primal problem of elastoplasticity summary the boundary value problem representing one time step of the primal formulation of elastoplasticity with positive hardening leads to a variational inequality of the second kind with some nondifferentiable functional this paper establishes an adaptive finite element algorithm for the solution of this variational inequality that yields the energy reduction and up to higher order terms the r linear convergence of the stresses with respect to the number of loops applications include several plasticity models linear isotropic kinematic hardening linear kinematic hardening and multisurface plasticity as model for nonlinear hardening laws for perfect plasticity the adaptive algorithm yields strong convergence of the stresses numerical examples confirm an improved linear convergence rate and study the performance of the algorithm in comparison with the more frequently applied maximum refinement rule copyright q 2006 john wiley sons ltd

a posteriori error estimation and mesh adaptation for finite element models in elasto plasticity a new approach to a posteriori error estimation and adaptive mesh design based on techniques from optimal control is presented for primal mixed finite element models in elasto plasticity this method uses global duality arguments for deriving weighted a posteriori error bounds for arbitrary functionals of the error representing physical quantities of interest in these estimates local residuals of the computed solution are multiplied by certain weights which are obtained by solving a linearized global dual problem numerically the resulting local error indicators are used in a feed back process for generating economical meshes this approach is developed here for the hencky and prandtl reuss models in linear elastic perfect plasticity its performance is demonstrated for a plane strain benchmark problem

a convergence analysis of an h version finite element method with high order elements for two dimensional elasto plasticity problems in this paper we will give an h version finite element method for a two dimensional nonlinear elasto plasticity problem a family of admissible constitutive laws based on the so called gauge function method is introduced first and then a high order h version semidiscretization scheme is presented the existence and uniqueness of the solution for the semidiscrete problem are guaranteed by using some special properties of the constitutive law and finally we will show that as the maximum element size h longrightarrow 0 the solution of the semidiscrete problem will converge to the solution of the continuous problem the high order h version discretization scheme introduced here is unusual if the partition of the spatial space only has rectangles or parallelograms involved then there would not be any limit on the element degree however if the partition of the spatial space has some triangular elements then only certain combinations of finite element spaces for displacement and stress functions can be used the discretization scheme also provides a useful idea for applications of hp version or high order h version finite element methods for two dimensional problems where the elasto plastic body is not a polygon such as a disk or an annulus

spl alpha complete information in factor space in daily life we normally describe our concepts and problems in linguistic terms due to the vagueness of our natural languages the classical approach is unable to fully capture the properties factors of such concepts and problems and hence cannot provide decision makers complete information for making an appropriate decision therefore in this paper we first classify general fuzzy data of a problem which are presented by human linguistic terms into different categories and based on their properties each of them is described by an appropriate fuzzy set then by investigating the properties of a problem as factors of a system a fuzzy multiobjective linear programming fmolp model is proposed from the viewpoint of evidence theory and information theory to measure the uncertainty of a fuzzy problem a learning procedure is also designed to inquire the complete information according to the required level of sufficiency spl alpha finally an example of mobile phone service mps is presented to show that the proposed model can aid decision makers to identify representative significant factors and obtain complete information of the mps within a few steps

optimal rates of convergence for degenerate parabolic problems in two dimensions fully discrete implicit schemes for the solution of degenerate parabolic equations in two dimensions are shown to satisfy error estimates of the form o tau ln 1 h alpha h where tau is the time step size and h is the mesh size these results apply to both the stefan problem and the porous medium equation

regularity and rothe method error estimates for parabolic hemivariational inequality this paper deals with regularity of solutions to the abstract operator version of parabolic partial differential inclusion of the form u t au t j u t f t with the multivalued term given in the form of clarke subdifferential of a locally lipschitz functional j using the rothe method it is shown that under appropriate assumptions on the data the solution has the increased regularity three regularity theorems are given the first one concerns the regularity of solution in the besov space b2 1 2 0 t h the second theorem provides assumption under which the solution lies in the space h1 0 t h l 0 t v c 0 t vweak the last one shows that if the operator a is strongly monotone and the multivalued term satisfies the relaxed monotonicity assumption then the unique solution also belongs to h1 0 t v w1 0 t h in the last case the error estimates on the rothe method are also proved

the universality of the shuffle exchange network this paper has focused on the realization of every arbitrary permutation with the shuffle exchange network permutation properties of shuffle exchange networks are studied and are used to demonstrate several universal networks it is concluded that 3 log2 n 1 passes through a single stage regular shuffle exchange network are sufficient to realize every arbitrary permutation where n is network size a routing algorithm is also developed to calculate control settings of the shuffle exchange switches for the permutation realization three optimal universal networks namely expanded direct connection shuffle exchange network multiple pass omega network and modified shuffle exchange network are then exploited for better interconnection purposes in addition this work specifies the inherent relationship between the shuffle exchange network and the benes binary network so that designers can have a broad prospect

