a multiscale direct solver for the approximation of flows in high contrast porous media abstract we consider a non overlapping domain decomposition approach to approximate the solution of elliptic boundary value problems with high contrast in their coefficients we propose a method such that initially local solutions subject to robin boundary conditions in each primal subdomain are constructed with locally conservative finite element or finite volume methods then a novel approach is introduced to obtain a discontinuous global solution in terms of linear combination of the local subdomain solutions in the proposed algorithm the computation of local solutions for unions of subdomains are localized at nearest neighbor subdomain boundaries thus avoiding the solution of global interface problems we remove discontinuities in a smoothing step that is defined on a staggered grid or dual subdomains the resulting algorithm is naturally parallelizable and can be employed as a parallel direct solver offering great potential for the numerical solution of large problems in fact subdomains can be considered small enough to fit well in gpus and the proposed procedure can handle adaptive in space simulations effectively numerical simulations are presented and discussed we demonstrate the effectiveness of the proposed approach with two and three dimensional high contrast and channelized coefficients that lead to challenging approximation problems the new procedure although designed for parallel processing is also of value for serial calculations

the construction of preconditioners for elliptic problems by substructuring i in earlier parts of this series of papers we constructed preconditioners for the discrete systems of equations arising from the numerical approximation of elliptic boundary value problems the resulting algorithms are well suited for implementation on computers with parallel architecture in this paper we will develop a technique which utilizes these earlier methods to derive even more efficient preconditioners the iterative algorithms using these new preconditioners converge to the solution of the discrete equations with a rate that is independent of the number of unknowns these preconditioners involve an incomplete chebyshev iteration for boundary interface conditions which results in a negligible increase in the amount of computational work theoretical estimates and the results of numerical experiments are given which demonstrate the effectiveness of the methods

a mixed integer linear programming approach to minimize the number of late jobs with and without machine availability constraints this study investigates scheduling problems that occur when the weighted number of late jobs that are subject to deterministic machine availability constraints have to be minimized these problems can be modeled as a more general job selection problem cases with resumable non resumable and semi resumable jobs as well as cases without availability constraints are investigated the proposed efficient mixed integer linear programming approach includes possible improvements to the model notably specialized lifted knapsack cover cuts the method proves to be competitive compared with existing dedicated methods numerical experiments on randomly generated instances show that all 350 job instances of the test bed are closed for the well known problem 1 r i sum w iu i for all investigated problem types 98 4 of 500 job instances can be solved to optimality within one hour

genetic algorithms to minimize the weighted number of late jobs on a single machine the general one machine scheduling problem is strongly np hard when the objective is to minimize the weighted number of late jobs few methods exist to solve this problem in an other paper we developed a lagrangean relaxation algorithm which gives good results on many instances however there is still room for improvement and a metaheuristic might lead to better results in this paper we decided to use a genetic algorithm ga although a ga is somewhat easy to implement many variations exist and we tested some of them to design the best ga for our problem three different engines to evaluate the fitness of a chromosome are considered together with four types of crossover operators and three types of mutation operators an improved ga is also proposed by applying local search on solutions determined from the chromosome by the engine numerical experiments on different tests of instances are reported they show that starting from an initial population already containing a good solution is very effective 2003 elsevier b v all rights reserved

domain decomposition algorithms for mixed methods for second order elliptic problems domain decomposition algorithms for mixed finite element methods for linear second order elliptic problems in r 2 and r 3 are developed a convergence theory for two level and multilevel schwarz methods applied to the algorithms under consideration is given it is shown that the condition number of these iterative methods is bounded uniformly from above in the same manner as in the theory of domain decomposition methods for conforming and nonconforming finite element methods for the same differential problems numerical experiments are presented to illustrate the present techniques

properties of the voice transform of the blaschke group and connections with atomic decomposition results in the weighted bergman spaces abstract feichtinger and grochenig described a unified approach to atomic decomposition through integrable group representations in banach spaces studying the properties of a special voice transform of the blascke group outlined by the general theory developed by feichtinger and grochenig we obtain that every function from the minimal mobius invariant space will generate an atomic decomposition in the weighted bergman spaces in the unified approach of the atomic decomposition a useful tool is the q density the v separated property and the bounded uniform partitions of the unity of the locally compact group using the hyperbolic metric we can describe the q density from right and the separation from right in the blaschke group using this we can give an example of bounded uniform partitions of the unity from right in the general theory of atomic decomposition it is used the q density from the left this is the reason why we will make a small modification in the discretizing operator which corresponds to the q density from the right in order to obtain atomic decomposition in the weighted bergman spaces

minimizing tardy jobs in a flowshop with common due date abstract this paper considers the two machine flowshop scheduling problem where the total time for which a shop is available to complete a given number of jobs is constrained to a known number this problem is equivalent to the flowshop scheduling problem to minimize the total number of tardy jobs against a common due date it has been recently proven to be np hard in the ordinary sense a compact multidimensional knapsack problem formulation of the problem is introduced together with several structural properties a branch and bound procedure is proposed to find an optimal solution to the problem computational results show that the proposed algorithm is capable of finding optimal solutions to problems with up to 900 jobs

