indifference zone free selection of the best many procedures have been proposed in the literature to select the simulated alternative with the best mean performance from a finite set of alternatives among these procedures frequentist procedures are typically designed under either the subset selection ss formulation or the indifference zone iz formulation both formulations may encounter problems when the goal is to select the unique best alternative for any configuration of the means in particular ss procedures may return a subset that contains more than one alternative and iz procedures hinge on the relationship between the chosen iz parameter and the true mean differences that is unknown to decision makers a priori in this paper we propose a new formulation that guarantees to select the unique best alternative with a user specified probability of correct selection pcs as long as the means of alternatives are unique and we design a class of fully sequential procedures under this formulation these procedures are parameterized by the

the numerical range theory and boundedness of solutions of the complementarity problem abstract using the numerical range theory of an operator defined on a hilbert space we study the boundedness of the solution set for the complementarity problem defined in a hilbert space

fast and high accuracy multigrid solution of the three dimensional poisson equation we employ a fourth order compact finite difference scheme fos with the multigrid algorithm to solve the three dimensional poisson equation we test the influence of different orderings of the grid space and different grid transfer operators on the convergence and efficiency of our high accuracy algorithm fourier smoothing analysis is conducted to show that fos has a smaller smoothing factor than the traditional second order central difference scheme cds a new method of fourier smoothing analysis is proposed for the partially decoupled red black gauss seidel relaxation with fos numerical results are given to compare the computed accuracy and the computational efficiency of fos with multigrid against cds with multigrid

myopic allocation policy with asymptotically optimal sampling rate in this note we consider the statistical ranking and selection problem of finding the best alternative when the performances of each alternative must be estimated by sampling we provide a myopic allocation policy that asymptotically achieves the sampling ratios given by the optimal computing budget allocation an approximate solution of the optimal large deviations rate for the decreasing probability of false selection we analyze the asymptotic sampling ratio for both known variances and unknown variances under a bayesian framework numerical results substantiate the theoretical results

a second order accurate symmetric discretization of the poisson equation on irregular domains in this paper we consider the variable coefficient poisson equation with dirichlet boundary conditions on an irregular domain and show that one can obtain second order accuracy with a rather simple discretization moreover since our discretization matrix is symmetric it can be inverted rather quickly as opposed to the more complicated nonsymmetric discretization matrices found in other second order accurate discretizations of this problem multidimensional computational results are presented to demonstrate the second order accuracy of this numerical method in addition we use our approach to formulate a second order accurate symmetric implicit time discretization of the heat equation on irregular domains then we briefly consider stefan problems

a supra convergent finite difference scheme for the variable coefficient poisson equation on non graded grids we introduce a method for solving the variable coefficient poisson equation on non graded cartesian grids that yields second order accuracy for the solutions and their gradients we employ quadtree in 2d and octree in 3d data structures as an efficient means to represent the cartesian grid allowing for constraint free grid generation the schemes take advantage of sampling the solution at the nodes vertices of each cell in particular the discretization at one cell s node only uses nodes of two 2d or three 3d adjacent cells producing schemes that are straightforward to implement numerical results in two and three spatial dimensions demonstrate supra convergence in the l norm

acceleration of steady state lattice boltzmann simulations on non uniform mesh using local time step method in this paper the local time step method is applied to the lattice boltzmann method lbm on non uniform grid generalized form of interpolation supplemented lbm gilbm for steady flow simulations the local time step method is known to be an effective technique to accelerate the solution to the converged steady state on non uniform grid first code validation for global time step method is performed by solving flow around a cylinder at low reynolds numbers our results show good agreement with previous studies two dimensional flow simulations around an airfoil were performed in order to validate the code using the local time step method and the results are compared with the global time step solutions the pressure distribution and the aerodynamic coefficients of global and local time step results are in good agreement they are also consistent with the previous studies at the same time cpu time required to obtain the steady state solutions using the local time step are reduced by 70 80 compared with that using global time step

nonlinear complementarity problem and galerkin method etude du probleme de complementarite non lineaire dans des espaces de dimensions infinies en utilisant l approximation de galerkin et une generalisation de l hypothese de karamardian on obtient plusieurs resultats d existence pour une forme speciale du probleme ou f x x l x t x l etant un operateur lineaire et t un operateur non lineaire