transfer operators for evolving meshes in small strain elasto placticity abstract together with error evaluation and mesh refinement transfer operators represent the essential component of the adaptive procedure applied to history dependent materials aspects of the transfer operation discussed in this work relate to equilibrium conditions consistency with the constitutive equation geometric issues and diffusion of state variables between successive meshes in this paper attention is restricted to small strain rate independent elasto plasticity numerical examples are presented to illustrate some practical features of the computational procedure

gradient structures for the thermomechanics of shape memory materials abstract we investigate the variational structure of a phenomenological model for the coupled thermomechanical behavior of shape memory polycrystalline materials the nonisothermal evolution of the medium is reformulated as a generalized gradient flow of the entropy with respect to an entropy production potential based on this reformulation a semi implicit time discretization of the fully coupled thermomechanical problem is presented and proved to be unconditionally stable and convergent the flexibility and robustness of the numerical method is assessed via both uniaxial and multiaxial computational tests

analysis of transfer procedures in elastoplasticity based on the error in the constitutive equations theory and numerical illustration the aim of this work is to illustrate a methodology for the assessment of adaptive strategies for the solution of associative rate independent plasticity problems solved by employing the incremental displacement conforming finite element method this is the first step towards a more rational definition of transfer operators in terms of the ensuing error the motivating idea is the observation that change of data and or finite element mesh from one time interval to the other can be both related to a discontinuity jump of the approximate solution across the time instant t n thus reliable a posteriori estimates will have to depend not only on the time step and finite element mesh size but also on the value of the jump a new error estimate based on the error in the constitutive equations is developed which allows characterization of the discontinuity jump

lyapunov stability and performance analysis of the implicit discrete sliding mode control discrete time sliding mode controllers with an implicit discretization of the signum function are considered with a proper choice of the equivalent part of the control the resulting controller is shown to be lyapunov stable with finite time convergence of the sliding variable to 0 the convergence of the control input as the sampling period goes to 0 to the continuous time one is shown the robustness with respect to matching perturbations is also investigated the discretization performance in terms of the error order is studied for different discretizations of the equivalent part of the input numerical and experimental results illustrate and support the analysis

a robust and efficient linearization scheme for doubly nonlinear and degenerate parabolic problems arising in flow in porous media we study a nonlinear degenerate convection diffusion model problem having an application in groundwater aquifer and petroleum reservoir simulation the true solution typically possesses low regularity and therefore special numerical techniques for its approximation are needed we design a robust efficient and reliable linear relaxation approximation scheme we prove the convergence of iterations at each time step in the h 1 omega norm finally the convergence of the approximate solution in corresponding functional spaces to its exact counterpart for the parabolic problem is shown

an improved error bound for a finite element approximation of a model for phase separation of a multi component alloy with a concentration dependent mobility matrix using a slightly different discretization scheme in time and adapting the approach in nochetto et al 1998 for analysing the time discretization error in the backward euler method we improve on the error bounds derived in i barrett and blowley 1998 and ii barrett and blowey 1999c for a fully practical piecewise linear finite element approximation of a model for phase separation of a multi component alloy with a concentration dependent mobility matrix and i a logarithmic free energy and ii a non smooth free energy the deep quench limit respectively moreover the improved error bound in the deep quench limit is optimal numerical experiments with three components illustrating the above error bounds are also presented

dynamic plasticity models the evolution of an elastic plastic material is modeled as an initial boundary value problem consisting of the dynamic momentum equation coupled with a constitutive law for which the hysteretic dependence between stress and strain is described by a system of variational inequalities this system is posed as an evolution equation in hilbert space for which is proved the existence and uniqueness of three classes of solutions which are distinguished by their regularity

error estimates for a mixed finite element discretization of some degenerate parabolic equations we consider a numerical scheme for a class of degenerate parabolic equations including both slow and fast diffusion cases a particular example in this sense is the richards equation modeling the flow in porous media the numerical scheme is based on the mixed finite element method mfem in space and is of one step implicit in time the lowest order raviart thomas elements are used here we extend the results in radu et al siam j numer anal 42 1452 1478 2004 schneid et al numer math 98 353 370 2004 to a more general framework by allowing for both types of degeneracies we derive error estimates in terms of the discretization parameters and show the convergence of the scheme the features of the mfem especially of the lowest order raviart thomas elements are now fully exploited in the proof of the convergence the paper is concluded by numerical examples

an easily controlled network for frequently used permutations a network which is a concatenation of 2 networks 2 along with a simple control algorithm is proposed this network is capable of performing all network realizable permutations and the bit permute complement bpc class of permutations 5 in 0 log n time the control algorithm is actually a multiple pass control algorithm on the network which is more general than pease s lu decomposition method 6 and lenfant s decomposition method 4

