the discontinuous enrichment method for medium frequency helmholtz problems with a spatially variable wavenumber numerical dispersion or what is often referred to as the pollution effect presents a challenge to an efficient finite element discretization of the helmholtz equation in the medium frequency regime to alleviate this effect and improve the unsatisfactory pre asymptotic convergence of the classical galerkin finite element method based on piecewise polynomial basis functions several discretization methods based on plane wave bases have been proposed among them is the discontinuous enrichment method that has been shown to offer superior performance to the classical galerkin finite element method for a number of constant wavenumber helmholtz problems and has also outperformed two representative methods that use plane waves the partition of unity and the ultra weak variation formulation methods in this paper the discontinuous enrichment method is extended to the variable wavenumber helmholtz equation to this effect the concept of enrichment functions based on free space solutions of the homogeneous form of the governing differential equation is enlarged to include free space solutions of approximations of this equation obtained in this case by successive taylor series expansions of the wavenumber around a reference point this leads to plane wave enrichment functions based on the piece wise constant approximation of the wavenumber and to airy wave enrichment functions several elements based on these enrichment functions are constructed and evaluated on benchmark problems modeling sound hard scattering by a disk submerged in an acoustic fluid where the speed of sound varies in space all these elements are shown to outperform by a substantial margin their continuous polynomial counterparts

a local projection type stabilization with exponential enrichments applied to one dimensional advection diffusion equations abstract we consider the local projection stabilization lps for solving a singularly perturbed advection diffusion two point boundary value problem in its classical one level variant the lps uses polynomial bubble functions to enrich the standard finite element spaces of continuous piecewise polynomial functions as recently shown the two level approach can be considered also as a one level method however with piecewise polynomial enrichments here we study the question under which condition a linearly independent h1 function can serve as an enrichment for the standard space of continuous piecewise polynomials of degree r leading to the same type of error estimates for the solution as the original one and two level approaches moreover in the constant coefficient case we derive formulas for the user chosen stabilization parameter which guarantee that the piecewise linear part of the solution becomes nodal exact finally we choose exponential enrichments based on the asymptotic expansion of the solution and show by numerical tests that compared to the classical one level variant of the lps a considerable improvement of the accuracy of the solution on non layer adapted meshes can be achieved

an efficient newton barrier method for minimizing a sum of euclidean norms a new newton barrier method is proposed for minimizing a sum of euclidean norms msn f x sum i 1 k a i t x b i 2 msn is a nonsmooth problem because f is not differentiable at any point x where any of the norms is zero the method used is based on approximating f with a smooth function which in the limit has the same optimal value as f msn is shown to have a dual problem with properties very similar to duality theory in linear programming this is used in the development of the method and to give a proof of when an optimal solution for the smooth approximation is epsilon optimal measured in the duality gap for the original problem an implementation of the algorithm is described for large sparse problems and numerical results are presented for problems with more than 270 000 nonlinear variables these problems arise from plastic collapse analysis

a hybrid discontinuous galerkin method for computing the ground state solution of bose einstein condensates a numerical method for computing the ground state solution of bose einstein condensates modeled by the gross pitaevskii equation is presented in this method the three dimensional computational domain is divided into hexahedral elements in which the solution is approximated by a sum of basis functions both polynomial and plane wave bases are considered for this purpose and lagrange multipliers are introduced to weakly enforce the interelement continuity of the solution the ground state is computed by an iterative procedure for minimizing the energy the performance results obtained for several numerical experiments demonstrate that the proposed method is more computationally efficient than similar solution approaches based on the standard higher order finite element method

model predictive control of discrete hybrid stochastic automata this paper focuses on optimal and receding horizon control of a class of hybrid dynamical systems called discrete hybrid stochastic automata dhsa whose discrete state transitions depend on both deterministic and stochastic events a finite time optimal control approach optimistically determines the trajectory that provides the best tradeoff between tracking performance and the probability of the trajectory to actually execute under possible chance constraints the approach is also robustified less optimistically to ensure that the system satisfies a set of constraints for all possible realizations of the stochastic events or alternatively for those having enough probability to realize sufficient conditions for asymptotic convergence in probability are given for the receding horizon implementation of the optimal control solution the effectiveness of the suggested stochastic hybrid control techniques is shown on a case study in supply chain management

multi agent motion planning for nonlinear gaussian systems in this paper a multi agent motion planner is developed for nonlinear gaussian systems using a combination of probabilistic approaches and a rapidly exploring random tree rrt algorithm a closed loop model consisting of a controller and estimation loops is used to predict future distributions to manage the level of uncertainty in the path planner the closed loop model assumes the existence of a feedback control law that drives the actual system towards a nominal system this ensures the uncertainty in the evolution does not grow significantly and the tracking errors are bounded to trade conservatism with the risk of infeasibility and failure we use probabilistic constraints to limit the probability of constraint violation the probability of leaving the configuration space is included by using a chance constraint approach and the probability of closeness between two agents is imposed using an overlapping coefficient approach we augment these approaches with the rrt algorithm to develop a robust pat

a discontinuous hp finite element method for diffusion problems 1 d analysis abstract this paper presents the mathematical analysis of a new variant of the discontinuous galerkin method which is applicable to the numerical solution of diffusion problems not requiring auxiliary variables such as those used in mixed methods the focus of this study is on a class of linear second order boundary value problems for which we prove stability and a priori error estimates in both the finite and infinite dimensional spaces