a fully sequential elimination procedure for indifference zone ranking and selection with tight bounds on probability of correct selection we consider the indifference zone iz formulation of the ranking and selection problem with independent normal samples in this problem we must use stochastic simulation to select the best among several noisy simulated systems with a statistical guarantee on solution quality existing iz procedures sample excessively in problems with many alternatives in part because loose bounds on probability of correct selection lead them to deliver solution quality much higher than requested consequently existing iz procedures are seldom considered practical for problems with more than a few hundred alternatives to overcome this we present a new sequential elimination iz procedure called biz bayes inspired indifference zone whose lower bound on worst case probability of correct selection in the preference zone is tight in continuous time and nearly tight in discrete time to the author s knowledge this is the first sequential elimination procedure with tight bounds on worst case preference zone probability of correct selection for more than two alternatives theoretical results for the discrete time case assume that variances are known and have an integer multiple structure but the biz procedure itself can be used when these assumptions are not met in numerical experiments the sampling effort used by biz is significantly smaller than that of another leading iz procedure the kn procedure especially on the largest problems tested 214 16 384 alternatives

a multigrid solver for the discrete boltzmann equation this paper introduces a nonlinear multigrid solution approach for the discrete boltzmann equation discretized by an implicit second order finite difference scheme for simplicity we restrict the discussion to the stationary case a numerical example shows the drastically improved efficiency in comparison to the widely used lattice bathnagar gross krook lbgk approach

an adaptive multigrid technique for the incompressible navier stokes equations an automatic adaptive refinement technique has been coupled to the multigrid approach to produce an efficient and stable solution strategy for solving the steady state incompressible navier stokes equations solutions have been obtained for the driven cavity and flow over a backward facing step for reynolds numbers up to 5000 and 800 respectively the refinement criterion is based on the local truncation error the solution error is monitored and automatic refinement can continue until it is reduced to a satisfactory level for driven cavity flow at re 1000 the adaptive refinement approach reduced the computer memory and cpu time to 20 and 40 of the requirements of the pure multigrid method the primitive variable formulation of the navier stokes equations is used so the method can be extended easily to three dimensions application to other nonlinear elliptic problems is equally possible

constrained optimization in expensive simulation novel approach this article presents a novel heuristic for constrained optimization of computationally expensive random simulation models one output is selected as objective to be minimized while other outputs must satisfy given threshold values moreover the simulation inputs must be integer and satisfy linear or nonlinear constraints the heuristic combines i sequentialized experimental designs to specify the simulation input combinations ii kriging or gaussian process or spatial correlation modeling to analyze the global simulation input output data resulting from these designs and iii integer nonlinear programming to estimate the optimal solution from the kriging metamodels the heuristic is applied to an s s inventory system and a call center simulation and compared with the popular commercial heuristic optquest embedded in the arena versions 11 and 12 in these two applications the novel heuristic outperforms optquest in terms of number of simulated input combinations and quality of the estimated optimum

comparison of second and fourth order discretizations for multigrid poisson solvers we combine a compact high order difference approximation with multigrid v cycle algorithm to solve the two dimensional poisson equation with dirichlet boundary conditions this scheme along with several different orderings of grid space and projection operators is compared with the five point formula to show the dramatic improvement in computed accuracy on serial and vector machines

bayesian optimization via simulation with pairwise sampling and correlated prior beliefs this paper addresses discrete optimization via simulation we show that allowing for both a correlated prior distribution on the means e g with discrete kriging models and sampling correlation e g with common random numbers or crn can significantly improve the ability to quickly identify the best alternative these two correlations are brought together for the first time in a highly sequential knowledge gradient sampling algorithm which chooses points to sample using a bayesian value of information voi criterion we provide almost sure convergence guarantees as the number of samples grows without bound when parameters are known and provide approximations that allow practical implementation including a novel use of the voi s gradient rather than the response surface s gradient we demonstrate that crn leads to improved optimization performance for voi based algorithms in sequential sampling environments with a combinatorial number of alternatives and costly samples

