external boundary conditions for three dimensional problems of computational aerodynamics we consider an unbounded steady state flow of viscous fluid over a three dimensional finite body or configuration of bodies for the purpose of solving this flow numerically we discretize the governing equations navier stokes on a finite difference grid prior to the discretization we obviously need to truncate the original unbounded domain by introducing an artificial computational boundary at a finite distance from the body otherwise the number of discrete variables will not be finite this artificial boundary is typically the external boundary of the domain covered by the grid the flow problem both continuous and discretized formulated on the finite computational domain is clearly subdefinite unless supplemented by some artificial boundary conditions abcs at the external computational boundary in this paper we present an innovative approach to constructing highly accurate abcs for three dimensional flow computations the approach extends our previous technique developed for the two dimensional case it employs the finite difference counterparts to calderon s pseudodifferential boundary projections calculated in the framework of the difference potentials method dpm of ryaben kii the resulting abcs appear spatially nonlocal but are particularly easy to implement along with the existing flow solvers the new boundary conditions have been successfully combined with the nasa developed production code tlns3d and used for the analysis of wing shaped configurations in subsonic and transonic flow regimes as demonstrated by the computational experiments and comparison with the standard local methods the dpm based abcs allow one to greatly reduce the size of the computational domain while still maintaining high accuracy of the numerical solution moreover they may provide for a noticeable speedup of multigrid convergence

validation analysis of mirror descent stochastic approximation method the main goal of this paper is to develop accuracy estimates for stochastic programming problems by employing stochastic approximation sa type algorithms to this end we show that while running a mirror descent stochastic approximation procedure one can compute with a small additional effort lower and upper statistical bounds for the optimal objective value we demonstrate that for a certain class of convex stochastic programs these bounds are comparable in quality with similar bounds computed by the sample average approximation method while their computational cost is considerably smaller

adjustable robust solutions of uncertain linear programs we consider linear programs with uncertain parameters lying in some prescribed uncertainty set where part of the variables must be determined before the realization of the uncertain parameters non adjustable variables while the other part are variables that can be chosen after the realization adjustable variables we extend the robust optimization methodology 1 3 6 9 13 14 to this situation by introducing the adjustable robust counterpart arc associated with an lp of the above structure often the arc is significantly less conservative than the usual robust counterpart rc however in most cases the arc is computationally intractable np hard this difficulty is addressed by restricting the adjustable variables to be affine functions of the uncertain data the ensuing affinely adjustable robust counterpart aarc problem is then shown to be in certain important cases equivalent to a tractable optimization problem typically an lp or a semidefinite problem and in other cases having a tight approximation which is tractable the aarc approach is illustrated by applying it to a multi stage inventory management problem

the importance of eigenvectors for local preconditioners of the euler equations the design of local preconditioners to accelerate the convergence to a steady state for the compressible euler equations has so far been solely based on eigenvalue analysis however numerical evidence exists that the eigenvector structure also has an influence on the performance of preconditioners and should therefore be included in the design process in this paper we present the mathematical framework for the eigenvector analysis of local preconditioners for the multi dimensional euler equations the non normality of the preconditioned system is crucial in determining the potential for transient amplification of perturbations several existing local preconditioners are shown to possess a highly non normal structure for low mach numbers this non normality leads to significant robustness problems at stagnation points a modification to these preconditioners which eliminates the non normality is suggested and numerical results are presented showing the marked improvement in robustness

robust stochastic approximation approach to stochastic programming in this paper we consider optimization problems where the objective function is given in a form of the expectation a basic difficulty of solving such stochastic optimization problems is that the involved multidimensional integrals expectations cannot be computed with high accuracy the aim of this paper is to compare two computational approaches based on monte carlo sampling techniques namely the stochastic approximation sa and the sample average approximation saa methods both approaches the sa and saa methods have a long history current opinion is that the saa method can efficiently use a specific say linear structure of the considered problem while the sa approach is a crude subgradient method which often performs poorly in practice we intend to demonstrate that a properly modified sa approach can be competitive and even significantly outperform the saa method for a certain class of convex stochastic problems we extend the analysis to the case of convex concave stochastic saddle point problems and present in our opinion highly encouraging results of numerical experiments

navier stokes equations for almost incompressible flow the isentropic navier stokes equations at low mach numbers describe almost incompressible flow by a variable transformation the equations take a symmetric form suitable for computation estimates of the solution and its derivatives are obtained for the linearized equations on domains with open boundaries this is a necessary basis for the application of any numerical method whenever some part of the computational boundary is not a solid wall a semi implicit difference approximation is applied to the nonlinear equations for computation of flow over a backward facing step

