two agent scheduling in a flowshop abstract in this paper we study two agent scheduling in a two machine flowshop the cost function is the weighted sum of some common regular functions including the makespan and the total completion time specifically we consider two problems namely the problem to minimize the weighted sum of both agents makespan and the problem to minimize the weighted sum of one agent s total completion time and the other agent s makespan for the first problem we give an ordinary np hardness proof and a pseudo polynomial time algorithm we also analyze the performance of treating the problem using johnson s rule and propose an approximation algorithm based on johnson s rule for the second problem we propose an approximation algorithm based on linear programming relaxation of the problem finally we show that some simple algorithms can be used to solve special cases of the two problems

solution of high order compact discretized 3d elliptic partial differential equations by an accelerated multigrid method abstract a robust and efficient numerical solver for three dimensional linear elliptic partial differential equations without cross derivative terms but variable coefficients is presented the proposed algorithm is based on a general meshsize fourth order compact finite difference scheme and an accelerated geometric multigrid solver the former not only increases the accuracy of the discretization but also does not affect the bandwidth of the common second order finite difference scheme which is relevant for distributed memory parallel implementations of the multigrid preconditioner the acceleration technique on the other hand allows for a dramatic reduction of the number of cycles and smoothing steps required to achieve convergence furthermore it is found that depending on the coefficients of the elliptic partial differential equation the multigrid preconditioned solver can be the only way to obtain a reliable numerical solution or attain convergence

extrapolation methods for vector sequences this is an expository paper that describes and compares five methods for extrapolating to the limit or anti limit of a vector sequence without explicit knowledge of the sequence generator the methods are the minimal polynomial extrapolation mpe studied by cabay and jackson mesina and skelboe the reduced rank extrapolation rre of eddy which we show to be equivalent to mesina s version of mpe the vector and scalar versions of the epsilon algorithm vea sea introduced by wynn and extended by brezinski and gekeler and the topological epsilon algorithm tea of brezinski we cover the derivation and error analysis of iterated versions of the algorithms as applied to both linear and nonlinear problems and we show why these versions tend to converge quadratically we also present samples from extensive numerical testing that has led us to the following conclusions a tea in spite of its role as a theoretical link between the polynomial type and the epsilon type methods has no practical appl

multi agent scheduling on a single machine with max form criteria we consider multi agent scheduling on a single machine where the objective functions of the agents are of the max form for the feasibility model we show that the problem can be solved in polynomial time even when the jobs are subject to precedence restrictions for the minimality model we show that the problem is strongly np hard in general but can be solved in pseudo polynomial time when the number of agents is a given constant we then identify some special cases of the minimality model that can be solved in polynomial time

accelerated multigrid convergence and high reynolds recirculating flows techniques are developed for accelerating multigrid convergence in general and for advection diffusion and incompressible flow problems with small viscosity in particular it is shown by analysis that the slowing down of convergence is due mainly to poor coarse grid correction to certain error components and means for dealing with this problem are suggested analyzed and tested by numerical experiments showing very significant improvement in convergence rates at little cost

multilevel sparse approximate inverse preconditioners for adaptive mesh refinement abstract we present an efficient and effective preconditioning method for time dependent simulations with dynamic adaptive mesh refinement and implicit time integration adaptive mesh refinement greatly improves the efficiency of simulations where the solution develops steep gradients in small regions of the computational domain that change over time unfortunately adaptive mesh refinement also introduces a number of problems for preconditioning in parallel iterative linear solvers as the changes in the mesh lead to structural changes in the linear systems we must solve hence we may need to compute a new preconditioner at every time step since this would be expensive we propose preconditioners that are cheap to adapt for dynamic changes to the mesh more specifically we propose preconditioners that require only localized changes to the preconditioner for localized changes in the mesh our preconditioners combine sparse approximate inverses and multilevel techniques we demonstrate significant improvements in convergence rates of krylov subspace methods and significant reductions of the overall runtime furthermore we demonstrate experimentally level independent convergence rates for various problems

