characteristic based time dependent maxwell equation solvers on a general curvilinear frame four cell centered finite volume characteristic based procedures for solving time dependent three dimensional maxwell equations on a general curvilinear frame are developed and implemented on a spherical coordinate system these methods generate simulations or an oscillating electric dipole without wave reflection from the truncated computational domain through a comparative study it is established that an upwind biased third order scheme demonstrates less dispersive and dissipative errors than second order schemes

a new mesh generation scheme for arbitrary planar domains this paper describes a new algorithm to generate interior nodes within any arbitrary multi connected regions the boundary nodes and the interior nodes are then linked up to form the best possible triangular elements by a completely revised technique in an efficient and stable manner owing to the generality of the central generation program the global domain is allowed to be divided into as many irregular subdomains as desired in order to model closely the actual physical situation moreover the boundaries of the sub domains are updated from time to time when necessary to include the possibilities of progressive refinement around a sharp corner generating radiating mesh from a prescribed node generating mesh between two circular arcs etc despite its flexibility and capabilities data for triangulation have been kept to a minimum by a logical input module no connectivity information between subregions is needed and common boundaries are defined once only all these features have contributed to a powerful method to generate 3 node or 6 node triangular element meshes of great variety within the most irregular heterogeneous regions

implicit time stepping methods for the navier stokes equations a novel two factor approximate factorization for three dimensional flows is described the method uses a preconditioned conjugate gradient solver for one of the factors and this solution is based on a method developed for two dimensional flows this two dimensional method is described and its performance is summarized for steady and unsteady flows the two factor method is then given larger time steps can be used with this method than is possible with the more conventional three factor method test results for the transonic steady flow over the onera m6 wing are given

approximation algorithms for single source unsplittable flow in the single source unsplittable flow problem we are given a network g a source vertex s and k commodities with sinks ti and real valued demands rho i 1 leq i leq k we seek to route the demand rho i of each commodity i along a single s ti flow path so that the total flow routed across any edge e is bounded by the edge capacity ue the conceptual difficulty of this np hard problem arises from combining packing constraints due to the existence of capacities with path selection in a graph of arbitrary topology in this paper we give a generic framework which yields approximation algorithms that are simpler than those previously known and achieve significant improvements upon the approximation ratios our framework with appropriate subroutines applies to all optimization versions previously considered and unlike previous work treats in a unified manner directed and undirected graphs we provide extensions of our algorithms which yield the best possible approximation guarantees for restricted sets of demand values and an associated scheduling problem

a new routing algorithm for multirate rearrangeable clos networks in this paper we study the problem of finding routing algorithms on the multirate rearrangeable clos networks which use as few number of middle stage switches as possible we propose a new routing algorithm called the grouping algorithm this is a simple algorithm which uses fewer middle stage switches than all known strategies given that the number of input stage switches and output stage switches are relatively small compared to the size of input and output switches in particular the grouping algorithm implies that m 2n n 1 2k is a sufficient number of middle stage switches for the symmetric three stage clos network c n m r to be multirate rearrangeable where k is any positive integer and r n 2k 1

efficient use of direct solvers for the calculation of compressible flows while the direct solution of systems of linear equations resulting from fluid dynamic problems has generally not been practical in the past it is presently demonstrated that the direct method is often more efficient than the most popular iterative schemes when constructed in such a way as to take advantage of presently available vector processing capabilities and large memory the vertical line gauss seidel algorithm was chosen as the iterative method to be compared with the direct method it is fond that the direct method becomes efficient only when large residual reductions are desired

nonblocking multirate networks an extension of the classical theory of connection networks is defined and studied this extension models systems in which multiple connections of differing data rates share the links within a network conditions under which the clos and cantor networks are strictly nonblocking for multirate traffic are determined the authors also determine conditions under which the benes network and variants of the cantor and clos networks are rearrangeable it is found that strictly nonblocking operation can be obtained for multirate traffic with essentially the same complexity as in the classical context

boundary conditions for surface reactions in lattice boltzmann simulations a surface reaction boundary condition in multicomponent lattice boltzmann simulations is developed the method is applied to a test case with nonlinear reaction rates and nonlinear density profiles the results are compared to the corresponding analytical solution which shows that the error of the method scales with the square of the lattice spacing

nonlinear relaxation navier stokes solver for three dimensional high speed internal flows an efficient implicit navier stokes method for computing steady three dimensional flowfields characteristic of high speed propulsion systems is presented a nonlinear iteration strategy based on planar gauss siedel sweeps is used to drive the solution toward a steady state with approximate factorization error within a crossflow plane reduced by the application of a quasi newton technique a hybrid discretization approach is employed with flux vector splitting used in the streamwise direction and central differences with artificial dissipation used for the transverse fluxes convergence histories and comparisons with experimental dara are presented for several three dimensional shock boundary layer interactions

implicit lambda methods for three dimensional compressible flow this paper derives the three dimensional lambda formula tion equations for a general orthogonal curvilinear coordinate system and provides various block explicit and block implicit methods for solving them numerically three model problems characterized by subsonic supersonic and transonic flow conditions are used to assess the reliability and compare the efficiency of the proposed methods

the generalized assignment problem with minimum quantities abstract we consider a variant of the generalized assignment problem gap where the amount of space used in each bin is restricted to be either zero if the bin is not opened or above a given lower bound a minimum quantity we provide several complexity results for different versions of the problem and give polynomial time exact algorithms and approximation algorithms for restricted cases for the most general version of the problem we show that it does not admit a polynomial time approximation algorithm unless p np even for the case of a single bin this motivates to study dual approximation algorithms that compute solutions violating the bin capacities and minimum quantities by a constant factor when the number of bins is fixed and the minimum quantity of each bin is at least a factor 1 larger than the largest size of an item in the bin we show how to obtain a polynomial time dual approximation algorithm that computes a solution violating the minimum quantities and bin capacities by at most a factor 1 1 and 1 1 respectively and whose profit is at least as large as the profit of the best solution that satisfies the minimum quantities and bin capacities strictly in particular for 2 we obtain a polynomial time 1 2 approximation algorithm

a faster strongly polynomial minimum cost flow algorithm in this paper we present a new strongly polynomial time algorithm for the minimum cost flow problem based on a refinement of the edmonds karp scaling technique our algorithm solves the uncapacitated minimum cost flow problem as a sequence of on log n shortest path problems on networks with n nodes and m arcs and runs in on log nm n log n time using a standard transformation this approach yields an om log nm n log n algorithm for the capacitated minimum cost flow problem this algorithm improves the best previous strongly polynomial time algorithm due to z galil and e tardos by a factor of n2 m our algorithm for the capacitated minimum cost flow problem is even more efficient if the number of arcs with finite upper bounds say m is much less than m in this case the running time of the algorithm is om n log nm n log n

