sufficient conditions for pseudo lipschitz property in convex semi infinite vector optimization problems abstract this paper is devoted to the study of the pseudo lipschitz property of the efficient pareto solution map for the perturbed convex semi infinite vector optimization problem csvo we establish sufficient conditions for the pseudo lipschitz property of the efficient solution map of csvo under continuous perturbations of the right hand side of the constraints and functional perturbations of the objective function examples are given to illustrate the obtained results

simultaneous primal dual right hand side sensitivity analysis from a strictly complementary solution of a linear program this paper establishes theorems about the simultaneous variation of right hand sides and cost coefficients in a linear program from a strictly complementary solution some results are extensions of those that have been proven for varying the right hand side of the primal or the dual but not both other results are new in addition changes in the optimal partition and what that means in economic terms are related to the basis driven approach notably to the theory of compatibility in addition to new theorems about this relation the transition graph is extended to provide another visualization of the underlying economics

numerical study of pseudospectral methods in shock wave applications abstract in this paper we use shock capturing spectral methods to simulate compressible flows in the presence of shock waves three applications are considered the first is an interaction of a one dimensional shock with an entropy wave the second case deals with interactions between shock wave and an entropy wave in two space dimensions and the third case is two dimensional shock vortex interactions the first two applications are found in the study of turbulence in high speed flow the last application is a key element in understanding the acoustic dynamics in aeroacoustic and in design of supersonic jet in aerodynamics the purpose of this study is to show the feasibility of simulating shocked flow with spectral methods the numerical methods involved are the chebyshev and fourier collocation methods the euler equations of gas dynamics is discretized by pseudospectral collocation methods in space and a nonlinearly stable third order runge kutta methods in time the fluxes are evaluated pointwise directly and not by the cell averaging technique a significant reduction in cpu time and storage usage are achieved by incorporating several well established numerical techniques such as grid transformation and filtering into the spectral algorithm the results of this study indicate that spectral method is well suited not only for smooth problems but also for those with discontinuity

kernel methods in machine learning we review machine learning methods employing positive definite kernels these methods formulate learning and estimation problems in a reproducing kernel hilbert space rkhs of functions defined on the data domain expanded in terms of a kernel working in linear spaces of function has the benefit of facilitating the construction and analysis of learning algorithms while at the same time allowing large classes of functions the latter include nonlinear functions as well as functions defined on nonvectorial data we cover a wide range of methods ranging from binary classifiers to sophisticated methods for estimation with structured data

semi infinite programming theory methods and applications starting from a number of motivating and abundant applications in 2 including control of robots eigenvalue computations mechanical stress of materials and statistical design the authors describe a class of optimization problems which are referred to as semi infinite because their constraints bound functions of a finite number of variables on a whole region in 3 5 first and second order optimality conditions are derived for general nonlinear problems as well as a procedure for reducing the problem locally to one with only finitely many constraints another main effort for achieving simplification is through duality in 6 there algebraic properties of finite linear programming are brought to bear on duality theory in semi infinite programming section 7 treats numerical methods based on either discretization or local reduction with the emphasis on the design of superlinearly convergent sqp type methods taking this differentiable point of view this paper can be considered to be complementar

spectral simulation of supersonic reactive flows we present in this paper numerical simulations of reactive flows interacting with shock waves we argue that spectral methods are suitable for these problems and review the recent developments in spectral methods that have made them a powerful numerical tool appropriate for long term integrations of complicated flows even in the presence of shock waves a spectral code is described in detail and the theory that leads to each of its components is explained results of interactions of hydrogen jets with shock waves are presented and analyzed and comparisons with eno finite difference schemes are carried out

the role of linear semi infinite programming in signal adapted qmf bank design we consider the problem of designing a perfect reconstruction fir quadrature mirror filter qmf bank h g adapted to input signal statistics with the coding gain as the adaptation criterion maximization of the coding gain has so far been viewed as a difficult nonlinear constrained optimization problem it is shown that the coding gain depends only on the product filter p z h z h z sup 1 and this transformation leads to a stable class of linear optimization problems having finitely many variables and infinitely many constraints termed linear semi infinite programming sip problems the sought for original filter h z is obtained by deflation and spectral factorization of p z with the sip formulation every locally optimal solution is also globally optimal and can be computed using reliable numerical algorithms the natural regularity properties inherent in the sip formulation enhance the performance of these algorithms we present a comprehensive theoretical analysis of the sip problem and its dual characterize the optimal filters and analyze uniqueness and sensitivity issues all these properties are intimately related to those of the input signal and bring considerable insight into the nature of the adaptation process we present discretization and cutting plane algorithms and apply both methods to several examples