a relaxation procedure for domain decomposition methods using finite elements we present the convergence analysis of a new domain decomposition technique for finite element approximations this technique was introduced in 11 and is based on an iterative procedure among subdomains in which transmission conditions at interfaces are taken into account partly in one subdomain and partly in its adjacent no global preconditioner is needed in the practice but simply single domain finite element solvers are required an optimal strategy for an automatic selection of a relaxation parameter to be used at interface subdomains is indicated applications are given to both elliptic equations and incompressible stokes equations

on the use of rational iterations and domain decomposition methods for the helmholtz problem an iterative algorithm for the numerical solution of the helmholtz problem is considered it is difficult to solve the problem numerically in particular when the imaginary part of the wave number is zero or small we develop a parallel iterative algorithm based on a rational iteration and a nonoverlapping domain decomposition method for such a non hermitian non coercive problem algorithm parameters artificial damping and relaxation are introduced to accelerate the convergence speed of the iteration convergence analysis and effective strategies for finding efficient algorithm parameters are presented numerical results carried out on an ncube2 are given to show the efficiency of the algorithm to reduce the boundary reflection we employ a hybrid absorbing boundary condition abc which combines the first order abc and the physical q abc computational results comparing the hybrid abc with non hybrid ones are presented

minimizing late jobs in the general one machine scheduling problem abstract in this paper the problem of minimizing the number of late jobs on one machine is investigated the general problem is considered i e with release dates and different due dates a lower bound is first proposed based on the relaxation of a mixed integer linear programming formulation of the problem a heuristic is then presented its effectiveness is computationally studied by comparison with the lower bound

a branch and bound algorithm to minimize the number of late jobs in a permutation flow shop abstract the problem of scheduling n jobs in an m machine permutation flow shop is considered each job requires processing on machines 1 m in that order the processing order of jobs is to be the same for each machine a due date for each job is specified that represents the time by which it should ideally be completed the objective is to schedule the jobs so that the number completed after their due dates is minimized a lower bound which is obtained by solving a single machine subproblem is derived also two improvement procedures which consider all subproblems together are developed a branch and bound algorithm that uses these lower bounds is described computational experience with the algorithm is reported

a non overlapping domain decomposition method with non matching grids for modeling large finite antenna arrays a non overlapping domain decomposition method ddm is proposed herein to solve maxwell equations in r 3 in this work the maxwell equations are discretized using a vector finite element method with hierarchical h curl vector basis functions there are two major ingredients in the proposed non overlapping ddm a a proper 1st order transmission condition to enforce field continuity across domain boundaries and b a cement technique to allow non matching grids for neighboring domains moreover a detail fourier analysis of the transmission condition for a canonical half space example is presented the analysis provides significant insights into the convergence behavior of the proposed non overlapping ddm for solving electromagnetic radiation problems such as the large finite antenna arrays particularly for the antenna arrays the proposed non overlapping ddm is extremely efficient since the formulation can easily incorporate geometrical repetitions exponentially tapered notch vivaldi antenna arrays with size up to 100x100 elements are solved on a common pc to validate the proposed non overlapping ddm

mixed finite elements for second order elliptic problems in three variables two families of mixed finite elements one based on simplices and the other on cubes are introduced as alternatives to the usual raviart thomas nedelec spaces these spaces are analogues of those introduced by brezzi douglas and marini in two space variables error estimates inl2 andh s are derived

the multiscale robin coupled method for flows in porous media abstract a multiscale mixed method aiming at the accurate approximation of velocity and pressure fields in heterogeneous porous media is proposed the procedure is based on a new domain decomposition method in which the local problems are subject to robin boundary conditions the domain decomposition procedure is defined in terms of two independent spaces on the skeleton of the decomposition corresponding to interface pressures and fluxes that can be chosen with great flexibility to accommodate local features of the underlying permeability fields the well posedness of the new domain decomposition procedure is established and its connection with the method of douglas et al 1993 12 is identified also allowing us to reinterpret the known procedure as an optimized schwarz or two lagrange multiplier method the multiscale property of the new domain decomposition method is indicated and its relation with the multiscale mortar mixed finite element method mmmfem and the multiscale hybrid mixed mhm finite element method is discussed numerical simulations are presented aiming at illustrating several features of the new method initially we illustrate the possibility of switching from mmmfem to mhm by suitably varying the robin condition parameter in the new multiscale method then we turn our attention to realistic flows in high contrast channelized porous formations we show that for a range of values of the robin condition parameter our method provides better approximations for pressure and velocity than those computed with either the mmmfem and the mhm this is an indication that our method has the potential to produce more accurate velocity fields in the presence of rough realistic permeability fields of petroleum reservoirs

domain decomposition methods for nonlinear problems in fluid dynamics abstract the numerical solution of finite element approximations of complicated two and three dimensional nonlinear problems can be a most formidable task in order to overcome this difficulty related to dimensionality domain splitting methods can be very effective particularly in view of obtaining a fast and economical conjugate gradient solver which can be used to precondition the solution of nonlinear problems by optimization methods via nonlinear least squares or weighted residual formulations a new technique of this type will be introduced and analysed and its efficiency will be discussed from numerical experiments concerning the numerical simulation of transonic flows for compressible inviscid fluids and incompressible viscous flows modelled by the navier stokes equations