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

a lattice boltzmann model for elliptic equations with variable coefficient abstract a lattice boltzmann model is proposed to solve elliptic equations with variable coefficient compared with the previous model the present model is a more effective solver to the ellipse equation with variable coefficient and the ellipse equation is exactly recovered to order o e 2 the relaxation time is not fixed and is determined by the coefficient of the equation the limited numerical results show that the present model is valid for ellipse equations

a multiple attribute utility theory approach to ranking and selection managers of large industrial projects often measure performance by multiple attributes for example our paper is motivated by the simulation of a large industrial project called a land seismic survey in which project performance is based on duration cost and resource utilization to address these types of problems we develop a ranking and selection procedure for making comparisons of systems e g project configurations that have multiple performance measures the procedure combines multiple attribute utility theory with statistical ranking and selection to select the best configuration from a set of possible configurations using the indifference zone approach we apply our procedure to results generated by the simulator for a land seismic survey that has six performance measures and describe a particular type of sensitivity analysis that can be used as a robustness check

sequential selection procedures using sample means to improve efficiency abstract two stage selection procedures have been widely studied and applied to determine appropriate sample sizes for selecting the best of k designs however standard indifference zone procedures are derived with a statistically conservative least favorable configuration assumption the enhanced two stage selection etss is a procedure that takes into account not only the variance of samples but also the difference between sample means when determining the sample sizes this paper discusses an implementation of sequential ranking and selection procedures due to the etss procedure to avoid relying too much on information obtained in just one stage we show that the needed ratios of sample sizes to maximize the probability of correct selection is approximately maintained at all iterations an experimental performance evaluation demonstrates the efficiency of our sequential procedures

an error minimized pseudospectral penalty direct poisson solver this paper presents a direct poisson solver based on an error minimized chebyshev pseudospectral penalty formulation for problems defined on rectangular domains in this study the penalty parameters are determined analytically such that the discrete l 2 error is minimized numerical experiments are conducted and the results show that the penalty scheme computes numerical solutions with better accuracy compared to the traditional approach with boundary conditions enforced strongly

steady state convergence acceleration of the generalized lattice boltzmann equation with forcing term through preconditioning several applications exist in which lattice boltzmann methods lbm are used to compute stationary states of fluid motions particularly those driven or modulated by external forces standard lbm being explicit time marching in nature requires a long time to attain steady state convergence particularly at low mach numbers due to the disparity in characteristic speeds of propagation of different quantities in this paper we present a preconditioned generalized lattice boltzmann equation glbe with forcing term to accelerate steady state convergence to flows driven by external forces the use of multiple relaxation times in the glbe allows enhancement of the numerical stability particular focus is given in preconditioning external forces which can be spatially and temporally dependent in particular correct forms of moment projections of source forcing terms are derived such that they recover preconditioned navier stokes equations with non uniform external forces as an illustration we solve an extended system with a preconditioned lattice kinetic equation for magnetic induction field at low magnetic prandtl numbers which imposes lorentz forces on the flow of conducting fluids computational studies particularly in three dimensions for canonical problems show that the number of time steps needed to reach steady state is reduced by orders of magnitude with preconditioning in addition the preconditioning approach resulted in significantly improved stability characteristics when compared with the corresponding single relaxation time formulation

selection procedures with frequentist expected opportunity cost bounds selection procedures help identify the best of a finite set of simulated alternatives most work has measured the quality of a selection with the probability of correct selection p cs but the expected opportunity cost of a potentially incorrect decision makes more sense in business contexts this paper analyzes the first selection procedures that guarantee an upper bound for the expected opportunity cost in a frequentist sense of a potentially incorrect selection the paper therefore bridges a gap between the indifference zone approach with frequentist guarantees but for the p cs and the bayesian approach to selection procedures which has considered the opportunity cost we also provide unexpected expected opportunity cost guarantees for several existing indifference zone selection procedures that were originally designed to provide p cs guarantees

multigrid lattice boltzmann method for accelerated solution of elliptic equations a new solver for second order elliptic partial differential equations pdes based on the lattice boltzmann method lbm and the multigrid mg technique is presented several benchmark elliptic equations are solved numerically with the inclusion of multiple grid levels in two dimensional domains at an optimal computational cost within the lb framework the results are compared with the corresponding analytical solutions and numerical solutions obtained using the stone s strongly implicit procedure the classical pdes considered in this article include the laplace and poisson equations with dirichlet boundary conditions with the latter involving both constant and variable coefficients a detailed analysis of solution accuracy convergence and computational efficiency of the proposed solver is given it is observed that the use of a high order stencil for smoothing improves convergence and accuracy for an equivalent number of smoothing sweeps the effect of the type of scheduling cycle v or w cycle on the performance of the mg lbm is analyzed next a parallel algorithm for the mg lbm solver is presented and then its parallel performance on a multi core cluster is analyzed lastly a practical example is provided wherein the proposed elliptic pde solver is used to compute the electro static potential encountered in an electro chemical cell which demonstrates the effectiveness of this new solver in complex coupled systems several orders of magnitude gains in convergence and parallel scaling for the canonical problems and a factor of 5 reduction for the multiphysics problem are achieved using the mg lbm