a monotone finite element method with test space of legendre polynomials this paper is concerned with the development of a multi dimensional monotone scheme to deal with erroneous oscillations in regions where sharp gradients exist the strategy behind the underlying finite element analysis is the accommodation of the m matrix to the petrov galerkin finite element model an irreducible diagonal dominated coefficient matrix is rendered through the use of exponential weighting functions with a priori knowledge capable of leading to a monotone matrix the analysis model is well conditioned with the monotonicity preserving property in order to stress the effectiveness of test functions in resolving oscillations we considered two classes of the convection diffusion problem as seen from the computed results we can classify the proposed finite element model as legitimate for the problem free of boundary layer also through the use of this model we can capture the solution for the problem involving a high gradient in this study we are interested in a cost effective method which ensures monotonicity irrespective of the value of the peclet number throughout the entire domain to gain access to these desired properties it is tempting to bring in the legendre polynomials and the characteristic information so that by virtue of the inherent orthogonal property the integral can be obtained exactly by two gaussian integration points along each spatial direction while maintaining stability in the m matrix satisfaction sense

efficient adaptive integration of functions with sharp gradients and cusps in n dimensional parallelepipeds summary in this paper we study the efficient numerical integration of functions with sharp gradients and cusps an adaptive integration algorithm is presented that systematically improves the accuracy of the integration of a set of functions the algorithm is based on a divide and conquer strategy and is independent of the location of the sharp gradient or cusp the error analysis reveals that for a c0 function derivative discontinuity at a point a rate of convergence of n 1 is obtained in rn two applications of the adaptive integration scheme are studied first we use the adaptive quadratures for the integration of the regularized heaviside function a strongly localized function that is used for modeling sharp gradients then the adaptive quadratures are employed in the enriched finite element solution of the all electron coulomb problem in crystalline diamond the source term and enrichment functions of this problem have sharp gradients and cusps at the nuclei we show that the optimal rate of convergence is obtained with only a marginal increase in the number of integration points with respect to the pure finite element solution with the same number of elements the adaptive integration scheme is simple robust and directly applicable to any generalized finite element method employing enrichments with sharp local variations or cusps in n dimensional parallelepiped elements copyright 2012 john wiley sons ltd

extension of karmarkar s algorithm onto convex quadratically constrained quadratic problems convex quadratically constrained quadratic problems are considered it is shown that such problems can be transformed to aconic form the feasible set of the conic form is the intersection of a direct product of standard quadratic cones intersected with a hyperplane the analogue of a simplex and a linear subspace for a problem of such form the analogue of karmarkar s projective transformation and logarithmic barrier function are built this allows us to extend word by word the method of karmarkar for lp to qcqp and allows us to obtain a similar polynomial worst case bound for the number of iterations

robust state feedback stabilization of discrete time uncertain dynamical systems the problem of stabilization of a class of discrete time dynamic systems containing uncertain elements using the direct method of lyapunov is considered state feedback controllers that guarantee uniform boundedness and uniform ultimate boundedness of the closed loop system are proposed

a nonlinear primal dual method for total variation based image restoration we present a new method for solving total variation tv minimization problems in image restoration the main idea is to remove some of the singularity caused by the nondifferentiability of the quantity nabla u in the definition of the tv norm before we apply a linearization technique such as newton s method this is accomplished by introducing an additional variable for the flux quantity appearing in the gradient of the objective function which can be interpreted as the normal vector to the level sets of the image u our method can be viewed as a primal dual method as proposed by conn and overton a primal dual interior point method for minimizing a sum of euclidean norms preprint 1994 and andersen ph d thesis odense university denmark 1995 for the minimization of a sum of euclidean norms in addition to possessing local quadratic convergence experimental results show that the new method seems to be globally convergent

a discontinuous enrichment method for three dimensional multiscale harmonic wave propagation problems in multi fluid and fluid solid media an evanescent wave occurs when a propagating incident wave impinges on an interface between two fluid solid or fluid solid media at a subcritical angle mathematical properties of such a wave make it difficult to capture with standard finite element discretization schemes for this reason the discontinuous enrichment method dem developed in comput methods appl mech eng 2001 190 6455 6479 comput methods appl mech eng 2003 192 1389 1419 comput methods appl mech eng 2003 192 3195 3210 int j numer meth engng 2004 61 1938 1956 wave motion 2004 39 4 307 317 int j numer meth engng 2006 66 2086 2114 int j numer meth engng 2006 66 796 815 is extended here to the solution of a class of three dimensional evanescent wave problems in the frequency domain to this effect new dem elements for three dimensional elastodynamic problems are first proposed then these and other dem elements previously developed for the efficient solution of the helmholtz problem are further enriched with free space solutions of model evanescent wave problems in order to achieve high accuracy at practical mesh resolution for fluid fluid and fluid solid applications the performance of the extended dem elements is reported to be better than that of its basic helmholtz and navier counterparts and superior to that achieved by the classical high order polynomial finite element method copyright 2008 john wiley sons ltd

a new method for optimal truss topology design truss topology optimization formulated in terms of displacements and bar volumes results in a large nonconvex optimization problem for the case of maximization of stiffness for a prescribed volume this paper presents a new equivalent an unconstrained and convex minimization problem in displacements only where the function to be minimized is the sum of terms each of which is the maximum of two convex quadratic functions existence of solutions is proved as is the convergence of a nonsmooth steepest descent type algorithm for solving the topology optimization problem the algorithm is computationally attractive and has been tested on a large number of examples some of which are presented

