a preconditioner for the steady state navier stokes equations we present a new method for solving the sparse linear system of equations arising from the discretization of the linearized steady state navier stokes equations also known as the oseen equations the solver is an iterative method of krylov subspace type for which we devise a preconditioner through a heuristic argument based on the fundamental solution tensor for the oseen operator the preconditioner may also be conceived through a weaker heuristic argument involving differential operators computations indicate that convergence for the preconditioned discrete oseen problem is only mildly dependent on the viscosity inverse reynolds number and most importantly that the number of iterations does not grow as the mesh size is reduced indeed since the preconditioner is motivated through analysis of continuous operators the number of iterations decreases for smaller mesh size which accords with better approximation of these operators

lower and upper bounds for the allocation problem and other nonlinear optimization problems we demonstrate the impossibility of strongly polynomial algorithms for the allocation problem in the comparison model and in the algebraic tree computation model that follow from lower bound results consequently there are no strongly polynomial algorithms for nonlinear concave separable optimization over a totally unimodular constraint matrix this is in contrast to the case when the objective is linear we present scaling based algorithms that use a greedy algorithm as a subroutine the algorithms are polynomial for the allocation problem and its extensions and are also optimal for the sample allocation problem and the generalized upper bounds allocation problem in that the complexity meets the lower bound derived from the comparison model for other extensions of the allocation problem the scaling based algorithms presented here are the fastest known these algorithms are also polynomial time algorithms for solving with e accuracy the allocation problem and its extension in continuous variables

variational and projection methods for the volume constraint in finite deformation elasto plasticity this paper focuses on the treatment of volume constraints which in the context of elasto plasticity typically arise as a result of assuming volume preserving plastic flow projection methods based on the modification of the discrete gradient operator b often proposed on an ad hoc basis are systematically obtained in the variational context furnished by a three field hu washizu principle the fully nonlinear formulation proposed here is based on a local multiplicative split of the deformation gradient into volume preserving and dilatational parts without relying on rate forms of the weak form of momentum balance this approach fits naturally in a formulation of plasticity based on the multiplicative decomposition of the deformation gradient and enables one to exactly enforce the condition of volume preserving plastic flow within the framework proposed in this paper rate forms and incrementally objective algorithms are entirely bypassed

a nonlinear mixed finite eelement method for a degenerate parabolic equation arising in flow in porous media we study a model nonlinear degenerate advection diffusion equation having application in petroleum reservoir and groundwater aquifer simulation the main difficulty is that the true solution is typically lacking in regularity therefore we consider the problem from the point of view of optimal approximation through time integration we develop a mixed variational form that respects the known minimal regularity and then we develop and analyze two versions of a mixed finite element approximation a simpler semidiscrete time continuous version and a fully discrete version our error bounds are optimal in the sense that all but one of the bounding terms reduce to standard approximation error the exceptional term is a nonstandard approximation error term we also consider our new formulation for the nondegenerate problem showing the usual optimal l 2 error bounds moreover superconvergence is obtained under special circumstances

mixed displacement rotation pressure formulations for linear elasticity abstract we propose a new locking free family of mixed finite element and finite volume element methods for the approximation of linear elastostatics formulated in terms of displacement rotation vector and pressure the unique solvability of the three field continuous formulation as well as the well definiteness and stability of the proposed galerkin and petrov galerkin methods is established thanks to the babuska brezzi theory optimal a priori error estimates are derived using norms robust with respect to the lame constants turning these numerical methods particularly appealing for nearly incompressible materials we exemplify the accuracy in a suitably weighted norm as well the applicability of the new formulation and the mixed schemes by conducting a number of computational tests in 2d and 3d also including cases not covered by our theoretical analysis

a novel alpha finite element method αfem for exact solution to mechanics problems using triangular and tetrahedral elements abstract the paper presents an alpha finite element method fem for computing nearly exact solution in energy norm for mechanics problems using meshes that can be generated automatically for arbitrarily complicated domains three node triangular fem t3 and four node tetrahedral fem t4 elements with a scale factor are formulated for two dimensional 2d and three dimensional 3d problems respectively the essential idea of the method is the use of a scale factor 0 1 to obtain a combined model of the standard fully compatible model of the fem and a quasi equilibrium model of the node based smoothed fem n sfem this novel combination of the fem and n sfem makes the best use of the upper bound property of the n sfem and the lower bound property of the standard fem using meshes with the same aspect ratio a unified approach has been proposed to obtain a nearly exact solution in strain energy for linear problems the proposed elements are also applied to improve the accuracy of the solution of nonlinear problems of large deformation numerical results for 2d using fem t3 and 3d using fem t4 problems confirm that the present method gives the much more accurate solution comparing to both the standard fem and the n sfem with the same number of degrees of freedom and similar computational efforts for both linear and nonlinear problems

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 alternative alpha finite element method aαfem for free and forced structural vibration using triangular meshes an alternative alpha finite element method email protected using triangular elements is proposed that significantly improves the accuracy of the standard triangular finite elements and provides a superconvergent solution in the energy norm for the static analysis of two dimensional solid mechanics problems in the email protected the piecewise constant strain field of linear triangular fem models is enhanced by additional strain terms with an adjustable parameter a which results in an effectively softer stiffness formulation compared to a linear triangular element the element is further extended to the free and forced vibration analyses of solids several numerical examples show that the email protected achieves high reliability compared to other existing elements in the literature