computation of limit loads for computing the collapse state of a perfect plastic continuum we suggest a mixed finite element approximation to the infinite dimensional mathematical programming problem of limit analysis the convergence of the limit load to the exact solution is discussed as well as solution methods for the discrete problem finally the method is applied to a classical problem in plane strain

polynomial interpolation results in sobolev spaces abstract in this paper we derive new results related to the lagrange polynomial interpolation on the nodes of gauss type quadrature formulas in particular we obtain asymptotic error estimates of the same order as the distance to the best fit in the polynomial space

the inverse scattering problem for time harmonic acoustic waves the inverse scattering problem we are considering in this paper is to determine the shape of a sound soft bounded connected obstacle from a knowledge of the time harmonic incident wave with frequency in the resonance region and the far field pattern of the scattered wave after some introductory remarks we begin by describing the method of integral equations and the null field method for solving the direct scattering problem this enables us to define an operator t mapping the boundary of the scattering obstacle and the incident field onto the far field pattern the inverse scattering problem is to invert this operator in order to do this we first must examine the range of t i e to characterize the class of far field patterns and to establish the existence of t on the range of t i e to show the uniqueness of the solution to the inverse scattering problem this analysis shows that for a given measured far field pattern in general no solution exists to the inverse scattering problem and if a solution does exist it does not depend continuously on the measured data i e the problem is improperly posed this motivates us to consider a linearized model and to examine various methods for studying linearized improperly posed problems based on the ideas of a priori assumptions and compactness arguments we then consider a simple model problem that focuses on the nonlinear character of the inverse scattering problem and motivated by our study of the linearized model reformulate the inverse scattering problem as a problem in constrained optimization we conclude by considering the numerical solution of this nonlinear optimization problem approach your problems from the right end and begin with the answers then one day perhaps you will find the final question from the hermit clad in crane feathers in the chinese maze murders by r van gulik

filtering in legendre spectral methods we discuss the impact of modal filtering in legendre spectral methods both on accuracy and stability for the former we derive sufficient conditions on the filter to recover high order accuracy away from points of discontinuity computational results confirm that less strict necessary conditions appear to be adequate we proceed to discuss a instability mechanism in polynomial spectral methods and prove that filtering suffices to ensure stability the results are illustrated by computational experiments

the slater conundrum duality and pricing in infinite dimensional optimization duality theory is pervasive in finite dimensional optimization there is growing interest in solving infinite dimensional optimization problems and hence a corresponding interest in duality theory in infinite dimensions unfortunately many of the intuitions and interpretations common to finite dimensions do not extend to infinite dimensions in finite dimensions a dual solution is represented by a vector of dual prices that index the primal constraints and have a natural economic interpretation in infinite dimensions we show that this simple dual structure and its associated economic interpretation may fail to hold for a broad class of problems with constraint vector spaces that are riesz spaces ordered vector spaces with a lattice structure that either are sigma order complete or satisfy the projection property in these spaces we show that the existence of interior points required by common constraint qualifications for zero duality gap such as slater s condition implies the existence of

dealiasing techniques for high order spectral element methods on regular and irregular grids high order methods are becoming increasingly attractive in both academia and industry especially in the context of computational fluid dynamics however before they can be more widely adopted issues such as lack of robustness in terms of numerical stability need to be addressed particularly when treating industrial type problems where challenging geometries and a wide range of physical scales typically due to high reynolds numbers need to be taken into account one source of instability is aliasing effects which arise from the nonlinearity of the underlying problem in this work we detail two dealiasing strategies based on the concept of consistent integration the first uses a localised approach which is useful when the nonlinearities only arise in parts of the problem the second is based on the more traditional approach of using a higher quadrature the main goal of both dealiasing techniques is to improve the robustness of high order spectral element methods thereby reducing aliasing driven instabilities we demonstrate how these two strategies can be effectively applied to both continuous and discontinuous discretisations where in the latter both volumetric and interface approximations must be considered we show the key features of each dealiasing technique applied to the scalar conservation law with numerical examples and we highlight the main differences in terms of implementation between continuous and discontinuous spatial discretisations