a branch and bound to minimize the number of late jobs on a single machine with release time constraints this paper presents a branch and bound algorithm for the single machine scheduling problem 1 ri ui where the objective function is to minimize the number of late jobs lower bounds based on a lagrangian relaxation and no reductions to polynomially solvable cases are proposed efficient elimination rules together with strong dominance relations are also used to reduce the search space a branch and bound exploiting these techniques solves to optimality instances with up to 200 jobs improving drastically the size of problems that could be solved by exact methods up to now

extension theorems for plate elements with applications extension theorems for plate elements are established their applications to the analysis of nonoverlapping domain decomposition methods for solving the plate bending problems are presented numerical results support our theory

banach spaces related to integrable group representations and their atomic decompositions i abstract we present a general theory of banach spaces which are invariant under the action of an integrable group representation and give their atomic decompositions with respect to coherent states i e the atoms arise from a single element under the group action several well known decomposition theories are contained as special examples and are unified under the aspect of group theory

an iterative procedure with interface relaxation for domain decomposition methods a domain decomposition method for second order elliptic problems is considered an iterative procedure that reduces the problem to a sequence of mixed boundary value problems on each subdomain is proposed at each iteration a relaxation is accomplished at the subdomain interfaces in several circumstances a value of the relaxation parameter that yields exact convergence in a finite number of iterations is explicitly found moreover when such a value is not available an appropriate strategy for the automatic selection of the relaxation parameter at each iteration is indicated and analyzed this iterative method is then applied to the spectral collocation approximation of the differential problem the same kind of convergence results are proven many numerical experiments show the effectiveness of the method proposed here

the optimized schwarz method with a coarse grid correction optimized schwarz methods osms use robin transmission conditions across the subdomain interfaces the robin parameter can then be optimized to obtain the fastest convergence a new formulation is presented with a coarse grid correction the optimal parameter is computed for a model problem on a cylinder together with the corresponding convergence factor which is smaller than that of classical schwarz methods a new coarse space is presented suitable for osm numerical experiments illustrating the effectiveness of osm with a coarse grid correction both as an iteration and as a preconditioner are reported

a genetic algorithm for an industrial multiprocessor flow shop scheduling problem with recirculation abstract we propose in this paper an effective heuristic algorithm to solve a scheduling problem that comes from industry the workshop is an hybrid flow shop with recirculation and the problem is to perform jobs between a release date and a due date in order to minimize the weighted number of tardy jobs firstly an integer linear programming formulation of the problem is proposed then a lower bound a greedy algorithm and a genetic algorithm are described as approximate methods to evaluate these heuristics experiences on instances like industrial ones are computed and show the efficiency of the genetic algorithm

branch and bound crossed with ga to solve hybrid flowshops this article deals with an optimal methods for solving a k stage hybrid flowshop scheduling problem this problem is known to be np hard in 1991 brah and hunsucker proposed a branch and bound algorithm to solve this problem however for some medium size problems the computation time is not acceptable the aim of this article is to present an improvement of this algorithm as a matter of fact we prove that the value of their lower bound lb may decrease along a path of the search tree first of all we present an improvement of their lb then we introduce several heuristics at the beginning of the search in order to compute an initial upper bound and genetic algorithm ga to improve during the search the value of the upper bound more precisely our ga takes into account the set of partial decisions made by the branch and bound and builds a series of populations of complete solutions with the aim of improving the upper bound the best found criterion value corresponding to a complete solution experimentation show that the optimality of branch and bound is more often reached and the value of criterion is improved when our improvements are taken into account

balancing neumann neumann methods for incompressible stokes equations this paper describes the unerlying mathematical model and the balancing neumann neumann methods are introduced and studied for incompressible stokes equations discretized with mixed finite or spectral elements with discontinuous pressures after decomposing the original domain of the problem into nonoverlapping subdomains the interior unknowns which are the interior velocity component and all except the constant pressure component of each subdomain problem are implicitly eliminated the resulting saddle point schur complement is solved with a krylov space method with a balancing neumann neumann preconditioner based on the solution of a coarse stokes problem with a few degrees of freedom per subdomain and on the solution of local stokes problems with natural neumann velocity and essential boundary conditions on the subdomains this preconditioner is of hybrid form in which the coarse problem is treated multiplicatively while the local problems are treated additively the condition number of the preconditioned operator is independent of the number of subdomains and is bounded from above by the product of the square of the logarithm of the local number of unknowns in each subdomain and the inverse of the inf sup constants of the discrete problem and of the coarse subproblem numerical results show that the method is quite fast they are also fully consistent with the theory

coupling of viscous and inviscid stokes equations via a domain decomposition method for finite elements a generalized stokes problem is addressed in the framework of a domain decomposition method in which the physical computational domain is partitioned into two subdomains 1 and 2 three different situations are covered in the former the viscous terms are kept in both subdomains then we consider the case in which viscosity is dropped out everywhere in finally a hybrid situation in which viscosity is dropped out only in 1 is addressed the latter is motivated by physical applications in all cases correct transmission conditions across the interface between 1 and 2 are devised and an iterative procedure involving the successive resolution of two subproblems is proposed the numerical discretization is based upon appropriate finite elements and stability and convergence analysis is carried out we also prove that the iteration by subdomain algorithms which are associated with the various domain decomposition approaches converge with a rate independent of the finite element mesh size

