co volume methods for degenerate parabolic problems a complementary volume co volume technique is used to develop a physically appealing algorithm for the solution of degenerate parabolic problems such as the stefan problem it is shown that these algorithms give rise to a discrete semigroup theory that parallels the continuous problem in particular the discrete stefan problem gives rise to nonlinear semigroups in both the discretel 1 andh 1 spaces

on spectral multigrid methods for the time dependent navier stokes equations a new splitting scheme is proposed for the numerical solution of the time dependent incompressible navier stokes equations by spectral methods a staggered grid is used for the pressure improved intermediate boundary conditions are employed in the split step for the velocity and spectral multigrid techniques are used for the solution of the implicit equations

finite element preconditioning for spectral multigrid methods abstract the good performance of finite element preconditioning for the algebraic spectral systems is demonstrated different types of multigrid strategies are compared the most efficient strategy consists of a pure richardson relaxation preconditioned by one v cycle of a finite element multigrid method the good smoothing properties of line relaxation become obvious the computational work for the various methods is estimated

preconditioned minimal residual methods for chebyshev spectral calculations abstract the problem of preconditioning the pseudospectral chebyshev approximation of an elliptic operator is considered the numerical sensitivity to variations of the coefficients of the operator are investigated for two classes of preconditioning matrices one arising from finite differences the other from finite elements the preconditioned system is solved by a conjugate gradient type method and by a dufort frankel method with dynamical parameters the methods are compared on some test problems with the richardson method 13 and with the minimal residual richardson method 21

chebyshev pseudospectral solution of second order elliptic equations with finite element preconditioning abstract a new chebyshev pseudospectral algorithm for second order elliptic equations using finite element preconditioning is proposed and tested on various problems bilinear and biquadratic lagrange elements are considered as well as bicubic hermite elements the numerical results show that bilinear elements produce spectral accuracy with the minimum computational work l shaped regions are treated by a subdomain approach

multigrid methods for combined finite difference and fourier problems abstract multigrid methods for combined finite difference and fourier pseudospectral problems are considered applications to two and three dimensional elliptic systems are given suitable relaxation schemes for isotropic and anisotropic problems are presented numerical results demonstrate the efficiency of these methods

efficient pseudospectral flow simulations in moderately complex geometries a computationally efficient pseudospectral method is developed for incompressible flow simulations in two dimensional geometries involving periodicity in one direction and significant surface deformations a pseudoconformal mapping is used to map the flow domain into a rectangle thereby establishing an orthogonal curvilinear coordinate system within which the governing equations are formulated the time integration of the spectrally discretized two dimensional momentum equations is performed by a second order mixed explicit implicit time integration scheme the satisfaction of the continuity equation is obtained through the solution of a poisson equation for the pressure and the use of the influence matrix technique a highly efficient iterative solver has been developed for the solution of a generalized stokes problem at each time step based on a spectrally preconditioned biconjugate gradient algorithm which exhibits almost linear scalability requiring an ordernlog2nnumber of operations wherenis the number of unknowns numerical results are presented for two dimensional steady oscillatory and peristaltic flows within an undulating channel which agree well with previous results that have appeared in the literature

multiobjective programming in optimization of interval objective functions a generalized approach abstract we generalize known concepts those introduced by ishihuchi and tanaka 1 and rommerlfanger et al 2 of the solution of the linear programming problem with interval coefficients in the objective function based on preference relations between intervals we unify all the discussed concepts as well as the corresponding solution methods into one general framework

multistate components assignment problem with optimal network reliability subject to assignment budget abstract the typical assignment problem for finding the optimal assignment of a set of components to a set of locations in a system has been widely studied in practical applications however this problem mainly focuses on maximizing the total profit or minimizing the total cost without considering component s failure in practice each component should be multistate due to failure partially failure or maintenance that is each component has several capacities with a probability distribution and may fail when a set of multistate components is assigned to a system the system can be treated as a stochastic flow network the network reliability is the probability that d units of homogenous commodity can be transmitted through the network successfully the multistate components assignment problem to maximize the network reliability is never discussed therefore this paper focuses on solving this problem under an assignment budget constraint in which each component has an assignment cost the network reliability under a components assignment can be evaluated in terms of minimal paths and state space decomposition subsequently an optimization method based on genetic algorithm is proposed the experimental results show that the proposed algorithm can be executed in a reasonable time

