preconditioning for dual time stepping simulations of the shallow water equations including coriolis and bed friction effects diagonal preconditioners for implicit unsteady and steady discretizations of the shallow water equations at low and high rossby and drag number limits are analyzed for each case sub and supercritical flow conditions are also considered based on the analysis a preconditioner is derived for use with a multigrid cycle that performs as well as possible under all conditions in addition a streamwise upwind petrov galerkin discretization of the system is presented that is derived from the preconditioned system using this discretization it is demonstrated that for most conditions the preconditioner gives rapid convergence that is independent of the grid resolution and the flow parameters practical tests including an equatorial rossby soliton and tide propagation over variable bathymetry are simulated to demonstrate the performance of this approach

the minimum cost flow problem a unifying approach to dual algorithms and a new tree search algorithm this paper is concerned with the minimum cost flow problem it is shown that the class of dual algorithms which solve this problem consists of different variants of a common general algorithm we develop a new variant which is in fact a new form of the primal dual algorithm and which has several interesting properties it uses explicitly only dual variables the slope of the change in the dual objective is monotone the bound on the maximum number of iterations to solve a problem with integral bounds on the flow is better than bounds for other algorithms

convex separable optimization is not much harder than linear optimization the polynomiality of nonlinear separable convex concave optimization problems on linear constraints with a matrix with small subdeterminants and the polynomiality of such integer problems provided the inteter linear version of such problems ins polynomial is proven this paper presents a general purpose algorithm for converting procedures that solves linear programming problems the conversion is polynomial for constraint matrices with polynomially bounded subdeterminants among the important corollaries of the algorithm is the extension of the polynomial solvability of integer linear programming problems with totally unimodular constraint matrix to integer separable convex programming an algorithm for finding a e accurate optimal continuous solution to the nonlinear problem that is polynomial in log 1 e and the input size and the largest subdeterminant of the constraint matrix is also presented these developments are based on proximity results between the continuous and integral optimal solutions for problems with any nonlinear separable convex objective function the practical feature of our algorithm is that is does not demand an explicit representation of the nonlinear function only a polynomial number of function evaluations on a prespecified grid

a fully semi lagrangian discretization for the 2d incompressible navier stokes equations in the vorticity streamfunction formulation abstract a numerical method for the two dimensional incompressible navier stokes equations in vorticity streamfunction form is proposed which employs semi lagrangian discretizations for both the advection and diffusion terms thus achieving unconditional stability without the need to solve linear systems beyond that required by the poisson solver for the reconstruction of the streamfunction a description of the discretization of dirichlet boundary conditions for the semi lagrangian approach to diffusion terms is also presented numerical experiments on classical benchmarks for incompressible flow in simple geometries validate the proposed method

relaxation methods for monotropic programs we propose a dual descent method for the problem of minimizing a convex possibly nondifferentiable separable cost subject to linear constraints the method has properties reminiscent of the gauss seidel method in numerical analysis and uses the e complementary slackness mechanism introduced in bertsekas hosein and tseng 1987 to ensure finite convergence to near optimality as special cases we obtain the methods in bertsekas hosein and tseng 1987 for network flow programs and the methods in tseng and bertsekas 1987 for linear programs

in plane vibrations of an elastically cantilevered circular arc with a tip mass abstract upper and lower bounds are determined for the fundamental frequency of in plane transverse vibration of the structural system described in the title in the case of constant cross section and moment of inertia the upper bound is determined by approximating the fundamental mode shape with a polynomial co ordinate function in the angular co ordinate which includes an exponential optimization parameter the fundamental frequency equation is generated by means of the rayleigh ritz method and the resulting upper bound is minimized with respect to the previously mentioned exponential parameter the lower bound for the frequency coefficient is obtained by means of an extension of dunkerley s method it is felt that the methodologies developed in the present study are especially useful in the case of variable cross section of the arch structure presence of internal supports etc

exact solution of in plane vibrations of circular arches with account taken of axial extension transverse shear and rotatory inertia effects exact solution of free in plane vibrations of circular arches of uniform cross section is given by considering axial extension transverse shear and rotatory inertia effects in contrast with kirchhoff s beam theory the restrictions of perpendicular cross section and inextensible arc length are removed the principal axes of the cross section are assumed to coincide with the principal normal and binormal vectors of the centerline of the beam a solution procedure is applied to obtain the fundamental matrix for various end conditions natural frequencies and mode shapes are given in figures and tables

concave generalized flows with applications to market equilibria we consider a nonlinear extension of the generalized network flow model with the flow leaving an arc being an increasing concave function of the flow entering it as proposed by truemper truemper k 1978 optimal flows in nonlinear gain networks networks 8 1 17 36 and by shigeno shigeno m 2006 maximum network flows with concave gains math programming 107 3 439 459 we give a polynomial time combinatorial algorithm for solving corresponding flow maximization problems finding an e approximate solution in o m m log n log mum e arithmetic operations where m and u are upper bounds on simple parameters and is the complexity of a value oracle query for the gain functions this also gives a new algorithm for linear generalized flows an efficient purely scaling variant of the fat path algorithm by goldberg et al goldberg av plotkin sa tardos e 1991 combinatorial algorithms for the generalized circulation problem math oper res 16 2 351 381 not using any cycle cancellations we sho