integer linear programming formulations of multiple salesman problems and its variations in this paper we extend the classical multiple traveling salesman problem mtsp by imposing a minimal number of nodes that a traveler must visit as a side condition we consider single and multidepot cases and propose integer linear programming formulations for both with new bounding and subtour elimination constraints we show that several variations of the multiple salesman problem can be modeled in a similar manner computational analysis shows that the solution of the multidepot mtsp with the proposed formulation is significantly superior to previous approaches

a multi timestep robin robin domain decomposition method for time dependent advection diffusion problems abstract many physical processes present separated evolution time scales in different regions such as windblown sand in the desert the evolution of bed surface locally affects the sandy wind flow which erodes the sand in turns while few meters higher from the ground the airflow is almost stationary this and other applications suggest to improve the overall computational efficiency by locally adapting the time advancing step to the evolution in each region we propose a multi timestep robin robin domain decomposition method which uses mutually proportional time steps based on a predictor corrector strategy coupled with linear interpolation in time the resulting algorithm is completely segregated several numerical tests obtained by the finite volume code openfoam are reported to show its stability and convergence properties

domain decomposition iterative procedures for solving scalar waves in the frequency domain the propagation of dispersive waves can be modeled relevantly in the frequency domain a wave problem in the frequency domain is difficult to solve numerically in addition to having a complex valued solution the problem is neither hermitian symmetric nor coercive in a wide range of applications in geophysics or quantum mechanics in this paper we consider a parallel domain decomposition iterative procedure for solving the problem by finite differences or conforming finite element methods the analysis includes the decomposition of the domain into either the individual elements or larger subdomains blocks of finite elements to accelerate the speed of convergence we introduce relaxation parameters on the subdomain interfaces and an artificial damping iteration the convergence rate of the resulting algorithm turns out to be independent on the mesh size and the wave number numerical results carried out on an ncube2 parallel computer are presented to show the effectiveness of the method

global estimates for mixed methods for second order elliptic equations global error estimates in l2 92 l 9 and h s q 2 in r2 or a re derived for a mixed finite element method for the dirichlet problem for the elliptic operator lp div a grad p bp cp based on the raviart thomas nedelec space vh x wh c h div 92 x l2 g2 optimal order estimates are obtained for the approximation of p and the associated velocity field u a grad p bp in l2 g2 and h s 92 0 6 s k 1 and if q c r2 forp in lv2

a review of exact solution methods for the non preemptive multiprocessor flowshop problem abstract the hybrid or flexible flowshop problem is a generalization of the flowshop in such a way that every job can be processed by one among several machines on each machine stage in recent years a number of effective exact methods have been developed a major reason for this progress is the development of new job and machine based lower bounds as well as the rapidly increasing importance of constraint programming in this paper we provide the first comprehensive and uniform overview on exact solution methods for flexible flowshops with branching bounding and propagation of constraints under two different objective functions minimizing the makespan of a schedule and the mean flow time

flowshop scheduling with identical jobs and uniform parallel machines the single stage scheduling problem to minimize the makespan of identical jobs on uniform parallel machines is known to be solvable in polynomial time we extend this work to consider multi stage systems with flowshop configuration we show that the 2 stage problem may also be solved in polynomial time and for the number of stages greater than two the problem is shown to be np hard we present a branch and bound procedure which provides an optimal solution to the 3 stage problem and a fast heuristic procedure that is shown to provide good approximate solutions on sample problems this heuristic is a natural extension of the 2 stage polynomial time procedure we develop theoretical bounds showing that the maximum deviation between the solution derived by the heuristic procedure and the optimal solution is bounded by the maximum processing time of a machine at the second stage independent of the number of jobs and the processing times at the first and third stages we also show that the heuristic provides an approximate solution bounded by a ratio of 1 75 to the optimal solution

mixed approximation of a population diffusion equation abstract a numerical method is proposed to approximate the solution of a nonlinear and nonlocal system of integro differential equations describing age dependent population dynamics with spatial diffusion a finite difference method along the characteristic age time direction combined with mixed finite elements in the spatial variable is used for the approximation optimal order error estimates are derived for the relevant variables using nonnegativity of the discrete solution a stability of the method is also proved

an iterative method for elliptic problems on regions partitioned into substructures some new preconditioners for discretizations of elliptic boundary problems are studied with these preconditioners the domain under consideration is broken into subdomains and preconditioners are defined which only require the solution of matrix problems on the subdomains analytic estimates are given which guarantee that under appropriate hypotheses the preconditioned iterative procedure converges to the solution of the discrete equations with a rate per iteration that is independent of the number of unknowns numerical examples are presented which illustrate the theoretically predicted iterative convergence rates