a deferred correction multigrid algorithm based on a new smoother for the navier stokes equations abstract an algorithm which brings together the techniques of multigrid and deferred correction through their common relationship with imperfect newton iteration manages to combine the ease of calculation of a low order with the accuracy of a high order difference approximation of any given differential equation problem a stable explicit gauss seidel relaxation algorithm for the navier stokes equations based on an appropriate kind of upwinding of as well as derivatives especially developed for use as a multigrid smoother in this context is presented and the complete algorithm is tested on the standard conservative second order discretization of the driven cavity problem

upwind relaxation methods for the navier stokes equations using inner iterations an upwind line relaxation algorithm for the navier stokes equations which employs inner iterations is applied to a supersonic and a subsonic test problem the purpose of using inner iterations is to accelerate the convergence to steady state solutions thereby reducing the overall cpu time a convergence criterion is developed to assist in automating the inner iterative procedure the ability of the line inner iterative procedure to mimic the quadratic convergence of the direct solver method is confirmed in both test problems but some of the non quadratic inner iterative results were more efficient than the quadratic results in the supersonic test case the use of inner iterations was very efficient in reducing the residual to machine zero for this test problem the inner iteration method required only about 65 of the cpu time which was required by the most efficient line relaxation method without inner iterations in the subsonic test case poor matrix conditioning forced the use of under relaxation in order to obtain convergence of the inner iterations resulting in an overall method which was less efficient than line relaxation methods which employ a more conventional cpu savings strategy 23 refs 9 figs

implicit flux split schemes for the euler equations progress in the development of implicit algorithms for the euler equations using the flux vector splitting method is described comparisons of the relative efficiency of relaxation and spatially split approximately factored methods on a vector processor for transonic and supersonic twodimensional channel flows are made a hybrid threedimensional algorithm is developed that uses relaxation in one coordinate direction and approximate factorization in the crossflow plane the scheme is completely vectorizable and recovers conventional space marching schemes for fully supersonic flows the method is applied to a forebody shape in supersonic flow with an embedded pocket of subsonic flow

an efficient approximation scheme for variable sized bin packing in the classical bin packing problem one is required to pack a given list of items into the smallest possible number of unit sized bins because this problem is np complete researchers have tried to find efficient approximation algorithms that solve this problem in a reasonable amount of time if we let a i be the number of bins used by algorithm a to pack a list of items i and textit opt i be the minimum number of bins necessary to pack i one defines the asymptotic performance ratio of a to be a i textit opt i as textit opt i tends to infinity de la vega and lueker presented an approximation scheme which for any in 0 yields an approximation algorithm with performance ratio 1 varepsilon this scheme has time complexity polynomial in n the number of items but exponential in 1 varepsilon karmarkar and karp extended this scheme to one that has time complexity polynomial in n and 1 varepsilon in the variable sized bin packing problem one

nonlinear relaxation quasi newton algorithm for the compressible navier stokes equations a highly efficient implicit method for the computation of steady two dimensional compressible navier stokes flowfields is presented the discretization of the governing equations is hybrid in nature with flux vector splitting utilized in the streamwise direction and central differences with flux limited artificial dissipation used for the transverse fluxes line jacobi relaxation is used to provide a suitable initial guess for a new nonlinear iteration strategy based on line gauss seidel sweeps the applicability of quasi newton methods as convergence accelerators for this and other line relaxation algorithms is discussed and efficient implementations of such techniques are presented convergence histories and comparisons with experimental data are presented for supersonic flow over a flat plate and for several high speed compression corner interactions results indicate a marked improvement in computational efficiency over more conventional upwind relaxation strategies particularly for flowfields containing large pockets of streamwise subsonic flow

finite volume solution of the two dimensional euler equations on a regular triangular mesh the two dimensional euler equations have been solved on a triangular grid by a multigrid scheme using the finite volume approach by careful construction of the dissipative terms the scheme is designed to be secondorder accurate in space provided the grid is smooth except in the vicinity of shocks where it behaves as firstorder accurate in its present form the accuracy and convergence rate of the triangle code are comparable to that of the quadrilateral mesh code of jameson

a polynomial approximation scheme for scheduling on uniform processors using the dual approximation approach in this paper we present a polynomial approximation scheme for the minimum makespan problem on uniform parallel processors more specifically the problem is to find a schedule for a set of independent jobs on a collection of machines of different speeds so that the last job to finish is completed as quickly as possible we give a family of polynomial time algorithms a such that a delivers a solution that is within a relative error of e of the optimum the technique employed is the dual approximation approach where infeasible but superoptimal solutions for a related dual problem are converted to the desired feasible but possibly suboptimal solution

improved approximation guarantees for packing and covering integer programs several important np hard combinatorial optimization problems can be posed as packing covering integer programs the randomized rounding technique of raghavan and thompson is a powerful tool with which to approximate them well we present one elementary unifying property of all these integer linear programs and use the fkg correlation inequality to derive an improved analysis of randomized rounding on them this yields a pessimistic estimator thus presenting deterministic polynomial time algorithms for them with approximation guarantees that are significantly better than those known

an approximation algorithm for the generalized assignment problem the generalized assignment problem can be viewed as the following problem of scheduling parallel machines with costs each job is to be processed by exactly one machine processing jobj on machinei requires timep ij and incurs a cost ofc ij each machinei is available fort i time units and the objective is to minimize the total cost incurred our main result is as follows there is a polynomial time algorithm that given a valuec either proves that no feasible schedule of costc exists or else finds a schedule of cost at mostc where each machinei is used for at most 2t i time units we also extend this result to a variant of the problem where instead of a fixed processing timep ij there is a range of possible processing times for each machine job pair and the cost linearly increases as the processing time decreases we show that these results imply a polynomial time 2 approximation algorithm to minimize a weighted sum of the cost and the makespan i e the maximum job completion time we also consider the objective of minimizing the mean job completion time we show that there is a polynomial time algorithm that given valuesm andt either proves that no schedule of mean job completion timem and makespant exists or else finds a schedule of mean job completion time at mostm and makespan at most 2t

boundary scheme for linear heterogeneous surface reactions in the lattice boltzmann method a boundary scheme is proposed to treat the linear heterogeneous surface reaction i e general robin boundary condition for the lattice boltzmann method lbm in this study the basic idea of the present scheme is to compute the scalar variable gradient in the boundary condition with the moment of the nonequilibrium distribution functions the unknown distribution functions on the boundary can then be obtained on the basis of the given boundary condition for a straight wall where the lattice nodes are located on the boundaries both the scalar variable and its gradient can be expressed in terms of the distribution functions at the boundary node and the scheme is purely local the scheme is also extended to problems with a curved wall in which a linear extrapolation is employed to realize the exact boundary position a common feature of the two schemes lies in the easy treatment of the heterogenous reactions in comparison with existing methods a number of simulations are performed to test the accuracy of the schemes the results show that for flat walls the scheme can achieve second order accuracy while for curved walls the order of the accuracy is between 1 0 and 1 5