spectral methods for initial boundary value problems an alternative approach mea this paper presents a new approach to spectral methods for initial boundary value problems a filtered version of the partial differential equation and the initial and boundary conditions at an overdetermined set of points are collocated as an approximate solution the function is chosen that belongs to an appropriate finite dimensional space and minimizes a weighted average of the residuals at these points it is proved that the approximate solution converges to the actual solution at a spectral rate of accuracy in both space and time the proof is based on a priori energy estimates that have been proved for such systems although this method is restricted here to hyperbolic initial boundary value problems and chebyshev polynomials it generalizes to general initial boundary value problems boundary value problems and gegenbauer polynomials

a spectral collocation method for two dimensional compressible convection abstract a fourier chebyshev spectral simulation of two dimensional compressible convection is presented the fluid is a perfect gas with constant dynamic viscosity and thermal conductivity both slippery and rigid boundary conditions for the velocity are used here the temperature is maintained fixed at the upper and lower boundaries an explicit adams bashforth predictor corrector numerical scheme is used in order to overcome the courant friedriechs lewy condition the nonlinear diffusion terms are handled by an iterative method with finite differences or spectral preconditioning steady state solutions have been obtained for both types of boundary conditions critical exponents are found to be the same as in the incompressible case at least for a weak value of the stratification parameter

konvergenzaussagen fur kollokationsverfahren bei elliptischen randwertaufgaben we examine the convergence of collocation with polynomials for elliptic problems the general theory is imbedded in thel p theory from which known results of existence and regularity are adopted convergence results are deduced in the cases of periodic dirichlet and mixed boundary conditions it becomes obvious that the order of convergence essentially depends on the smoothness of the solution

an alternating crank nicolson method for decoupling the ginzburg landau equations the time dependent ginzburg landau model of superconductors consists of coupled nonlinear partial differential equations which presents difficulties in the numerical solution we present an alternating crank nicolson method for this model that leads to two decoupled algebraic subsystems one is linear and the other is semilinear both have nice numerical properties and can be solved by efficient matrix solvers we show the stability and convergence and derive error estimates for this scheme numerical results are also reported

anisotropic singular perturbations the vectorial case we obtain the l 1 limit of the sequence where e e is the family of anisotropic perturbations of the nonconvex functional of vector valued functions the proof relies on the blow up argument introduced by fonseca and muller

on comparing interval numbers abstract this paper first presents a brief survey of the existing works on comparing and ranking any two interval numbers on the real line and then on the basis of this gives two approaches to compare any two interval numbers the first one describes a value judgement index along with a discussion on its strength and weakness over the other approaches this index has also been called an optimistic decision maker s preference index the other approach defines strict and fuzzy preference ordering between any two interval numbers from a pessimistic decision maker s point of view choice of different decision makers with different degrees of pessimism has also been considered

phase field computations of single needle crystals crystal growth and motion by mean curvature the phase field model for free boundaries consists of a system of parabolic differential equations in which the variables represent a phase or order parameter and temperature respectively the parameters in the equations are related directly to the physical observables including the interfacial width epsilon which we can regard as a free parameter in computation the phase field equations can be used to compute a wide range of sharp interface problems including the classical stefan model its modification to incorporate surface tension and or surface kinetic terms the cahn allen motion by mean curvature the hele shaw model etc also included is anisotropy in the equilibrium and dynamical forms generally considered by materials scientists by adjusting the parameters the computations can be varied continuously from single needle dendritic to faceted crystals the computational method consists of smoothing a sharp interface problem within the scaling of distinguished limits of the phase field e

computational simulation of flux trapping and vortex pinning in type ii superconductors effects of pointwise thickness variations and material inhomogeneities in the dynamics of vorticies are investigated by means of appropriately formulated time dependent ginzburg landau tdgl based models for inhomogeneous thin films having constant thickness and homogeneous thin films having variable thickness the resulting models are solved numerically using a nonstandard finite difference method for spatial discretization and a modified forward euler method for temporal discretization in particular vortex pinning and flux trapping phenomena in both types of films are investigated our numerical simulations indicate that the dynamics of vortices are mostly affected by inhomogeneities introduced in the chemical composition of a material as compared to variations introduced in thickness of the material