a dirichlet robin iteration by subdomain method for an anisotropic nonisothermal two phase transport model of pem fuel cell with micro porous layer in this paper we present a nonoverlapping domain decomposition method dirichlet robin type alternately iteration by subdomain method for a 3d anisotropic nonisothermal multiphysics two phase transport model of proton exchange membrane fuel cell pemfc particularly bearing micro porous layer mpl and wet gas channel gc in this method the necessary transmission conditions are introduced by nonlinear dirichlet robin interfacial boundary conditions at the interfaces of some specific subdomains i e of gas diffusion layer gdl and mpl due to the discontinuous liquid saturation pasaogullari and wang 2004 therein and of gdl and gc due to the discontinuous kirchhoff transformation arising from wet gas channel sun et al 2009 we then use these transmission conditions to design a type of nonoverlapping domain decomposition method with the combined finite element upwind finite volume discretizations to deal with water transports amongst such multi layer diffusion media kirchhoff transformation and its inverse techniques are employed to overcome the discontinuous and degenerate water diffusivity in the coexisting single and two phase regions numerical simulations demonstrate that the present techniques are effective to obtain a fast and convergent nonlinear iteration for such a 3d multiphysics pemfc model in contrast to the oscillatory and nonconvergent iteration conducted by a standard finite element method

an algorithm for a singly constrained class of quadratic programs subject to upper and lower bounds this paper gives an o n algorithm for a singly constrained convex quadratic program using binary search to solve the kuhn tucker system computational results indicate that a randomized version of this algorithm runs in expected linear time and is suitable for practical applications for the nonconvex case ane approximate algorithm is proposed which is based on convex and piecewise linear approximations of the objective function

tight bounds on indefinite separable singly constrained quadratic programs in linear time non convex knapsack separable quadratic optimization with compact box constraints is an np hard problem we present tight lower and upper bounding procedures that are computationally efficient as the problem size grows the lower bound is based on lagrangian relaxation and it is computed in linear time when the bound is not an exact global solution a worst case bound quality measure is developed moreover the lower bounding lb solution is improved to construct a feasible solution leading to an upper bound ub on the given problem the ub is based on fixing the convex variables and a subset of non convex and linear variables at the lb solution and considering the remaining problem which is always feasible the ub is computable with linear time complexity and it is the global optimum in certain verifiable cases when the duality gap is zero in our limited computational experiments the ub has very small relative gap with an exact global optimum solution when there is a nonzero duality gap performance of the bounds is demonstrated through a broad range of randomly generated problem instances and comparisons with existing global and non global solvers the proposed method on these indefinite problems of extremely large size is an order of magnitude faster than the alternative solvers including ibm s commercial software cplex12 6

a formulation for the 4 node quadrilateral element a formulation for the plane 4 node quadrilateral finite element is developed based on the principle of virtual displacements for a deformable body incompatible modes are added to the standard displacement field then expressions for gradient operators are obtained from an expansion of the basis functions into a second order taylor series in the physical co ordinates the internal degrees of freedom of the incompatible modes are eliminated on the element level a modified change of variables is used to integrate the element matrices for a linear elastic material the element stiffness matrix can be separated into two parts these are equivalent to a stiffness matrix obtained from underintegration and a stabilization matrix the formulation includes the cases of plane stress and plane strain as well as the analysis of incompressible materials further the approach is suitable for non linear analysis there an application is given for the calculation of inelastic problems in physically non linear elasticity the element is efficient to implement and it is frame invariant locking effects and zero energy modes are avoided as well as singularities of the stiffness matrix due to geometric distortion a high accuracy is obtained for numerical solutions in displacements and stresses

monotonic optimization problems and solution approaches problems of maximizing or minimizing monotonic functions of n variables under monotonic constraints are discussed a general framework for monotonic optimization is presented in which a key role is given to a property analogous to the separation property of convex sets the approach is applicable to a wide class of optimization problems including optimization problems dealing with functions representable as differences of increasing functions d i functions

algorithms for separable nonlinear resource allocation problems we consider a simple resource allocation problem with a single resource constraint the objective function is composed of separable convex performance functions one for each activity likewise the constraint has separable convex resource usage functions one for each activity the objective is to minimize the sum of the performance functions subject to satisfying the resource constraint and nonnegativity constraints this problem extends the well studied problem in which the resource constraint is linear we present several algorithms to solve the problem these algorithms extend approaches developed for the linearly constrained problem they can readily solve large problems and find the optimal solution in a number of iterations that does not exceed the number of variables we provide several examples for illustration purposes present computational results and highlight the similarities and differences among the algorithms

approximation algorithms for indefinite quadratic programming we consider approximation schemes for indefinite quadratic programming we argue that such an approximation can be found in polynomial time for fixed andt wheret denotes the number of negative eigenvalues of the quadratic term our algorithm is polynomial in 1 for fixedt and exponential int for fixed we next look at the special case of knapsack problems showing that a more efficient polynomial int approximation algorithm exists

fully polynomial approximation schemes for single item capacitated economic lot sizing problems np hard cases of the single item capacitated lot sizing problem have been the topic of extensive research and continue to receive considerable attention however surprisingly few theoretical results have been published on approximation methods for these problems to the best of our knowledge until now no polynomial approximation method is known that produces solutions with a relative deviation from optimality that is bounded by a constant in this paper we show that such methods do exist by presenting an even stronger result the existence of fully polynomial approximation schemes the approximation scheme is first developed for a quite general model which has concave backlogging and production cost functions and arbitrary monotone holding cost functions subsequently we discuss important special cases of the model and extensions of the approximation scheme to even more general models