multiblock multigrid grid generation algorithms overcoming multigrid anisotropy abstract the paper presents multiblock multigrid algorithms for the generation of boundary fitted grids bfgs able to avoid undesired multigrid anisotropy arises the algorithms combine a domain decomposition technique the elliptic grid generation and the multigrid computation and provide satisfactory numerical solutions and fast convergence block matching based on two surface overlapping saves grid characteristics through the block boundaries we assume two and three dimensional generation systems allowing line spacing control and we design block by block multigrid computation to solve the transformed finite difference systems we identify anisotropy as an undesirable multigrid effect and we overcome anisotropic behaviors by investigation over coefficients of the generating systems they can provide information to select appropriate relaxation algorithms a wide series of performance evaluation results is available one block and multiblock so as one grid and multi grid algorithms have been evaluated and meaningful results are collected in tables visualizations of 2d and 3d computed grids and displays of convergence histories comparing multigrid components are shown by figures

boundary fitted coordinate systems for numerical solution of partial differential equations a review a comprehensive review of methods of numerically generating curvilinear coordinate systems with coordinate lines coincident with all boundary segments is given some general mathematical framework and error analysis common to such coordinate systems is also included the general categories of generating systems are those based on conformal mapping orthogonal systems nearly orthogonal systems systems produced as the solution of elliptic and hyperbolic partial differential equations and systems generated algebraically by interpolation among the boundaries also covered are the control of coordinate line spacing by functions embedded in the partial differential operators of the generating system and by subsequent stretching transformation dynamically adaptive coordinate systems coupled with the physical solution and time dependent systems that follow moving boundaries are treated references reporting experience using such coordinate systems are reviewed as well as those covering the system development

fundamental mode shape and its derivatives in structural damage localization abstract various techniques for structural damage detection involving modal parameters have widely been used over the past few decades this is because the modal parameters of a structure can easily be obtained from forced free or ambient vibration measurements in many of these techniques mode shape curvature has been used for localization of damage in this paper a mathematical basis is provided to show the correlation between a structural damage and a change in the fundamental mode shape and its derivatives this has been achieved by deriving the expression of a damaged mode shape utilizing a perturbation approach for a cantilever shear beam discretized into a large number of elements this approach demonstrates that the change in the fundamental mode shape due to any damage is an excellent indicator of damage localization as it is found to be discontinuous at the location of damage further the change in higher derivatives i e slope and curvature of the fundamental mode shape is shown to be sensitive enough in damage localization a numerical study involving a shear building and a steel moment resisting frame is conducted to show the effectiveness of the proposed approach in damage localization it has been found from this study that spline fitting of mode shapes in case of a limited number of degrees of freedom which is generally adopted for plotting mode shapes and their derivatives may lead to false detection of damage

a multigrid method for grid generation with line spacing control a multigrid method for grid generation on two dimensional regions and its applications to test problems are presented the multigrid algorithm deals with the solution of elliptic differential problems which occur in the computation of boundary fitted grids the solution of elliptic systems of partial differential equations which correspond to transformed poisson systems is carried out by a full approximation storage fas algorithm the components of the method such as the relaxation for error smoothing and the coarsening strategy are evaluated on problems in which sources of attractions are considered and the generated grids are shown by figures

polynomial methods for separable convex optimization in unimodular linear spaces with applications we consider the problem of minimizing a separable convex objective function over the linear space given by a system mx 0 with m a totally unimodular matrix in particular this generalizes the usual minimum linear cost circulation and cocirculation problems in a network and the problems of determining the euclidean distance from a point to the perfect bipartite matching polytope and the feasible flows polyhedron we first show that the idea of minimum mean cycle canceling originally worked out for linear cost circulations by goldberg and tarjan j assoc comput mach 36 1989 pp 873 886 and extended to some other problems t r ervolina and s t mccormick discrete appl math 46 1993 pp 133 165 a frank and a v karzanov technical report rr 895 m laboratoire artemis imag universite joseph fourier grenoble france 1992 t ibaraki a v karzanov and h nagamochi private communication 1993 m hadjiat technical report groupe intelligence artificielle faculte des sciences de luminy marseille france 1994 can be generalized to give a combinatorial method with geometric convergence for our problem we also generalize the computationally more efficient cancel and tighten method we then consider objective functions that are piecewise linear pure and piecewise quadratic or piecewise mixed linear and quadratic and we show how both methods can be implemented to find exact solutions in polynomial time strongly polynomial in the piecewise linear case these implementations are then further specialized for finding circulations and cocirculations in a network we finish by showing how to extend our methods to find optimal integer solutions to linear spaces of larger fractionality and to the case when the objective functions are given by approximate oracles

combinatorial algorithms for the generalized circulation problem we consider a generalization of the maximum flow problem in which the amounts of flow entering and leaving an arc are linearly related more precisely if x e units of flow enter an arc e x e e units arrive at the other end for instance nodes of the graph can correspond to different currencies with the multipliers being the exchange rates we require conservation of flow at every node except a given source node the goal is to maximize the amount of flow excess at the source this problem is a special case of linear programming and therefore can be solved in polynomial time in this paper we present the first polynomial time combinatorial algorithms for this problem the algorithms are simple and intuitive