a cartesian grid embedded boundary method for poisson s equation on irregular domains we present a numerical method for solving poisson s equation with variable coefficients and dirichlet boundary conditions on two dimensional regions the approach uses a finite volume discretization which embeds the domain in a regular cartesian grid we treat the solution as a cell centered quantity even when those centers are outside the domain cells that contain a portion of the domain boundary use conservative differencing of second order accurate fluxes on each cell volume the calculation of the boundary flux ensures that the conditioning of the matrix is relatively unaffected by small cell volumes this allows us to use multigrid iterations with a simple point relaxation strategy we have combined this with an adaptive mesh refinement amr procedure we provide evidence that the algorithm is second order accurate on various exact solutions and compare the adaptive and nonadaptive calculations

lattice boltzmann model for the axisymmetric electro thermo convection abstract a lattice boltzmann model for the axisymmetric electro thermo convection is proposed in this paper the axisymmetric governing equations in the cylindrical coordinate system including the navier stokes equations the energy equation the conservation equation of charge density and the poisson s equation for electric potential are solved by the lattice boltzmann method in the cartesian coordinate system all additional source terms can be calculated locally the present model is validated by three simple numerical examples the electro thermo convection in an annulus between two coaxial vertical cylinders is also investigated by the present model the effect of the electric rayleigh number on heat transfer enhancement is discussed

generalized lattice boltzmann equation with forcing term for computation of wall bounded turbulent flows in this paper we present a framework based on the generalized lattice boltzmann equation glbe using multiple relaxation times with forcing term for eddy capturing simulation of wall bounded turbulent flows due to its flexibility in using disparate relaxation times the glbe is well suited to maintaining numerical stability on coarser grids and in obtaining improved solution fidelity of near wall turbulent fluctuations the subgrid scale sgs turbulence effects are represented by the standard smagorinsky eddy viscosity model which is modified by using the van driest wall damping function to account for reduction of turbulent length scales near walls in order to be able to simulate a wider class of problems we introduce forcing terms which can represent the effects of general nonuniform forms of forces in the natural moment space of the glbe expressions for the strain rate tensor used in the sgs model are derived in terms of the nonequilibrium moments of the glbe to include such forcing terms which comprise a generalization of those presented in a recent work yu et al comput fluids 35 957 2006 variable resolutions are introduced into this extended glbe framework through a conservative multiblock approach the approach whose optimized implementation is also discussed is assessed for two canonical flow problems bounded by walls viz fully developed turbulent channel flow at a shear or friction reynolds number re of 183 6 based on the channel half width and three dimensional 3d shear driven flows in a cubical cavity at a re of 12 000 based on the side length of the cavity comparisons of detailed computed near wall turbulent flow structure given in terms of various turbulence statistics with available data including those from direct numerical simulations dns and experiments showed good agreement the glbe approach also exhibited markedly better stability characteristics and avoided spurious near wall turbulent fluctuations on coarser grids when compared with the single relaxation time srt based approach moreover its implementation showed excellent parallel scalability on a large parallel cluster with over a thousand processors

multigrid method and fourth order compact scheme for 2d poisson equation with unequal mesh size discretization abstract a fourth order compact difference scheme with unequal mesh sizes in different coordinate directions is employed to discretize a two dimensional poisson equation in a rectangular domain multigrid methods using a partial semicoarsening strategy and line gauss seidel relaxation are designed to solve the resulting sparse linear systems numerical experiments are conducted to test the accuracy of the fourth order compact difference scheme and to compare it with the standard second order difference scheme convergence behavior of the partial semicoarsening and line gauss seidel relaxation multigrid methods is examined experimentally

a lower bound for the correct subset selection probability and its application to discrete event system simulations ordinal optimization concentrates on finding a subset of good designs by approximately evaluating a parallel set of designs and reduces the required simulation time dramatically for discrete event simulation and optimization the estimation of the confidence probability cp that the selected designs contain at least one good design is crucial to ordinal optimization however it is very difficult to estimate this probability in des simulation especially for complicated des with large number of designs this paper proposes two simple lower bounds for quantifying the confidence probability numerical testing is presented