the low frequency axisymmetric modal sound radiation efficiency of an elastically supported annular plate abstract this paper deals with the sound radiation efficiency of a vibrating thin elastically supported annular plate embedded into a flat rigid baffle the free axisymmetric time harmonic vibrations have been considered for a single mode it has been assumed that the influence of the air column above the plate on the plate s vibrations is negligible first the sound radiation efficiency has been formulated as an integral further rigorous mathematical manipulations have been carried out based on the theory of summation of multiple expansion series containing the hypergeometric functions as a result the formulations have been expressed as some fast convergent expansion series containing only the bessel and struve functions of integer order and the spherical bessel functions the presented formulations of sound radiation efficiency of an elastically supported annular plate are useful for numerical calculations within the low frequency range what is important for practical reasons the formulations are valid for axisymmetric boundary conditions and they enable changing the values of boundary stiffness constants consequently the analysis of influence of the plate s edge attachment on the sound radiation efficiency has been performed the limiting transitions have also been performed from formulations valid for the elastically supported annular plates to the formulations valid for annular plates with classical boundary conditions clamped simply supported and free at one edge or at both edges

on the short wave acoustic radiation from planar panels or beams of rectangular shape an exact representation which involves single as opposed to double integrals is established for the time average power output generated by individual modes of normal surface velocity on a simply supported and baffled rectangular panel fluid loading is not taken into account the representation enables analytical estimates to be found in the short wavelength range and provides details hitherto unresolved by numerical analysis

semi implicit extension of a godunov type scheme based on low mach number asymptotics i one dimensional flow a single scale multiple space scale asymptotic analysis provides detailed insight into the low mach number limit behavior of solutions of the compressible euler equations we use the asymptotics as a guideline for developing a low mach number extension of an explicit higher order shock capturing scheme this semi implicit scheme involves multiple pressure variables large scale differencing and averaging procedures that are discretized versions of standard operations in multiple scales asymptotic analysis advection and acoustic wave propagation are discretized explicitly and upwind and only one scalar elliptic equation is to be solved implicitly at each time step this equation is a pressure correction equation for incompressible flows when the mach number is zero in the low mach number limit the time step is restricted by a courant number based essentially on the maximum flow velocity for moderate and large mach numbers the scheme reduces to the underlying explicit higher order shock capturing algorithm

introduction to convex optimization in financial markets convexity arises naturally in financial risk management in risk preferences concerning random cash flows convexity corresponds to the fundamental diversification principle convexity is a basic property also of budget constraints both in classical linear models as well as in more realistic models with transaction costs and constraints moreover modern securities markets are based on trading protocols that result in convex trading costs the first part of this paper gives an introduction to certain basic concepts and principles of financial risk management in simple optimization terms the second part reviews some convex optimization techniques used in mathematical and numerical analysis of financial optimization problems

axisymmetric vibration of circular plates in contact with fluid abstract this paper is concerned with the effect of fluid on the natural frequencies of circular plates vibrating axisymmetrically in contact with fluid the ratio between the natural frequencies in fluid and the natural frequencies in air is a function of so called added virtual mass incremental avmi factor which reflects the increase of inertia due to the presence of fluid in this paper the non dimensionalized added virtual mass incremental navmi factor for circular plates having simply supported clamped and free edges is obtained by employing the integral transformation technique in conjunction with the dual integral equation method it is shown that the effect of fluid on the natural frequencies decreases with order

low mach number limit of viscous polytropic fluid flows abstract this paper studies the singular limit of the non isentropic navier stokes equations with zero thermal coefficient in a two dimensional bounded domain as the mach number goes to zero a uniform existence result is obtained in a time interval independent of the mach number provided that the initial data satisfy the bounded derivative conditions that is the time derivatives up to order two are bounded initially and navier s slip boundary condition is imposed

duality and martingales a stochastic programming perspective on contingent claims the hedging of contingent claims in the discrete time discrete state case is analyzed from the perspective of modeling the hedging problem as a stochastic program application of conjugate duality leads to the arbitrage pricing theorems of financial mathematics namely the equivalence of absence of arbitrage and the existence of a probability measure that makes the price process into a martingale the model easily extends to the analysis of options pricing when modeling risk management concerns and the impact of spreads and margin requirements for writers of contingent claims however we find that arbitrage pricing in incomplete markets fails to model incentives to buy or sell options an extension of the model to incorporate pre existing liabilities and endowments reveals the reasons why buyers and sellers trade in options the model also indicates the importance of financial equilibrium analysis for the understanding of options prices in incomplete markets