applications of the pseudo residual free bubbles to the stabilization of convection diffusion problems abstract residual free bubbles have been recently introduced in order to compute optimal values for the stabilization methods a la hughes franca however unless in very special situations one dimensional problems limit cases etc they require the actual solution of pde problems the bubble problems in each element thus they are very difficult to be used in practice in this paper we present for the special case of convection dominated elliptic problems a cheap way to compute approximately the solution of the bubble problem in each element this provides as a consequence a cheap way to compute good approximations for the optimal values of the stabilization parameters

stochastic mpc with inequality stability constraints stochastic uncertainty is a common feature of many control engineering problems and is also present in a wider class of applications e g finance and sustainable development recent work proposed a constrained mpc approach that took explicit account of the distributions of uncertain model parameters but used terminal equality constraints to ensure stability the present paper reformulates the problem in order to relax the stability constraints by invoking appropriate terminal inequalities the application of the proposed strategy and its advantages over earlier work are illustrated by means of a numerical example

streamline design of stability parameters for advection diffusion problems the dependence of the computation of advective diffusive transport phenomena on the orientation of the mesh with respect to the flow direction is analyzed poor performance of the classical galerkin finite element method in the convection dominated regime is alleviated by stabilization we propose definitions of the stability parameter that rationally incorporate the flow direction numerical tests compare the performance of the proposed methods with established techniques

a novel exponentially fitted triangular finite element method for an advection diffusion problem with boundary layers in this paper we develop an exponentially fitted finite element method for a singularly perturbed advection diffusion problem with a singular perturbation parameter this finite element method is based on a set of novel piecewise exponential basis functions constructed on unstructured triangular meshes the basis functions can not be expressed explicitly but the values of each of them and its associated flux at a point are determined by a set of two point boundary value problems which can be solved exactly a method for evaluating elements of the stiffness matrix is also proposed for the case that is small numerical results presented to validate the method show that the method is stable for a large range of it is also shown by the numerical results that the rate of convergence of the method in an energy norm is of orderh1 2when is small

convexity and convex approximations of discrete time stochastic control problems with constraints we investigate constrained optimal control problems for linear stochastic dynamical systems evolving in discrete time we consider minimization of an expected value cost subject to probabilistic constraints we study the convexity of a finite horizon optimization problem in the case where the control policies are affine functions of the disturbance input we propose an expectation based method for the convex approximation of probabilistic constraints with polytopic constraint function and a linear matrix inequality lmi method for the convex approximation of probabilistic constraints with ellipsoidal constraint function finally we introduce a class of convex expectation type constraints that provide tractable approximations of the so called integrated chance constraints performance of these methods and of existing convex approximation methods for probabilistic constraints is compared on a numerical example

a new finite element formulation for computational fluid dynamics viii the galerkin least squares method for advective diffusive equations abstract galerkin least squares finite element methods are presented for advective diffusive equations galerkin least squares represents a conceptual simplification of supg and is in fact applicable to a wide variety of other problem types a convergence analysis and error estimates are presented

exponential finite elements for diffusion advection problems a new finite element method for the solution of the diffusion advection equation is proposed the method uses non isoparametric exponentially varying interpolation functions based on exact one and two dimensional solutions of the laplace transformed differential equation two eight noded elements are developed and tested for convergence stability peclet number limit anisotropy material heterogeneity dirichlet and neumann boundary conditions and tolerance for mesh distortions their performance is compared to that of conventional eight and 12 noded polynomial elements the exponential element based on two dimensional analytical solutions fails basic tests of convergence the one based on one dimensional solutions performs particularly well it reduces by about 75 the number of elements and degrees of freedom required for convergence yielding an error that is one order of magnitude smaller than that of the eight noded polynomial element the exponential element is stable and robust under relatively high degrees of heterogeneity anisotropy and mesh distortions copyright 2005 john wiley sons ltd

higher order extensions of a discontinuous galerkin method for mid frequency helmholtz problems recently a discontinuous galerkin method with plane wave basis functions and lagrange multiplier degrees of freedom was proposed for the efficient solution of helmholtz problems in the mid frequency regime in this paper this method is extended to higher order elements performance results obtained for various two dimensional problems highlight the advantages of these elements over classical higher order galerkin elements such as q2 and q4 for the discretization of interior and exterior helmholtz problems copyright 2004 john wiley sons ltd

an efficient primal dual interior point method for minimizing a sum of euclidean norms the problem of minimizing a sum of euclidean norms dates from the 17th century and may be the earliest example of duality in the mathematical programming literature this nonsmooth optimization problem arises in many different kinds of modern scientific applications we derive a primal dual interior point algorithm for the problem by applying newton s method directly to a system of nonlinear equations characterizing primal and dual feasibility and a perturbed complementarity condition the main work at each step consists of solving a system of linear equations the schur complement equations this schur complement matrix is not symmetric unlike in linear programming we incorporate a mehrotra type predictor corrector scheme and present some experimental results comparing several variations of the algorithm including as one option explicit symmetrization of the schur complement with a skew corrector term we also present results obtained from a code implemented to solve large sparse problems using a symmetrized schur complement this has been applied to problems arising in plastic collapse analysis with hundreds of thousands of variables and millions of nonzeros in the constraint matrix the algorithm typically finds accurate solutions in less than 50 iterations and determines physically meaningful solutions previously unobtainable