numerical algorithm for the calculation of nonsymmetric dipolar and rotating monopolar vortex structures a numerical iteration scheme is presented for the calculation of coherent vortex structures steady solutions of the euler vorticity equation are found using a variational characterization for dipolar and monopolar vortices as relative equilibria of the poisson system the variational principle for the vorticity is solved by a numerical method for nonconvex optimization besides the variational principle for the vorticity an optimization process is used for the multipliers that appear in the description the free boundary is solved implicitly in the iteration process

numerical study of quantized vortex interaction in complex ginzburg landau equation on bounded domains in this paper we study numerically quantized vortex dynamics and their interaction in the two dimensional complex ginzburg landau equation cgle with a dimensionless parameter e 0 on bounded domains under either dirichlet or homogeneous neumann boundary condition we begin with a review of the reduced dynamical laws rdls for time evolution of quantized vortex centers in cgle and show how to solve these nonlinear ordinary differential equations numerically then we present efficient and accurate numerical methods for solving the cgle on either a rectangular or a disk domain under either dirichlet or homogeneous neumann boundary condition based on these efficient and accurate numerical methods for cgle and the rdls we explore rich and complicated quantized vortex dynamics and interaction of cgle with different e and under different initial physical setups including single vortex vortex pair vortex dipole and vortex lattice compare them with those obtained from the corresponding rdls and identify the cases where the rdls agree qualitatively and or quantitatively as well as fail to agree with those from cgle on vortex interaction finally we also obtain numerically different patterns of the steady states for quantized vortex lattices in the cgle dynamics on bounded domains

splitting techniques for the pseudospectral approximation of the unsteady stokes equations a pseudospectral or collocation approximation of the unsteady stokes equations is considered using the uzawa algorithm the spectral system is decoupled into a helmholtz equation and an equation with a pseudo laplace operator it is proven that the eigenvalues of the pseudo laplacian are real and negative except one zero eigenvalue belonging to the constant mode the pseudospectral method avoids spurious modes since the pressure is approximated with lower order two degrees lower polynomials than the velocity only one grid no staggered grids with the standard chebyshev gauss lobatto nodes is used for discretization for the iterative solution of the spectral system an effective preconditioner is necessary here effective finite difference preconditioners for the spectral pseudo laplacian are presented

spectral multigrid methods for domain decomposition problems using patching techniques abstract we consider spectral domain decomposition problems that use patching techniques the resulting discrete systems are solved by the very efficient spectral multigrid methods for relaxation we employ a preconditioned richardson iteration effective preconditioning is achieved by one or more steps of a line relaxation method for the corresponding finite difference scheme numerical results are presented for rectangular and l shaped domains furthermore a cross point problem is considered

analysis and approximation of the ginzburg landau model of superconductivity the authors consider the ginzburg landau model for superconductivity first some well known features of superconducting materials are reviewed and then various results concerning the model the resultant differential equations and their solution on bounded domains are derived then finite element approximations of the solutions of the ginzburg landau equations are considered and error estimates of optimal order are derived

a lyapunov type theorem for dissipative numerical integrators with adaptive time stepping the asymptotic behavior of continuous dissipative systems and dissipative numerical integrators with fixed time stepping can be fully investigated by a lyapunov type theorem on continuous and discrete dynamical systems respectively however once adaptive time stepping is involved such theories cease to work and usually the dynamics should be investigated from the past instead of the standard forward way such as in terms of pullback attractors in this paper we present a different approach we stick to a forward definition of limit sets and show that still we can establish a lyapunov type theorem which reveals the precise asymptotic behavior of adaptive time stepping integrators in the presence of a discrete lyapunov functional

a spectral multigrid method for the stokes problem in streamfunction formulation abstract suitable spectral multigrid components for the stokes problem in streamfunction formulation are presented we split the stokes problem into a system of two equations with the laplace operator we discretize by means of a collocation or pseudo spectral method preconditioning with finite differences is employed numerical results for the spectral multigrid method are presented