motzkin decomposition of closed convex sets theodore motzkin proved in 1936 that any polyhedral convex set can be expressed as the minkowski sum of a polytope and a polyhedral convex cone this paper provides five characterizations of the larger class of closed convex sets in finite dimensional euclidean spaces which are the sum of a compact convex set with a closed convex cone these characterizations involve different types of representations of closed convex sets as the support functions dual cones and linear systems whose relationships are also analyzed in the paper the obtaining of information about a given closed convex set f and the parametric linear optimization problem with feasible set f from each of its different representations including the motzkin decomposition is also discussed

comments on filter based stabilization of spectral element methods p fischer and j mullen 3 have recently proposed a stabilization technique for the solution of the unsteady navier stokes equations with the spectral element method it is based on interpolations in physical space given the values of a function u on a gauss lobatto legendre gll mesh with n 1 d nodes per element where d is the space dimension and n is the degree of the polynomial approximation in each direction in each element one uses the polynomial interpolant to compute u at the n d nodes gll mesh so that one obtains a new polynomial approximation the degree of which in each direction is then n 1 combined with a relaxation method this filtering of the highest frequencies is applied at each time step an important advantage of the technique is that interelement continuity and boundary conditions are preserved its efficiency for high reynolds number flows was demonstrated from results of numerical simulations in the present note we point out that this technique finds a simple interpretation in legendre spectral space and that this interpretation remains true when a chebyshev polynomial approximation is used although the result is easy to obtain it is not a priori obvious so that to our knowledge this viewpoint has not yet been clearly stated moreover we emphasize the link only briefly mentioned in the conclusion of 3 to the filtering procedure suggested in 2 and finally we consider the case of the fourier spectral method by extension to the trigonometric polynomials without loss of generality we can restrict ourselves to the one dimensional situation let 1 1 pn n n the space of the polynomials of maximum degree n defined on li n i 0 the set of the n 1 legendre polynomials of degree i and n i n i 0 the set of the gll nodes associated with pn i e those that solve 1 x2 l n x 0

sensitivity analysis in linear optimization invariant support set intervals abstract sensitivity analysis is one of the most interesting and preoccupying areas in optimization many attempts are made to investigate the problem s behavior when the input data changes usually variation occurs in the right hand side of the constraints and or the objective function coefficients degeneracy of optimal solutions causes considerable difficulties in sensitivity analysis in this paper we briefly review three types of sensitivity analysis and consider the question what is the range of the parameter where for each parameter value an optimal solution exists with exactly the same set of positive variables that the current optimal solution has this problem is coming from managerial requirements managers want to know in what range of variation of sources or prices in the market can they keep the installed production lines active and only production s levels would change

legendre pseudospectral viscosity method for nonlinear conservation laws in this paper the legendre spectral viscosity sv method for the approximate solution of initial boundary value problems associated with nonlinear conservation laws is studied the authors prove that by adding a small amount of sv bounded solutions of the legendre sv method converge to the exact scalar entropy solution the convergence proof is based on compensated compactness arguments and therefore applies to certain 2 times 2 systems finally numerical experiments for scalar as well as the one dimensional system of gas dynamics equations are presented which confirm the convergence of the legendre sv method moreover these numerical experiments indicate that by post processing the sv approximation one can recover the entropy solution within spectral accuracy

de aliasing on non uniform grids algorithms and applications we present de aliasing rules to be used when evaluating non linear terms with polynomial spectral methods on non uniform grids analogous to the de aliasing rules used in fourier spectral methods they are based upon the idea of super collocation followed by a galerkin projection of the non linear terms we demonstrate through numerical simulation that both accuracy and stability can be greatly enhanced through the use of this approach we begin by deriving from the numerical quadrature rules used by galerkin type projection methods the number of quadrature points and weights needed for quadratic and cubic non linearities we then present a systematic study of the effects of super collocation when using both a continuous galerkin and a discontinuous galerkin method to solve the one dimensional viscous burgers equation we conclude by examining three direct numerical simulation flow examples incompressible turbulent flow in a triangular duct incompressible turbulent flow in a channel at re 395 and compressible flow past a pitching airfoil at re 45 000

concentration phenomena of a semilinear elliptic equation with large advection in an ecological model abstract we consider a reaction diffusion advection equation arising from a biological model of migrating species the qualitative properties of the globally attracting solution are studied and in some cases the limiting profile is determined in particular a conjecture of cantrell cosner and lou on concentration phenomena is resolved under mild conditions applications to a related parabolic competition system are also discussed