an approach to output feedback mpc of stochastic linear discrete time systems in this paper we propose an output feedback model predictive control mpc algorithm for linear discrete time systems affected by a possibly unbounded additive noise and subject to probabilistic constraints in case the noise distribution is unknown the probabilistic constraints on the input and state variables are reformulated by means of the chebyshev cantelli inequality the recursive feasibility is guaranteed the convergence of the state to a suitable neighbor of the origin is proved under mild assumptions and the implementation issues are thoroughly addressed two examples are discussed in detail with the aim of providing an insight into the performance achievable by the proposed control scheme

the scenario approach for stochastic model predictive control with bounds on closed loop constraint violations many practical applications in control require that constraints on the inputs and states of the system are respected while some performance criterion is optimized in the presence of model uncertainties or disturbances it is often sufficient to satisfy the state constraints for at least a prescribed share of the time such as in building climate control or load mitigation for wind turbines for such systems this paper presents a new method of scenario based model predictive control scmpc the basic idea is to optimize the control inputs over a finite horizon subject to robust constraint satisfaction under a finite number of random scenarios of the uncertainty and or disturbances previous scmpc approaches have suffered from a substantial gap between the rate of constraint violations specified in the optimal control problem and that actually observed in closed loop operation of the controlled system this paper identifies the two theoretical explanations for this gap first accounting for the special structure of the optimal control problem leads to a substantial reduction of the problem dimension second the probabilistic constraints have to be interpreted as average in time rather than pointwise in time based on these insights a novel scmpc method can be devised for general linear systems with additive and multiplicative disturbances for which the number of scenarios is significantly reduced the presented method retains the essential advantages of the general scmpc approach namely a low computational complexity and the ability to handle arbitrary probability distributions moreover the computational complexity can be adjusted by a sample and remove strategy

a hybrid discontinuous in space and time galerkin method for wave propagation problems summary medium frequency regime and multi scale wave propagation problems have been a subject of active research in computational acoustics recently new techniques have attempted to overcome the limitations of existing discretization methods that tend to suffer from dispersion one such technique the discontinuous enrichment method incorporates features of the governing partial differential equation in the approximation in particular the solutions of the homogeneous form of the equation here based on this concept and by extension of a conventional space time finite element method a hybrid discontinuous galerkin method dgm for the numerical solution of transient problems governed by the wave equation in two and three spatial dimensions is described the discontinuous formulation in both space and time enables the use of solutions to the homogeneous wave equation in the approximation in this contribution within each finite element the solutions in the form of polynomial waves are employed the continuity of these polynomial waves is weakly enforced through suitably chosen lagrange multipliers results for two dimensional and three dimensional problems in both low frequency and medium frequency regimes show that the proposed dgm outperforms the conventional space time finite element method copyright 2014 john wiley sons ltd

a discontinuous galerkin method with lagrange multipliers for spatially dependent advection diffusion problems abstract a higher accuracy discontinuous galerkin method with lagrange multipliers dglm is presented for the solution of the advection diffusion equation with a spatially varying advection field in the high peclet number regime where the classical polynomial finite element method fem produces spurious oscillations in the solution at practical mesh resolutions the proposed dglm method is based on discontinuous polynomial shape functions that are attached to an element rather than its nodes it overcomes the aforementioned spurious oscillation issue by enriching these functions with approximate free space solutions of homogeneous equations derived from an asymptotic analysis of the governing partial differential equation inspired by prandtl s boundary layer theory these enrichment functions are capable of resolving exponential parabolic and corner boundary layers at relatively coarse mesh resolutions the proposed method enforces a weak continuity of the solution approximation across inter element boundaries using polynomial lagrange multipliers which makes it a hybrid method however unlike other hybrid methods it operates directly on the second order form of the advection diffusion equation and does not require any stabilization its intrinsic performance and its superiority over the higher order polynomial fem are demonstrated for several test problems at peclet numbers ranging from one thousand to one billion

applications of second order cone programming in a second order cone program socp a linear function is minimized over the intersection of an affine set and the product of second order quadratic cones socps are nonlinear convex problems that include linear and convex quadratic programs as special cases but are less general than semidefinite programs sdps several efficient primaldual interior point methods for socp have been developed in the last few years after reviewing the basic theory of socps we describe general families of problems that tan be recast as socps these include robust linear programming and robust leastsquares problems problems involving sums or maxima of norms or with convex hyperbolic constraints we discuss a variety of engineering applications such as filter design antenna array weight design truss design and grasping forte optimization in robotics we describe an efficient primaldual interior point method for solving socps which shares many of the features of primaldual interior point methods for linear program

brief a probabilistically constrained model predictive controller we propose a novel control algorithm probabilistically constrained predictive control to deal with the uncertainties of system disturbances the output is to be controlled in the constrained range with a desired probability under the assumption of a linear system the formulated joint probabilistically constrained problem is convex thus it can be solved with a nonlinear programming solver the probabilities and gradients of the constraints composed of disturbance sequences with multivariate normal distribution are computed using an efficient simulation approach the results of a test problem show the effectiveness of the proposed algorithm