genetic algorithm for asymmetric traveling salesman problem with imprecise travel times this paper presents a variant of the asymmetric traveling salesman problem atsp in which the traveling time between each pair of cities is represented by an interval of values wherein the actual travel time is expected to lie instead of a fixed deterministic value as in the classical atsp here the atsp with interval objective is formulated using the usual interval arithmetic to solve the interval atsp i atsp a genetic algorithm with interval valued fitness function is proposed for this purpose the existing revised definition of order relations between interval numbers for the case of pessimistic decision making is used the proposed algorithm is based on a previously published work and includes some new features of the basic genetic operators to analyze the performance and effectiveness of the proposed algorithm and different genetic operators computational studies of the proposed algorithm on some randomly generated test problems are reported

a dynamic programming approach to nonlinear boundary control problems of parabolic type abstract in this paper we study a hamilton jacobi equation related to the boundary control of a parabolic equation with neumann boundary conditions the state space of this problem is a hilbert space and the equation is defined classically only on a dense subset of the state space moreover the hamiltonian appearing in the equation contains fractional powers of an unbounded operator these facts render the problem difficult in this paper we give a revised definition of a viscosity solution to accommodate the unboundness of the hamiltonian we then obtain existence and uniqueness results for viscosity solutions in particular we show that under suitable assumptions the value function of the boundary control problem is the unique viscosity solution of the related hamilton jacobi equation

spectrally accurate numerical incompressible flows with deformed boundaries a finite volume preconditioning method spectrally accurate solutions of the stokes problem have been computed with finite volume preconditioning of a chebyshev collocation method it has been validated on two analytical test cases and applied to the resolution of the navier stokes equations in a deformed driven cavity configuration this numerical tool is ready for application to flows with deformed free surface

numerical methods for the transition to wavy taylor vortices abstract numerical methods for the analysis of the nonaxisymmetric stability of two dimensional axisymmetric flows are discussed the relative merits of a fully spectral approach are compared with methods which are spectral in one direction and finite difference in the other the results are applied to the onset of waviness in taylor vortices it is shown that the methods described are capable of finding accurate eigenvalues for taylor numbers up to fifty times critical

fast accurate and small scale direct trajectory optimization using a gegenbauer transcription method this paper reports a novel direct gegenbauer ultraspherical transcription method gtm for solving continuous time optimal control oc problems ctocps with linear nonlinear dynamics and path constraints in elgindy et al 2012 1 we presented a gtm for solving nonlinear ctocps directly for the state and the control variables and the method was tailored to find the best path for an unmanned aerial vehicle mobilizing in a stationary risk environment this article extends the gtm to deal further with problems including higher order time derivatives of the states by solving the ctocp directly for the control u t and the highest order time derivative x n t n z the state vector and its derivatives up to the n 1 th order derivative can then be stably recovered by successive integration moreover we present our solution method for solving linear quadratic regulator lqr problems as we aim to cover a wider collection of ctocps with the concrete aim of comparing the efficiency of the current work with other classical discretization methods in the literature the proposed numerical scheme fully parameterizes the state and the control variables using gegenbauer expansion series for problems with various order time derivatives of the state variables arising in the cost function dynamical system or path terminal constraints the gtm seeks to fully parameterize the control variables and the highest order time derivatives of the state variables the time horizon is mapped onto the closed interval 0 1 the dynamical system characterized by differential equations is transformed into its integral formulation through direct integration the resulting problem on the finite interval is then transcribed into a nonlinear programming nlp problem through collocation at the gegenbauer gauss gg points the integral operations are approximated by optimal gegenbauer quadratures in a certain optimality sense the reduced nlp problem is solved in the gegenbauer spectral space and the state and the control variables are approximated on the entire finite horizon the proposed method achieves discrete solutions exhibiting exponential convergence using relatively small scale number of collocation points the advantages of the proposed direct gtm over other traditional discretization methods are shown through four well studied oc test examples the present work is a major breakthrough in the area of computational oc theory as it delivers significantly more accurate solutions using considerably smaller numbers of collocation points states and controls expansion terms moreover the gtm produces very small scale nlp problems which can be solved very quickly using the modern nlp software