two families of mixed finite elements for second order elliptic problems two families of mixed finite elements one based on triangles and the other on rectangles are introduced as alternatives to the usual raviart thomas nedelec spaces error estimates inl 2 andh 5 are derived for these elements a hybrid version of the mixed method is also considered and some superconvergence phenomena are discussed

finite element methods for the simulation of waves in composite saturated poroviscoelastic media this work presents and analyzes a collection of finite element procedures for the simulation of wave propagation in a porous medium composed of two weakly coupled solids saturated by a single phase fluid the equations of motion formulated in the space frequency domain include dissipation due to viscous interaction between the fluid and solid phases with a correction factor in the high frequency range and intrinsic anelasticity of the solids modeled using linear viscoelasticity this formulation leads to the solution of a helmholtz type boundary value problem for each temporal frequency for the spatial discretization nonconforming finite element spaces are employed for the solid phases while for the fluid phase the vector part of the raviart thomas nedelec mixed finite element space is used optimal a priori error estimates for global standard and hybridized galerkin finite element procedures are derived an iterative nonoverlapping domain decomposition procedure is also presented and convergence results are derived numerical experiments showing the application of the numerical procedures to simulate wave propagation in partially frozen porous media are presented

minimizing the weighted number of tardy jobs on a single machine with release dates abstract in this paper we describe an exact algorithm to minimize the weighted number of tardy jobs on a single machine with release dates the algorithm uses branch and bound a surrogate relaxation resulting in a multiple choice knapsack provides the bounds extensive computational experiments indicate the proposed exact algorithm solves either weighted or unweighted problems it solves the hardest problems to date indeed it solves all previously unsolved instances its run time is the shortest to date scope and purpose in many industrial sectors satisfying due dates is a critical issue thus lateness related measures such as the weighted number of tardy jobs are relevant performance measures of schedules in these industries our paper studies minimizing the weighted number of tardy jobs on a single machine with release and due dates and proposes a new exact algorithm for both weighted and unweighted problems the exact algorithm solves the largest problems to date

an optimal parallel nonoverlapping domain decomposition iterative procedure a nonoverlapping domain decomposition iterative procedure is developed and analyzed for second order elliptic problems in mathbb r n its convergence is proved the method is based on a robin type consistency condition with two parameters called a transmission coefficient and a penalty coefficient as a transmission condition together with a derivative free transmission data updating technique on the artificial interfaces then the method is applied to the nonconforming finite element problems a nonoverlapping domain decomposition iterative procedure for solving the nonconforming finite element problems of second order partial differential equations is developed and analyzed which is directly presented to the nonconforming finite element problems without introducing any lagrange multipliers its convergence is demonstrated and the convergence rate is derived the convergence analyses imply that the convergence rate is independent of the finite element meshes size while choosing the right parameters furthermore the conclusions are extended to the unstructured finite element meshes for both continuous problems and discrete problems the method of this paper can be applied to general multisubdomain decompositions and implemented on parallel machines with local communications naturally the method also allows choosing subdomains very flexibly even as small as an individual element for finite element problems

scheduling a two stage hybrid flowshop with separable setup and removal times abstract this paper considers the two stage flowshop scheduling problem where each stage consists of several identical parallel machines and the setup and removal times of each job at each stage are separated from the processing times a polynomial optimization algorithm is developed for the special case where the first stage contains only one machine and the number of identical parallel machines at the second stage is equal to or greater than the total number of jobs in view of the np completeness of this problem four heuristic algorithms are developed for the case where there is one machine at stage 1 and the number of identical parallel machines at the second stage is less than the total number of jobs the proposed heuristic algorithms are empirically tested to determine their effectiveness in finding an optimal schedule

space time domain decomposition methods for diffusion problems in mixed formulations this paper is concerned with global in time nonoverlapping domain decomposition methods for the mixed formulation of the diffusion problem two approaches are considered one uses the time dependent steklov poincare operator and the other uses optimized schwarz waveform relaxation oswr based on robin transmission conditions for each method a mixed formulation of an interface problem on the space time interfaces between subdomains is derived and different time grids are employed to adapt to different time scales in the subdomains demonstrations of the well posedness of the robin subdomain problems involved in the oswr method and a convergence proof of the oswr algorithm are given for the mixed formulation numerical results for two dimensional problems with strong heterogeneities are presented to illustrate the performance of the two methods

global lower bounds for flow shops with multiple processors abstract flow shop with multiple processors fsmp scheduling involves sequencing jobs in a flow shop where at any processing stage there exists one or more identical processors any methodology to determine the optimal makespan for this type of problem is np complete this necessitates the use of sub optimal heuristic methods to address problems of moderate to large scale this paper presents global lower bounds on fsmp makespan problems which may be used to assess the quality of heuristic solutions when the optimal solution is unknown