improving the low mach number steady state convergence of the cascaded lattice boltzmann method by preconditioning abstract cascaded lattice boltzmann method lbm involves the use of central moments in a multiple relaxation time formulation in prescribing the collision step when the goal is to simulate low mach number stationary flows the greater the disparity between the magnitude of fluid speed and the sound speed the higher is the numerical stiffness which results in relatively large number of time steps for convergence of the lbm one way to improve the steady state convergence of the scheme is to precondition the cascaded lbm which reduces the disparities between the characteristic speeds or equivalently those between the eigenvalues of the system in this paper we present a new preconditioned two dimensional cascaded lbm where a preconditioning parameter is introduced into the equilibrium moments as well as the forcing terms particular focus is given to preconditioning differently the moments due to forcing at first and second orders so as to avoid any spurious effects in the emergent macroscopic equations a chapman enskog analysis performed on this approach shows consistency to the preconditioned navier stokes equations this modified central moment based scheme is then validated for accuracy by comparison against prior analytical or numerical results for certain benchmark problems including those involving spatially variable body forces finally significant steady state convergence acceleration of the preconditioned cascaded lbm is demonstrated for a set of characteristic parameters

a boundary condition capturing method for poisson s equation on irregular domains interfaces have a variety of boundary conditions or jump conditions that need to be enforced the ghost fluid method gfm was developed to capture the boundary conditions at a contact discontinuity in the inviscid euler equations and has been extended to treat more general discontinuities such as shocks detonations and deflagrations and compressible viscous flows in this paper a similar boundary condition capturing approach is used to develop a new numerical method for the variable coefficient poisson equation in the presence of interfaces where both the variable coefficients and the solution itself may be discontinuous this new method is robust and easy to implement even in three spatial dimensions furthermore the coefficient matrix of the associated linear system is the standard symmetric matrix for the variable coefficient poisson equation in the absence of interfaces allowing for straightforward application of standard black box solvers

a complementarity problem in mathematical programming in banach space abstract an existence and uniqueness theorem for the nonlinear complementarity problem over arbitrary closed convex cones in a reflexive real banach space is established

economic analysis of simulation selection problems ranking and selection procedures are standard methods for selecting the best of a finite number of simulated design alternatives based on a desired level of statistical evidence for correct selection but the link between statistical significance and financial significance is indirect and there has been little or no research into it this paper presents a new approach to the simulation selection problem one that maximizes the expected net present value of decisions made when using stochastic simulation we provide a framework for answering these managerial questions when does a proposed system design whose performance is unknown merit the time and money needed to develop a simulation to infer its performance for how long should the simulation analysis continue before a design is approved or rejected we frame the simulation selection problem as a stoppable version of a bayesian bandit problem that treats the ability to simulate as a real option prior to project implementation for a single proposed system we solve a free boundary problem for a heat equation that approximates the solution to a dynamic program that finds optimal simulation project stopping times and that answers the managerial questions for multiple proposed systems we extend previous bayesian selection procedures to account for discounting and simulation tool development costs

preconditioned lattice boltzmann method for steady flows in this paper we propose a preconditioned lattice boltzmann lb method for steady incompressible flows for steady flows the macroscopic equations derived from this lb model are equivalent to those from the standard lb model but with an improved eigenvalue system the proposed model can be viewed as an explicit solver for preconditioned compressible navier stokes equations linear stability analysis is performed and the results show that the stability of the model is the same as that of the standard lb model for low mach numbers the proposed model retains the structure of the standard lb model and hence possesses all the advantages numerical tests show that the convergence rate can be enhanced as much as an order of magnitude compared to the standard lattice boltzmann method the accuracy of the solutions is improved as well

a new lattice boltzmann model for the laplace equation in this paper a new lattice boltzmann equation which is independent of time is proposed based on the new lattice boltzmann equation some steady problems can be modeled by the lattice boltzmann method in the further study the laplace equation is investigated with the method of the higher order moment of equilibrium distribution functions and a series of partial differential equations in different space scales the numerical results show that the new method is effective

information collection on a graph we derive a knowledge gradient policy for an optimal learning problem on a graph in which we use sequential measurements to refine bayesian estimates of individual edge values in order to learn about the best path this problem differs from traditional ranking and selection in that the implementation decision the path we choose is distinct from the measurement decision the edge we measure our decision rule is easy to compute and performs competitively against other learning policies including a monte carlo adaptation of the knowledge gradient policy for ranking and selection