numerical methods for convection dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures finite element and finite difference methods are combined with the method of characteristics to treat a parabolic problem of the form cu t bu x au x x f optimal order error estimates in l 2 and w 1 2 are derived for the finite element procedure various error estimates are presented for a variety of finite difference methods the estimates show that for convection dominated problems b gg a these schemes have much smaller time truncation errors than those of standard methods extensions to n space variables and time dependent or nonlinear coefficients are indicated along with applications of the concepts to certain problems described by systems of differential equations

determination of bed elevation in the enhanced lattice boltzmann method for the shallow water equations the bed slope in the shallow water equations reflects the bed topography it is not a flow variable and cannot be determined in the solution to the flow equations an immovable nonflat bed affects a flow as a force term but the flow has no effect on it only when the bed term is correctly represented in a numerical method can it generate an accurate solution in the enhanced lattice boltzmann method for the shallow water equations elabswe using an individual chapman enskog analysis it is found that such a correct representation can be achieved by retaining c 2 in which c is the coefficient for bed elevation in the lattice boltzmann equation and is that for the water depth in the local equilibrium distribution function the finding has been validated through simulations of a water at rest in a dish shaped lake a wind induced shallow flow in the same lake and a steady flow over a two dimensional bed hump

stability accuracy and efficiency of a semi implicit method for three dimensional shallow water flow abstract the stability analysis the accuracy and the efficiency of a semi implicit finite difference scheme for the numerical solution of a three dimensional shallow water model are presented and discussed the governing equations are the three dimensional reynolds equations in which pressure is assumed to be hydrostatic the pressure gradient in the momentum equations and the velocities in the vertically integrated continuity equation are discretized with the method with being an implicitness parameter it is shown that the method is stable for 1 2 1 unstable for 1 2 and highest accuracy and efficiency is achieved when 1 2 the resulting algorithm is mass conservative and naturally allows for the simulation of flooding and drying of tidal flats

a domain decomposition and overlapping method for the generation of three dimensional boundary fitted coordinate systems abstract a new method is presented for numerically generating boundary fitted coordinate systems for arbitrarily shaped three dimensional regions in the method the three dimensional region of interest is decomposed into several hexahedrons each of which has two grid surfaces overlapped with each of the neighboring hexahedrons based on this method a new computer program grid 3d has been developed which allows the generation of an unlimitted number of different types of coordinate systems application to a variety of geometries confirms that grid 3d is a convenient and efficient tool in the generation of boundary fitted coordinate systems even for a considerably complicated configuration consisting of many different components

euler s predictor corrector technique for solving the depth integrated shallow water equations abstract euler s predictor corrector technique combined with finite analysis method is applied to solve 2d advection diffusion shallow water equations in this algorithm the momentum equations are calculated by the finite analysis method based on a single mesh while the continuity equation is solved by euler s predictor corrector technique to verify the performance of this approach the simulation of tidal flow in the huangpu estuary is carried out the numerical results are found to be consistent with the field results implying that this proposed method is effective and applicable

nondegenerate piecewise linear systems a finite newton algorithm and applications in machine learning we investigate newton type optimization methods for solving piecewise linear systems plss with nondegenerate coefficient matrix such systems arise for example from the numerical solution of linear complementarity problem which is useful to model several learning and optimization problems in this letter we propose an effective damped newton method pls dn to find the exact up to machine precision solution of nondegenerate plss pls dn exhibits provable semiiterative property that is the algorithm converges globally to the exact solution in a finite number of iterations the rate of convergence is shown to be at least linear before termination we emphasize the applications of our method in modeling from a novel perspective of plss some statistical learning problems such as box constrained least squares elitist lasso kowalski torreesani 2008 and support vector machines cortes vapnik 1995 numerical results on synthetic and benchmark data sets are presented to demonstrate the effectiveness and efficiency of pls dn on these problems

semi implicit semi lagrangian modelling for environmental problems on staggered cartesian grids with cut cells in this paper we propose an extension of semi implicit models for the shallow water or euler equations on staggered cartesian meshes to handle the presence of cut cells at the boundaries of the computational domain semi lagrangian advection algorithms are also extended to staggered cartesian meshes with cut boundary cells a linear reconstruction algorithm and radial basis function interpolation are used respectively to compute approximate trajectories and to recover an accurate velocity field in cells intersected by the boundary the effective accuracy of radial basis function interpolators for semi lagrangian algorithms is assessed by simple numerical experiments timestep control techniques in the computation of the semi lagrangian trajectories are also discussed the accuracy of the resulting models for environmental flows is demonstrated by a number of test cases simulating nonlinear open channel flows and baroclinic flows over an isolated obstacle

on the complexity of computing the handicap of a sufficient matrix the class of sufficient matrices is important in the study of the linear complementarity problem lcp some interior point methods ipm s for lcp s with sufficient data matrices have complexity polynomial in the bit size of the matrix and its handicap in this paper we show that the handicap of a sufficient matrix may be exponential in its bit size implying that the known complexity bounds of interior point methods are not polynomial in the input size of the lcp problem we also introduce a semidefinite programming based heuristic that provides a finite upper bond on the handicap for the sub class of mathcal p matrices where all principal minors are positive