flow shop scheduling algorithms for minimizing the completion time variance and the sum of squares of completion time deviations from a common due date abstract we consider two problems of m machine flow shop scheduling in this paper one with the objective of minimizing the variance of completion times of jobs and the other with the objective of minimizing the sum of squares of deviations of job completion times from a common due date lower bounds on the sum of squares of deviations of job completion times from the mean completion time of jobs for a given partial sequence are first presented using these lower bounds a branch and bound algorithm based on breadth first search procedure for scheduling n jobs on m machines with the objective of minimizing completion time variance ctv is developed to obtain the best permutation sequence we also present two lower bounds and thereafter a branch and bound algorithm with the objective of minimizing the sum of squares of deviations of job completion times from a given common due date called the msd problem the computational experience with the working of the two proposed branch and bound algorithms is also reported two heuristics one for each of the two problems are developed the computational experience on the evaluation of the heuristics is discussed

mixed finite element domain decomposition for nonlinear parabolic problems abstract fully discrete mixed finite element method is considered to approximate the solution of a nonlinear second order parabolic problem a massively parallel iterative procedure based on domain decomposition technique is presented to solve resulting nonlinear algebraic equations robin type boundary conditions are used to transmit information between subdomains the convergence of the iteration for each time step is demonstrated optimal order error estimates are also derived numerical examples are given

domain decomposition for fourth order problems multidomain pseudospectral approximation of fourth order boundary value problems are considered different patching conditions at the interfaces are analyzed convergence results are given an iterative method with interface relaxation is investigated numerical results are presented for two or more domains

analysis of finite element methods and domain decomposition algorithms for a fluid solid interaction problem this paper is concerned with the finite element galerkin approximations for a fluid solid interaction model proposed in x feng p lee and y wei appl anal submitted both continuous time and discrete time approximations are formulated and analyzed optimal order a priori estimates for the errors in l infty h 1 and l infty l 2 are derived the main difficulty for the error estimates is caused by the interface conditions which describe the interaction between a fluid and a solid on their contact surface and it is overcome by using a boundary duality argument of douglas and dupont numer math 20 1973 pp 213 237 to handle the terms involving the interface conditions parallelizable domain decomposition algorithms are also proposed and analyzed for efficiently solving the finite element systems

overlapping schwarz methods on unstructured meshes using non matching coarse grids we consider two level overlapping schwarz domain decomposition methods for solving the finite element problems that arise from discretizations of elliptic problems on general unstructured meshes in two and three dimensions standard finite element interpolation from the coarse to the fine grid may be used our theory requires no assumption on the substructures that constitute the whole domain so the substructures can be of arbitrary shape and of different size the global coarse mesh is allowed to be non nested to the fine grid on which the discrete problem is to be solved and neither the coarse mesh nor the fine mesh need be quasi uniform in addition the domains defined by the fine and coarse grid need not be identical the one important constraint is that the closure of the coarse grid must cover any portion of the fine grid boundary for which neumann boundary conditions are given in this general setting our algorithms have the same optimal convergence rate as the usual two level overlapping domain decomposition methods on structured meshes the condition number of the preconditioned system depends only on the possibly small overlap of the substructures and the size of the coarse grid but is independent of the sizes of the subdomains

nonconforming finite element methods for the simulation of waves in viscoelastic solids the propagation of waves in two and three dimensional bounded viscoelastic media is described in the space frequency domain leading to a helmholtz type boundary value problem which is noncoercive non hermitian and complex valued first order absorbing boundary conditions are derived and used to minimize spurious reflections from the artificial boundaries the paper consists of two parts in part i we describe the global procedures for the approximate solution of the problem simplicial and rectangular nonconforming finite element methods are employed for the spatial discretization optimal error estimate in a broken energy and l2 norms are derived using a bootstrapping argument of schatz also a hybridization of these procedures is analyzed in part ii we define and analyze nonoverlapping domain decomposition iterative methods convergence results are derived and numerical experiments showing the potential applicability in seismology are presented

a petrov galerkin finite element method for interface problems arising in sensitivity computations continuous sensitivity equation methods have been applied to a variety of applications ranging from optimal design to fast algorithms in computational fluid dynamics to the quantification of uncertainty in order to make use of these methods for interface problems one needs fast and accurate numerical methods for computing sensitivities for problems defined by partial differential equations with solutions that have spatial discontinuities such as shocks and interfaces in this paper we develop a discontinuous petrov galerkin finite element scheme for solving the sensitivity equation resulting from a 1d interface problem the 1d example is sufficient to motivate the theoretical and computational issues that arise when one derives the corresponding boundary value problem for the sensitivities in particular the sensitivity boundary value problem must be formulated in a very weak sense and the resulting variational problem provides a natural framework for developing and analyzing numerical schemes numerical examples are presented to illustrate the benefits of this approach

branch and bound algorithm for the flow shop with multiple processors abstract the sequencing of a flow shop with multiple processors at each stage is a general case of the flow shop problem it involves sequencing n jobs in a flow shop where for at least one stage the facility has one or more identical machines the purpose of this paper is to present a branch and bound algorithm to solve scheduling problems of such facilities for optimizing the maximum completion time the lower bounds and elimination rules developed in this research are based upon the generalization of the flow shop problem furthermore a computational algorithm along with results is also presented the branch and bound algorithm can also be used to optimize other measures of performance in a flow shop with multiple processors