modeling studies and efficient numerical methods for proton exchange membrane fuel cell abstract in this paper a three dimensional 3d nonisothermal multiphysics two phase steady state transport model and its efficient numerical methods are systematically studied for a full proton exchange membrane fuel cell pemfc in the sense of efficiency and accuracy the conservation equations of mass momentum species charge and energy are fully addressed in view of nonisothermality and multiphase characteristics in addition from an accurate numerical discretization s point of view we present some new formulations for species equations by investigating the interactions among the species in a framework of the combined finite element upwind finite volume method some efficient numerical methods are developed in terms of kirchhoff transformation for the sake of a fast and convergent numerical simulation the 3d simulations demonstrate that the convergent solutions can be attained within 80 nonlinear iterations in contrast to the oscillating and nonconvergent iterations conducted by commercial flow solvers or in house code with standard finite element volume methods numerical convergence tests are carried out to verify the efficiency and accuracy of our numerical algorithms and techniques

a unified method for a class of convex separable nonlinear knapsack problems abstract in this paper a unified algorithm is proposed for solving a class of convex separable nonlinear knapsack problems which are characterized by positive marginal cost pmc and increasing marginal loss cost ratio imlcr by taking advantage of these two characteristics the proposed algorithm is applicable to the problem with equality or inequality constraints in contrast to the methods based on karush kuhn tucker kkt conditions our approach has linear computation complexity numerical results are reported to demonstrate the efficacy of the proposed algorithm for different problems

analysis of preconditioners for saddle point problems mixed finite element formulations give rise to large sparse block linear systems of equations the solution of which is often sought via a preconditioned iterative technique in this work we present a general analysis of block preconditioners based on the stability conditions inherited from the formulation of the finite element method the babuska brezzi or inf sup conditions the analysis is motivated by the notions of norm equivalence and field of values equivalence of matrices in particular we give sufficient conditions for diagonal and triangular block preconditioners to be norm and field of values equivalent to the system matrix

optimal multiple objective resource allocation using hybrid particle swarm optimization and adaptive resource bounds technique the multiple objective resource allocation problem morap seeks for an allocation of resource to a number of activities such that a set of objectives are optimized simultaneously and the resource constraints are satisfied morap has many applications such as resource distribution project budgeting software testing health care resource allocation etc this paper addresses the nonlinear morap with integer decision variable constraint to guarantee that all the resource constraints are satisfied we devise an adaptive resource bound technique to construct feasible solutions the proposed method employs the particle swarm optimization pso paradigm and presents a hybrid execution plan which embeds a hill climbing heuristic into the pso for expediting the convergence to cope with the optimization problem with multiple objectives we evaluate the candidate solutions based on dominance relationship and a score function experimental results manifest that the hybrid pso derives solution sets which are very close to the exact pareto sets the proposed method also outperforms several representatives of the state of the art algorithms on a simulation data set of the morap

the nonlinear resource allocation problem in this paper we study the nonlinear resource allocation problem defined as the minimization of a convex function over one convex constraint and bounded integer variables this problem is encountered in a variety of applications including capacity planning in manufacturing and computer networks production planning capital budgeting and stratified sampling despite its importance to these and other applications the nonlinear resource allocation problem has received little attention in the literature therefore we develop a branch and bound algorithm to solve this class of problems first we present a general framework for solving the continuous variable problem then we use this framework as the basis for our branch and bound method we also develop reoptimization procedures and a heuristic that significantly improve the performance of the branch and bound algorithm in addition we show how the algorithm can be modified to solve nonconvex problems so that a concave objective function can be handled

solving knapsack problems with s curve return functions we consider the allocation of a limited budget to a set of activities or investments in order to maximize return from investment in a number of practical contexts e g advertising the return from investment in an activity is effectively modeled using an s curve where increasing returns to scale exist at small investment levels and decreasing returns to scale occur at high investment levels we demonstrate that the resulting knapsack problem with s curve return functions is np hard provide a pseudo polynomial time algorithm for the integer variable version of the problem and develop efficient solution methods for special cases of the problem we also discuss a fully polynomial time approximation algorithm for the integer variable version of the problem

fast and accurate 4 node quadrilateral an accurate and variationally consistent 4 node quadrilateral element is introduced where high coarse mesh accuracy and low mesh distortion sensitivity are characteristic qualities even when incompressibility is approached for plane strain one point quadrature integration procedure is adopted and a new improved stabilization technique is developed orthogonality conditions are utilized so that the patch test is satisfied for arbitrary quadrilaterals several numerical examples including a convergence rate study are presented which confirm the excellent performance of this element copyright c 2004 john wiley sons ltd

algorithms for the continuous nonlinear resource allocation problem new implementations and numerical studies patriksson 2008 provided a then up to date survey on the continuous separable differentiable and convex resource allocation problem with a single resource constraint since the publication of that paper the interest in the problem has grown several new applications have arisen where the problem at hand constitutes a subproblem and several new algorithms have been developed for its efficient solution this paper therefore serves three purposes first it provides an up to date extension of the survey of the literature of the field complementing the survey in patriksson 2008 with more then 20 books and articles second it contributes improvements of some of these algorithms in particular with an improvement of the pegging that is variable fixing process in the relaxation algorithm and an improved means to evaluate subsolutions third it numerically evaluates several relaxation primal and breakpoint dual algorithms incorporating a variety of pegging strategies as well as a quasi newton method our conclusion is that our modification of the relaxation algorithm performs the best at least for problem sizes up to 30 million variables the practical time complexity for the breakpoint and relaxation algorithms is linear

analysis of expanded mixed finite element methods for a nonlinear parabolic equation modeling flow into variably saturated porous media we present an analysis of expanded mixed finite element methods applied to richards equation a nonlinear parabolic partial differential equation modeling the flow of water into a variably saturated porous medium we consider the full range of saturated to completely unsaturated media in the case of the lowest order raviart thomas spaces and the range of all possible saturations we bound the h 1 norm of the error in capacity in terms of approximation error this estimate uses a time integrated scheme and the kirchhoff transformation to handle a degeneracy in the case of completely unsaturated flow optimal convergence is then shown for a nonlinear form related to the error in the capacity for the case of saturated to partially saturated flow convergence rates depending on the holder continuity of the capacity term are derived last optimal convergence of pressures and fluxes is stated for the case of strictly partially saturated flow