a unifying polyhedral approximation framework for convex optimization we propose a unifying framework for polyhedral approximation in convex optimization it subsumes classical methods such as cutting plane and simplicial decomposition but also includes new methods and new versions extensions of old methods such as a simplicial decomposition method for nondifferentiable optimization and a new piecewise linear approximation method for convex single commodity network flow problems our framework is based on an extended form of monotropic programming a broadly applicable model which includes as special cases fenchel duality and rockafellar s monotropic programming and is characterized by an elegant and symmetric duality theory our algorithm combines flexibly outer and inner linearization of the cost function the linearization is progressively refined by using primal and dual differentiation and the roles of outer and inner linearization are reversed in a mathematically equivalent dual algorithm we provide convergence results for the general case where outer and inner linearization are combined in the same algorithm

new algorithms for generalized network flows this paper of which a preliminary version appeared in istcs 92 is concerned with generalized network flow problems in a generalized network each edgee u v has a positive flow multiplier a e associated with it the interpretation is that if a flow ofx e enters the edge at nodeu then a flow ofa e x e exits the edge atv the uncapacitated generalized transshipment problem ugt is defined on a generalized network where demands and supplies real numbers are associated with the vertices and costs real numbers are associated with the edges the goal is to find a flow such that the excess or deficit at each vertex equals the desired value of the supply or demand and the sum over the edges of the product of the cost and the flow is minimized adler and cosares operations research 39 1991 955 960 reduced the restricted uncapacitated generalized transshipment problem where only demand nodes are present to a system of linear inequalities with two variables per inequality the algorithms presented by the authors in siam journal on computing to appear result in a faster algorithm for restricted ugt generalized circulation is defined on a generalized network with demands at the nodes and capacity constraints on the edges i e upper bounds on the amount of flow the goal is to find a flow such that the excesses at the nodes are proportional to the demands and maximized we present a new algorithm that solves the capacitated generalized flow problem by iteratively solving instances of ugt the algorithm can be used to find an optimal flow or an approximation thereof when used to find a constant factor approximation the algorithm is not only more efficient than previous algorithms but also strongly polynomial it is believed to be the first strongly polynomial approximation algorithm for generalized circulation the existence of such an approximation algorithm is interesting since it is not known whether the exact problem has a strongly polynomial algorithm

an epsilon relaxation method for separable convex cost network flow problems we propose a new method for the solution of the single commodity separable convex cost network flow problem the method generalizes the epsilon relaxation method developed for linear cost problems and reduces to that method when applied to linear cost problems we show that the method terminates with a near optimal solution and we provide an associated complexity analysis we also present computational results showing that the method is much faster than earlier relaxation methods particularly for ill conditioned problems

a polynomial time descent method for separable convex optimization problems with linear constraints we propose a polynomial algorithm for a separable convex optimization problem with linear constraints we do not make any additional assumptions about the structure of the objective function except for polynomial computability that is the objective function can be non differentiable the running time of our algorithm is polynomial in the size of the input consisting of an instance of the problem and the accuracy with which the problem is to be solved our algorithm uses an oracle for solving auxiliary systems of linear inequalities this oracle can be any polynomial algorithm for linear programming

closed form solutions for dynamic analysis of extensional circular timoshenko beams with general elastic boundary conditions abstract closed form solutions for dynamic analysis of extensional circular timoshenko beams with general elastic boundary conditions are derived taking the laplace transform and some procedures the system composed of three coupled governing differential equations and six coupled boundary conditions is uncoupled and reduced to a single equation in terms of the angle of rotation due to bending the explicit relations between the inward radial displacement the tangential displacement and the angle of rotation due to bending are revealed six exact normalized fundamental solutions of the uncoupled governing differential equation are obtained by the frobenius method the exact transformed general solution of the uncoupled system is expressed in terms of the six fundamental solutions using the generalized green function given by lin the systems based on the rayleigh and bernoulli euler beam theories can be obtained by taking the corresponding limiting procedures without the laplace transform the exact solutions for the steady and free vibrations of the general system are obtained the effects of the spring constants the opening angle the rotary inertia and the shear deformation on the natural frequencies are investigated

multicolor iccg methods for vector computers this paper considers the incomplete choleski conjugate gradient method for symmetric positive definite linear systems the goal is to obtain implementations of this method suitable for vector computers which require long vectors for efficiency this is achieved by a multicoloring strategy which allows efficient solution of the triangular systems of the preconditioning as well as efficient matrix vector multiplication numerical results are given for three model problems on a cyber 205

a decomposition approach for the general lotsizing and scheduling problem for parallel production lines abstract this paper presents a novel solution heuristic to the general lotsizing and scheduling problem for parallel production lines glsppl the glsppl addresses the problem of simultaneously deciding about the sizes and schedules of production lots on parallel heterogeneous production lines with respect to scarce capacity sequence dependent setup times and deterministic dynamic demand of multiple products its objective is to minimize inventory holding sequence dependent setup and production costs the new heuristic iteratively decomposes the multi line problem into a series of single line problems which are easier to solve different approaches for decomposition and for the iteration between a modified multi line master problem and the single line subproblems are proposed they are compared with an existing solution method for the glsppl by means of medium sized and large practical problem instances from different types of industries the new methods prove to be superior with respect to both solution quality and computation time