methodology for calculating aerodynamic sensitivity derivatives a general procedure is developed for calculating aerodynamic sensitivity coefficients using the full equations of inviscid fluid flow where the focus of the work is the treatment of geometric shape design variables using an upwind cell centered finite volume approximation to represent the euler equations sensitivity derivatives are determined by direct differentiation of the resulting set of coupled nonlinear algebraic equations that model the fluid flow

incremental multigrid strategy for the fluid dynamic equations abstract this paper provides a novel incremental multigrid strategy for the equations of fluid dynamics the time dependent governing equations are discretized in time by means of a two level implicit euler scheme and linearized using taylor series and the incremental delta form of beam and warming the coefficients and the right hand side of the resulting linear systems are evaluated always at the finest grid level whereas the delta unknowns are computed approximately by a single relaxation sweep on a sequence of coarser meshes at every grid level the computed deltas are interpolated up to the finest grid level and used to update the solution as well as the coefficients and the right hand side of the linear systems this process is repeated sweeping all grid levels successively until a satisfactory convergence criterion is met the validity of the proposed approach is demonstrated by solving a simple linear problem and the vorticity stream function navier stokes equations using line relaxation methods as smoothers and the lambda formulation euler equations in conjunction with a simple explicit smoother in all cases the proposed multigrid strategy provides a considerable efficiency gain over the corresponding single grid methods

high reynolds number separated flow solutions using navier stokes and approximate equations simulation d ecoulements laminaires faiblement decolles incompressibles stationnaires a nombre de reynolds eleve on montre qu un code bien concu peut resoudre les equations completes de navier stokes et les equations de vorticite parabolisees avec la meme vitesse de convergence on resoud egalement les equations de couche limite sous forme vorticite fonction de courant

stochastic packing integer programs with few queries we consider a stochastic variant of the packing type integer linear programming problem which contains random variables in the objective vector we are allowed to reveal each entry of the objective vector by conducting a query and the task is to find a good solution by conducting a small number of queries we propose a general framework of adaptive and non adaptive algorithms for this problem and provide a unified methodology for analyzing the performance of those algorithms we also demonstrate our framework by applying it to a variety of stochastic combinatorial optimization problems such as matching matroid and stable set problems

upwind relaxation algorithms for the navier stokes equations analyse des erreurs de troncature de la differenciation spatiale et analyse de la stabilite de l algorithme de relaxation calcul pour une serie d ecoulements a l aide de la forme couche mince des equations calcul du decollement de couche limite induit par chocs

faster approximation algorithms for the unit capacity concurrent flow problem with applications to routing and finding sparse cuts this paper describes new algorithms for approximately solving the concurrent multicommodity flow problem with uniform capacities these algorithms are much faster than algorithms discovered previously besides being an important problem in its own right the uniform capacity concurrent flow problem has many interesting applications leighton and rao used uniform capacity concurrent flow to find an approximately sparsest cut in a graph and thereby approximately solve a wide variety of graph problems including minimum feedback arc set minimum cut linear arrangement and minimum area layout however their method appeared to be impractical as it required solving a large linear program this paper shows that their method might be practical by giving an o m 2 log m expected time randomized algorithm for their concurrent flow problem on an m edge graph raghavan and thompson used uniform capacity concurrent flow to solve approximately a channel width minimization problem in very large scale integration an o k 3 2 m n log n expected time randomized algorithm and an o k min n k m n log n log k deterministic algorithm is given for this problem when the channel width is omega log n where k denotes the number of wires to be routed in an n node m edge network

consistent second order boundary implementations for convection diffusion lattice boltzmann method in this study an alternative second order boundary scheme is proposed under the framework of the convection diffusion lattice boltzmann lb method for both straight and curved geometries with the proposed scheme boundary implementations are developed for the dirichlet neumann and linear robin conditions in a consistent way the chapman enskog analysis and the hermite polynomial expansion technique are first applied to derive the explicit expression for the general distribution function with second order accuracy then the macroscopic variables involved in the expression for the distribution function is determined by the prescribed macroscopic constraints and the known distribution functions after streaming see the paragraph after eq 29 for the discussions of the streaming step in lb method after that the unknown distribution functions are obtained from the derived macroscopic information at the boundary nodes for straight boundaries boundary nodes are directly placed at the physical boundary surface and the present scheme is applied directly when extending the present scheme to curved geometries a local curvilinear coordinate system and first order taylor expansion are introduced to relate the macroscopic variables at the boundary nodes to the physical constraints at the curved boundary surface in essence the unknown distribution functions at the boundary node are derived from the known distribution functions at the same node in accordance with the macroscopic boundary conditions at the surface therefore the advantages of the present boundary implementations are i the locality i e no information from neighboring fluid nodes is required ii the consistency i e the physical boundary constraints are directly applied when determining the macroscopic variables at the boundary nodes thus the three kinds of conditions are realized in a consistent way it should be noted that the present focus is on two dimensional cases and theoretical derivations as well as the numerical validations are performed in the framework of the two dimensional five velocity lattice model

parameterized approximation scheme for the multiple knapsack problem the multiple knapsack problem mkp is a well known generalization of the classical knapsack problem we are given a set a of n items and set b of m bins knapsacks such that each item a in a has a size size a and a profit value profit a and each bin b in b has a capacity c b the goal is to find a subset u subset a of maximum total profit such that u can be packed into b without exceeding the capacities the decision version of mkp is strongly np complete since it is a generalization of the classical knapsack and bin packing problem furthermore mkp does not admit a fully time polynomial time approximation scheme fptas even if the number m of bins is two kellerer gave a polynomial time approximation scheme ptas for mkp with identical capacities and chekuri and khanna presented a ptas for mkp with general capacities with running time n o log 1 epsilon epsilon 8 in this paper we propose an efficient ptas eptas with parameterized running time 2 o log 1 epsilon epsilon 5 cdot poly n o m for mkp this also solves an open question by chekuri and khanna

iteration strategy for upwind relaxation solutions to the thin layer navier stokes equations an efficient iteration strategy for supersonic flow solutions to the parabolized and thin layer navier stokes equations is described modifications are made to a previously developed upwind relaxation algorithm to suppress the upstream influence within the subsonic part of the boundary layer through restriction of the streamwise pressure gradient a parabolized solution then is efficiently obtained by marching downstream and locally iterating each crossflow plane to convergence the parabolized solution fully conservative and second order accurate provides an excellent solution for problems without strong adverse streamwise pressure gradients if necessary the thin layer solution may be recovered by further iteration using the original upwind relaxation algorithm