knapsack problems with sigmoid utilities approximation algorithms via hybrid optimization we study a class of non convex optimization problems involving sigmoid functions we show that sigmoid functions impart a combinatorial element to the optimization variables and make the global optimization computationally hard we formulate versions of the knapsack problem the generalized assignment problem and the bin packing problem with sigmoid utilities we merge approximation algorithms from discrete optimization with algorithms from continuous optimization to develop approximation algorithms for these np hard problems with sigmoid utilities

efficient preconditioning of the linearized navier stokes equations for incompressible flow we outline a new class of robust and efficient methods for solving subproblems that arise in the linearization and operator splitting of navier stokes equations we describe a very general strategy for preconditioning that has two basic building blocks a multigrid v cycle for the scalar convection diffusion operator and a multigrid v cycle for a pressure poisson operator we present numerical experiments illustrating that a simple implementation of our approach leads to an effective and robust solver strategy in that the convergence rate is independent of the grid robust with respect to the time step and only deteriorates very slowly as the reynolds number is increased

error estimates for a combined finite volume finite element method for nonlinear convection diffusion problems the subject of this paper is the analysis of error estimates of the combined finite volume finite element fv fe method for the numerical solution of a scalar nonlinear conservation law equation with a diffusion term nonlinear convective terms are approximated with the aid of a monotone finite volume scheme considered over the finite volume mesh dual to a triangular grid whereas the diffusion term is discretized by piecewise linear conforming triangular finite elements under the assumption that the exact solution possesses some regularity properties and the triangulations are of a weakly acute type with the aid of the discrete maximum principle and a priori estimates error estimates of the method are proved

entropy based optimization of nonlinear separable discrete decision models this paper develops a new way to help solve difficult linear and nonlinear discrete optimization decision models more efficiently by introducing a problem difficulty metric that uses the concept of entropy from information theory our entropy metric is employed to devise rules for problem partitioning within an implicit enumeration method where branching is accomplished based on the subproblem complexity the only requirement for applying our metric is the availability of upper bounds on branching subproblems which are often computed within most implicit enumeration methods such as branch and bound or cutting plane based methods focusing on problems with a relatively small number of constraints but with a large number of variables we develop a hybrid partitioning and enumeration solution scheme by combining the entropic approach with the recently developed improved surrogate constraint isc method to produce the new method we call iscent our computational results indicate that iscent can be an order of magnitude more efficient than commercial solvers such as cplex for convex instances with no more than eight constraints furthermore for nonconvex instances iscent is shown to be significantly more efficient than other standard global solvers this paper was accepted by dimitris bertsimas optimization

a survey on the continuous nonlinear resource allocation problem our problem of interest consists of minimizing a separable convex and differentiable function over a convex set defined by bounds on the variables and an explicit constraint described by a separable convex function applications are abundant and vary from equilibrium problems in the engineering and economic sciences through resource allocation and balancing problems in manufacturing statistics military operations research and production and financial economics to subproblems in algorithms for a variety of more complex optimization models this paper surveys the history and applications of the problem as well as algorithmic approaches to its solution the most common techniques are based on finding the optimal value of the lagrange multiplier for the explicit constraint most often through the use of a type of line search procedure we analyze the most relevant references especially regarding their originality and numerical findings summarizing with remarks on possible extensions and future research 2006 elsevier b v all rights reserved

nonconvex piecewise linear knapsack problems this paper considers the minimization version of a class of nonconvex knapsack problems with piecewise linear cost structure the items to be included in the knapsack have a divisible quantity and a cost function an item can be included partially in the given quantity range and the cost is a nonconvex piecewise linear function of quantity given a demand the optimization problem is to choose an optimal quantity for each item such that the demand is satisfied and the total cost is minimized this problem and its close variants are encountered in manufacturing planning supply chain design volume discount procurement auctions and many other contemporary applications two separate mixed integer linear programming formulations of this problem are proposed and are compared with existing formulations motivated by different scenarios in which the problem is useful the following algorithms are developed 1 a fast polynomial time near optimal heuristic using convex envelopes 2 exact pseudo polynomial time dynamic programming algorithms 3 a 2 approximation algorithm and 4 a fully polynomial time approximation scheme a comprehensive test suite is developed to generate representative problem instances with different characteristics extensive computational experiments show that the proposed formulations and algorithms are faster than the existing techniques

nonlinear integer programming for optimal allocation in stratified sampling a stratified random sampling plan is one in which the elements of the population are first divided into nonoverlapping groups and then a simple random sample is selected from each group in this paper we focus on determining the optimal sample size of each group we show that various versions of this problem can be transformed into a particular nonlinear program with a convex objective function a single linear constraint and bounded variables two branch and bound algorithms are presented for solving the problem the first algorithm solves the transformed subproblems in the branch and bound tree using a variable pegging procedure the second algorithm solves the subproblems by performing a search to identify the optimal lagrange multiplier of the single constraint we also present linearization and dynamic programming methods that can be used for solving the stratified sampling problem computational testing indicates that the pegging branch and bound algorithm is fastest for some classes of problems and the linearization method is fastest for other classes of problems