natural frequencies of a non uniform beam with multiple cracks via modified fourier series abstract a new method is presented in this paper for computing the natural frequencies of a non uniform beam with an arbitrary number of transverse open cracks the essence of this new method lies in the use of a kind of modified fourier series mfs which is specially developed for a beam with transverse open cracks unlike conventional fourier series modified fourier series can approach a function with internal geometrical discontinuities based on the modified fourier series one can treat the cracked beam in the most usual way and thus reduce the problem to a simple one the beam can be of non uniform cross section and the number of cracks can be arbitrary by using the present method only standard linear eigenvalue equations rather than non linear algebraic equations need to be solved all the formulae are expressed in matrix form which renders the programming quite straightforward

third order conservative sign preserving and steady state preserving time integrations and applications in stiff multispecies and multireaction detonations abstract in this paper we develop third order conservative sign preserving and steady state preserving time integrations and seek their applications in multispecies and multireaction chemical reactive flows in this problem the density and pressure are nonnegative and the mass fraction for the ith species denoted as z i 1 i m should be between 0 and 1 where m is the total number of species there are four main difficulties in constructing high order bound preserving techniques for multispecies and multireaction detonations first of all most of the bound preserving techniques available are based on euler forward time integration therefore for problems with stiff source the time step will be significantly limited secondly the mass fraction does not satisfy a maximum principle and hence it is not easy to preserve the upper bound 1 thirdly in most of the previous works for gaseous denotation the algorithm relies on second order strang splitting methods where the flux and stiff source terms can be solved separately and the extension to high order time discretization seems to be complicated finally most of the previous ode solvers for stiff problems cannot preserve the total mass and the positivity of the numerical approximations at the same time in this paper we will construct third order conservative sign preserving rugne kutta and multistep methods to overcome all these difficulties the time integrations do not depend on the strang splitting i e we do not split the flux and the stiff source terms moreover the time discretization can handle the stiff source with large time step and preserves the steady state numerical experiments will be given to demonstrate the good performance of the bound preserving technique and the stability of the scheme for problems with stiff source terms

a fully implicit domain decomposition algorithm for shallow water equations on the cubed sphere popular approaches for solving shallow water equations swes for climate modeling are explicit and semiimplicit methods and both have certain constraints on the time step size in this paper we propose and study a fully implicit method which imposes no limit on the time step size but requires the solution of a large sparse nonlinear system of equations at every time step the focus of the paper is a parallel fully coupled newton krylov ras algorithm with a jacobian matrix explicitly calculated on a weakly nonmatching cubed sphere mesh here ras is a restricted additive schwarz method we show numerically that with such a preconditioned nonlinearly implicit method the time step size is no longer constrained by the cfl condition and we report superlinear speedup of the algorithm on machines with thousands of processors for problems with smooth and nonsmooth solutions

a barely implicit correction for flux corrected transport abstract the barely implicit correction bic removes the stringent limit on the timestep imposed by the sound speed in explicit methods this is done by adding one elliptic equation which has to be solved implicitly bic is combined with the flux corrected transport algorithm in order to represent sharp gradients in subsonic flows accurately the resultant conservative algorithm costs about the same per timestep as a single explicit timestep calculated using an optimized fct module several examples show the technique s ability to solve nearly incompressible flows very economically

a staggered semi implicit spectral discontinuous galerkin scheme for the shallow water equations a spatially arbitrary high order semi implicit spectral discontinuous galerkin dg scheme for the numerical solution of the shallow water equations on staggered control volumes is derived and discussed the free surface elevation and the momentum are expressed in terms of the same polynomials that are used as basis and as test functions each unknown is however defined on a different set of control volumes that are spatially staggered with respect to each other a semi implicit time integration yields a stable and efficient mass conservative algorithm the use of a staggered mesh has the advantage that after substitution of the momentum equations into the mass conservation equation only one single block penta diagonal system must be solved for the new free surface location which is a scalar quantity subsequently the new momentum components are directly obtained the staggered semi implicit approach makes the present dg scheme different from other published dg schemes the sparse linear system of the resulting discrete wave equation for the free surface can be conveniently solved by a matrix free gmres algorithm furthermore for the shallow water equations the proposed scheme can be written as a quadrature free method where all surface and volume integrals can be precomputed once and for all on the reference element and assembled into universal matrices and tensors for the special case n 0 the proposed method reduces to a classical semi implicit finite difference scheme the proposed semi implicit scheme is particularly well suited for low froude number flows the method is validated on some typical academic benchmark problems using polynomial degrees of up to n 20

a strongly polynomial algorithm for a special class of linear programs we extend the list of linear programming problems that are known to be solvable in strongly polynomial time to include a class of lps which contains special cases of the generalized transshipment problem the result is facilitated by exploiting some special properties associated with leontief substitution systems and observing that a feasible solution to the system ax b x 0 in which no variable appears in more than two equations can be found in strongly polynomial time for b belonging to some set

curvature based beam elements for the analysis of timoshenko and shear deformable curved beams abstract curved beam elements with six degrees of freedom and two three four and five node timoshenko straight beam elements with four five six and seven degrees of freedom respectively are proposed to eliminate stiffness locking when applied to the dynamic analysis of the beams the elements are based on curvature assumptions so that they can represent the bending energy accurately and the shear strain energy is incorporated into the formulation by way of the equilibrium equation eigenvalue problems of timoshenko and shear deformable curved beams are analyzed by using the elements the results of the eigen analysis show that the curvature based beam elements are free of locking and are efficient