a practical approach to algebraic grid adaption algebraic grid adaption is discussed and a method with the capability to simultaneously adapt to several variables is described this method makes it possible to resolve several gradients in a flow field such as gradients in velocity pressure and mach number the method is incorporated into an algorithm and applied to hypersonic flow computations about two blunt bodies the algorithm is called practical because it allows a user to specify the resolution of several variables in a solution in an interactive manner

solving multiple knapsack problems by cutting planes in this paper we consider the multiple knapsack problem which is defined as follows given a set n of items with weights f i i in n a set m of knapsacks with capacities f k k in m and a profit function c ik i in n k in m find an assignment of a subset of the set of items to the set of knapsacks that yields minimum cost we consider the multiple knapsack problem from a polyhedral point of view the inequalities that we describe here serve as the theoretical basis for a cutting plane algorithm we present some of the implementation details of this algorithm including a discussion and evaluation of different separation and primal heuristics our algorithm is applied to practical problem instances arising in the design of main frame computers in the layout of electronic circuits and in sugar cane alcohol production

a high order difference method for the steady state navier stokes equations a stable high order difference method is developed for solving the heated cavity and the driven cavity problems governed by the steady state navier stokes equations the numerical results compared favorably with other methods coordinate transformations were also used to reflect the boundary layer phenonmena without requiring many mesh points the methods used in this paper are accurate stable and applicable to other flow problems governed by the navier stokes equations

approximating the single source unsplittable min cost flow problem in the single source unsplittable min cost flow problem commodities must be routed simultaneously from a common source vertex to certain destination vertices in a given graph with edge capacities and costs the demand of each commodity must be routed along a single path so that the total flow through any edge is at most its capacity moreover the total cost must not exceed a given budget this problem has been introduced by kleinberg 7 and generalizes several np complete problems from various areas in combinatorial optimization such as packing partitioning scheduling load balancing and virtual circuit routing kolliopoulos and stein 9 and dinitz garg and goemans 4 developed algorithms improving the first approximation results of kleinberg for the problem of minimizing the violation of edge capacities and for other variants however known techniques do not seem to be capable of providing solutions without also violating the cost constraint we give the first approximation results with hard cost constraints moreover all our results dominate the best known bicriteria approximations finally we provide results on the hardness of approximation for several variants of the problem

an approximately factored incremental strategy for calculating consistent discrete aerodynamic sensitivity derivatives in this study involving advanced fluid flow codes an incremental iterative formulation also known as the delta or correction form together with the well known spatially split approximate factorization algorithm is presented for solving the very large sparse systems of linear equations which are associated with aerodynamic sensitivity analysis for smaller 2d problems a direct method can be applied to solve these linear equations in either the standard or the incremental form in which case the two are equivalent iterative methods are needed for larger 2d and future 3d applications however because direct methods require much more computer memory than is currently available iterative methods for solving these equations in the standard form are generally unsatisfactory due to a lack of diagonal dominance and perhaps ill conditioning of the coefficient matrix this problem can be overcome when these equations are cast in the incremental form these and other benefits are discussed herein the methodology is successfully implemented and tested in 2d using an upwind cell centered finite volume formulation applied to the thin layer navier stokes equations results are presented for two sample airfoil problems 1 subsonic low reynolds number laminar flow and 2 transonic high reynolds number turbulent flow

sensitivity derivatives for three dimensional supersonic euler code using incremental iterative strategy in a recent work an incremental strategy was proposed to iteratively solve the very large systems of linear equations that are required to obtain quasianalytical sensitivity derivatives from advanced computational fluid dynamics cfd codes the technique was sucessfully demonstrated for two large two dimensional problems a subsonic and a transonic airfoil the principal feature of this incremental iterative stategy is that it allows the use of the identical approximate coefficient matrix operator and algorithm to solve the nonlinear flow and the linear sensitivity equations at convergence the accuracy of the sensitivity derivatives is not compromised this feature allows a comparatively straightforward extension of the methodology to three dimensional problems this extension is successfully demonstrated in the present study for a space marching solution of the three dimensional euler equations over a mach 2 4 blended wing body configuration

approximating disjoint path problems using packing integer programs in a packing integer program we are given a matrix a and column vectors b c with nonnegative entries we seek a vector x of nonnegative integers which maximizes c t x subject to ax leq b the edge and vertex disjoint path problems together with their unsplittable flow generalization are np hard problems with a multitude of applications in areas such as routing scheduling and bin packing these two categories of problems are known to be conceptually related but this connection has largely been ignored in terms of approximation algorithms we explore the topic of approximating disjoint path problems using polynomial size packing integer programs motivated by the disjoint paths applications we introduce the study of a class of packing integer programs called column restricted we develop improved approximation algorithms for column restricted programs a result that we believe is of independent interest additional approximation algorithms for disjoint paths are presented that are simple to implement and achieve good performance when the input has a special structure

primitive variable strongly implicit calculation procedure for viscous flows at all speeds a coupled solution procedure is described for solving the compressible form of the time dependent twodimensional navier stokes equations in body fitted curvilinear coordinates this approach employs the strong conservation form of the governing equations but uses primitive variables m v p t rather than the more traditional conservative variables p pw pv et as unknowns a coupled modified strongly implicit procedure cmsip is used to efficiently solve the newton linearized algebraic equations it appears that this procedure is effective for mach numbers ranging from the incompressible limit mx 0 01 to supersonic generally smoothing was not needed to control spatial oscillations in pressure for subsonic flows despite the use of central differences dual time stepping was found to further accelerate convergence for steady flows sample calculations including steady and unsteady low mach number internal and external flows and a steady shock boundarylayer interaction flow illustrate the capability of the present solution algorithm

using dual approximation algorithms for scheduling problems theoretical and practical results the problem of scheduling a set of n jobs on m identical machines so as to minimize the makespan time is perhaps the most well studied problem in the theory of approximation algorithms for np hard optimization problems in this paper the strongest possible type of result for this problem a polynomial approximation scheme is presented more precisely for each e an algorithm that runs in time o n e 1 e 2 and has relative error at most e is given in addition more practical algorithms for e 1 5 2 k and e 1 6 2 k which have running times o n k log n and o n km 4 log n are presented the techniques of analysis used in proving these results are extremely simple especially in comparison with the baroque weighting techniques used previously the scheme is based on a new approach to constructing approximation algorithms which is called dual approximation algorithms where the aim is to find superoptimal but infeasible solutions and the performance is measured by the degree of infeasibility allowed this notion should find wide applicability in its own right and should be considered for any optimization problem where traditional approximation algorithms have been particularly elusive