numerical methods for flows through porous media i the degenerate parabolic equation aut v oulvvu v 1 has been used to model the flow of gas through a porous medium error estimates for continuous and discrete time finite element procedures to approximate the solution of this equation are proved and several new regularity results are given 1 a porous medium equation introduction we shall study the porous medium equation 1 1 au at v i u i vu on 2 x 0 t 1 2 au an 0 on aa x o t 1 3 u x 0 uo x on 2 where v 1 is a parameter and q is a bounded domain in rn n 3 with a smooth boundary the initial function u0 is assumed to be nonnegative and four times continuously differentiable on u notice that the compatibility condition auo an 0 holds on asa our main result is the derivation of error estimates for numerical approximations to the problem 1 1 1 3 which we shall refer to as the porous medium equation or ipme the pme does not in general admit classical solutions existence and uniqueness of weak solutions was proved in one space dimension by oleinik kalashnikov and czou 15 16 and in several space dimensions by lions 12 these proofs concern the pme with different boundary conditions but the arguments carry over to the pme 1 1 1 3 the maximum principle implies that since u0 is nonnegative on 92 u x t is nonnegative for all x t e q x 0 t see 15 16 if u0 is nonzero the neumann boundary condition implies that u will eventually become strictly positive and 1 1 will become nondegenerate for all time t to to sufficiently large we can rewrite 1 1 in the form 1 4 au at ak u on qx 0 t received may 11 1979 revised july 24 1981 1980 mathematics subject classification primary 35k65 65n30 65n15 current address reservoir engineering branch petroleum engineering division bp exploration dos britannic house moore lane london ec2y 9bu united kingdom d1983 american mathematical society 0025 5718 82 0000 1 063 08 25 435 this content downloaded from 157 55 39 55 on tue 23 aug 2016 04 12 54 utc all use subject to http about jstor org terms

inverse optimization for linearly constrained convex separable programming problems abstract in this paper we study inverse optimization for linearly constrained convex separable programming problems that have wide applications in industrial and managerial areas for a given feasible point of a convex separable program the inverse optimization is to determine whether the feasible point can be made optimal by adjusting the parameter values in the problem and when the answer is positive find the parameter values that have the smallest adjustments a sufficient and necessary condition is given for a feasible point to be able to become optimal by adjusting parameter values inverse optimization formulations are presented with l 1 and l 2 norms these inverse optimization problems are either linear programming when l 1 norm is used in the formulation or convex quadratic separable programming when l 2 norm is used

quadrilateral membrane element family formulated by the quadrilateral area coordinate method abstract the quadrilateral area coordinate qac method is a new tool for developing quadrilateral finite element models compared with those traditional elements using isoparametric coordinates models formulated by qac method are less sensitive to mesh distortion in this paper a family of quadrilateral membrane elements with 4 8 nodes are successfully developed by employing the qac method the generalized conforming conditions and internal parameters all the displacement fields of these elements possess second order completeness in cartesian coordinates so they are more accurate and robust in various distorted meshes numerical results show that the presented elements exhibit excellent performance in all benchmark problems such as macneal s beam thin curved beam problems etc which the traditional isoparametric elements can not easily achieve the efficiency of the qac method for developing simple effective and reliable serendipity plane membrane elements is again demonstrated

a novel galerkin like weakform and a superconvergent alpha finite element method sαfem for mechanics problems using triangular meshes a carefully designed procedure is presented to modify the piecewise constant strain field of linear triangular fem models and to reconstruct a strain field with an adjustable parameter a a novel galerkin like weakform derived from the hellinger reissner variational principle is proposed for establishing the discretized system equations the new weak form is very simple possesses the same good properties of the standard galerkin weakform and works particularly well for strain construction methods a superconvergent alpha finite element method email protected is then formulated by using the constructed strain field and the galerkin like weakform for solid mechanics problems the implementation of the email protected is straightforward and no additional parameters are used we prove theoretically and show numerically that the email protected always achieves more accurate and higher convergence rate than the standard fem of triangular elements t3 and even more accurate than the four node quadrilateral elements q4 when the same sets of nodes are used the email protected can always produce both lower and upper bounds to the exact solution in the energy norm for all elasticity problems by properly choosing an a in addition a email protected approach has also been devised to produce very accurate solutions for both displacement and energy norms and a superconvergent rate in the energy error norm furthermore a model based selective scheme is proposed to formulate a combined email protected ns fem model that handily overcomes the volumetric locking problems intensive numerical studies including singularity problems have been conducted to confirm the theory and properties of the email protected

a particle swarm optimization approach to the nonlinear resource allocation problem the resource allocation problem seeks to find an optimal allocation of a limited amount of resource to a number of activities for optimizing the objective under the resource constraint most existing methods use mathematical programming techniques but they may fail to derive exact solutions for large sized problems with reasonable time an alternative is to use meta heuristic algorithms for obtaining approximate solutions this paper presents a particle swarm optimization pso algorithm for conquering the nonlinear resource allocation problem to ensure the resource constraint is satisfied we propose adaptive resource bounds for guiding the search the experimental results manifest that the proposed method is more effective and efficient than a genetic algorithm the convergence behavior of the proposed method is analyzed by observing the variations of particle entropy finally a worst case analysis is conducted to provide a reliable performance guarantee

fast nonsymmetric iterations and preconditioning for navier stokes equations discretization and linearization of the steady state navier stokes equations gives rise to a nonsymmetric indefinite linear system of equations in this paper we introduce preconditioning techniques for such systems with the property that the eigenvalues of the preconditioned matrices are bounded independently of the mesh size used in the discretization we confirm and supplement these analytic results with a series of numerical experiments indicating that krylov subspace iterative methods for nonsymmetric systems display rates of convergence that are independent of the mesh parameter in addition we show that preconditioning costs can be kept small by using iterative methods for some intermediate steps performed by the preconditioner

block triangular preconditioners for nonsymmetric saddle point problems field of values analysis a preconditioned minimal residual method for nonsymmetric saddle point problems is analyzed the proposed preconditioner is of block triangular form the aim of this article is to show that a rigorous convergence analysis can be performed by using the field of values of the preconditioned linear system as an example a saddle point problem obtained from a mixed finite element discretization of the oseen equations is considered the convergence estimates obtained by using a field of values analysis are independent of the discretization parameter h several computational experiments supplement the theoretical results and illustrate the performance of the method