problems with different time scales for nonlinear partial differential equations consider a system of partial differential equations u t varepsilon 1 p 0 p 1 u here 0 varepsilon ll 1 is a small constant p 0 p 0 partial partial x is a differential operator with constant coefficients and p 1 p 1 x t u partial partial x is a quasilinear operator the coefficients of p 0 p 1 are of order o 1 it is shown how to prepare the initial data such that the solutions u x t and their derivatives can be bounded independently of varepsilon applications are discussed

analysis of artificial pressure equations in numerical simulations of a turbulent channel flow abstract recently several methods have been proposed to simulate incompressible fluid flows using an artificial pressure evolution equation avoiding the resolution of a poisson equation these methods can be seen as various levels of approximation of the compressible navier stokes equation in the low mach number limit we study the simulation of incompressible wall bounded flows using several artificial pressure equations in order to determine the most relevant approximations the simulations are stable using a finite difference method in a staggered grid system even without diffusive term and converge to the incompressible solution both in direct numerical simulations and for coarser meshes to be used in large eddy simulations a pressure equation with a convective and a diffusive term produces a more accurate solution than a compressible solver or methods involving more approximations this suggests that it is near to an optimal level of approximation the presence of a convective term in the pressure evolution equation is in particular crucial for the accuracy of the method the rate of convergence of the solution in terms of artificial mach number is studied numerically and validates the theoretical quadratic convergence rate we demonstrate that this property can be used to accelerate the rate of convergence using an extrapolation in terms of artificial mach number since the approach is based on an explicit and local system of equations the numerical procedure is massively parallelisable and has low memory requirements

weakly compressible high order i stable central difference schemes for incompressible viscous flows abstract in this paper we propose a weakly compressible model for numerical simulation of the incompressible viscous flows this model asymptotically approximates the incompressible navier stokes equations when the mach number tends to zero the main advantage of this model is that its numerical discretization avoids any poisson solver thus is very attractive for problems with complicated geometries this model is discretized by high order center differences in space and the so called i stable method for time the linear stability region of an i stable method contains part of the imaginary axis when solving a system of convection diffusion equations with a small viscosity the i stable method allows a very large cell reynolds number thus is particularly suitable for the simulation of fluid flows with large reynolds numbers numerical experiments illustrate the efficiency and robustness of this approach

incompressible limits of the navier stokes equations for all time abstract we study the asymptotic behaviors of the regular solutions to the compressible navier stokes equations for well prepared initial data for all time as the mach number tends to zero by deriving a differential inequality with certain decay property the estimates obtained in this paper are uniform both in time and mach number

epi convergent discretizations of multistage stochastic programs in many dynamic stochastic optimization problems in practice the uncertain factors are best modeled as random variables with an infinite support this results in infinite dimensional optimization problems that can rarely be solved directly therefore the random variables stochastic processes are often approximated by finitely supported ones scenario trees which result in finite dimensional optimization problems that are more likely to be solvable by available optimization tools this paper presents conditions under which such finite dimensional optimization problems can be shown to epi converge to the original infinite dimensional problem epi convergence implies the convergence of optimal values and solutions as the discretizations are made finer our convergence result applies to a general class of convex problems where neither linearity nor complete recourse are assumed

free vibrations of annular plates coupled with fluids abstract the natural frequencies of annular plates on an aperture of an infinite rigid wall and in contact with a fluid on one side are theoretically obtained by using the added mass approach the fluid is assumed to be incompressible and inviscid and the velocity potential describes its irrotational motion the hankel transform is applied to solve the fluid plate coupled system boundary conditions are expressed by integral equations mode shapes are first assumed not to be modified by the fluid accurate numerical results are given for different plate boundary conditions they are suitable for engineering applications the accuracy of the assumed modes approach is theoretically studied by using the rayleigh ritz method that removes the simplifying hypothesis that dry and wet mode shapes are the same eigenfunctions of the plate vibrating in vacuum are assumed as admissible functions and the rayleigh quotient for coupled vibration is used to obtain a galerkin equation it was found that the fundamental mode and frequency for all the plate boundary conditions considered is well estimated by the assumed modes approach higher modes are computed with less accuracy by this formula and for some enhanced applications the rayleigh ritz approach is necessary