improved approximation algorithms for shop scheduling problems in the job shop scheduling problem there are m machines and n jobs a job consists of a sequence of operations each of which must be processed on a specified machine and the aim is to complete all jobs as quickly as possible this problem is strongly cal np hard even for very restrictive special cases the authors give the first randomized and deterministic polynomial time algorithms that yield polylogarithmic approximations to the optimal length schedule these algorithms also extend to the more general case where a job is given not by a linear ordering of the machines on which it must be processed but by an arbitrary partial order comparable bounds can also be obtained when there are m types of machines a specified number of machines of each type and each operation must be processed on one of the machines of a specified type as well as for the problem of scheduling unrelated parallel machines subject to chain precedence constraints

an incremental block line gauss seidel method for the navier stokes equations a block line gauss seidel lgs method is developed for solving the incompressible and compressible navier stokes equations in two dimensions the method requires only one block tridiagonal solution process per iteration and is consequently faster per step than the linearized block adi methods results are presented for both incompressible and compressible separated flows in all cases the proposed block lgs method is more efficient than the block adi methods furthermore for high reynolds number weakly separated incompressible flow in a channel which proved to be an impossible task for a block adi method solutions have been obtained very efficiently by the new scheme

locally implicit total variation diminishing schemes on unstructuredtriangular meshes a numerical solution procedure that includes locally implicit total variation diminishing schemes and adaptive mesh generation techniques has been developed in this work in a cartesian coordinate system the euler equations are solved by using a cell centered finite volume algorithm a new construction of symmetric total variation diminishing schemes on unstructured triangular meshes is presented the validation of the present solution adaptive methods is confirmed by comparison with related numerical results for inviscid flows around an isolated naca 0012 airfoil and passing through a channel with a circular arc bump in transonic and supersonic flow regimes to further prove the feasibility of this approach a two element airfoil flow is also investigated furthermore one unsteady transonic channel flow is studied to demonstrate the reliability and capability of the present solution procedure for a time accurate calculation

the travelling wave scheme for the navier stokes equations a new scheme is developed for the one dimensional compressible navier stokes equations the method is a deviation from traditional explicit methods in that the hyperbolic and parabolic parts are treated as a single entity and travelling waves are used as approximating tools the scheme is used mainly for computation in the regime where the mesh size is of the same order as the ratio of the viscosity varepsilon to the characteristic speed a viscous riemann solver is designed that solves the local riemann problems

parabolized navier stokes algorithm for solving supersonic flows with upstream influences a new parabolized navier stokes pns algorithm has been developed to efe ciently compute supersonic e ows with embedded regions that produce upstream effects innovative techniques are used to automatically detect and measure the extent of the embedded regions within the embedded regions the pns equations are globally iterated to duplicate the results that would be obtained with the complete navier stokes ns equations once an embedded region is computed the algorithm returns to the standard space marching pns mode until the next embedded region is encountered this procedure has been successfully incorporated into nasa s upwind pns code and it has been validated by its application to several two dimensional test cases all of these test cases include embedded regions that produce signie cant upstream effects the present numerical results arein excellent agreement with previous ns computations and experimental data in addition these calculations demonstrate the signie cant reduction in computer time and storage that can be achieved by the use of this approach

a fast asymptotic approximation scheme for bin packing with rejection bin packing with rejection is the following problem given a list of items with associated sizes and rejection costs find a packing into unit bins of a subset of the list such that the number of bins used plus the sum of rejection costs of unpacked items is minimized we show that bin packing with rejection can be reduced to n multiple knapsack problems and based on techniques for the multiple knapsack problem we give a fast asymptotic polynomial time approximation scheme reject pack with time complexity o n o e 2 this improves a recent approximation scheme given by epstein which has time complexity o n o e 4 e 1 we also show that reject pack can be extended to variable sized bin packing with rejection and give an asymptotic polynomial time approximation scheme

taylor series approximation of geometric shape variation for the euler equations references free turbulent shear flows nasa sp 321 1973 launder b e morse a rodi w and spalding d b prediction of free shear flows a comparison of the performance of six turbulence models free turbulent shear flows nasa sp 321 1973 pp 361 426 birch s f and eggers j m a critical review of the experimental data for developed free turbulent shear layers free turbulent shear flows nasa sp 321 1973 pp 11 40 dash s m weilerstein g and vaglio laurin r compressibility effects in free turbulent shear flows air force office of scientific research afosr tr 75 1436 aug 1975 chuech s g lai m c and faeth g m structure of turbulent sonic underexpanded free jets aiaa journal no 5 vol 27 1989 pp 549 559 sarkar s erlebacher g hussaini m y and kreiss h o the analysis and modeling of dilatational terms in compressible turbulence journal of fluid mechanics vol 227 1991 pp 473 493 zeman o dilation dissipation the concept and application in modeling compressible mixing layers physics of fluids a vol 2 no 2 1990 pp 178 188 kim s c new mixing length model for supersonic shear layers aiaa journal vol 28 no 11 1990 pp 1999 2000 brescianini c p morgan r g and stalker r j numerical modeling of sidewall injected scramjet experiments in a high enthalpy airflow shock tunnel studies of scramjet phenomena supplement 6 dept of mechanical engineering univ of queensland brisbane queensland australia 1990 bogdanoff d w compressibility effects in turbulent shear layers aiaa journal vol 21 no 6 1983 pp 926 927 papamoschou d and roshko a the compressible shear layer an experimental study journal of fluid mechanics vol 197 1988 pp 453 477 samimy m and elliott g s effects of compressibility on the characteristics of free shear layers aiaa journal vol 28 no 3 1990 pp 439 445 rodi w a review of experimental data for uniform density free turbulent boundary layers studies in convection vol 1 academic press london 1975 pp 79 165

upper and lower bounding procedures for the multiple knapsack assignment problem abstract we formulate the multiple knapsack assignment problem mkap as an extension of the multiple knapsack problem mkp as well as of the assignment problem except for small instances mkap is hard to solve to optimality we present a heuristic algorithm to solve this problem approximately but very quickly we first discuss three approaches to evaluate its upper bound and prove that these methods compute an identical upper bound in this process reference capacities are derived which enables us to decompose the problem into mutually independent mkps these mkps are solved euristically and in total give an approximate solution to mkap through numerical experiments we evaluate the performance of our algorithm although the algorithm is weak for small instances we find it prospective for large instances indeed for instances with more than a few thousand items we usually obtain solutions with relative errors less than 0 1 within one cpu second

approximation algorithms for the m dimensional 0 1 knapsack problem worst case and probabilistic analyses abstract we describe a polynomial approximation scheme for an m constraint 0 1 integer programming problem m fixed based on the use of the dual simplex algorithm for linear programming we also analyse the asymptotic properties of a particular random model