eulerian lagrangian solution of the convection dispersion equation in natural coordinates the vast majority of numerical investigations of transport phenomena use an eulerian formulation for the convenience that the computational grids are fixed in space an eulerian lagrangian method elm of solution for the convection dispersion equation is discussed and analyzed the elm uses the lagrangian concept in an eulerian computational grid system the values of the dependent variable off the grid are calculated by interpolation when a linear interpolation is used the method is a slight improvement over the upwind difference method at this level of approximation both the elm and the upwind difference method suffer from large numerical dispersion however if second order lagrangian polynomials are used in the interpolation the elm is proven to be free of artificial numerical dispersion for the convection dispersion equation the concept of the elm is extended for treatment of anisotropic dispersion in natural coordinates in this approach the anisotropic properties of dispersion can be conveniently related to the properties of the flow field several numerical examples are given to further substantiate the results of the present analysis

enhancement of the labswe for shallow water flows in the lattice boltzmann method for the shallow water equations labswe the force term involves the first order derivative related to a bed slope which has to be determined using the centred scheme for an accurate solution however such calculation contradicts the spirit of only simple arithmetic calculations required in the lattice boltzmann method this paper shows how to remove this drawback from the labswe by incorporating the bed level into the lattice boltzmann equation in a consistent manner with the lattice boltzmann approach three numerical tests have been presented to verify the proposed method

change in instantaneous eigenproperties due to yielding of a structure this paper presents an insight into the pattern of change in instantaneous eigenproperties of a building as a result of reduction in tangent stiffness due to yielding of different members of the building using a perturbation approach it is found that for a shear building a reduction in instantaneous stiffness due to a yielding occurring in the bottom story will cause a greater absolute percentage change in eigenvalues squared frequencies of a lower mode than that of a higher mode in contrast for a reduction in instantaneous stiffness due to a yielding occurring in the top story this absolute percentage change in the eigenvalues increases with a increase in mode number starting from the fundamental mode a numerical study with a four story shear building and a four story and an eight story steel moment resisting frame models representative of existing buildings demonstrates that the trends in change in eigenproperties obtained from the analytical study works well for these buildings the findings of this study may be utilized to improve the design practices of buildings as well as non structural components attached to buildings

finding minimum cost circulations by canceling negative cycles a classical algorithm for finding a minimum cost circulation consists of repeatedly finding a residual cycle of negative cost and canceling it by pushing enough flow around the cycle to saturate an arc we show that a judicious choice of cycles for canceling leads to a polynomial bound on the number of iterations in this algorithm this gives a very simple strongly polynomial algorithm that uses no scaling a variant of the algorithm that uses dynamic trees runs in o nm log n min log nc m log n time on a network of n vertices m arcs and arc costs of maximum absolute value c this bound is comparable to those of the fastest previously known algorithms

maximum network flows with concave gains this paper deals with a generalized maximum flow problem with concave gains which is a nonlinear network optimization problem optimality conditions and an algorithm for this problem are presented the optimality conditions are extended from the corresponding results for the linear gain case the algorithm is based on the scaled piecewise linear approximation and on the fat path algorithm described by goldberg plotkin and tardos for linear gain cases the proposed algorithm solves a problem with piecewise linear concave gains faster than the naive solution by adding parallel arcs

a high order semi implicit discontinuous galerkin method for the two dimensional shallow water equations on staggered unstructured meshes a well balanced spatially arbitrary high order accurate semi implicit discontinuous galerkin scheme is presented for the numerical solution of the two dimensional shallow water equations on staggered unstructured non orthogonal grids the semi implicit method is derived in such a fashion that all relevant integrals can be precomputed and stored in a preprocessing stage so that the extension to curved isoparametric elements is natural and does not increase the computational effort of the simulation at runtime for p 0 the resulting scheme becomes a generalization of the classical semi implicit finite volume finite difference scheme of casulli and walters 2000 25 but with less conditions on the grid geometry the method proposed in this paper allows large time steps with respect to the surface wave speed gh and is thus particularly suitable for low froude number flows the approach is validated on some typical academic benchmark problems using polynomial degrees up to p 6

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

an e out of kilter method for monotropic programming the out of kilter method was first proposed by fulkerson 1961 for linear cost network flow and independently by minty 1961 for piecewise linear cost network flow and was then extended by rockafellar 1984 section 11k to piecewise linear cost monotropic programming we propose an extension of this method based on rockafellar s work and on ideas from e relaxation methods for convex cost network flow bertsekas et al 1997a de leone et al 1999 to monotropic programming in general the proposed method is amenable to a complexity analysis and its convergence is based on essentially a monotone decrease in vertical distance to the characteristic curve for each index

relaxation methods for network flow problems with convex arc costs we consider the standard single commodity network flow problem with both linear and strictly convex possibly nondifferentiable arc costs for the case where all arc costs are strictly convex we study the convergence of a dual gauss seide type relaxation method that is well suited for parallel computation we then extend this method to the case where some of the arc costs are linear as a special case we recover a relaxation method for the linear minimum cost network flow problem proposed in bertsekas 1 and bertsekas and tseng 2