positive steady states of reaction diffusion advection competition models in periodic environment abstract in this paper we consider the positive steady states for reaction diffusion advection competition models in the whole space with a spatially periodic structure under the spatially periodic setting we establish sufficient conditions for the existence of positive steady states of this model respectively by investigating the sign of the principal eigenvalue for some linearized eigenvalue problems as an application a lotka volterra reaction diffusion advection model for two competing species in a spatially periodic environment is considered finally some numerical simulations are presented to seek dynamical behaviors

on the gibbs phenomenon and its resolution the nonuniform convergence of the fourier series for discontinuous functions and in particular the oscillatory behavior of the finite sum was already analyzed by wilbraham in 1848 this was later named the gibbs phenomenon this article is a review of the gibbs phenomenon from a different perspective the gibbs phenomenon as we view it deals with the issue of recovering point values of a function from its expansion coefficients alternatively it can be viewed as the possibility of the recovery of local information from global information the main theme here is not the structure of the gibbs oscillations but the understanding and resolution of the phenomenon in a general setting the purpose of this article is to review the gibbs phenomenon and to show that the knowledge of the expansion coefficients is sufficient for obtaining the point values of a piecewise smooth function with the same order of accuracy as in the smooth case this is done by using the finite expansion series to construct a different rapidly convergent approximation

a stabilised nodal spectral element method for fully nonlinear water waves we present an arbitrary order spectral element method for general purpose simulation of non overturning water waves described by fully nonlinear potential theory the method can be viewed as a high order extension of the classical finite element method proposed by cai et al 1998 5 although the numerical implementation differs greatly features of the proposed spectral element method include nodal lagrange basis functions a general quadrature free approach and gradient recovery using global l 2 projections the quartic nonlinear terms present in the zakharov form of the free surface conditions can cause severe aliasing problems and consequently numerical instability for marginally resolved or very steep waves we show how the scheme can be stabilised through a combination of over integration of the galerkin projections and a mild spectral filtering on a per element basis this effectively removes any aliasing driven instabilities while retaining the high order accuracy of the numerical scheme the additional computational cost of the over integration is found insignificant compared to the cost of solving the laplace problem the model is applied to several benchmark cases in two dimensions the results confirm the high order accuracy of the model exponential convergence and demonstrate the potential for accuracy and speedup the results of numerical experiments are in excellent agreement with both analytical and experimental results for strongly nonlinear and irregular dispersive wave propagation the benefit of using a high order possibly adapted spatial discretisation for accurate water wave propagation over long times and distances is particularly attractive for marine hydrodynamics applications

a new method for chebyshev approximation of complex valued functions problems of this type appear in many connections and have been treated by various authors cf 2 12 13 considering the computation of best rational chebyshev approximations to complex valued functions by descent algorithms ellacott and williams 6 report that the main portion of computer time is spent in the solution of the linear subproblems they have applied the very slowly convergent lawson algorithm to these subproblems and they remark that a fast linear algorithm would bring about a significant improvement in efficiency in our paper we describe a new algorithm which seems to be the first one which works for the continuous case where t is not a finite set too in our method we transform the complex approximation problem into a real linear optimization problem with infinitely many constraints a so called semi infinite program sip cf 5 8 10 this is solved by a two step procedure in the first step we apply the stabilized simplex algorithm to a discrete approximation of the sip and in the second we make use of the newton raphson method in order to obtain very rapidly the solution of the sip and thus of our original approximation problem

hybridizable discontinuous galerkin projection methods for navier stokes and boussinesq equations schemes for the incompressible navier stokes and boussinesq equations are formulated and derived combining the novel hybridizable discontinuous galerkin hdg method a projection method and implicit explicit runge kutta imex rk time integration schemes we employ an incremental pressure correction and develop the corresponding hdg finite element discretization including consistent edge space fluxes for the velocity predictor and pressure correction we then derive the proper forms of the element local and hdg edge space final corrections for both velocity and pressure including the hdg rotational correction we also find and explain a consistency relation between the hdg stability parameters of the pressure correction and velocity predictor we discuss and illustrate the effects of the time splitting error we then detail how to incorporate the hdg projection method time split within standard imex rk time stepping schemes our high order hdg projection schemes are implemented for arbitrary mixed element unstructured grids with both straight sided and curved meshes in particular we provide a quadrature free integration method for a nodal basis that is consistent with the hdg method to prevent numerical oscillations we develop a selective nodal limiting approach its applications show that it can stabilize high order schemes while retaining high order accuracy in regions where the solution is sufficiently smooth we perform spatial and temporal convergence studies to evaluate the properties of our integration and selective limiting schemes and to verify that our solvers are properly formulated and implemented to complete these studies and to illustrate a range of properties for our new schemes we employ an unsteady tracer advection benchmark a manufactured solution for the steady diffusion and stokes equations and a standard lock exchange boussinesq problem