global properties of pseudospectral methods abstract we apply polynomial interpolation methods both to the approximation of functions and to the numerical solutions of hyperbolic and elliptic partial differential equations the derivative matrix for a general sequence of collocation points is explicitly constructed we explore the effect of several factors on the performance of these methods we show that global methods cannot be interpreted in terms of local methods for example the accuracy of the approximation differs when large gradients of the function occur near the center of the region or in the vicinity of the boundary this difference does not depend on the density of the collocation points near the boundaries hence intuition based on finite difference methods can lead to false results

multigrid sinc methods a galerkin method using whittaker cardinal or sinc functions as basis functions is described for the solution of boundary value problems when the solution is analytic in the interior of the domain the error of approximation using 2n 1 points is o e c n 1 2 even if derivatives of the solution are singular at the boundaries a multigrid method with overall complexity o nlogn is used to solve the discrete equations this paper contains a description of the multigrid sinc algorithm along with some preliminary numerical results for two point boundary value problems

finite element methods for the time dependent ginzburg landau model of superconductivity abstract the initial boundary value problem for the time dependent ginzburg landau equations that model the macroscopic behavior of superconductors is considered the convergence of finite dimensional semidiscrete galerkin approximations is studied as is a fully discrete scheme the results of some computational experiments are presented

improved spectral multigrid methods for periodic elliptic problems abstract the spectral multigrid method for periodic elliptic problems is examined several modifications are introduced including a midpoint pseudospectral discretization which eliminates the need for filtering the highest fourier mode and new relaxation schemes for isotropic and anisotropic problems numerical results are presented demonstrating substantial increases in efficiency and accuracy over previous methods

relaxation schemes for spectral multigrid methods the effectiveness of relaxation schemes for solving the systems of algebraic equations which arise from spectral discretizations of elliptic equations is examined iterative methods are an attractive alternative to direct methods because fourier transform techniques enable the discrete matrix vector products to be computed almost as efficiently as for corresponding but sparse finite difference discretizations preconditioning is found to be essential for acceptable rates of convergence preconditioners based on second order finite difference methods are used a comparison is made of the performance of different relaxation methods on model problems with a variety of conditions specified around the boundary the investigations show that iterations based on incomplete lu decompositions provide the most efficient methods for solving these algebraic systems

a direct spectral collocation poisson solver in polar and cylindrical coordinates in this paper we present a direct spectral collocation method for the solution of the poisson equation in polar and cylindrical coordinates the solver is applied to the poisson equations for several different domains including a part of a disk an annulus a unit disk and a cylinder unlike other poisson solvers for geometries such as unit disks and cylinders no pole condition is involved for the present solver the method is easy to implement fast and gives spectral accuracy we also use the weighted interpolation technique and nonclassical collocation points to improve the convergence

spectral collocation methods and polar coordinate singularities this paper considers the numerical solution of elliptic differential equations on the unit disk using polar coordinates the disk is mapped onto a rectangle the resulting transformed problem is solved by a method related to collocation since the origin is a coordinate singularity some natural trial functions are singular there and a special technique is applied to use zero as a collocation point for poisson and helmholtz equations a fast algorithm with an operation count of o n2 log n is presented numerical results show the different stability and convergence properties of the algorithms

on semi infinite spectral elements for poisson problems with re entrant boundary singularities abstract a spectral element method is described which enables poisson problems defined in irregular infinite domains to be solved as a set of coupled problems over semi infinite rectangular regions two choices of trial functions are considered namely the eigenfunctions of the differential operator and chebyshev polynomials the coefficients in the series expansions are obtained by imposing weak c1 matching conditions across element interfaces singularities at re entrant corners are treated by a post processing technique which makes use of the known asymptotic behaviour of the solution at the singular point accurate approximations are obtained with few degrees of freedom

unconditional superconvergence analysis of a linearized crank nicolson galerkin fem for generalized ginzburg landau equation abstract in this paper we study an effective numerical method for the generalized ginzburg landau equation gle based on the linearized crank nicolson difference method in time and the standard galerkin finite element method with bilinear element in space the time discrete and space time discrete systems are both constructed we focus on a rigorous analysis and consideration of unconditional superconvergence error estimates of the discrete schemes firstly by virtue of the temporal error results the regularity for the time discrete system is presented secondly the classical ritz projection is used to obtain the spatial error with order o h 2 in the sense of l 2 norm thanks to the relationship between the ritz projection and the interpolated projection the superclose estimate with order o 2 h 2 in the sense of h 1 norm is derived thirdly it follows from the interpolated postprocessing technique that the global superconvergence result is deduced finally some numerical results are provided to confirm the theoretical analysis