multigrid line smoothers for higher order upwind discretizations of convection dominated problems in this paper we present new multigrid line smoothers for the solution of higher order discretizations of convection dominated problems directly the behavior of the smoothers is analyzed theoretically with fourier smoothing and two grid analysis a parallel tri line variant is presented and evaluated the smoothers are applied to scalar convection diffusion problems discretized with limiters and systems of incompressible navier stokes and euler equations

krylov subspace acceleration of nonlinear multigrid with application to recirculating flows this paper deals with the combination of two solution methods multigrid and gmres siam j sci comput 14 1993 pp 856 869 the generality and parallelizabili nonlinear pdes as the preconditioner for a nonlinear krylov subspace method we use the full approximation storage fas scheme math comp 31 1977 pp 333 390 a nonlinear multigrid method the nonlinear krylov acceleration is applied also on coarse grids so that recirculating incompressible flow problems discretized with a higher order upwind scheme can be solved efficiently

minimization of the makespan in a two machine problem under given resource constraints in the paper the classical two machine flow shop problem was generalized to the case when job processing times may be reduced linearly by the application of a limited continuously divisible resource e g financial outlay energy fuel catalyzer etc it is proved that the decision form of this problem is np complete even for the fixed job processing times on one of the machines and identical job reduction rates on another some polynomially solvable cases of the problem are identified four simple and modified approximate algorithms are presented together with their worst case and experimental analysis also a fast exact algorithm of the branch and bound type based on the shown elimination properties of the problem considered is presented some computational results and generalizations e g bicriterial approach are included as well

anderson acceleration for fixed point iterations this paper concerns an acceleration method for fixed point iterations that originated in work of d g anderson j assoc comput mach 12 1965 pp 547 560 which we accordingly call anderson acceleration here this method has enjoyed considerable success and wide usage in electronic structure computations where it is known as anderson mixing however it seems to have been untried or underexploited in many other important applications moreover while other acceleration methods have been extensively studied by the mathematics and numerical analysis communities this method has received relatively little attention from these communities over the years a recent paper by h fang and y saad numer linear algebra appl 16 2009 pp 197 221 has clarified a remarkable relationship of anderson acceleration to quasi newton secant updating methods and extended it to define a broader anderson family of acceleration methods in this paper our goals are to shed additional light on anderson acceleration and to draw further attention to its usefulness as a general tool we first show that on linear problems anderson acceleration without truncation is essentially equivalent in a certain sense to the generalized minimal residual gmres method we also show that the type 1 variant in the fang saad anderson family is similarly essentially equivalent to the arnoldi full orthogonalization method we then discuss practical considerations for implementing anderson acceleration and illustrate its performance through numerical experiments involving a variety of applications

scheduling two agents with controllable processing times abstract we consider several two agent scheduling problems with controllable job processing times where agents a and b have to share either a single machine or two identical machines in parallel while processing their jobs the processing times of the jobs of agent a are compressible at additional cost the objective function for agent b is always the same namely a regular function f max several different objective functions are considered for agent a including the total completion time plus compression cost the maximum tardiness plus compression cost the maximum lateness plus compression cost and the total compression cost subject to deadline constraints the imprecise computation model all problems are to minimize the objective function of agent a subject to a given upper bound on the objective function of agent b these problems have various applications in computer systems as well as in operations management we provide np hardness proofs for the more general problems and polynomial time algorithms for several special cases of the problems

job shop scheduling with resource time models of operations abstract the job shop problems with allocation of continuously divisible nonrenewable resource is considered the mathematical models of operations are linear decreasing functions with respect to an amount of resource the objective is sequencing operations and allocation of constrained resource such that the project duration is minimized thus the problem considered is a generalization of the classical job shop problem some properties of the optimal solution are presented the algorithm of solving this problem is based on the disjunctive graphs theory and branch and bound technique the theory of the algorithm is based on the critical path concept using the segment system approach the special feature of the algorithm is that it gives a complete solution which is associated with each node of the enumeration tree possible generalizations of the results presented are indicated