fibonacci heaps and their uses in improved network optimization algorithms in this paper we develop a new data structure for implementing heaps priority queues our structure fibonacci heaps abbreviated f heaps extends the binomial queues proposed by vuillemin and studied further by brown f heaps support arbitrary deletion from an n item heap in o log n amortized time and all other standard heap operations in o 1 amortized time using f heaps we are able to obtain improved running times for several network optimization algorithms in particular we obtain the following worst case bounds where n is the number of vertices and m the number of edges in the problem graph o n log n m for the single source shortest path problem with nonnegative edge lengths improved from o m log m n 2 n o n 2 log n nm for the all pairs shortest path problem improved from o nm log m n 2 n o n 2 log n nm for the assignment problem weighted bipartite matching improved from o nm log m n 2 n o m m n for the minimum spanning tree problem improved from o m log log m n 2 n where m n min i u log i n m n note that m n log n if m n of these results the improved bound for minimum spanning trees is the most striking although all the results give asymptotic improvements for graphs of appropriate densities

on rearrangeability of multirate clos networks chung and ross siam j comput 20 1991 pp 726 736 conjectured that the multirate three stage clos network c n 2n 1 r is rearrangeable in the general discrete bandwidth case i e each connection has a weight chosen from a given finite set p1 p2 pk where 1 geq p 1 p 2 cdots p k 0 and pi is an integer multiple of pi denoted by p k mid p i for 1 leq i leq k 1 in this paper we prove that multirate three stage clos network c n 2n 1 r is rearrangeable when each connection has a weight chosen from a given finite set p1 p2 pk where 1 geq p 1 p 2 cdots p h 1 2 geq p h 1 cdots p k 0 and ph 2 ph 1 ph 3 ph 2 pk ph 1 we also prove that c n 2n 1 r is two rate rearrangeable and c n lceil frac 7n 3 rceil r is three rate rearrangeable

stable high order methods for differential equations with small coefficients for the second order terms abstract stable high order methods are developed for solving differential equations with small coefficients for the second order terms in particular second fourth and sixth order methods are developed the methods are developed for general linear two point boundary value problems and proved to be stable and accurate results are presented for the one dimensional convection diffusion equation involving problems with and without boundary layers the methods converged for all values of parameters attempted and the results compared favorably with other methods the methods developed in this paper are accurate stable easy to use and applicable to other problems

locally implicit hybrid algorithm for steady and unsteady viscous flows a locally implicit hybrid finite volume algorithm on mixed type of triangular and quadrilateral meshes for the two dimensional steady and unsteady viscous flows has been developed the unsteady full navier stokes equations are solved in the cartesian coordinate system a new construction of a total variation diminishing formulation on triangles is used to obtain high resolution results in the convective dominated flow region in the viscous dominated part a second and fourth order dissipative model on quadrilateral grids is employed to minimize the numerical dissipation

approximation algorithms for disjoint paths and related routing and packing problems given a network and a set of connection requests on it we consider the maximum edge disjoint paths and related generalizations and routing problems that arise in assigning paths for these requests we present improved approximation algorithms and or integrality gaps for all problems considered the central theme of this work is the underlying multicommodity flow relaxation applications of these techniques to approximating families of packing integer programs are also presented

navier stokes solutions for vortical flows over a tangent ogive cylinder reynolds number re effects on low speed vortical flows over 3 5 caliber tangent ogive cylinders at two angles of attack 20 and 30 deg are computationally assessed for re d 0 2 3 million d maximum diameter the flowfield results are steady state solution to the three dimensional incompressible navier stokes equations in their thin layer approximation for the first time a crossflow separation pattern which consists of a laminar separation bubble with a subsequent transition in the separating shear layer that forms a primary vortex has been modeled

a new approach to the maximum flow problem all previously known efficient maximum flow algorithms work by finding augmenting paths either one path at a time as in the original ford and fulkerson algorithm or all shortest length augmenting paths at once using the layered network approach of dinic an alternative method based on the preflow concept of karzanov is introduced a preflow is like a flow except that the total amount flowing into a vertex is allowed to exceed the total amount flowing out the method maintains a preflow in the original network and pushes local flow excess toward the sink along what are estimated to be shortest paths the algorithm and its analysis are simple and intuitive yet the algorithm runs as fast as any other known method on dense graphs achieving an o n 3 time bound on an n vertex graph by incorporating the dynamic tree data structure of sleator and tarjan we obtain a version of the algorithm running in o nm log n 2 m time on an n vertex m edge graph this is as fast as any known method for any graph density and faster on graphs of moderate density the algorithm also admits efficient distributed and parallel implementations a parallel implementation running in o n 2 log n time using n processors and o m space is obtained this time bound matches that of the shiloach vishkin algorithm which also uses n processors but requires o n 2 space

multirate rearrangeable clos networks and a generalized edge coloring problem on bipartite graphs chung and ross siam j comput 20 1991 pp 726 736 conjectured that the minimum number m n r of middle stage switches for the symmetric 3 stage clos network c n m n r r to be rearrangeable in the multirate environment is at most 2n 1 this problem is equivalent to a generalized version of the bipartite graph edge coloring problem the best bounds known so far on this function m n r are 11n 9 leq m n r leq 41n 16 o 1 for n r geq 2 derived by du et al siam j comput 28 1999 pp 464 471 in this paper we make several contributions first we give evidence to show that even a stronger result might hold in particular we give a coloring algorithm to show that m n r leq lceil r 1 n 2 rceil which implies m n 2 leq lceil 3n 2 rceil stronger than the conjectured value of 2n 1 second we derive that m 2 r 3 by an elegant argument last we improve both the best upper and lower bounds given above lceil 5n 4 rceil leq m n r leq 2n 1 lceil r 1 2 rceil

comparing apples and oranges query trade off in submodular maximization fast algorithms for submodular maximization problems have a vast potential use in applicative settings such as machine learning social networks and economics though fast algorithms were known for some special cases only recently such algorithms were considered in the general case of maximizing a monotone submodular function subject to a matroid independence constraint the known fast algorithm matches the best possible approximation guarantee while trying to reduce the number of value oracle queries the algorithm performs our main result is a new algorithm for this general case that establishes a surprising trade off between two seemingly unrelated quantities the number of value oracle queries and the number of matroid independence queries performed by the algorithm specifically one can decrease the former by increasing the latter and vice versa while maintaining the best possible approximation guarantee such a trade off is very useful since various applications might incur significantly diff

a numerical method for viscous perturbations of hyperbolic conservation laws a high resolution numerical scheme for the computation of viscous shock layers is introduced the novel feature consists in the use of travelling wave solutions as approximating tools this is a departure from previous methods which are based on splitting the viscous part from the hyperbolic part of the equation stability and accuracy results and numerical tests for one dimensional models are presented