numerical approximations of the ginzburg landau models for superconductivity in this paper we review various methods for the numerical approximations of the ginzburg landau models of superconductivity particular attention is given to the different treatment of gauge invariance in both the finite element finite difference and finite volume settings representative theoretical results typical numerical simulations and computational challenges are presented generalizations to other relevant models are also discussed

analysis of chebyshev collocation methods for parabolic equations time discretizations of both the heat equation and the advection diffusion equation in two space variables are analyzed for space approximation the pseudospectral chebyshev method which enjoys infinite order of accuracy for smooth solutions is used the equation is collocated at the gauss chebyshev points and derivatives are computed by the pseudospectral differencing technique at any time interval the pseudospectral solution which is a polynomial of degree n is advanced in time using the implicit theta method for the diffusive part of the equation while the advective term is dealt with explicitly we prove unconditional stability and optimal error bounds depending on both n and delta t the time step in the norms of the weighted sobolev spaces the method considered here is the most commonly used spectral method for parabolic equations to solve the linear system arising at any time interval efficient iterative techniques with scaling are presented

a survey of algorithms for the generalized assignment problem abstract this paper surveys algorithms for the well known problem of finding the minimum cost assignment of jobs to agents so that each job is assigned exactly once and agents are not overloaded all approaches seem to be based on branch and bound with bound supplied through heuristics and through relaxations of the primal problem formulation from the survey one can select building blocks for the design of one s own tailor made algorithm the survey also reveals that although just about every mathematical programming technique was tried on this problem there is still a lack of a representative set of test problems on which competing enumeration algorithms can be compared as well as a shortage of effective heuristics

splitting techniques for the unsteady stokes equations a pseudospectral or collocation approximation of the unsteady stokes equations is presented using the uzawa algorithm the spectral system is decoupled into helmholtz equations for the velocity components and an equation with the pseudo laplacian for the pressure both the velocity components and the pressure are approximated by polynomials of the same degree n compatible velocity and pressure approximations are constructed to ensure that the discrete problem is well posed the resulting discrete velocity field is identically divergence free only one grid no staggered grids with the standard chebyshev gauss lobatto nodes is used here we further compare our treatment with an inhomogeneous neumann condition for the pressure this scheme was proposed in g karniadakis m israeli and s a orszag j comp phys 97 1991 pp 414 443 the comparison shows that the neumann condition yields somewhat better approximations for the pressure in the time discretization a high order backward differentiation scheme for the intermediate velocity is combined with a high order extrapolant for the pressure it is numerically shown that a stable third order method in time can be achieved in the case of periodic boundary conditions this result is confirmed by fourier analysis

an application of genetic algorithm in a marketing oriented inventory model with interval valued inventory costs and three component demand rate dependent on displayed stock level the objective of this research is to investigate an inventory model for a single item with imprecise inventory costs by considering the impact of marketing strategies such as pricing and advertising on three component demand rate this rate is dependent on selling price frequency of advertisement and displayed stock level dsl in a show room shop here the impreciseness of inventory costs like carrying cost purchase cost ordering cost and advertisement cost has been represented by interval valued numbers analyzing the relative size of the storage capacity of the show room shop and the stock level dependency parameters of demand different scenarios with sub scenarios of each have been mentioned then for each sub scenario the model has been formulated as a constrained optimization problem with interval objective to solve these problems an advanced genetic algorithm ga for mixed integer non linear programming has been developed with interval valued fitness function in this developed ga the order relations of interval valued numbers have been used with respect to pessimistic decision maker s point of view this approach has been used in the ranked based selection process for selecting better chromosomes individuals for the next generation and also for finding the best chromosomes individuals in each generation finally the model has been illustrated with some numerical examples and the performance of the ga has been tested by computing appropriate statistical measures and the computing time

line relaxation for spectral multigrid methods abstract spectral multigrid methods for elliptic problems with dirichlet and periodic boundary conditions are examined the multigrid convergence is improved by certain line relaxation techniques which are suggested by a smoothing analysis furthermore several choices of relaxation parameters are compared numerical results are presented showing the gain in efficiency and accuracy over previous methods