a riccati based interior point algorithm for the computation in constrained stochastic mpc we propose a fast algorithm for the linear quadratic control problem with probabilistic constraints that is repeatedly solved in stochastic model predictive control under the assumption of affine state feedback and gaussian noise the finite horizon control problem is converted to an equivalent deterministic problem using the mean and covariance matrix as the state a line search interior point method is proposed to solve this optimization problem where the step direction can be quickly computed via a riccati difference equation numerical examples show that this algorithm has linear complexity in the horizon length

stabilizing model predictive control of stochastic constrained linear systems this paper investigates stochastic stabilization procedures based on quadratic and piecewise linear lyapunov functions for discrete time linear systems affected by multiplicative disturbances and subject to linear constraints on inputs and states a stochastic model predictive control smpc design approach is proposed to optimize closed loop performance while enforcing constraints conditions for stochastic convergence and robust constraints fulfillment of the closed loop system are enforced by solving linear matrix inequality problems off line performance is optimized on line using multistage stochastic optimization based on enumeration of scenarios that amounts to solving a quadratic program subject to either quadratic or linear constraints in the latter case an explicit form is computable to ease the implementation of the proposed smpc law the approach can deal with a very general class of stochastic disturbance processes with discrete probability distribution the effectiveness of the proposed smpc formulation is shown on a numerical example and compared to traditional mpc schemes

two level finite element method and its application to the helmholtz equation a two level finite element method is introduced and its application to the helmholtz equation is considered the method retains the desirable features of the galerkin method enriched with residual free bubbles while it is not limited to discretizations using elements with simple geometry the method can be applied to other equations and to irregular shaped domains

brief paper explicit use of probabilistic distributions in linear predictive control the guarantee of feasibility given feasibility at initial time is an issue that has been overlooked by many of the recent papers on stochastic model predictive control effective solutions have recently been proposed but these carry considerable online computational load and a degree of conservativism for the case that the elements of the random additive disturbance vector are independent the current paper ensures that probabilistic constraints are met and that a quadratic stability condition is satisfied a numerical example illustrates the efficacy of the proposed algorithm which achieves tight satisfaction of constraints and thereby attains near optimal performance

probabilistic tubes in linear stochastic model predictive control this paper considers constrained control of linear systems with additive and multiplicative stochastic uncertainty and linear input state constraints both hard and soft constraints are considered and bounds are imposed on the probability of soft constraint violation assuming the plant parameters to be finitely supported a method of constraint handling is proposed in which a sequence of tubes corresponding to a sequence of confidence levels on the predicted future plant state is constructed online around nominal state trajectories a set of linear constraints is derived by imposing bounds on the probability of constraint violation at each point on an infinite prediction horizon through constraints on one step ahead predictions a guarantee of the recursive feasibility of the online optimization ensures that the closed loop system trajectories satisfy both the hard and probabilistic soft constraints the approach is illustrated by a numerical example

stochastic tubes in model predictive control with probabilistic constraints stochastic model predictive control mpc strategies can provide guarantees of stability and constraint satisfaction but their online computation can be formidable this difficulty is avoided in the current technical note through the use of tubes of fixed cross section and variable scaling a model describing the evolution of predicted tube scalings facilitates the computation of stochastic tubes furthermore this procedure can be performed offline the resulting mpc scheme has a low online computational load even for long prediction horizons thus allowing for performance improvements the efficacy of the approach is illustrated by numerical examples

model predictive control for systems with stochastic multiplicative uncertainty and probabilistic constraints abstract robust predictive control handles constrained systems that are subject to stochastic uncertainty but propagating the effects of uncertainty over a prediction horizon can be computationally expensive and conservative this paper overcomes these issues through an augmented autonomous prediction formulation and provides a method of handling probabilistic constraints and ensuring closed loop stability through the use of an extension of the concept of invariance namely invariance with probability p

a logarithmic barrier function algorithm for quadratically constrained convex quadratic programming an interior point method for quadratically constrained convex quadratic programming is presented that is based on a logarithmic barrier function approach and terminates at a required accuracy of an approximate solution in polynomial time this approach generates a sequence of unconstrained optimization problems each of which is approximately solved by taking a single step in a newton direction

bubble functions prompt unusual stabilized finite element methods a second order linear scalar differential equation including a zero th order term is approximated using first the standard galerkin method enriched with bubble functions static condensation of the bubbles suggest an unusual stabilized finite element method for which we establish a convergence study and obtain successful numerical simulations the method is generalized to allow for a convection operator in the equation this work may be employed as a starting point for simulation of nonlinear equations governing turbulence phenomena flows with chemical reactions and other important problems

three dimensional discontinuous galerkin elements with plane waves and lagrange multipliers for the solution of mid frequency helmholtz problems recently a discontinuous galerkin finite element method with plane wave basis functions and lagrange multiplier degrees of freedom was proposed for the efficient solution in two dimensions of helmholtz problems in the mid frequency regime in this paper this method is extended to three dimensions and several new elements are proposed computational results obtained for several wave guide and acoustic scattering model problems demonstrate one to two orders of magnitude solution time improvement over the higher order galerkin method