sensitivity analysis in linear semi infinite programming perturbing cost and right hand side coefficients this paper analyzes the effect on the optimal value of a given linear semi infinite programming problem of the kind of perturbations which more frequently arise in practical applications those which affect the objective function and the right hand side coefficients of the constraints in particular we give formulae which express the exact value of a perturbed problem as a linear function of the perturbation

optimality conditions in convex multiobjective sip the purpose of this paper is to characterize the weak efficient solutions the efficient solutions and the isolated efficient solutions of a given vector optimization problem with finitely many convex objective functions and infinitely many convex constraints to do this we introduce new and already known data qualifications conditions involving the constraints and or the objectives in order to get optimality conditions which are expressed in terms of either karusk kuhn tucker multipliers or a new gap function associated with the given problem

convergence of spectral methods for nonlinear conservation laws we discuss the convergence of fourier methods for scalar nonlinear conservation laws that exhibit spontaneous shock discontinuities numerical tests indicate that the convergence may and in fact in some cases we prove it must fail with or without post processing of the numerical solution instead we introduce here a new kind of spectrally accurate vanishing viscosity to augment the fourier approximation of such nonlinear conservation laws using compensated compactness arguments augmented by the assumption of l infty stability we show for the inviscid burgers model equation that this spectral viscosity method prevents oscillations and convergence to the unique entropy solution follows

a general parametric analysis approach and its implication to sensitivity analysis in interior point methods adler and monteiro 1992 developed a parametric analysis approach that is naturally related to the geometry of the linear program this approach is based on the availability of primal and dual optimal solutions satisfying strong complementarity in this paper we develop an alternative geometric approach for parametric analysis which does not require the strong complementarity condition this parametric analysis approach is used to develop range and marginal analysis techniques which are suitable for interior point methods two approaches are developed namely the lu factorization approach and the affine scaling approach

a stochastic galerkin method for the boltzmann equation with uncertainty we develop a stochastic galerkin method for the boltzmann equation with uncertainty the method is based on the generalized polynomial chaos gpc approximation in the stochastic galerkin framework and can handle random inputs from collision kernel initial data or boundary data we show that a simple singular value decomposition of gpc related coefficients combined with the fast fourier spectral method in velocity space allows one to compute the high dimensional collision operator very efficiently in the spatially homogeneous case we first prove that the analytical solution preserves the regularity of the initial data in the random space and then use it to establish the spectral accuracy of the proposed stochastic galerkin method several numerical examples are presented to illustrate the validity of the proposed scheme

stable zero duality gaps in convex programming complete dual characterisations with applications to semidefinite programs the zero duality gap that underpins the duality theory is one of the central ingredients in optimisation in convex programming it means that the optimal values of a given convex program and its associated dual program are equal it allows in particular the development of efficient numerical schemes however the zero duality gap property does not always hold even for finite dimensional problems and it frequently fails for problems with non polyhedral constraints such as the ones in semidefinite programming problems over the years various criteria have been developed ensuring zero duality gaps for convex programming problems in the present work we take a broader view of the zero duality gap property by allowing it to hold for each choice of linear perturbation of the objective function of the given problem globalising the property in this way permits us to obtain complete geometric dual characterisations of a stable zero duality gap in terms of epigraphs and conjugate functions for convex semidefinite programs we establish necessary and sufficient dual conditions for stable zero duality gaps as well as for a universal zero duality gap in the sense that the zero duality gap property holds for each choice of constraint right hand side and convex objective function zero duality gap results for second order cone programming problems are also given our approach makes use of elegant conjugate analysis and fenchel s duality

sensitivity analysis in linear programming just be careful in this paper we review the topic of sensitivity analysis in linear programming we describe the problems that may occur when using standard software and advocate a framework for performing complete sensitivity analysis three approaches can be incorporated within it one using bases an approach using the optimal partition and one using optimal values we elucidate problems and solutions with an academic example and give results from an implementation of these approaches to a large practical linear programming model of an oil refinery this shows that the approaches are viable and useful in practice