discrete gauge invariant approximations of a time dependent ginzburg landau model of superconductivity we present here a mathematical analysis of a nonstandard difference method for the numerical solution of the time dependent ginzburg landau models of superconductivity this type of method has been widely used in numerical simulations of the behavior of superconducting materials we also illustrate some of their nice properties such as the gauge invariance being retained in discrete approximations and the discrete order parameter having physically consistent pointwise bound

memory effects in homogenisation linear second order equations the theory of homogenisation treats the question if the solutions u of the problems a u f converge weakly to the function u 0 can an operator a 0 be found such that u 0 is a solution of the problem a 0 u 0 f and is a 0 of the same type as a we study an example where the answer is negative we take a a varepsilon t text partial x 2 b varepsilon t text partial x c varepsilon t and show that a 0 a text eff t text partial x 2 b text eff t text partial x c text eff t k is an integrodifferential operator the expression for k is deduced under two different sets of assumptions bounds in l 1 or l 2 the l 2 setting uses the fourier transform and natural assumptions on the coefficients a b and c boundedness in l and uniform ellipticity the answer in the l 1 setting is obtained only under additional assumptions which seem to be unnecessary finally the description of the memory term is given for a problem on a bounded interval by using the eigenfunction expansion and a representation theorem for nevanlinna functions in one space dimension the equation a varepsilon t text partial x 2 u varepsilon x t b varepsilon t text partial x u varepsilon x t c varepsilon t text u varepsilon x t f x t is studied while in several space dimensions x 2 is replaced by the laplace operator computations are done in several examples

elitist genetic algorithm for assignment problem with imprecise goal the objective of this research paper is to solve a generalized assignment problem with imprecise cost s time s instead of precise one by elitist genetic algorithm ga here the impreciseness of cost s time s has been represented by interval valued numbers as interval valued numbers are the best representation than others like random variable representation with a known probability distribution and fuzzy representation to solve these types of problems an elitist ga has been developed with interval valued fitness function in this developed ga the existing ideas about the order relations of interval valued numbers have been modified from the point of view of two types of decision making viz optimistic decision making and pessimistic decision making this modified approach has been used in the selection process for selecting better chromosomes individuals for the next generation and in finding the best as well as the worst chromosomes individuals in each generation here two new crossover schemes and two new mutation schemes have been introduced in order to maintain the feasibility with crossover operations a repair algorithm has been suggested extensive comparative computational studies based on different parameters of our developed algorithm on one illustrative example have also been reported

spectral methods with sparse matrices spectral methods employ global polynomials for approximation hence they give very accurate approximations for smooth solutions unfortunately for dirichlet problems the matrices involved are dense and have condition numbers growing aso n 4 for polynomials of degree n in each variable we propose a new spectral method for the helmholtz equation with a symmetric and sparse matrix whose condition number grows only aso n 2 certain algebraic spectral multigrid methods can be efficiently used for solving the resulting system numerical results are presented which show that we have probably found the most effective solver for spectral systems

a pseudospectral method for solution of the three dimensional incompressible navier stokes equations abstract a new chebyshev pseudospectral technique based on the projection method that was previously applied by the authors to the solution of two dimensional incompressible navier stokes equations in primitive variables for nonperiodic boundary conditions is extended to solve the three dimensional navier stokes equations the crucial point of the method is the requirement that the continuity equation be satisfied everywhere in the domain on the boundaries as well as in the interior the key feature of the work presented in this paper is that the computer storage requirements of the full matrix inversion resulting from direct solution of the pressure poisson equation in three dimensions is greatly reduced by considering an eigenfunction decomposition the method was tested on a two dimensional driven cavity flow and the results were compared with those of the most accurate finite difference calculation the three dimensional driven cavity flow was then calculated at the same reynolds numbers as the two dimensional cases i e re 100 400 and 1000 in the calculated results three dimensional boundary effects were observed in all cases and became more apparent with increasing reynolds number