a higher order discontinuous enrichment method for the solution of high peclet advection diffusion problems on unstructured meshes a higher order discontinuous enrichment method dem with lagrange multipliers is proposed for the efficient finite element solution on unstructured meshes of the advection diffusion equation in the high peclet number regime following the basic dem methodology the usual galerkin polynomial approximation is enriched with free space solutions of the governing homogeneous partial differential equation pde in this case these are exponential functions that exhibit a steep gradient in a specific flow direction exponential lagrange multipliers are introduced at the element interfaces to weakly enforce the continuity of the solution the construction of several higher order dem elements fitting this paradigm is discussed in detail numerical tests performed for several two dimensional benchmark problems demonstrate their computational superiority over stabilized galerkin counterparts especially for high peclet numbers copyright 2009 john wiley sons ltd

ltv models in mpc for sustainable development recent work has formulated an mpc strategy for a sustainable development problem focused on the control of a stochastic non linear economic model called prometheus this work also takes prometheus to be the system to use mpc an analytic approximation of prometheus is required with previous work focusing on linear and non linear time invariant models global optimality of the solution could not be guaranteed since to achieve reasonable accuracy in iterative fitting was required which destroyed convexity of the optimization in this paper an ltv model is considered and is shown to reduce the approximation error it is demonstrated that the model can be finitely parameterized and that the predominant time variation in prometheus is from a decaying exponential weighting on the predicted input sequence it is suggested that this variation is a representation of inflation the sustainable development mpc methodology is recast for such a model convexity of the mpc optimization with an ltv model guarantees

a discontinuous galerkin method with lagrange multipliers for the solution of helmholtz problems in the mid frequency regime we present a discontinuous galerkin method dgm for the solution of the helmholtz equation in the mid frequency regime our approach is based on the discontinuous enrichment method in which the standard polynomial field is enriched within each finite element by a non conforming field that contains free space solutions of the homogeneous partial differential equation to be solved hence for the helmholtz equation the enrichment field is chosen here as the superposition of plane waves we enforce a weak continuity of these plane waves across the element interfaces by suitable lagrange multipliers preliminary results obtained for two dimensional model problems discretized by uniform meshes reveal that the proposed dgm enables the development of elements that are far more competitive than both the standard linear and the standard quadratic galerkin elements for the discretization of helmholtz problems

an efficient algorithm for minimizing a sum of euclidean norms with applications in recent years rich theories on polynomial time interior point algorithms have been developed these theories and algorithms can be applied to many nonlinear optimization problems to yield better complexity results for various applications in this paper the problem of minimizing a sum of euclidean norms is studied this problem is convex but not everywhere differentiable by transforming the problem into a standard convex programming problem in conic form we show that an epsilon optimal solution can be computed efficiently using interior point algorithms as applications to this problem polynomial time algorithms are derived for the euclidean single facility location problem the euclidean multifacility location problem and the shortest network under a given tree topology in particular by solving the newton equation in linear time using em gaussian elimination on leaves of a tree we present an algorithm which computes an epsilon optimal solution to the shortest network under a given full steiner topology interconnecting n regular points in o n sqrt n log bar c epsilon log n arithmetic operations where bar c is the largest pairwise distance among the given points the previous best known result on this problem is a graphical algorithm which requires o n2 arithmetic operations under certain conditions

a discontinuous enrichment method for capturing evanescent waves in multiscale fluid and fluid solid problems abstract an evanescent wave is produced when a propagating incident wave impinges on an interface between two media or materials at a sub critical angle the sub scale nature of such a wave makes it difficult to be captured computationally in this paper the discontinuous enrichment method dem developed in c farhat i harari l p franca the discontinuous enrichment method comput methods appl mech engrg 190 2001 6455 6479 c farhat i harari u hetmaniuk a discontinuous galerkin method with lagrange multipliers for the solution of helmholtz problems in the mid frequency regime comput methods appl mech engrg 192 2003 1389 1419 c farhat i harari u hetmaniuk the discontinuous enrichment method for multiscale analysis comput methods appl mech engrg 192 2003 3195 3210 c farhat r tezaur p weidemann goiran higher order extensions of a discontinuous galerkin method for mid frequency helmholtz problems int j numer methods engrg 61 2004 1938 1956 c farhat p wiedemann goiran r tezaur a discontinuous galerkin method with plane waves and lagrange multipliers for the solution of short wave exterior helmholtz problems on unstructured meshes new computational methods for wave propagation wave motion 39 4 2004 307 317 l zhang r tezaur c farhat the discontinuous enrichment method for elastic wave propagation in the medium frequency regime int j numer methods engrg 66 2006 2086 2114 r tezaur c farhat three dimensional discontinuous galerkin elements with plane waves and lagrange multipliers for the solution of mid frequency helmholtz problems int j numer methods engrg 66 2006 796 815 is extended to a class of evanescent wave problems new dem elements are constructed by enriching polynomial approximations with free space evanescent solutions in order to achieve high accuracy for problems with fluid fluid or fluid solid interfaces on which evanescent waves may occur the new dem elements are applied to the solution of various two dimensional model problems with evanescent waves their performance is observed to be better than that of the basic helmholtz type dem elements and superior to that of the classical higher order polynomial finite element method