a semi implicit semi lagrangian p adaptive discontinuous galerkin method for the shallow water equations a semi implicit and semi lagrangian discontinuous galerkin method for the shallow water equations is proposed for applications to geophysical scale flows a non conservative formulation of the advection equation is employed in order to achieve a more treatable form of the linear system to be solved at each time step the method is equipped with a simple p adaptivity criterion that allows to adjust dynamically the number of local degrees of freedom employed to the local structure of the solution numerical results show that the method captures well the main features of gravity and inertial gravity waves as well as reproducing correct solutions in nonlinear test cases with analytic solutions the accuracy and effectiveness of the method are also demonstrated by numerical results obtained at high courant numbers and with automatic choice of the local approximation degree

exact vibration solutions for nonuniform timoshenko beams with attachments the exact solution for the free vibration of a symmetric nonuniform timoshenko beam with tip mass at one end and elastically restrained at the other end of the beam is derived the two coupled governing characteristic differential equations are reduced into one complete fourth order ordinary differential equation with variable coefficients in the angle of rotation due to bending the frequency equation is derived in terms of the four normalized fundamental solutions of the differential equation it can be shown that if the coefficients of the reduced differential equation can be expressed in polynomial form the exact fundamental solutions can be found by the method of frobenius finally several limiting cases are studied and the results are compared with those in the existing literature a x e x g x i x j x

faster algorithms for the generalized network flow problem we consider the generalized network flow problem each arc e in the network has a gain factor e if f e units of flow enter arc e then f e e units arrive at the other end of e the objective is to maximize the net flow into one specific node the sink the constraints are the conservation of flow at nodes and the capacities of arcs we present a combinatorial algorithm which solves this problem in o m2 m n log log b log b time where n is the number of nodes m is the number of arcs and b is the largest integer used to represent the gain factors the capacities and the initial supplies at the nodes if m is o n4 3 e and b is not extremely large then our bound is better than the previous best upper bound for this problem we also improve the best known upper bound for the approximate generalized flow problem by showing that a solution whose value is within a factor of 1 from the optimum can be computed in o m m n log log b log 1 time plus o mn2 log b time for preprocessing

vibration and stability analysis of non uniform timoshenko beams under axial and distributed tangential loads two sets of governing equations for transverse vibration of non uniform timoshenko beam subjected to both axial and tangential loads have been presented in the first set the axial and tangential loads were taken perpendicular to the shearing force i e normal to the cross section inclined at an angle while in the second set the axial force is assumed to be tangential to the axis of the beam column for each case there exist a pair of differential equations coupled in terms of the flexural displacement and the angle of rotation due to bending the two coupled second order governing differential equations were combined into one fourth order ordinary differential equation with variable coefficients the parameters of the frequency equation were determined for different boundary conditions the exact fundamental solutions could be found by expressing the coefficients of the reduced differential equation in a polynomial form before applying the frobenius method several illustrative examples of uniform and non uniform beams with various boundary conditions such as clamped supported elastically supported and free end mass and pinned end mass have been presented the stability analysis for the variation of the natural frequencies of the uniform and non uniform beams with the axial force has also been investigated moreover the present work illustrates the frequency behavior of the beam under a tangential load

relaxation methods for minimum cost ordinary and generalized network flow problems we propose a new class of algorithms for linear cost network flow problems with and without gains these algorithms are based on iterative improvement of a dual cost and operate in a manner that is reminiscent of coordinate ascent and gauss seidel relaxation methods we compare our coded implementations of these methods with mature state of the art primal simplex and primal dual codes and find them to be several times faster on standard benchmark problems and faster by an order of magnitude on large randomly generated problems our experiments indicate that the speedup factor increases with problem dimension

out of plane dynamic responses of non circular curved beams by numerical laplace transform abstract the paper presents a systematic method for analyzing the out of plane dynamic behaviours of non circular curved beams the governing equations of which take into account the effects of shear deformation rotary inertia and viscous damping the procedure consists of formulating an analytical solution for the transformed governing equations in the laplace transform domain and computing the responses in the time domain by means of numerical laplace inversion as key elements in the dynamic stiffness method the first known transformed dynamic stiffness matrix and equivalent nodal loading vector for non circular curved beams subjected to distributed external loading are established from the analytical solution developed using the famous frobenius method with a simple modification the formulation of the solution is also suitable for free vibration analysis which results in an exact solution as numerical examples for transient analysis time responses of displacement components and stress resultants are found for a two span elliptic beam subjected to a rectangular impulse the behaviours of the response due to the variation of the ratio of the long axis to the short one are investigated

semi implicit finite difference methods for the two dimensional shallow water equation abstract in this paper a semi implicit finite difference method for the 2 dimensional shallow water equations is derived and discussed a characteristic analysis of the governing equations is carried out first in order to determine those terms to be discretized implicitly so that the stability of the method will not depend upon the celerity such terms are the gradient of the water surface elevation in the momentum equations and the velocity divergence in the continuity equation the convective terms are discretized explicitly the simpler explicit discretization for the convective terms is the upwind discretization which is conditionally stable and introduces some artificial viscosity it is shown that the stability restriction is eliminated and the artificial viscosity is reduced when an eulerian lagrangian approach with large time steps is used to discretize the convective terms this method at each time step requires the solution of a linear symmetric 5 diagonal system such a system is diagonally dominant with positive elements on the main diagonal and negative ones elsewhere thus existence and uniqueness of the numerical solution is assured the resulting algorithm is mass conservative and fully vectorizable for an efficient implementation on modern vector computers the performance of this method is further improved when used in combination with an adi technique which results in two sets of simpler linear 3 diagonal systems and maintains all the properties described above