approximation of analytic functions a method of enhanced convergence we deal with a method of enhanced convergence for the approximation of analytic functions this method introduces conformal transformations in the approximation problems in order to help extract the values of a given analytic function from its taylor expansion around a point an instance of this method based on the euler transform has long been known recently we introduced more general versions of it in connection with certain problems in wave scattering in 2 we present a general discussion of this approach as is known in the case of the euler transform conformal transformations can enlarge the region of convergence of power series and can enhance substantially the convergence rates inside the circles of convergence we show that conformal maps can also produce a rather dramatic improvement in the conditioning of pade approximation this improvement which we discuss theoretically for stieltjes type functions is most notorious in cases of very poorly conditioned pade problems in many instances an application of enhanced convergence in conjunction with pade approximation leads to results which are many orders of magnitude more accurate than those obtained by either classical pade approximants or the summation of a truncated enhanced series

relaxation heuristics for a generalized assignment problem abstract we propose relaxation heuristics for the problem of maximum profit assignment of n tasks to m agents n m such that each task is assigned to only one agent subject to capacity constraints on the agents using lagrangian or surrogate relaxation the heuristics perform a subgradient search obtaining feasible solutions relaxation considers a vector of multipliers for the capacity constraints the resolution of the lagrangian is then immediate for the surrogate the resulting problem is a multiple choice knapsack that is again relaxed for continuous values of the variables and solved in polynomial time relaxation multipliers are used with an improved heuristic of martello and toth or a new constructive heuristic to find good feasible solutions six heuristics are tested with problems of the literature and random generated problems best results are less than 0 5 from the optimal with reasonable computational times for an at 386 computer it seems promising even for problems with correlated coefficients

chebyshev expansion methods for the solution of elliptic partial differential equations abstract in a recent paper haidvogel and zang j comput phys 30 1979 167 described a method based on an expansion in chebyshev polynomials for the solution of poisson s equation in a rectangle they also indicated how the method might be extended to more general equations in this note we give a comparison of the method with the global element method delves and hall j inst math appl 23 1979 223 and give numerical results for those problems treated by haidvogel and zang

spectral multigrid methods for elliptic equations ii a detailed description of spectral multigrid methods is provided this includes the interpolation and coarse grid operators for both periodic and dirichlet problems the spectral methods for periodic problems use fourier series and those for dirichlet problems are based upon chebyshev polynomials an improved preconditioning for dirichlet problems is given numerical examples and practical advice are included

defect correction for convection dominated flow a defect correction scheme with the first order upwind preconditioner is considered by fourier analysis the preconditioning properties for the second order upwind scheme the central scheme and spectral methods are examined since the eigenvalues of the preconditioned operator are complex the generalized minimal residual iteration is used for the iterative solution this procedure is applied to the boussinesq flow problem in vorticity streamfunction formulation numerical results are presented for increasing rayleigh numbers

a 3d spectral multigrid method we consider a 3d spectral multigrid method for 3d elliptic problems with arbitrary anisotropies the smoothing method is a preconditioned richardson iteration where a pseudospectral discretization is used on the right hand side and a finite difference discretization on the left hand side in each step of this iteration a finite difference problem is solved approximately by plane relaxation sweeps the plane relaxation requires the solution of 2d finite difference problems these problems are solved approximately using 2d multigrid cycles

a phase field approach in the numerical study of the elastic bending energy for vesicle membranes in this paper we compute the equilibrium configurations of a vesicle membrane under elastic bending energy with prescribed volume and surface area a variational phase field method is developed for such a problem discrete finite difference approximations and numerical simulations are carried out in the axial symmetrical cases different energetic bifurcation phenomena are discussed

analysis and convergence of a covolume approximation of the ginzburg landau model of superconductivity in this paper we present the mathematical analysis of a covolume method for the approximations of the ginzburg landau gl model for superconductivity a nice feature of this approach is that the gauge invariance properties are retained in discrete approximations based on triangular grids we also use properties of discrete vector fields to study issues such as the gauge choices and their enforcement

multiobjective programming in optimization of the interval objective function abstract in this paper the mathematical programming problem whose objective function has interval coefficients is investigated to maximize the interval objective function the order relations which represent the decision maker s preference between interval profits are defined by the right limit the left limit the center and the width of an interval the maximization problem with the interval objective function is converted into a multiobjective problem using the order relations the minimization problem is also converted into a multiobjective problem using the order relations which represent the decision maker s preference between interval costs