min max control of constrained uncertain discrete time linear systems for discrete time uncertain linear systems with constraints on inputs and states we develop an approach to determine state feedback controllers based on a min max control formulation robustness is achieved against additive norm bounded input disturbances and or polyhedral parametric uncertainties in the state space matrices we show that the finite horizon robust optimal control law is a continuous piecewise affine function of the state vector and can be calculated by solving a sequence of multiparametric linear programs when the optimal control law is implemented in a receding horizon scheme only a piecewise affine function needs to be evaluated on line at each time step the technique computes the robust optimal feedback controller for a rather general class of systems with modest computational effort without needing to resort to gridding of the state space

comments on a new robust control for a class of uncertain discrete time systems a completed proof for a theorem on the robust controller design proposed in wang and ghosh ibid vol 43 1997 is presented in this paper

a high order generalized fem for through the thickness branched cracks this paper presents high order implementations of a generalized finite element method for through the thickness three dimensional branched cracks this approach can accurately represent discontinuities such as triple joints in polycrystalline materials and branched cracks independently of the background finite element mesh representative problems are investigated to illustrate the accuracy of the method in combination with various discretizations and refinement strategies the combination of local refinement at crack fronts and high order continuous and discontinuous enrichments proves to be an excellent combination which can deliver convergence rates close to that of problems with smooth solutions copyright 2007 john wiley sons ltd

the discontinuous enrichment method for elastic wave propagation in the medium frequency regime the discontinuous enrichment method dem is specified and developed for the solution of two dimensional elastic wave propagation problems in the frequency domain the classical finite element polynomial approximation of the displacement field is enriched by the superposition of discontinuous pressure and shear wave functions the continuity of the solution across the element interfaces is weakly enforced by suitable lagrange multipliers higher order rectangular dem elements are constructed and benchmarked against the standard higher order polynomial galerkin elements for two dimensional problems in the medium frequency regime in general it is found that for such applications dem can achieve the same accuracy as the p finite element method using a similar computational complexity but with about 10 times fewer degrees of freedom this highlights the potential of this hybrid method for problems where the scale of vibrations is very small compared to the characteristic dimension of the physical medium copyright 2006 john wiley sons ltd

a stable galerkin reduced order model for coupled fluid structure interaction problems summary a stable reduced order model rom of a linear fluid structure interaction fsi problem involving linearized compressible inviscid flow over a flat linear von karman plate is developed separate stable roms for each of the fluid and the structure equations are derived both roms are built using the continuous galerkin projection approach in which the continuous governing equations are projected onto the reduced basis modes in a continuous inner product the mode shapes for the structure rom are the eigenmodes of the governing linear plate equation the fluid rom basis is constructed via the proper orthogonal decomposition for the linearized compressible euler fluid equations a symmetry transformation is required to obtain a stable formulation of the galerkin projection step in the model reduction procedure stability of the galerkin projection of the structure model in the standard l2 inner product is shown the fluid and structure roms are coupled through solid wall boundary conditions at the interface plate boundary an a priori energy linear stability analysis of the coupled fluid structure system is performed it is shown that under some physical assumptions about the flow field the fsi rom is linearly stable a priori if a stabilization term is added to the fluid pressure loading on the plate the stability of the coupled rom is studied in the context of a test problem of inviscid supersonic flow past a thin square elastic rectangular panel that will undergo flutter once the non dimensional pressure parameter exceeds a certain threshold this a posteriori stability analysis reveals that the fsi rom can be numerically stable even without the addition of the aforementioned stabilization term moreover the rom constructed for this problem properly predicts the maintenance of stability below the flutter boundary and gives a reasonable prediction for the instability growth rate above the flutter boundary copyright 2013 john wiley sons ltd

overview of the discontinuous enrichment method the ultra weak variational formulation and the partition of unity method for acoustic scattering in the medium frequency regime and performance comparisons

a discontinuous enrichment method for variable coefficient advection diffusion at high peclet number a discontinuous galerkin method with lagrange multipliers is presented for the solution of variable coefficient advection diffusion problems at high peclet number in this method the standard finite element polynomial approximation is enriched within each element with free space solutions of a local constant coefficient homogeneous counterpart of the governing partial differential equation hence in the two dimensional case the enrichment functions are exponentials each exhibiting a sharp gradient in a carefully chosen flow direction the continuity of the enriched approximation across the element interfaces is enforced weakly by the aforementioned lagrange multipliers numerical results obtained for two benchmark problems demonstrate that elements based on the proposed discretization method are far more competitive for variable coefficient advection diffusion analysis in the high peclet number regime than their standard galerkin and stabilized finite element comparables copyright 2010 john wiley sons ltd

stochastic receding horizon control with output feedback and bounded controls we study the problem of receding horizon control for stochastic discrete time systems with bounded control inputs and incomplete state information given a suitable choice of causal control policies we first present a slight extension of the kalman filter to estimate the state optimally in mean square sense we then show how to augment the underlying optimization problem with a negative drift like constraint yielding a second order cone program to be solved periodically online we prove that the receding horizon implementation of the resulting control policies renders the state of the overall system mean square bounded under mild assumptions we also discuss how some quantities required by the finite horizon optimization problem can be computed off line thus reducing the on line computation

discrete time robust control via state feedback for single input systems a nonlinear robust state feedback controller for discrete time uncertain systems is proposed the uncertainties in the system must satisfy the matching condition but only their bounds need to be known the controller is designed via the second method of lyapunov the detailed derivation of the controller for single input systems is given the system response remains in the neighborhood of the zero state if uncertainties are small the uncertainty bound for the stability condition is derived