hydrodynamic modeling of short channel devices using an upwind flux vector splitting scheme upwind flux vector splitting is presented for hydrodynamic modeling of 1d and 2d deep submicron semiconductor devices this approach splits the jacobian matrices of the hydrodynamic system into two parts corresponding to forward and backward running fluxes and an upwind difference is applied to each split flux influences of the boundary discontinuity of electric field and velocity on transport results in the 2d deep submicron devices are discussed the study demonstrates that the developed method is capable of handling large discontinuity of the boundary conditions and highly non linear source terms in short channel semiconductor devices

a polynomial time approximation scheme for the multiple knapsack problem the multiple knapsack problem mkp is a natural and well known generalization of the single knapsack problem and is defined as follows we are given a set of n items and m bins knapsacks such that each item i has a profit p i and a size s i and each bin j has a capacity c j the goal is to find a subset of items of maximum profit such that they have a feasible packing in the bins mkp is a special case of the generalized assignment problem gap where the profit and the size of an item can vary based on the specific bin that it is assigned to gap is apx hard and a 2 approximation for it is implicit in the work of shmoys and tardos math program a 62 1993 pp 461 474 and thus far this was also the best known approximation for mkp the main result of this paper is a polynomial time approximation scheme ptas for mkp apart from its inherent theoretical interest as a common generalization of the well studied knapsack and bin packing problems it appears to be the strongest special case of gap that is not apx hard we substantiate this by showing that slight generalizations of mkp are apx hard thus our results help demarcate the boundary at which instances of gap become apx hard an interesting aspect of our approach is a ptas preserving reduction from an arbitrary instance of mkp to an instance with o log n distinct sizes and profits

characteristic based rotated upwind scheme for the euler equations a rotated upwind scheme is developed that calculates shock waves oblique to the grid with nearly the same resolution as shocks that are aligned with the grid the scheme applies flux difference splitting along two orthogonal directions for each cell face with the directions computed on the basis of pressure gradient data rotated extrapolations and flux limiting are used to generate second order spatial accuracy a filtering of the pressure gradient data allows the convergence of the rotated scheme with continuously updated upwinding angles at a rate comparable to classical schemes flux evaluations based on characteristi c variables and characteristic boundary conditions are discussed and implemented the method has been tested on two simple shock reflection problems and formally second order results capture the oblique shocks with only two to three cells in the shock transition region

improved bounds on nonblocking 3 stage clos networks we consider a generalization of edge coloring bipartite graphs in which every edge has a weight in 0 1 and the coloring of the edges must satisfy that the sum of the weights of the edges incident to a vertex v of any color must be at most 1 for unit weights konig s theorem says that the number of colors needed is exactly the maximum degree for this generalization we show that 2 557 n o n colors are sufficient where n is the maximum total weight adjacent to any vertex improving the previously best bound of 2 833n o 1 due to du et al our analysis is interesting on its own and involves a novel decomposition result for bipartite graphs and the introduction of an associated continuous one dimensional bin packing instance which we can prove allows perfect packing this question is motivated by the question of the rearrangeability of 3 stage clos networks in that context the corresponding parameter n of interest in the edge coloring problem is the maximum over all vertices of the number of unit sized bins needed to pack the weights of the incident edges in that setting we are able to improve the bound to 2 5480 n o n also improving a bound of 2 5625n o 1 of du et al we also consider the online version of this problem in which edges have to be colored as soon as they are revealed in this context we can show that 5n colors are enough this contrasts with the best known lower bound of 3n 2 by tsai wang and hwang but improves upon the previous best upper bound of 5 75n obtained by gao and hwang additionally we show several improved bounds for more restricted versions of the problem these online bounds are achieved by simple and easy to implement algorithms inspired by the first fit heuristic for bin packing

temporal and acoustic accuracy of an implicit upwind method for ducted flows an implicit time accurate method for ducted flow aeroacoustics is presented the method is unfactored using line gauss seidel relaxation and multiple axial sweeps for convergence of each time step

approximation algorithms for scheduling unrelated parallel machines we consider the following scheduling problem there arem parallel machines andn independent jobs each job is to be assigned to one of the machines the processing of jobj on machinei requires timep ij the objective is to find a schedule that minimizes the makespan our main result is a polynomial algorithm which constructs a schedule that is guaranteed to be no longer than twice the optimum we also present a polynomial approximation scheme for the case that the number of machines is fixed both approximation results are corollaries of a theorem about the relationship of a class of integer programming problems and their linear programming relaxations in particular we give a polynomial method to round the fractional extreme points of the linear program to integral points that nearly satisfy the constraints in contrast to our main result we prove that no polynomial algorithm can achieve a worst case ratio less than 3 2 unlessp np we finally obtain a complexity classification for all special cases with a fixed number of processing times

a faster combinatorial approximation algorithm for scheduling unrelated parallel machines we consider the problem of scheduling n independent jobs on m unrelated parallel machines without preemption job i takes processing time p i j on machine j and the total time used by a machine is the sum of the processing times for the jobs assigned to it the objective is to minimize makespan the best known approximation algorithms for this problem compute an optimum fractional solution and then use rounding techniques to get an integral 2 approximation in this paper we present a combinatorial approximation algorithm that matches this approximation quality it is much simpler than the previously known algorithms and its running time is better this is the first time that a combinatorial algorithm always beats the interior point approach for this problem our algorithm is a generic minimum cost flow algorithm without any complex enhancements tailored to handle unsplittable flow it pushes unsplittable jobs through a two layered bipartite generalized network defined by the scheduling problem in our analysis we take advantage from addressing the approximation problem directly in particular we replace the classical technique of solving the lp relaxation and rounding afterwards by a completely integral approach we feel that this approach will be helpful also for other applications

stable high order methods for solving elliptic equations with large first order terms abstract stable high order methods are developed for solving elliptic partial differential equations with large first order terms in particular second order and fourth order methods are developed by stabilizing the central difference method the methods can solve second order linear elliptic partial differential equations and are found to be stable and accurate in all tested examples results are presented for the two dimensional convection diffusion equation involving problems with and without boundary layers the methods converged for all values of parameters attempted and the results compared favorably with other methods the methods developed in this paper are accurate stable easy to use and applicable to other problems

