A MUCLTI-PARAMETER SPLITTING EXTRAPOLATION AND A PARALLEL ALGORITHM

1.IntroductionConsidertheone-dimensionalDirichletproblemwherethecoefficientsoftheproblemaresmoothandsatisfyp(x)2c>0,q(x)30,xE(0,1).Let[0,1]bedividedintopsubintervalsT={(aj--1,aj):j=1,2,'',p},ac=0,ap--1.Oneach(aj--1)aj),auniformmeshrefinementwithsizehiisi…     

THE SPLITTING EXTRAPOLATION FOR FINITEELEMENT METHOD

1.IntroductionDespitethesignificantprogressmadeindigitalcomputersandcomputationalmethodsoaferthelasttwodecades,computationalworkaswellascomputerstoragerequiremelltintheappliedfieldissogreatthatsuper-computersarenotabletoaft'ord.111recentyears)thehotpoilltsincomputationalmathematicsarehowtodevelopanealcomPlltationalmethodwhichwouldfulfilthefollowingrequirelllents;1)ItshouldbeaparallelcomputationalIned]'>(lwhichcan11eimplementedonrnultiprocessorcomputersreqlliringminimalcommunicationanloll!{pro(…     

QUADRATURE AND EXTRAPOLATION FOR THE VARIABLE COEFFICIENT ELLIPTIC EIGENVALUE PROBLEM

For the variable coefficient elliptic eigenvalue problem on a smooth domain or aconvex polygonal domain,a numerical quadrature scheme over triangles is used for computingthe coefficient of the resulting linear finite element system.The effect of numerical integrationis studied.The corresponding discrete eigenvalue with linear finite elements is shown to admitasymptotic error expansions for certain classes of“uniform”meshes.Hence,the Richardsonextrapolation increases the accuracy of the scheme from second to fourth order.     

AN ANALYSIS OF SPLITTING EXTRAPOLATION FOR MULTIDIMENSIONAL PROBLEMS

The splitting extrapolation is an important technique for solving multidimensionalproblems.In the case that error u~h-u has an asymptotic expansion of form Σc_αh~(2α),whereα=(α_1,…,α_s) and h~α=h_1~(α_1),…h_s~(α_s),the method gives an approximation involving less computerstorage and less computational work in comparison with the classical Richardson extrapolation.In this paper we present a recurrence rule of the splitting extrapolation and discuss itsapplications in the fields of multiple integrals,multidimensional integral equations,partialdifferential equations and singular perturbation problems.     

GOAL PROGRAMMING ALGORITHM FOR A TYPE OF LEAST ABSOLUTE VALUE REGRESSION PROBLEM

This paper develops goal programming algorithm to solve a type of least absolute value (LAV) problem. Firstly, we simplify the simplex algorithm by proving the existence of solutions of the problem. Then, we present a goal programming algorithm on the basis of the original techniques. Theoretical analysis and numerical results indicate that the new method contains a lower number of deviation variables and consumes less computational time as compared to current LAV methods.     

PARALLEL COMPUTATION AND DOMAIN DECOMPOSITION FOR A CLASS OF HYPERBOLIC PROBLEMS

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OPTIMAL SWITCHING AND IMPULSE CONTROLS FOR DISTRIBUTED PARAMETER SYSTEMS

Optimal switching and impulse controls for a distributed parameter systems are considered.We prove that the value functions u_u(·) of approximating problems approach to the value functionu(·) of the original problem,while u_u(·) is the unique viscosity solution of the correspondingHamilton-Jacobi-Bellman system.We also construct an optimal control for the original problem viathe value function u(·).     

ERROR ESTIMATION OF THE APPROXIMATION ALGORITHM FOR THE WINDY POSTMAN PROBLEM

If we restrict the postman to traversing each edge at most twice in the windypostman problem (WPP), we will get a new problem: 2WPP. An approximation algorithmhas been posed by M. Guan for the WPP. In the present paper, we improve the estimatederror given by M. Guan and show that we can estimate the error for the 2WPP by findinga minimum cost circulation. We also pose a new sufficient condition for the equivalencebetween WPP and 2WPP, which can be checked in polynomial time steps.     

FUZZY MULTI-LEVEL WAREHOUSE LAYOUT PROBLEM： NEW MODEL AND ALGORITHM

1. Introduction As we know, in most manufactory, above all in large-scale manufactory, warehouse operation is an important part of a manufacturer's material handling operation. Effective warehouse planning can not only reduce material handling cost but also increase productivity. Hence, it is very important for the manufacturer to make the best plan to manage the warehouse. The warehouse layout problem concerns how to place different items into the warehouse so that people resources, equipment…     

A FULL-NEWTON STEP INFEASIBLE INTERIOR-POINT ALGORITHM FOR P＊（κ） LINEAR COMPLEMENTARITY PROBLEM

This paper proposes a new infeasible interior-point algorithm with full-Newton steps for P＊（κ） linear complementarity problem（LCP）,which is an extension of the work by Roos（SIAM J.Optim.,2006,16（4）：1110-1136）.The main iteration consists of a feasibility step and several centrality steps.The authors introduce a specific kernel function instead of the classic logarithmical barrier function to induce the feasibility step,so the analysis of the feasibility step is different from that of Roos＇ s.This kernel function has a finite value on the boundary.The result of iteration complexity coincides with the currently known best one for infeasible interior-point methods for P＊（κ） LCP.Some numerical results are reported as well.     

THE EXTRAPOLATION METHOD FOR A CLASS OF NON-SMOOTH FREDHOLM INTEGRAL EQUATIONS

For a class of non-smooth Fredholm integral equations we prove thatRichardson extrapolation method can be used to increase accuracy for finite ele-ment methods.On the basis of local refinement mesh,a superconvergence result isshown.Our theory also covers a class of non-smooth Wiener-Hopf equations andan application includes the calculation in certain linear elastic fracture problems.     

A NEWTON MULTIGRID METHOD FOR QUASILINEAR PARABOLIC EQUATIONS

A combination of the classical Newton Method and the multigrid method, i.e., a Newton multigrid method is given for solving quasilinear parabolic equations discretized by finite elements. The convergence of the algorithm is obtained for only one step Newton iteration per level. The asymptotically computational cost for quasilinear parabolic problems is O（NNk） similar to multigrid method for linear parabolic problems.     

EXTRAPOLATION FOR FINITE ELEMENT METHODS OF THE FIRST KIND FREDHOLM INTEGRAL EQUATIONS

In this paper,a numerical analysis of finite element methods for Fredholm equationsof the first kind,which is based upon regularization,is made.It shows that extrapolationalgorithms can accelerate the convergence of approximate solutions.     

SUPERCONVERGENCE OF THE MORTAR FINITE ELEMENT APPROXIMATION TO A PARABOLIC PROBLEM

1.IntroductionDomaindecompositionapproachesaremostimportanttechniqllesforsolvingpartialdifferentialequations.Suchreformulationsareusuallymotivatedbytheneedtocreatesolverswhichareeasilyparallelised,see[1]and[2].MostapplicationsusediscretizationsgridswhicharedeAnedgloballyoverthewholedomainandthensplitilltosubdomains.Inmechanics,.thisresultsinanoverallconformingapprotimatiollofthevelocityfield.However,itmightbemoreconvethelltandefficienttouseapproximationswhicharedefinedindependelltlyoneachsubd…