duality gaps in semi infinite linear programming an approximation problem this paper builds upon the relationship between the objective function of a semi infinite linear program and its constraints to identify a class of semi infinite linear programs which do not have a duality gap the key idea is to guarantee the approximation of the primal program by a sequence of linear programs where thenth approximating program is to minimize the objective function subject to the firstn constraints the paper goes on to show that any program not in the identified class can be linearly perturbed into it with the optimal value of the perturbed program converging to the optimal value of the original program the results are then extended to the case when an uncountable number of constraints are present by reducing this case to the countable case

strong duality and sensitivity analysis in semi infinite linear programming finite dimensional linear programs satisfy strong duality sd and have the dual pricing dp property the dp property ensures that given a sufficiently small perturbation of the right hand side vector there exists a dual solution that correctly prices the perturbation by computing the exact change in the optimal objective function value these properties may fail in semi infinite linear programming where the constraint vector space is infinite dimensional unlike the finite dimensional case in semi infinite linear programs the constraint vector space is a modeling choice we show that for a sufficiently restricted vector space both sd and dp always hold at the cost of restricting the perturbations to that space the main goal of the paper is to extend this restricted space to the largest possible constraint space where sd and dp hold once sd or dp fail for a given constraint space then these conditions fail for all larger constraint spaces we give sufficient conditions for when sd and dp hold in an extended constraint space our results require the use of linear functionals that are singular or purely finitely additive and thus not representable as finite support vectors we use the extension of the fourier motzkin elimination procedure to semi infinite linear systems to understand these linear functionals

sensitivity analysis in linear semi infinite programming via partitions this paper provides sufficient conditions for the optimal value function of a given linear semi infinite programming lsip problem to depend linearly on the size of the perturbations when these perturbations involve either the cost coefficients or the right hand side function or both and they are sufficiently small two kinds of partitions are considered the first concerns the effective domain of the optimal value as a function of the cost coefficients and consists of maximal regions on which this value function is linear the second class of partitions considered in this paper concerns the index set of the constraints through a suitable extension of the concept of optimal partition from ordinary to lsip these partitions provide convex sets in particular segments on which the optimal value is a linear function of the size of the perturbations for the three types of perturbations considered in this paper

advection mediated competition in general environments abstract we consider a reaction diffusion advection system of two competing species with one of the species dispersing by random diffusion as well as a biased movement upward along resource gradient while the other species by random diffusion only it has been shown that under some non degeneracy conditions on the environment function the two species always coexist when the advection is strong in this paper we show that for general smooth environment function in contrast to what is known there can be competitive exclusion when the advection is strong and we give a sharp criterion for coexistence that includes all previously considered cases moreover when the domain is one dimensional we derive in the strong advection limit a system of two equations defined on different domains uniqueness of steady states of this non standard system is obtained when one of the diffusion rates is large

generalised summation by parts operators and variable coefficients abstract high order methods for conservation laws can be highly efficient if their stability is ensured a suitable means mimicking estimates of the continuous level is provided by summation by parts sbp operators and the weak enforcement of boundary conditions recently there has been an increasing interest in generalised sbp operators both in the finite difference and the discontinuous galerkin spectral element framework however if generalised sbp operators are used the treatment of the boundaries becomes more difficult since some properties of the continuous level are no longer mimicked discretely interpolating the product of two functions will in general result in a value different from the product of the interpolations thus desired properties such as conservation and stability are more difficult to obtain here new formulations are proposed allowing the creation of discretisations using general sbp operators that are both conservative and stable thus several shortcomings that might be attributed to generalised sbp operators are overcome cf nordstrom and ruggiu 2017 38 and manzanero et al 2017 39

a stable penalty method for the compressible navier stokes equations i open boundary conditions the purpose of this paper is to present asymptotically stable open boundary conditions for the numerical approximation of the compressible navier stokes equations in three spatial dimensions the treatment uses the conservation form of the navier stokes equations and utilizes linearization and localization at the boundaries based on these variables the proposed boundary conditions are applied through a penalty procedure thus ensuring correct behavior of the scheme as the reynolds number tends to infinity the versatility of this method is demonstrated for the problem of a compressible flow past a circular cylinder