adaptive finite element methods in computational mechanics we present a general approach to adaptivity for finite element methods and give applications to linear elasticity non linear elasto plasticity and nonlinear conservation laws including numerical results

stiffly accurate runge kutta methods for nonlinear evolution problems governed by a monotone operator stiy accurate implicit runge kutta methods are studied for the time discretisation of nonlinear rst order evolution equations the equation is supposed to be governed by a time dependent hemicontinuous operator that is up to a shift monotone and coercive and fullls a certain growth condi tion it is proven that the piecewise constant as well as the piecewise linear interpolant of the time discrete solution converge towards the exact weak solu tion provided the runge kutta method is consistent and satises a stability criterion that implies algebraic stability examples are the radau iia and lo batto iiic methods the convergence analysis is also extended to problems involving a strongly continuous perturbation of the monotone main part

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

a posteriori error estimates for variable time step discretizations of nonlinear evolution equations we study the backward euler method with variable time steps for abstract evolution equations in hilbert spaces exploiting convexity of the underlying potential or the angle bounded condition thereby assuming no further regularity we derive novel a posteriori estimates of the discretization error in terms of computable quantities related to the amount of energy dissipation or monotonicity residual these estimators depend solely on the discrete solution and data and impose no constraints between consecutive time steps we also prove that they converge to zero with an optimal rate with respect to the regularity of the solution we apply the abstract results to a number of concrete strongly nonlinear problems of parabolic type with degenerate or singular character 2000 john wiley sons inc

parallel matrix and graph algorithms matrix multiplication algorithms for cube connected and perfect shuffle computers are presented it is shown that in both these models two n times n matrices can be multiplied in o n m log m time when n 2 m 1 leqq m leqq n processing elements pes are available when only m 2 1 leqq m leqq n pes are available two n times n matrices can be multiplied in o n 2 m m n m 2 61 time it is shown that many graph problems can be solved efficiently using the matrix multiplication algorithms

a pde approach to space time fractional parabolic problems we study solution techniques for parabolic equations with fractional diffusion and caputo fractional time derivative the latter being discretized and analyzed in a general hilbert space setting the spatial fractional diffusion is realized as the dirichlet to neumann map for a nonuniformly elliptic problem posed on a semi infinite cylinder in one more spatial dimension we write our evolution problem as a quasi stationary elliptic problem with a dynamic boundary condition we propose and analyze an implicit fully discrete scheme first degree tensor product finite elements in space and an implicit finite difference discretization in time we prove stability and error estimates for this scheme

a numerical approach to degenerate parabolic equations in this work we propose a numerical approach to solve some kind of degenerate parabolic equations the underlying idea is based on the maximum principle more precisely we locally perturb the initial and boundary data instead of the nonlinear diffusion coefficients so that the resulting problem is not degenerate the efficiency of this method is shown analytically as well as numerically the numerical experiments show that this new approach is comparable with the existing ones

numerical analysis of a steepest descent pde model for surface relaxation below the roughening temperature we study the numerical solution of a pde describing the relaxation of a crystal surface to a flat facet the pde is a singular nonlinear fourth order evolution equation which can be viewed as the gradient flow of a convex but nonsmooth energy with respect to the h per 1 inner product our numerical scheme uses implicit discretization in time and a mixed finite element approximation in space the singular character of the energy is handled using regularization combined with a primal dual method we study the convergence of this scheme both theoretically and numerically

numerical analysis of the primal problem of elastoplasticity with hardening the finite element method is a reasonable and frequently utilised tool for the spatial discretization within one time step in an elastoplastic evolution problem in this paper we analyse the finite element discretization and prove a priori and a posteriori error estimates for variational inequalities corresponding to the primal formulation of hencky plasticity the finite element method of lowest order consists in minimising a convex function on a subspace of continuous piecewise linear resp piecewise constant trial functions an a priori error estimate is established for the fully discrete method which shows linear convergence as the mesh size tends to zero provided the exact displacement field u is smooth near the boundary of the plastic domain which is unknown a priori it is most likely that u is non smooth in this situation automatic mesh refinement strategies are believed to improve the quality of the finite element approximation we suggest such an adaptive algorithm on the basis of a computable a posteriori error estimate this estimate is reliable and efficient in the sense that the quotient of the error by the estimate and its inverse are bounded from above the constants depend on the hardening involved and become larger for decreasing hardening

plasticity models and nonlinear semigroups abstract the evolution of an elastic plastic material is modeled as an initial boundary value problem consisting of the dynamic momentum equation coupled with a constitutive law for which the hysteretic dependence between stress and strain is described by a system of variational inequalities this system is posed as an evolution equation in hilbert space for which is proved the existence and uniqueness of three classes of solutions which are distinguished by their regularity weak solutions are obtained in a very general situation strong solutions arise in the presence of kinematic work hardening or viscosity and the solution is even more regular under a stability assumption connecting the constraint set with the divergence operator