performance evaluation of the general characteristics based off lattice boltzmann scheme and dugks for low speed continuum flows the general characteristics based off lattice boltzmann scheme proposed by bardow et al 1 hereafter bardow s scheme and the discrete unified gas kinetic scheme dugks 2 are two methods that successfully overcome the time step restriction by the collision time which is commonly seen in many other kinetic schemes in this work we first perform a theoretical analysis of the two schemes in the finite volume framework by comparing their numerical flux evaluations it is found that the effect of collision term is considered in the evaluation of the cell interface distribution function in both schemes which explains why they can overcome the time step restriction and can give accurate results even as the time step is much larger than the collision time the difference between the two schemes lies in the treatment of the integral of the collision term when evaluating the cell interface distribution function in which bardow s scheme uses the rectangular rule while dugks uses the trapezoidal rule the performance of the two schemes i e accuracy stability and efficiency are then compared by simulating several two dimensional flows including the unsteady taylorgreen vortex flow the steady lid driven cavity flow and the laminar boundary layer problem it is observed that dugks can give more accurate results than bardow s scheme with a same mesh size furthermore the numerical stability of bardow s scheme decreases as the courantfriedrichslewy cfl number approaches to 1 while the stability of dugks is not affected by the cfl number apparently as long as cfl 1 it is also observed that dugks is twice as expensive as the bardow s scheme with the same mesh size

selecting a selection procedure selection procedures are used in a variety of applications to select the best of a finite set of alternatives best is defined with respect to the largest mean but the mean is inferred with statistical sampling as in simulation optimization there are a wide variety of procedures which begs the question of which selection procedure to select the main contribution of this paper is to identify through extensive experimentation the most effective selection procedures when samples are independent and normally distributed we also a summarize the main structural approaches to deriving selection procedures b formalize new sampling allocations and stopping rules c identify strengths and weaknesses of the procedures d identify some theoretical links between them and e present an innovative empirical test bed with the most extensive numerical comparison of selection procedures to date the most efficient and easiest to control procedures allocate samples with a bayesian model for uncertainty about the means and use new adaptive stopping rules proposed here

a quantile based approach to system selection abstract we propose a quantile based ranking and selection r s procedure for comparing a finite set of stochastic systems via simulation our r s procedure uses a quantile set of the simulated probability distribution of a performance characteristic of interest that best represents the most appropriate selection criterion as the basis for comparison since this quantile set may represent either the downside risk upside risk or central tendency of the performance characteristic the proposed approach is more flexible than the traditional mean based approach to r s we first present a procedure that selects the best system from among k systems and then we modified that procedure for the case where k 1 systems are compared against a standard system we present a set of experiments to highlight the flexibility of the proposed procedures

geometric multigrid with applications to computational fluid dynamics an overview is given of the development of the geometric multigrid method with emphasis on applications in computational fluid dynamics over the last ten years both compressible and incompressible flow problems and their corresponding multigrid solution methods are discussed the state of the art is described with respect to methods employed in industry as well as the multigrid efficiency obtained in academic applications

on the convergence rates of expected improvement methods we consider a ranking and selection problem with independent normal observations and we analyze the asymptotic sampling rates of expected improvement ei methods in this setting such methods often perform well in practice but a tractable analysis of their convergence rates is difficult because of the nonlinearity and nonconvexity of the ei calculations we present new results indicating that for known sampling noise variants of ei produce asymptotic simulation allocations that are essentially identical to those chosen by the optimal computing budget allocation ocba methodology which is known to yield near optimal asymptotic performance in ranking and selection this is the first general equivalence result between ei and ocba and it provides insight into the good practical performance of ei we also derive the limiting allocation for ei under unknown sampling variance

block implicit multigrid solution of navier stokes equations in primitive variables abstract a calculation procedure for rapid computation of steady multidimensional viscous flows is presented the method solves the navier stokes equations in primitive variables using a coupled block implicit multigrid procedure the procedure is applicable to finite difference formulations using staggered locations of the flow variables a smoothing technique called symmetrical coupled gauss seidel scgs is proposed and is empirically observed to provide good smoothing rates the viscous flow in a square cavity with a moving top wall is calculated for a range of reynolds numbers calculations with finite difference grids as large as 321 321 nodes have been made to test the accuracy and efficiency of the calculation scheme the cpu times for these calculations are observed to be significantly smaller than other solution algorithms with primitive variable formulation the calculated flow fields in the cavity are in good agreement with earlier studies of the same flow situation