new substructuring domain decomposition methods for advection diffusion equations abstract in this paper we consider a nonsymmetric elliptic problem and we use the techniques related to the steklov poincare operators to propose new substructuring iterative procedures in particular we propose two methods that generalize the well known neumann neumann and dirichlet neumann iterative procedures we prove that our methods that use symmetric and positive definite preconditioners lead to the construction of iterative schemes with optimal convergence properties numerical results for the finite element discretization are given

a domain decomposition method for the helmholtz equation and related optimal control problems we present an iterative domain decomposition method to solve the helmholtz equation and related optimal control problems the proof of convergence of this method relies on energy techniques this method leads to efficient algorithms for the numerical resolution of harmonic wave propagation problems in homogeneous and heterogeneous media

a flexible flowshop problem with total flow time minimization abstract in this study we consider total flow time problem in a flexible flowshop environment we develop a branch and bound algorithm to find the optimal schedule the efficiency of the algorithm is enhanced by upper and lower bounds and a dominance criterion computational experience reveals that the algorithm solves moderate sized problems in reasonable solution times

algorithms for scheduling a single machine to minimize the weighted number of late jobs this paper considers the problem of scheduling n jobs each having a processing time a due date and a weight on a single machine to minimize the weighted number of late jobs an o n log n algorithm is given for solving the linear programming problem obtained by relaxing the integrality constraints in a zero one programming formulation of the problem this linear programming lower bound is used in a reduction algorithm that eliminates jobs from the problem also a branch and bound algorithm that uses the linear programming lower bound is proposed computational results with branch and bound algorithms that use this and other lower bounds and with a dynamic programming algorithm for problems with up to 1000 jobs are given

condition number estimates for the nonoverlapping optimized schwarz method and the 2 lagrange multiplier method for general domains and cross points the optimized schwarz method and the closely related 2 lagrange multiplier method are domain decomposition methods which can be used to parallelize the solution of partial differential equations although these methods are known to work well in special cases e g when the domain is a square and the two subdomains are rectangles the problem has never been systematically stated nor analyzed for general domains with general subdomains the problem of cross points when three or more subdomains meet at a single vertex has been particularly vexing we introduce a 2 lagrange multiplier method for domain decompositions with cross points we estimate the condition number of the iteration and provide an optimized robin parameter for general domains we hope that this new systematic theory will allow broader utilization of optimized schwarz and 2 lagrange multiplier preconditioners

a finite element capacitance matrix method for the elliptic problem the capacitance matrix method for finite element approximation of the symmetric elliptic problem with the dirichlet condition on an arbitrary region is considered two variants of this method are presented which correspond to the situations when the single and double layer potential are used it is shown that the condition number of the capacitance matrix c is o h 1 for the first variant and the eigenvalues of c are positive and independent of h for the second variant where h is the mesh size of the triangulation

continuous and discrete wavelet transforms this paper is an expository survey of results on integral representations and discrete sum expansions of functions in l 2 bf r in terms of coherent states two types of coherent states are considered weyl heisenberg coherent states which arise from translations and modulations of a single function and affine coherent states called wavelets which arise as translations and dilations of a single function in each case it is shown how to represent any function in l 2 bf r as a sum or integral of these states most of the paper is a survey of literature most notably the work of i daubechies a grossmann and j morlet a few results of the authors are included

on accelerated convergence of nonoverlapping schwarz methods the schwarz alternating method can be used to solve elliptic boundary value problems on domains which consist of two or more overlapping subdomains the solution is approximated by an infinite sequence of functions which results from solving a sequence of elliptic boundary value problems in each subdomain schwarz methods for nonoverlapping subdomains also exist but they have not been popular because of their slow convergence these methods contain a free parameter in the robin boundary condition of each subdomain problem the slow convergence can be attributed to an improper choice of this parameter in this paper two models are proposed to give guidance to the choice of this parameter for the poisson equation on rectangular domains these models suggest very simple expressions for the parameter in terms of the dimensions of the subdomain numerical experiments verify their effectiveness when used as a preconditioner it is demonstrated numerically in some examples that the algorithm is quite efficient

artificial damping techniques for scalar waves in the frequency domain abstract an artificial damping algorithm for solving the helmholtz problem is considered when the imaginary part of the wave number is small the problem is known to be difficult to solve in this paper we propose an efficient artificial damping algorithm which can be viewed as a rational iteration each damped problem is solved incompletely by a nonoverlapping domain decomposition method convergence arguments are presented numerical results run on an ncube2 are presented to demonstrate the effectiveness of the method

some nonoverlapping domain decomposition methods the purpose of this paper is to give a unified investigation of a class of nonoverlapping domain decomposition methods for solving second order elliptic problems in two and three dimensions the methods under scrutiny fall into two major categories the substructuring type methods and the neumann neumann type methods the basic framework used for analysis is the parallel subspace correction method or additive schwarz method and other technical tools include local global and global local techniques the analyses for both two and three dimensional cases are carried out simultaneously some internal relationships between various algorithms are observed and several new variants of the algorithms are also derived

a gradient method approach to optimization based multidisciplinary simulations and nonoverlapping domain decomposition algorithms it has been shown recently that optimization based nonoverlapping domain decomposition algorithms are connected to many well known algorithms using a gradient type iterative strategy for the optimization problem we present further discussion on how to develop various algorithms that can integrate subdomain solvers into a solver for the problem in the whole domain in particular the algorithms we discuss can be used to develop efficient solvers of multidisciplinary problems which are constructed using existing subdomain solvers without the need for making changes in the latter