a flexible inner outer preconditioned gmres algorithm a variant of the gmres algorithm is presented that allows changes in the preconditioning at every step there are many possible applications of the new algorithm some of which are briefly discussed in particular a result of the flexibility of the new variant is that any iterative method can be used as a preconditioner for example the standard gmres algorithm itself can be used as a preconditioner as can cgnr or cgne the conjugate gradient method applied to the normal equations however the more appealing utilization of the method is in conjunction with relaxation techniques possibly multilevel techniques the possibility of changing preconditioners may be exploited to develop efficient iterative methods and to enhance robustness a few numerical experiments are reported to illustrate this fact

high re solutions for incompressible flow using the navier stokes equations and a multigrid method the vorticity stream function formulation of the two dimensional incompressible navierstokes equations is used to study the effectiveness of the coupled strongly implicit multigrid csi mg method in the determination of high re fine mesh flow solutions the driven flow in a square cavity is used as the model problem solutions are obtained for configurations with reynolds number as high as 10 000 and meshes consisting of as many as 257 x 257 points for re 1000 the 129 x 129 grid solution required 1 5 minutes of cpu time on the amdahl 470 v 6 computer because of the appearance of one or more secondary vortices in the flow field uniform mesh refinement was preferred to the use of one dimensional gridclustering coordinate transformations the past decade has witnessed a great deal of progress in the area of computational fluid dynamics developments in computer technology hardware as well as in advanced numerical algorithms have enabled attempts to be made towards analysis and numerical solution of highly complex flow problems for some of these applications the use of simple iterative techniques to solve the navier stokes equations leads to a rather slow convergence rate for the solutions the solution convergence rate can be seriously affected if the coupling among the various governing differential equations is not properly honored either in the interior of the solution domain or at its boundaries the rate of convergence is also generally strongly dependent on such problem parameters as the reynolds number the mesh size and the total number of computational points this has led several researchers to examine carefully the recently emerging multigrid mg technique as a useful means for enhancing the convergence rate of iterative numerical methods for solving discretized equations at a number of computational grid points so large as to be considered impractical previously

bicriterion single machine scheduling with resource dependent processing times a bicriterion problem of scheduling jobs on a single machine is studied the processing time of each job is a linear decreasing function of the amount of a common discrete resource allocated to the job a solution is specified by a sequence of the jobs and a resource allocation the quality of a solution is measured by two criteria f1 and f2 the first criterion is the maximal or total weighted resource consumption and the second criterion is a regular scheduling criterion depending on the job completion times both criteria have to be minimized general schemes for the construction of the pareto set and the pareto set epsilon approximation are presented computational complexities of problems to minimize f1 subject to f 2 le k and to minimize f2 subject to f 1 le k where k is any number are studied for various functions f1 and f2 algorithms for solving these problems and for the construction of the pareto set and the pareto set epsilon approximation for the corresponding bicriterion problems are presented

fast multigrid solution of the advection problem with closed characteristics the numerical solution of the advection diffusion problem in the inviscid limit with closed characteristics is studied as a prelude to an efficient high reynolds number flow solver it is demonstrated by a heuristic analysis and numerical calculations that using upstream discretization with downstream relaxation ordering in a multigrid cycle with appropriate residual weighting leads to an efficient solution process upstream finite difference approximations to the advection operator are derived whose truncation terms approximate physical laplacian viscosity thus avoiding spurious solutions to the homogeneous problem when the artificial diffusivity dominates the physical viscosity a brandt and i yavneh j comput phys 93 1991 pp 128 143

on recombining iterants in multigrid algorithms and problems with small islands this article deals with nearly singular problems and with problems having small islands or other small features not visible on a coarse grid in which cases usual multigrid solvers converge slowly or even diverge in these and many other problems the main difficulty is related to a few badly approximated components the numerical experiments reported below show that by recombining multigrid iterants such components are eliminated effectively and the usual multigrid asymptotic convergence rate is restored