truthful generalized assignments via stable matching in the generalized assignment problem gap a set of jobs seek to be assigned to a set of machines for every job machine pair there are a specific value and an accommodated capacity for the assignment the objective is to find an assignment that maximizes the total sum of values given that the capacity constraint of every machine is satisfied the gap is a classic optimization problem and has been studied extensively from the algorithmic perspective dughmi and ghosh dughmi s ghosh a 2010 truthful assignment without money acm conf electronic commerce acm new york 325 334 proposed the game theoretical framework in which every job is owned by a selfish agent who aims to maximize the value of his own assignment they gave a logarithmic approximation truthful in expectation mechanism and left open the problem whether there exists a truthful mechanism with a constant approximation factor in this paper we give an affirmative answer to this question and provide a constant approximation mechanism

approximation schemes for deal splitting and covering integer programs with multiplicity constraints we consider the problem of splitting an order for r goods r 1 among a set of sellers each having bounded amounts of the goods so as to minimize the total cost of the deal in deal splitting with packages dsp the sellers offer packages containing combinations of the goods in deal splitting with price tables dst the buyer can generate such combinations using price tables our problems which often occur in online reverse auctions generalize covering integer programs with multiplicity constraints cip where we must fill up an r dimensional bin by selecting with a bounded number of repetitions from a set of r dimensional items such that the overall cost is minimized thus both dsp and dst are np hard already for a single good and hard to approximate for arbitrary number of goods in this paper we focus on finding efficient approximations for dsp and dst instances where the number of goods is some fixed constant in particular we develop polynomial time approximation schemes ptas for several subclasses of instances of practical interest our results include a ptas for cip in fixed dimension and a more efficient combinatorial scheme for cip where the multiplicity constraints are omitted our approximation scheme for cip is based on a non trivial application of the fast scheme for the fractional covering problem proposed by fleischer l fleischer a fast approximation scheme for fractional covering problems with variable upper bounds in proc of the 15th acm siam symposium on discrete algorithm 2004 pp 994 1003

discrete shape sensitivity equations for aerodynamic problems intensive research and development in computational fluid dynamics cfd has recently produced many powerful cfd codes to simulate complex aerodynamic phenomena however in order to enhance the usefulness of these cfd codes for design practice development of design sensitivity equations compatible to these codes becomes very important this paper represents a part of such an effort to develop a sensitivity analysts methodology that enables the sensitivity equations to be implemented into existing cfd codes with minimal code modification the methodology is based upon a pre elimination procedure which accounts for consistently linearized boundary conditions formulations of both the direct differentiation and the adjoint variable methods will be presented in the paper

a fast algorithm for maximizing a non monotone dr submodular integer lattice function abstract in this paper we consider the problem of maximizing a non monotone and non negative dr submodular function on a bounded integer lattice b x 1 x n z n 0 x k b k 1 k n without any constraint where b b 1 b n z n we design an algorithm for the problem and measure its performance by its approximation ratio and the number of value oracle queries it needs where the latter one is the dominating term in the running time of an algorithm it has been showed that for the problem considered any algorithm achieving an approximation ratio greater than 1 2 requires an exponential number of value oracle queries in the literature there are two algorithms that reach 1 2 approximation guarantee the first algorithm needs o n b oracle queries the second one reduces its number of oracle queries to o n max 1 log b but it needs large storage in this paper we present a randomized approximation algorithm that has an approximation guarantee of 1 2 calls o n max 1 log b oracle queries and does not need large storage improving the results of the literature

conservation errors and convergence characteristics of iterative space marching algorithms the new iterative space marching algorithms for numerical solution of the parabolized navier stokes equations are critically examined it is shown by analysis and numerical examples that employing parabolized flux difference splitting in the marching direction can lead to serious conservation errors even though a finite volume formulation is employed schemes employing parabolized flux vector splitting in the marching direction are shown to be conservative the structure of the iterative algorithm is examined to determine what factors play important roles in the convergence of the local iteration

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

the demand matching problem we examine formulations for the well known b matching problem in the presence of integer demands on the edges a subset m of edges is feasible if for each node v the total demand of edges in m incident to v is at most bv we examine the system of star inequalities for this problem this system yields an exact linear description for b matchings in bipartite graphs for the demand version we show that the integrality gap for this system is at least 2 5 and at most 2 764 for general graphs the gap lies between 3 and 3 264 we also describe a 3 approximation algorithm 2 5 for bipartite graphs for the cardinality version of the problem a fully polynomial approximation scheme is also presented for the problem on a tree thus generalising a well known result for the knapsack problem recently the notion of demand matching has arisen in the design of clos network switches

parallel processing scheme for the navier stokes equations part 1 scheme development using a lower and upper decomposition procedure an implicit parallel processing scheme for the compressible navier stokes equations is developed in this scheme the solution for a multidimensional problem is obtained by the superposition of two independent solution cycles because of the independence of these two solutions they can be performed on separate processors simultaneously to confirm the analytical developments numerical results are obtained using the proposed scheme and compared with other available solutions and experimental data a study of other characteristics of the proposed scheme such as stability symmetry preserving and effects of domain decomposition on convergence and stability is also conducted

on multirate rearrangeable clos networks in the multirate switching environment each connection request is associated with a bandwidth weight we consider a three stage clos network and assume that each link has a capacity of one after normalization the network is rearrangeable if for all possible sets of requests such that each input and output link generates a total weight not exceeding one there always exists a set of paths one for each request such that the sum of weights of all paths going through a link does not exceed the link capacity the question is to determine the minimum number of center switches which guarantees rearrangeability we obtain a lower bound of 11n 9 and an upper bound of 41n 16 we then extend the result for the three stage clos network to the multistage clos network finally we propose the weighted version of the edge coloring problem which somehow has escaped the literature associated with our switching network problem

an improved upwind finite volume relaxation method for high speed viscous flows an improved upwind relaxation algorithm for the navier stokes equations is presented and results are given from the application of the method to two test problems including 1 a shock boundary layer interaction on a flat plate m sub infinity 2 0 and 2 a high speed inlet m sub infinity 5 0 the technique is restricted to high speed i e supersonic hypersonic viscous flows the new algorithm depends on a partitioning of the global domain into regions or sub domains where a relatively thin open quotes elliptic close quotes region is identified near each solid wall boundary and the remainder of the flowfield is identified to be a single larger open quotes hyperbolic close quotes i e hyperbolic parabolic in the stream wise direction region a direct solution procedure by lower upper factorization is applied to the elliptic region s the results of which are then coupled to a standard line gauss seidel relaxation sweep across the entire domain in the primary flow direction in the first test problem the new algorithm reduced total run times as much as 75 when compared to the standard alternating forward backward vertical line gauss seidel vlgs algorithm whereas in the second test problem a total savings as high as 20 was achieved essentially all of this improvement occurred only after the initial transientmore in the solution was overcome however in the second test problem a significant improvement in the computational performance of the standard forward backward vlgs algorithm was noted when overcoming the initial transient simply by converting from the use of conserved variables to primitive variables in the spatial discretization and linearization of all terms 22 refs 11 figs less