ekman layers of rotating fluids the case of general initial data in this paper we describe the weak solutions of the navier stokes equations with a large coriolis term as the rossby and the ekman numbers go to zero in a special domain with various boundary conditions this work extends the results in the case of well prepared initial data in 19 30 2000 john wiley sons inc

a semi implicit method for hyperbolic problems with different time scales hyperbolic systems with two different time scales are considered where the solutions vary on the slow scale only for this type of problem semi implicit difference methods are very natural and in this paper we analyze the leap frog backwards euler scheme in particular it is shown that when the ratio varepsilon between the slow and the fast scale tends to zero the solutions of the approximation converge to solutions of the reduced differential equation numerical experiments are included for illustration of the theoretical results

a simple justification of the singular limit for equatorial shallow water dynamics the equatorial shallow water equations at low froude number form a symmetric hyperbolic system with large variable coefficient terms although such systems are not covered by the classical klainerman majda theory of singular limits the first two authors recently proved that solutions exist uniformly and converge to the solutions of the long wave equations as the height and froude number tend to 0 their proof exploits the special structure of the equations by expanding solutions in series of parabolic cylinder functions a simpler proof of a slight generalization is presented here in the spirit of the classical theory 2008 wiley periodicals inc

epi convergent discretizations of multistage stochastic programs via integration quadratures this paper presents procedures for constructing numerically solvable discretizations of multistage stochastic programs that epi converge to the original problem as the discretizations are made finer epi convergence implies in particular that the cluster points of the first stage solutions of the discretized problems are optimal first stage solutions of the original problem the discretization procedures apply to a general class of nonlinear stochastic programs where the uncertain factors are driven by time series models using existing routines for numerical integration allows for an easy and efficient implementation of the procedures

a projection method for low speed flows we propose a decomposition applicable to low speed inviscid flows of all mach numbers less than 1 by using the hodge decomposition we may write the velocity field as the sum of a divergence free vector field and a gradient of a scalar function evolution equations for these parts are presented a numerical procedure based on this decomposition is designed using projection methods for solving the incompressible variables and a backward euler method for solving the potential variables numerical experiments are included to illustrate various aspects of our algorithm

a joint wavenumber time domain technique to determine the transient acoustic radiation loading on planar vibrators abstract a new method is presented to determine the transient radiation loading on planar vibrators mounted on rigid infinite baffles by using a wave vector time domain technique the specified non uniform velocity of the vibrator is expressed as a time dependent modal expansion where the modes are solutions to the homogeneous problem the time dependent acoustic modal forces can then be expressed as a sum of the modal radiation impulse responses convolved with the modal velocities in order to evaluate the radiation impulse responses the relationship between the fourier and hankel transforms of circular symmetric functions is first used to express the green s function for the problem as an integral over wave vector space the integral form of the green s function is then used to reduce the expression for the radiation impulse responses from a double surface integral over the vibrator to an integral over the wave vector space in contrast to the double surface integral which is difficult to evaluate the integral over the wave vector space can be evaluated easily numerical results are presented for clamped circular plates and simply supported square plates

singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids many interesting problems in classical physics involve the limiting behavior of quasilinear hyperbolic systems as certain coefficients become infinite using classical methods the authors develop a general theory of such problems this theory is broad enough to study a wide variety of interesting singular limits in compressible fluid flow and magneto fluid dynamics including new constructive local existence theorems for the time singular limit equations in particular the authors give an entirely self contained classical proof of the convergence of solutions of the compressible fluid equations to their incompressible limits as the mach number becomes small the theory depends upon a balance between certain inherently nonlinear structural conditions on the matrix coefficients of the system together with appropriate initialization procedures similar results are developed also for the compressible and incompressible navier stokes equations with periodic initial data independent of the viscosity coefficients as they tend to zero

asymptotic formulas for the acoustic radiation impedance of an elastically supported annular plate this paper deals with the normalized acoustic radiation impedance of an elastically supported annular plate in axisymmetric vibrations cauchy s theorem about residues and the stationary phase method have been used to approximate the corresponding integrals as a result elementary asymptotic formulas valid for axisymmetric boundary configurations of clamped guided simply supported and free annular plates as well as for all the intermediate boundary configurations have been obtained

log optimal and rapid paths in von neumann gale dynamical systems abstract von neumann gale dynamical systems are defined in terms of multivalued operators in spaces of random vectors possessing certain properties of convexity and homogeneity a central role in the theory of such systems is played by a special class of paths trajectories called rapid they grow over each time period t 1 t in a sense faster than others the paper establishes existence and characterization theorems for such paths showing in particular that any trajectory maximizing a logarithmic functional over a finite time horizon is rapid the proof of this result is based on the methods of convex analysis in spaces of measurable functions the study is motivated by the applications of the theory of von neumann gale dynamical systems to the modeling of capital growth in financial markets with friction