multi agent scheduling on a single machine to minimize total weighted number of tardy jobs we consider the feasibility model of multi agent scheduling on a single machine where each agent s objective function is to minimize the total weighted number of tardy jobs we show that the problem is strongly np complete in general when the number of agents is fixed we first show that the problem can be solved in pseudo polynomial time for integral weights and can be solved in polynomial time for unit weights then we present a fully polynomial time approximation scheme for the problem

an evaluation of parallel multigrid as a solver and a preconditioner for singularly perturbed problems in this paper we try to achieve h independent convergence with preconditioned gmres y saad and m h schultz siam j sci comput 7 1986 pp 856 869 and bicgstab h a van der vorst siam j sci comput 13 1992 pp 63 644 for two dimensional 2d singularly perturbed equations three recently developed multigrid methods are adopted as a preconditioner they are also used as solution methods in order to compare the performance of the methods as solvers and as preconditioners two of the multigrid methods differ only in the transfer operators one uses standard matrix dependent prolongation operators from j e dendy jr j comput phys 48 1982 pp 366 386 w hackbusch multi grid methods and applications springer berlin 1985 the second uses upwind prolongation operators developed in p m de zeeuw j comput appl math 33 1990 pp 1 27 both employ the galerkin coarse grid approximation and an alternating zebra line gauss seidel smoother the third method is based on the block lu decomposition of a matrix and on an approximate schur complement this multigrid variant is presented in a reusken a multigrid method based on incomplete gaussian elimination university of eindhoven the netherlands 1995 all three multigrid algorithms are algebraic methods the eigenvalue spectra of the three multigrid iteration matrices are analyzed for the equations solved in order to understand the convergence of the three algorithms furthermore the construction of the search directions for the multigrid preconditioned gmres solvers is investigated by the calculation and solution of the minimal residual polynomials for poisson and convection diffusion problems all solution methods are investigated and evaluated for finite volume discretizations on fine grids the methods have been parallelized with a grid partitioning technique and are compared on an mimd machine

inadequacy of first order upwind difference schemes for some recirculating flows spurious numerical solutions of problems with closed sub characteristics by upwind difference schemes in particular problems of recirculating incompressible flow at high reynolds numbers are proved to be due to the anisotropy of the artificial viscosity numerical examples are presented to show that even very simple problems including basic problems in fluid dynamics are not approximated well by schemes with anisotropic artificial viscosity regardless of numerical parameters 1991 academic press inc numerical methods for solving incompressible fluid flow equations are frequently tested on problems of recirculating flow quite often results obtained by different methods differ from each other significantly reliable experimental data is usually difficult to obtain and discrepancies between numerical two dimensional solutions and experimental data may be the result of the influence of walls in the experiments the problems in solving recirculating incompressible flows at high reynolds numbers are well known several researchers have pointed out that some of the methods employed to obtain stable discretization e g upwind differencing may lead to spurious results such results have been attributed to excessive artificial viscosity in the numerical scheme to multiple solutions of the non linear set of algebraic equations that is obtained from the numerical scheme and to poor resolution by grids that are too coarse 2 4 51 but spurious results occur even when none of these reasons are valid indeed a single linear partial differential equation may exhibit such behavior when the sub characteristics are closed this is true even when the mesh size is small enough to easily resolve the solution and truncation errors are genuinely small everywhere and even when the differential solution does not depend on the

monotone iterative technique for delay differential equations in abstract cones a monotone iterative technique is developed for delay differential equations in a banach space by utilizing the method of upper and lower solutions

positive half products and scheduling with controllable processing times we study the single machine scheduling problem with controllable job processing times to minimize a linear combination of the total weighted job completion time and the total weighted processing time compression we show that this scheduling problem is a positive half product minimization problem positive half products make up an interesting subclass of half products and are introduced in this paper to provide a conceptual framework for the problem with controllable job processing times as well as other problems this framework allows to readily derive in one fell swoop a number of results for the problem with controllable processing times from more general results obtained earlier for the half product we also present fast fully polynomial time approximation schemes for the problem with controllable processing times the schemes apply to all positive half products