on the solution of concave knapsack problems we consider a version of the knapsack problem which gives rise to a separable concave minimization problem subject to bounds on the variables and one equality constraint we characterize strict local miniimizers of concave minimization problems subject to linear constraints and use this characterization to show that although the problem of determining a global minimizer of the concave knapsack problem is np hard it is possible to determine a local minimizer of this problem with at most o n logn operations and 1 logn evaluations of the function if the function is quadratic this algorithm requires at most o n logn operations

accurate eight node hexahedral element based on the assumed strain method an eight node hexahedral element is proposed consistent choice of the fundamental element stiffness guarantees convergence and fulfillment of the patch test a priori in conjunction with a projection operator the higher order strain field becomes orthogonal to rigid body and linear displacement fields the higher order strain field in question is carefully selected to preserve correct rank for the element stiffness matrix also for distorted elements volumetric locking is also removed effectively by considerations of the bending energy improved accuracy is obtained even for coarse element meshes the choice of local co ordinate system aligned with the principal axes of inertia makes it possible to improve the performance even for distorted elements the strain driven format obtained is well suited for materials with non linear stress strain relations several numerical examples are presented where the excellent performance of the proposed eight node hexahedral is verified

a class of nonlinear nonseparable continuous knapsack and multiple choice knapsack problems this paper considers a general class of continuous nonlinear and nonseparable knapsack problems special cases of which arise in numerous operations and financial contexts we develop important properties of optimal solutions for this problem class based on the properties of a closely related class of linear programs using these properties we provide a solution method that runs in polynomial time in the number of decision variables while also depending on the time required to solve a particular one dimensional optimization problem thus for the many applications in which this one dimensional function is reasonably well behaved e g unimodal the resulting algorithm runs in polynomial time we next develop a related solution approach to a class of continuous nonlinear and nonseparable multiple choice knapsack problems this algorithm runs in polynomial time in both the number of variables and the number of variants per item while again dependent on the complexity of the same one dimensional optimization problem as for the knapsack problem computational testing demonstrates the power of the proposed algorithms over a commercial global optimization software package

a uniform strain hexahedron and quadrilateral with orthogonal hourglass control the treatment of zero energy modes which arise due to one point integration of first order isoparametric finite elements is addressed a method for precisely isolating these modes for arbitrary geometry is developed two hourglass control schemes viscous and elastic are presented and examined in addition a convenient one point integration scheme which analytically integrates the element volume and uniform strain modes is presented

some np complete problems in quadratic and nonlinear programming in continuous variable smooth nonconvex nonlinear programming we analyze the complexity of checking whether a a given feasible solution is not a local minimum and b the objective function is not bounded below on the set of feasible solutions we construct a special class of indefinite quadratic programs with simple constraints and integer data and show that checking a or b on this class is np complete as a corollary we show that checking whether a given integer square matrix is not copositive is np complete

a locking free finite difference method on staggered grids for linear elasticity problems abstract a finite difference method on staggered grids is constructed on general nonuniform rectangular partition for linear elasticity problems stability optimal order error estimates in discrete h 1 norms on general nonuniform grids and second order superconvergence on almost uniform grids have been obtained these theoretical results are uniform about the lame constant 0 so the finite difference method is locking free the method and theoretical results can be extended to three dimensional problems numerical experiments using the method show agreement of the numerical results with theoretical analysis

methods for global concave minimization a bibliographic survey the global concave minimization problem is to find the constrained global minimum of a concave function since such a function may have many local minima finding the global minimum is a computationally difficult problem in this bibliographic survey which includes most of the recent papers on constrained global concave minimization we have attempted to briefly summarize the main ideas in each paper these recent papers include those concerned with large scale global concave minimization and bilinear programming

a class of mixed assumed strain methods and the method of incompatible modes a three field mixed formulation in terms of displacements stresses and an enhanced strain field is presented which encompasses as a particular case the classical method of incompatible modes within this frame work incompatible elements arise as particular compatible mixed approximations of the enhanced strain field the conditions that the stress interpolation contain piece wise constant functions and be l2 ortho gonal to the enhanced strain interpolation ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation the preceding conditions are formulated in a form particularly convenient for element design as an illustration of the methodology three new elements are developed and shown to exhibit good performance a plane 3d elastic plastic quad an axisymmetric element and a thick plate bending quad the formulation described herein is suitable for non linear analysis

a domain decomposition method for two phase transport model in the cathode of a polymer electrolyte fuel cell using kirchhoff transformation we develop a dirichlet neumann alternating iterative domain decomposition method for a 2d steady state two phase model for the cathode of a polymer electrolyte fuel cell pefc which contains a channel and a gas diffusion layer gdl this two phase pefc model is represented by a nonlinear coupled system which typically includes a modified navier stokes equation with darcy s drag as an additional source term of the momentum equation and a convection diffusion equation for the water concentration with discontinuous and degenerate diffusivity for both cases of dry and wet gas channel we employ kirchhoff transformation and dirichlet neumann alternating iteration with appropriate interfacial conditions on the gdl channel interface to treat the jump nonlinearities in the water equation numerical experiments demonstrate that fast convergence as well as accurate numerical solutions are obtained simultaneously owing to the implementation of the above described numerical techniques along with a combined finite element upwind finite volume discretization to automatically control the dominant convection terms arising in the gas channel

necessary and sufficient condition for local minima of a class of nonconvex quadratic programs the author 1992 1993 earlier studied the equivalence of a class of 0 1 quadratic programs and their relaxed problems thus a class of combinatorial optimization problems can be solved by solving a class of nonconvex quadratic programs in this paper a necessary and sufficient condition for local minima of this class of nonconvex quadratic programs is given this will be the foundation for study of algorithms