the incompressible limit of the non isentropic euler equations we study the euler equations for slightly compressible fluids that is after rescaling the limits of the euler equations of fluid dynamics as the mach number tends to zero in this paper we consider the general non isentropic equations and general data we first prove the existence of classical solutions for a time independent of the small parameter then on the whole space d we prove that the solution converges to the solution of the incompressible euler equations

analysis of preconditioners for hyperbolic partial differential equations preconditioners for conjugate gradient cg like iterative methods are analyzed the systems of equations arise from discretizations of time dependent hyperbolic partial differential equations pdes in two space dimensions incomplete lu ilu and block ilu preconditioners are considered for a model problem subject to periodic boundary conditions the spectra of the preconditioned coefficient matrices are determined by fourier analysis it is found that the condition number is not improved by the ilu preconditioners furthermore the number of distinct eigenvalues is not decreased a semicirculant preconditioner applied to a problem subject to dirichlet boundary conditions at the inflow boundaries is also examined analytical formulas for the eigenvalues and the eigenvectors are derived for this purpose a special analysis based on spectral decomposition and residue theory is developed when the grid ratio in space is less than one the spectrum asymptotically becomes two finite curve segments which are independent of the number of gridpoints for the restarted generalized minimal residual gmres iteration a slight reduction of the grid ratio from one substantially improves the convergence rate this is also predicted by an asymptotic analysis

convex duality in stochastic optimization and mathematical finance this paper proposes a general duality framework for the problem of minimizing a convex integral functional over a space of stochastic processes adapted to a given filtration the framework unifies many well known duality frameworks from operations research and mathematical finance the unification allows the extension of some useful techniques from these two fields to a much wider class of problems in particular combining certain finite dimensional techniques from convex analysis with measure theoretic techniques from mathematical finance we are able to close the duality gap in some situations where traditional topological arguments fail

stochastic programs without duality gaps this paper studies dynamic stochastic optimization problems parameterized by a random variable such problems arise in many applications in operations research and mathematical finance we give sufficient conditions for the existence of solutions and the absence of a duality gap our proof uses extended dynamic programming equations whose validity is established under new relaxed conditions that generalize certain no arbitrage conditions from mathematical finance

expected utility penalty functions and duality in stochastic nonlinear programming we consider nonlinear programming problem p with stochastic constraints the lagrangean corresponding to such problems has a stochastic part which in this work is replaced by its certainty equivalent in the sense of expected utility theory it is shown that the deterministic surrogate problem ce p thus obtained contains a penalty function which penalizes violation of the constraints in the mean the approach is related to several known methods in stochastic programming such as chance constraints stochastic goal programming reliability programming and mean variance analysis the dual problem of ce p is studied for problems with stochastic righthand sides in the constraints and a comprehensive duality theory is developed by introducing a new certainty equivalent nce concept motivation for the nce and its potential role in decision theory are discussed as well as mean variance approximations

portfolio selection with transaction costs in this paper optimal consumption and investment decisions are studied for an investor who has available a bank account paying a fixed rate of interest and a stock whose price is a log normal diffusion this problem was solved by merton and others when transactions between bank and stock are costless here we suppose that there are charges on all transactions equal to a fixed percentage of the amount transacted it is shown that the optimal buying and selling policies are the local times of the two dimensional process of bank and stock holdings at the boundaries of a wedge shaped region which is determined by the solution of a nonlinear free boundary problem an algorithm for solving the free boundary problem is given

low mach number limit of full navier stokes equations in a 3d bounded domain abstract this paper studies the low mach number limit of the full compressible navier stokes equations in a three dimensional bounded domain where the velocity field and the temperature satisfy the slip boundary conditions and the neumann boundary condition respectively the uniform estimates in the mach number for the strong solutions are derived in a short time interval provided that the initial density and temperature are close to the constant states and satisfy the bounded derivative conditions thus the solutions of the full compressible navier stokes equations converge to the one of the isentropic incompressible navier stokes equations as the mach number vanishes

wave operators and the incompressible limit of the compressible euler equation in an exterior domain in rn n 2 the solution of the compressible euler equation is shown to converge to that of the incompressible euler equation when the mach number tends to 0 the initial layer appears