steady state and sign preserving semi implicit runge kutta methods for odes with stiff damping term in this paper we develop a family of second order semi implicit time integration methods for systems of ordinary differential equations odes with stiff damping term the important feature of the new methods resides in the fact that they are capable of exactly preserving the steady states as well as maintaining the sign of the computed solution under the time step restriction determined by the nonstiff part of the system only the new semi implicit methods are based on the modification of explicit strong stability preserving runge kutta ssp rk methods and are proven to have a formal second order of accuracy a alpha stability and stiff decay we illustrate the performance of the proposed ssp rk based semi implicit methods on both a scalar ode example and a system of odes arising from the semi discretization of the shallow water equations with stiff friction term the obtained numerical results clearly demonstrate that the ability of the introduced ode solver to exactly preserve equilibria plays

out of plane dynamic response of curved beams an analytical model abstract an analytical model for the vibration response of a curved beam is developed and presented the model is based on the solution closed solution of the dynamic differential equations of equilibrium for an infinitesimal element vibrating out of its initial plane of curvature and allows for inclusion of the effects of rotary inertia and or shear deformation final solutions are presented under the form of elements of the tip dynamic stiffness matrix for a free free beam the validity of the model is assessed by comparison of theoretical and experimental results for several examples of curved beams

distributed asynchronous relaxation methods for convex network flow problems we consider the solution of the single commodity strictly convex network flow problem in a distributed asynchronous computation environment the dual of this problem is unconstrained differentiable and well suited for solution via gauss seidel relaxation we show that the structure of the dual allows the successful application of a distributed asynchronous method whereby relaxation iterations are carried out in parallel by several processors in arbitrary order and with arbitrarily large interprocessor communication delays

polynomial time highest gain augmenting path algorithms for the generalized circulation problem this paper presents two new combinatorial algorithms for the generalized circulation problem after an initial step in which all flow generating cycles are canceled and excesses are created both algorithms bring these excesses to the sink via highest gain augmenting paths scaling is applied to the fixed amount of flow that the algorithms attempt to send to the sink and both node and arc excesses are used the algorithms have worst case complexities of om2m n log n log b where n is the number of nodes m is the number of arcs and b is the largest integer used to represent the gain factors and capacities in the network this bound is better than the previous best bound for a combinatorial algorithm for the generalized circulation problem and if m on4 3 e it is better than the previous best bound for any algorithm for this problem

nonconvergence of the plain newton min algorithm for linear complementarity problems with a p matrix the plain newton min algorithm to solve the linear complementarity problem lcp for short 0 leq x perp mx q geq0 can be viewed as a semismooth newton algorithm without globalization technique to solve the system of piecewise linear equations min x mx q 0 which is equivalent to the lcp when m is an m matrix of order n the algorithm is known to converge in at most n iterations we show in this paper that this result no longer holds when m is a p matrix of order 3 since then the algorithm may cycle p matrices are interesting since they are those ensuring the existence and uniqueness of the solution to the lcp for an arbitrary q incidentally convergence occurs for a p matrix of order 1 or 2

an e relaxation method for separable convex cost generalized network flow problems cover title the extended abstract of this article appeared in the proceedings of the 5th international ipco conference vancouver june 1996 p 1

the notion of a rational convex program and an algorithm for the arrow debreu nash bargaining game we introduce the notion of a rational convex program rcp and we classify the known rcps into two classes quadratic and logarithmic the importance of rationality is that it opens up the possibility of computing an optimal solution to the program via an algorithm that is either combinatorial or uses an lp oracle next we define a new nash bargaining game called adnb which is derived from the linear case of the arrow debreu market model we show that the convex program for adnb is a logarithmic rcp but unlike other known members of this class it is nontotal our main result is a combinatorial polynomial time algorithm for adnb it turns out that the reason for infeasibility of logarithmic rcps is quite different from that for lps and quadratic rcps we believe that our ideas for surmounting the new difficulties will be useful for dealing with other nontotal rcps as well we give an application of our combinatorial algorithm for adnb to an important fair throughput allocation problem on a wireless channel finally we present a number of interesting questions that the new notion of rcp raises

on newton type approach for piecewise linear systems we investigate effective newton type methods for solving piecewise linear systems we prove that under certain relaxed conditions the proposed newton type methods converge monotonically and have a finite termination property moreover we give some conclusions on the existence of solution for the piecewise linear systems

natural frequencies of a beam with varying section properties abstract non uniform beams with cross section varying in a continuous or non continuous manner along their lengths are used in many structural applications in an effort to achieve an optimum distribution of strength and weight the authors have investigated the problem of calculating the natural frequencies for beams with inertia area and mass varying in a general manner the procedure proposed allows the effect of each of these variables to be evaluated separately and leads to the concept of effective inertia effective area and effective mass it also enables one to determine the natural frequencies of a beam with varying section properties using a simple formula similar to the one used in practice for computing the natural frequencies for a uniform beam it is also shown that the effect of shear deformation upon the natural frequencies of a beam with classical boundary conditions can be estimated within the limits of practical accuracy by using a simple formula similar to the one used for simply supported beams an important feature of the results presented here is the simplicity and relative ease with which these expressions can be applied to beams with various types of boundary conditions the authors believe that a practicing engineer will find these results easy to apply in computing the natural frequencies of non uniform beams within practical limits