an iteration by subdomain overlapping dirichlet robin domain decomposition method for advection diffusion problems we present a new overlapping dirichlet robin domain decomposition method the method uses dirichlet and robin transmission conditions on the interfaces of an overlapping partitioning of the computational domain we derive interface equations to study the convergence of the method and show its properties through four numerical examples the mathematical framework is general and can be applied to derive overlapping versions of all the classical nonoverlapping methods

branch and bound experiments in convex nonlinear integer programming the branch and bound principle has long been established as an effective computational tool for solving mixed integer linear programming problems this paper investigates the computational feasibility of branch and bound methods in solving convex nonlinear integer programming problems the efficiency of a branch and bound method often depends on the rules used for selecting the branching variables and branching nodes among others the concepts of pseudo costs and estimations are implemented in selecting these parameters since the efficiency of the algorithm also depends on how fast an upper bound on the objective minimum is attained heuristic rules are developed to locate an integer feasible solution to provide an upper bound the different criteria for selecting branching variables branching nodes and heuristics form a total of 27 branch and bound strategies these strategies are computationally tested and the empirical results are presented

hourglass control in linear and nonlinear problems abstract mesh stabilization techniques for controlling the hourglass modes in under integrated hexahedral and quadrilateral elements are described it is shown that the orthogonal hourglass techniques previously developed can be obtained from simple requirements that insure the consistency of the finite element equations in the sense that the gradients of linear fields are evaluated correctly it is also shown that this leads to an hourglass control that satisfies the patch test the nature of the parameters which relate the generalized stresses and strains for controlling hourglass modes is examined by means of a mixed variational principle and some guidelines for their selection are discussed finally effective means of implementing these hourglass procedure in computer codes are described applications to both the laplace equation and the equations of solid mechanics in 2 and 3 dimensions are considered

quadrilateral membrane elements with analytical element stiffness matrices formulated by the new quadrilateral area coordinate method qacm ii a novel strategy for developing low order membrane elements with analytical element stiffness matrices is proposed first some complete low order basic analytical solutions for plane stress problems are given in terms of the new quadrilateral area coordinates method qacm ii then these solutions are taken as the trial functions for developing new membrane elements thus the interpolation formulae for displacement fields naturally possess second order completeness in physical space cartesian coordinates finally by introducing nodal conforming conditions new 4 node and 5 node membrane elements with analytical element stiffness matrices are successfully constructed the resulting models denoted as qac atf4 and qac atf5 have high computational efficiency since the element stiffness matrices are formulated explicitly and no internal parameter is added these two elements exhibit excellent performance in various bending problems with mesh distortion it is demonstrated that the proposed strategy possesses advantages of both the analytical and the discrete method and the qacm ii is a powerful tool for constructing high performance quadrilateral finite element models copyright 2008 john wiley sons ltd

on optimal allocation of indivisibles under uncertainty the optimal allocation of indivisible resources is formalized as a stochastic optimization problem involving discrete decision variables a general stochastic search procedure is proposed which develops the concept of the branch and bound method the main idea is to process large collections of possible solutions and to devote more attention to the most promising groups by gathering more information to reduce the uncertainty and by narrowing the search area the optimal solution can be found with probability one special techniques for calculating stochastic lower and upper bounds are discussed the results are illustrated by a computational experiment

about strongly polynomial time algorithms for quadratic optimization over submodular constraints we present new strongly polynomial algorithms for special cases of convex separable quadratic minimization over submodular constraints the main results are an o nm log n 2 m algorithm for the problemnetwork defined on a network onm arcs andn nodes an o n logn algorithm for thetree problem onn variables an o n logn algorithm for thenested problem and a linear time algorithm for thegeneralized upper bound problem these algorithms are the best known so far for these problems the status of the general problem and open questions are presented as well

an approximation approach for representing s shaped membership functions in general to formulate a fuzzy linear programming problem with n s shaped utility membership functions traditional methods require n or more extra binary variables because s shaped curves are neither convex nor concave in all places adding binary variables does not improve the bound of the linear programming relaxation on the contrary added binary variables increase the computational burden in the solution process if problems get large therefore a formulation without binary variables should be more efficient accordingly this study proposes a piecewise linear approach to formulate an s shaped membership function mf without adding any extra binary variables which improves the efficiency of fuzzy linear programming in solving decision management problems with s shaped mfs finally a computational experiment is provided to demonstrate the superiority of the proposed models an illustrative example is also provided to show the usefulness of the proposed method

two stage quadratic integer programs with stochastic right hand sides we consider two stage quadratic integer programs with stochastic right hand sides and present an equivalent reformulation using value functions we propose a two phase solution approach the first phase constructs value functions of quadratic integer programs in both stages the second phase solves the reformulation using a global branch and bound algorithm or a level set approach we derive some basic properties of value functions of quadratic integer programs and utilize them in our algorithms we show that our approach can solve instances whose extensive forms are hundreds of orders of magnitude larger than the largest quadratic integer programming instances solved in the literature

a heuristic algorithm for a chance constrained stochastic program a chance constrained stochastic program is considered that arises from an application to college enrollments and in which the objective function is the expectation of a linear function of the random variables when these random variables are independent and normally distributed with mean and variance that are linear in the decision variables the deterministic equivalent of the problem is a nonconvex nonlinear knapsack problem the optimal solution to this problem is characterized and a greedy type heuristic algorithm that exploits this structure is employed computational results show that the algorithm performs well especially when the normal random variables are approximations of binomial random variables