a high order discontinuous galerkin method with lagrange multipliers for advection diffusion problems abstract a high order discontinuous galerkin method with lagrange multipliers dglm is presented for the solution of advection diffusion problems on unstructured adaptive meshes unlike other hybrid discretization methods for transport problems it operates directly on the second order form the advection diffusion equation like the discontinuous enrichment method dem it chooses the basis functions among the free space solutions of the homogeneous form of the governing partial differential equation and relies on lagrange multipliers for enforcing a weak continuity of the approximated solution across the element interface boundaries however unlike dem the proposed hybrid discontinuous galerkin method approximates the lagrange multipliers in a space of polynomials instead of a space of traces on the element boundaries of the normal derivatives of a subset of the basis functions for a homogeneous problem the design of arbitrarily high order elements based on this dglm method is supported by a detailed mathematical analysis for a non homogeneous one the approximated solution is locally decomposed into its homogeneous and particular parts the homogeneous part is captured by the dglm elements designed for a homogenous problem the particular part is obtained analytically after the source term is projected onto an appropriate polynomial space this decoupling between the two parts of the solution is another differentiator between dglm and dem with attractive computational advantages an a posteriori error estimator for the proposed method is also derived to enable adaptive mesh refinement all theoretical results are illustrated by numerical simulations that furthermore highlight the potential of the proposed high order hybrid dg method for transport problems with steep gradients in the high peclet number regime

the discontinuous enrichment method we propose a finite element based discretization method in which the standard polynomial field is enriched within each element by a nonconforming field that is added to it the enrichment contains free space solutions of the homogeneous differential equation that are not represented by the underlying polynomial field continuity of the enrichment across element interfaces is enforced weakly by lagrange multipliers in this manner we expect to attain high coarse mesh accuracy without significant degradation of conditioning assuring good performance of the computation at any mesh resolution examples of application to acoustics and advection diffusion are presented

a high order discontinuous galerkin method for unsteady advection diffusion problems abstract a high order discontinuous galerkin method with lagrange multipliers is presented for the solution of unsteady advection diffusion problems in the high peclet number regime it operates directly on the second order form of the governing equation and does not require any stabilization its spatial basis functions are chosen among the free space solutions of the homogeneous form of the partial differential equation obtained after time discretization it also features lagrange multipliers for enforcing a weak continuity of the approximated solution across the element interface boundaries this leads to a system of differential algebraic equations which are time integrated by an implicit family of schemes the numerical stability of these schemes and the well posedness of the overall discretization method are supported by a theoretical analysis the performance of this method is demonstrated for various high peclet number constant coefficient model flow problems

cooperative distributed stochastic mpc for systems with state estimation and coupled probabilistic constraints a cooperative distributed stochastic model predictive control cdsmpc algorithm is given for multiple dynamically decoupled subsystems with additive stochastic disturbances and coupled probabilistic constraints for which states are not measurable cooperation between subsystems is promoted by a scheme in which a local subsystem designs hypothetical plans for others in some cooperating set and considers the weighted costs of these subsystems in its objective to achieve satisfaction of coupled probabilistic constraints in a distributed way only one subsystem is permitted to optimize at each time step in addition by using a lifting technique and the probabilistic information on additive disturbances measurement noise and the state estimation error a set of deterministic constraints is constructed for the predictions of nominal models recursive feasibility with respect to both local and coupled probabilistic constraints is guaranteed and stability for any choice of update sequence and any structure of cooperation is ensured numerical examples illustrate the efficacy of the proposed algorithm

concurrently coupled atomistic and xfem models for dislocations and cracks a method for the modeling of dislocations and cracks by atomistic continuum models is described the methodology combines the extended finite element method with the bridging domain method bdm the former is used to model crack surfaces and slip planes in the continuum whereas the bdm is used to link the atomistic models with the continuum the bdm is an overlapping domain decomposition method in which the atomistic and continuum energies are blended so that their contributions decay to their boundaries on the overlapping subdomain compatibility between the continua and atomistic domains is enforced by a continuous lagrange multiplier field the methodology allows for simulations with atomistic resolution near crack fronts and dislocation cores while retaining a continuum model in the remaining part of the domain and so a large reduction in the number of atoms is possible it is applied to the modeling of cracks and dislocations in graphene sheets energies and energy distributions compare very well with direct numerical simulations by strictly atomistic models copyright 2008 john wiley sons ltd

discontinuous galerkin methods for advection diffusion reaction problems on anisotropically refined meshes in this paper we consider the a posteriori and a priori error analysis of discontinuous galerkin interior penalty methods for second order partial differential equations with nonnegative characteristic form on anisotropically refined computational meshes in particular we discuss the question of error estimation for linear target functionals such as the outflow flux and the local average of the solution based on our a posteriori error bound we design and implement the corresponding adaptive algorithm to ensure reliable and efficient control of the error in the prescribed functional to within a given tolerance this involves exploiting both local isotropic and anisotropic mesh refinement the theoretical results are illustrated by a series of numerical experiments

optimal feedback control strategies for state space systems with stochastic parameters two different optimal feedback laws are derived for state space systems parametrized through an independent identically distributed vector sequence both feedback laws are obtained by minimizing the expectation of a multistep quadratic loss function at each time step they differ on the assumptions made about the future inputs the properties and implementability of the feedback laws are discussed for the infinite horizon case

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100