on the dimension of the set of rim perturbations for optimal partition invariance two new dimension results are presented for linear programs it is shown that the sum of the dimension of the optimal set and the dimension of the set of objective perturbations for which the optimal partition is invariant equals the number of variables a decoupling principle shows that the primal and dual results are additive the main result is then extended to convex quadratic programs but the dimension relationships are no longer dependent only on problem size furthermore although the decoupling principle does not extend completely the dimensions are additive as in the linear case

pseudo lipschitz property of linear semi infinite vector optimization problems this paper is devoted to the study of the pseudo lipschitz property of pareto solution map for the parametric linear semi infinite vector optimization problem lsvo we establish new sufficient conditions for the pseudo lipschitz property of the pareto solution map of lsvo under continuous perturbations of the right hand side of the constraints and linear perturbations of the objective function examples are given to illustrate the results obtained

the numerical solution of the inverse stefan problem in two space variables a method is given for solving the inverse stefan problem for the heat equation in two space variables the approach is based on using a complete family of solutions to the heat equation thus reducing the dimensionality of the problem by one and minimizing the maximal defect in the initial boundary data subject to regularizing constraints thus making the problem well posed in the sense that the solution now depends continuously on the data two numerical examples are given which make use of a linear semi infinite programming method recently developed by hettich and zencke

idempotent filtering in spectral and spectral element methods the comparison of numerical results for implicit explicit and fully explicit runge kutta time integration methods for a nozzle flow problem shows that filtering can significantly degrade the accuracy of the numerical solution for long time integration problems we demonstrate analytically and numerically that filtering in time errors become additive for u n x t k dt u n x t u n x t when nonidempotent filters are used and suggest the development and implementation of idempotent filters

stability of pseudospectral and finite difference methods for variable coefficient problems it is shown that pseudospectral approximation to a special class of variable coefficient one dimensional wave equations is stable and convergent even though the wave speed changes sign within the domain computer experiments indicate similar results are valid for more general problems similarly computer results indicate that the leapfrog finite difference scheme is stable even though the wave speed changes sign within the domain however both schemes can be asymptotically unstable in time when a fixed spatial mesh is used

analysis of the spectral vanishing viscosity method for periodic conservation laws the convergence of the spectral vanishing method for both the spectral and pseudospectral discretizations of the inviscid burgers equation is analyzed it is proved that this kind of vanishing viscosity is responsible for spectral decay of those fourier coefficients located toward the end of the computed spectrum consequently the discretization error is shown to be spectrally small independently of whether or not the underlying solution is smooth this in turn implies that the numerical solution remains uniformly bounded and convergence follows by compensated compactness arguments

does movement toward better environments always benefit a population abstract we study the effects of advection along environmental gradients on logistic reaction diffusion models for population growth the local population growth rate is assumed to be spatially inhomogeneous and the advection is taken to be a multiple of the gradient of the local population growth rate it is also assumed that the boundary acts as a reflecting barrier to the population we show that the effects of such advection depend crucially on the shape of the habitat of the population if the habitat is convex the movement in the direction of the gradient of the growth rate is always beneficial to the population while such advection could be harmful for certain non convex habitats

spectral methods for hyperbolic problems we review the current state of fourier and chebyshev collocation methods for the solution of hyperbolic problems with an eye to basic questions of accuracy and stability of the numerical approximations throughout the discussion we emphasize recent developments in the area such as spectral penalty methods the use of filters the resolution of the gibbs phenomenon and issues related to the solution of nonlinear conservations laws such as conservation and convergence we also include a brief discussion on the formulation of multi domain methods for hyperbolic problems and conclude with a few examples of the application of pseudospectral collocation methods for solving nontrivial systems of conservation laws

projection a unified approach to semi infinite linear programs and duality in convex programming fourier motzkin elimination is a projection algorithm for solving finite linear programs we extend fourier motzkin elimination to semi infinite linear programs which are linear programs with finitely many variables and infinitely many constraints applying projection leads to new characterizations of important properties for primal dual pairs of semi infinite programs such as zero duality gap feasibility boundedness and solvability extending the fourier motzkin elimination procedure to semi infinite linear programs yields a new classification of variables that is used to determine the existence of duality gaps in particular the existence of what the authors term dirty variables can lead to duality gaps our approach has interesting applications in finite dimensional convex optimization for example sufficient conditions for a zero duality gap such as the slater constraint qualification are reduced to guaranteeing that there are no dirty variables this leads to completely new proofs of such sufficient conditions for zero duality