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

simple and accurate four node axisymmetric element based on the assumed strain method a simple four node axisymmetric solid element is introduced the assumed strain field is carefully selected to preserve the correct rank of the element stiffness matrix and to achieve high accuracy the strain field is developed in conjunction with orthogonal projections and no matrix inversions are needed the coarse mesh accuracy in bending and in typical axisymmetric load cases is excellent even for nearly incompressible materials the strain driven format obtained is well suited for materials with non linear stress strain relations several numerical examples are presented where the excellent performance of the proposed simple element is verified copyright c 2006 john wiley sons ltd

the nonlinear knapsack problem algorithms and applications abstract we present a survey of algorithms and applications for the nonlinear knapsack problem or the nonlinear resource allocation problem in its most general form the nonlinear knapsack problem will be defined as a nonlinear optimization problem with just one constraint bounds on the variables and in some cases a set of specially structured constraints such as generalized upper bounds gubs this problem is encountered either directly or as a subproblem in a variety of applications including production planning financial modeling stratified sampling and capacity planning in manufacturing health care and computer networks by taking advantage of the special structure of the problem efficient solution methods can be developed problem classes addressed here include continuous and integer problems convex and nonconvex problems separable and nonseparable problems and problems with additional specially structured constraints

on stability convergence and accuracy of bes fem and bfs fem for nearly incompressible elasticity abstract we present in this paper a rigorous theoretical framework to show stability convergence and accuracy of improved edge based and face based smoothed finite element methods bes fem and bfs fem for nearly incompressible elasticity problems the crucial idea is that the space of piecewise linear polynomials used for the displacements is enriched with bubble functions on each element while the pressure is a piecewise constant function the meshes of triangular or tetrahedral elements required by these methods can be generated automatically the enrichment induces a softening in the bilinear form allowing the weakened weak w 2 procedure to produce a high quality solution free from locking and that does not oscillate we prove theoretically that both methods confirm the uniform inf sup and convergence conditions four numerical examples are given to validate the reliability of the bes fem and bfs fem

disaggregation and resource allocation using convex knapsack problems with bounded variables the allocation of a specific amount of a given resource among competitive alternatives can often be modelled as a knapsack problem this model formulation is extremely efficient because it allows convex cost representation with bounded variables to be solved without great computational efforts practical applications of this problem abound in the fields of operations management finance manpower planning marketing etc in particular knapsack problems emerge in hierarchical planning systems when a first level of decisions need to be further allocated among specific activities which have been previously treated in an aggregate way in this paper we provide a recursive procedure to solve such problems the method differs from classical optimization algorithms of convex programming in that it determines at each iteration the optimal value of at least one variable applications and computational results are presented

convergent lagrangian and contour cut method for nonlinear integer programming with a quadratic objective function in this paper we present an efficient exact solution method for solving nonlinear separable integer programming problems with a quadratic objective function the proposed method combines the lagrangian dual method with a duality reduction scheme using contour cut at each iteration of the algorithm lower and upper bounds of the problem are determined by the lagrangian dual search to eliminate the duality gap a novel cut and partition scheme is derived by exploring the special structure of the quadratic contour the method finds an exact solution of the problem in a finite number of iterations computational results are reported for problems with up to 2000 integer variables comparison results with other methods are also presented

rational approach for assumed stress finite elements a new method for the formulation of hybrid elements by the hellinger reissner principle is established by expanding the essential terms of the assumed stresses as complete polynomials in the natural coordinates of the element the equilibrium conditions are imposed in a variational sense through the internal displacements which are also expanded in the natural co ordinates the resulting element possesses all the ideal qualities i e it is invariant it is less sensitive to geometric distortion it contains a minimum number of stress parameters and it provides accurate stress calculations for the formulation of a 4 node plane stress element a small perturbation method is used to determine the equilibrium constraint equations the element has been proved to be always rank sufficient

algorithms for the solution of quadratic knapsack problems we consider the problem of minimizing a quadratic function with a knapsack constraint quadratic knapsack problems have numerous applications including the least distance problem quadratic programming defined on the convex hull of a set of points and the maximum clique problem we propose and analyze three algorithms for solving quadratic knapsack problems two algorithms are based on recently developed interior point methods the first solves convex quadratic problems and the second computes a stationary point for the indefinite case for both computational results on a variety of test problems are presented the third algorithm based on simplicial partitioning and convex underestimating functions can be used to compute the global optimum of indefinite quadratic knapsack problems

quasi newton updates with bounds we develop a quasi newton method which preserves known bounds on the jacobian matrix we show that this update can be computed with the same amount of work as competitive methods in particular we prove that the number of operations required to obtain this update is proportional to the number of nonzeros in the sparsity pattern of the jacobian matrix the method is also shown to share the local convergence properties of broyden s and schubert s method

a variationally consistent αfem vcαfem for solution bounds and nearly exact solution to solid mechanics problems using quadrilateral elements a variationally consistent alpha finite element method vc fem for quadrilateral isoparametric elements is presented by constructing an assumed strain field in which the gradient of the compatible strain field is scaled with a free parameter the assumed strain field satisfies the orthogonal condition and the hellinger reissner variational principle is used to establish the discretized system of equations it is shown that the strain energy is a second order continuous function of and the vc fem can produce both lower and upper bounds to the exact solution in the strain energy for all elasticity problems by choosing a proper 0 upper based on this bound property an exact approach has been devised to give an ultra accurate solution that is very close to the exact one in the strain energy furthermore the exact approach also works well for volumetric locking problems by simply replacing the strain gradient matrix by a stabilization matrix in addition a regularization approach has also been suggested to overcome possible hourglass instability intensive numerical studies have been conducted to confirm the properties of the present vc fem and a very good performance has been found in comparing to a large number of existing fem models copyright 2010 john wiley sons ltd