convergence analysis of domain decomposition algorithms with full overlapping for the advection diffusion problems the aim of this paper is to study the convergence properties of a time marching algorithm solving advection diffusion problems on two domains using incompatible discretizations the basic algorithm is first presented and theoretical or numerical results illustrate its convergence properties this study is based on spectral theory a priori estimates and a di giorgi nash maximum principle

a class of multi objective expected value decision making model with birandom coefficients and its application to flow shop scheduling problem in this paper we establish multi objective decision making models with birandom coefficients for the flow shop scheduling problem furthermore we introduce the general multi objective decision making model under a birandom environment and transform the birandom uncertain model into a deterministic model through an expected value operator and some properties of the expected value model are also researched we extend some theories of birandom variables and especially devote ourselves to researching the expected value of two kinds of birandom variables the expected value goal model is also proposed in order to compute the expected value of birandom variables birandom simulation is presented combined with the genetic algorithm it is applied in dealing with objective functions and constraint functions and to obtain the optimal solution finally an application to flow shop scheduling at geely haoqing automatic company is provided as an illustration

minimizing the weighted number of tardy jobs on a single machine abstract in this paper we describe an exact algorithm to solve the single machine weighted number of tardy jobs scheduling problem the algorithm uses branch and bound with the bounds obtained from a surrogate knapsack extensive computational experiments are carried out these experiments validate previous work on what constitutes a difficult instance and show that even difficult instances with 2500 jobs can be solved optimally in a reasonable amount of time

on the complexity of generalized due date scheduling problems abstract we study the recently identified class of generalized due date scheduling problems these are machine scheduling problems for which due dates are specified according to the position in which a job is completed rather than the identity of that job flexible manufacturing environments and public sector planning problems provide applications we study a wide variety of these problems with a view to determining their computational complexity in several instances a problem which is np hard under a traditional due date definition admits an efficient algorithm under the new definition as well as determining the complexity of many generalized due date scheduling problems including one published open problem we also describe several problems the complexity of which is still unresolved

preemptive hybrid flowshop scheduling problem of interval orders abstract the preemptive hybrid multi processor flowshop scheduling phfs problem consists in preemptively scheduling n jobs in a flowshop subject to precedence constraints with the objective of minimizing the makespan a special case of the general precedence constraints problems is np hard in the strong sense hoogeveen et al j a hoogeveen j k lenstra b veltman european journal of operational research 89 1996 172 in this paper a class of precedence constraints is proposed for which the problem is polynomially solvable the reported results demonstrate the feasibility and reliability of the proposed approach this should open future prospects for developing approximation algorithms for any class of precedence constraints

an efficient method for the navier stokes euler coupled equations via a collocation approximation the purpose of this paper is to propose an efficient iteration by subdomain method to solve the nonlinear incompressible navier stokes euler coupled equations the convergences are proven both in the differential case and in their spectral collocation counterpart detailed analysis shows that the iterative algorithms converge with a rate independent of the polynomial degree the numerical results presented are in good agreement with the theoretical investigation a validation study is carried out by simulating the flow past a cylinder

a parallel iterative procedure applicable to the approximate solution of second order partial differential equations by mixed finite element methods a parallelizable interative procedure based on domain decomposition techniques is defined and analyzed for mixed finite element methods for elliptic equations with the analysis being presented for the decomposition of the domain into the individual elements associated with the mixed method or into larger subdomains applications to time dependent problems are indicated

timely communicaton an analysis for a nonoverlapping domain decomposition iterative procedure an iterative procedure for nonoverlapping domain decomposition methods ddm is developed and analyzed which can be parallelly implemented with local communications it uses a robin boundary condition as its transmission condition on the interfaces the update of robin data of its transmission condition is a very simple relaxation between the preceding robin data and function value it need not find any derivatives at each iterative step this method can be easily applied to the discretization problems moreover it is shown that it is indeed a variant of the lions nonoverlapping ddm for the continuous problems also it can be regarded as a generalization of tang s generalized schwarz alternating method gsam in the nonoverlapping ddm

space time domain decomposition and mixed formulation for solving reduced fracture models in this paper we are interested in the fast path fracture and we aim to use global in time nonoverlapping domain decomposition methods to model flow and transport problems in a porous medium containing such a fracture we consider a reduced model in which the fracture is treated as an interface between the two subdomains two domain decomposition methods are considered one uses the time dependent steklovpoincare operator and the other uses optimized schwarz waveform relaxation oswr based on ventcell transmission conditions for each method a mixed formulation of an interface problem on the space time interface is derived and different time grids are employed to adapt to different time scales in the subdomains and in the fracture demonstrations of the well posedness of the ventcell subdomain problems is given for the mixed formulation an analysis for the convergence factor of the oswr algorithm is given in the case with fractures to compute the optimized parameters numerical results for two dimensional problems with strong heterogeneities are presented to illustrate the performance of the two methods