multiple comparison of several linear regression models research on multiple comparison during the past 50 years or so has focused mainly on the comparison of several population means several years ago spurrier considered the multiple comparison of several simple linear regression lines he constructed simultaneous confidence bands for all of the contrasts of the simple linear regression lines over the entire range when the models have the same design matrices this article extends spurrier s work in several directions first multiple linear regression models are considered and the design matrices are allowed to be different second the predictor variables are either unconstrained or constrained to finite intervals third the types of comparison allowed can be very flexible including pairwise many one and successive two simulation methods are proposed for the calculation of critical constants the methodologies are illustrated with examples

mixed finite element method for dirichlet boundary control problem governed by elliptic pdes in this paper we study the finite element approximation of dirichlet boundary control problems governed by elliptic pdes based on a mixed variational scheme we establish a mixed finite element approximation to the underlying optimal control problem we consider the optimal control problems posed on both polygonal and general smooth domains and we derive a priori error estimates for optimal control state and adjoint state the optimal and quasi optimal error estimates are obtained for problems on polygonal and smooth domains respectively numerical experiments are provided to confirm our theoretical results

the velocity tracking problem for navier stokes flows with bounded distributed controls we present some systematic approaches to the mathematical analysis and numerical approximation of the time dependent optimal control problem of tracking the velocity for navier stokes flows in bounded two dimensional domains with bounded distributed controls we study the existence of optimal solutions and derive an optimality system from which optimal solutions may be determined we also define and analyze semidiscrete in time and fully space time discrete approximations of the optimality system and a gradient method for the solution of the fully discrete system the results of some computational experiments are provided

control of flow separation over a forward facing step by model reduction abstract design and implementation of reduced order optimal controller for flow separation are investigated the reduced order controller design is based on proper orthogonal decomposition pod and galerkin projection detailed finite element simulations are performed and pod is applied to the resulting data to extract the most energetic eigenmodes these global eigenmodes are then used in conjunction with the galerkin projection to obtain a reduced order low dimensional model reduced order models are not only attractive for real time control computation but also crucial for detailed stability and bifurcation analysis we investigate the design of optimal controller for flow separation in a channel with this model where actuation is performed on a small part of the boundary two different types of surface actuation are considered tangential blowing and suction through a single slot best locations for actuation and adaptive procedure for reduced order model are explored the proposed approaches are evaluated by investigating the control of flow separation over a forward facing step channel our methods are found to be efficient and fast and our methods demonstrate a significant reduction in computational time and feasibility dramatic separation delays are observed on all cases it is found that the tangential blowing is more efficient in mitigating flow separation and reducing wake spread

a penalized neumann control approach for solving an optimal dirichlet control problem for the navier stokes equations we introduce a penalized neumann boundary control approach for solving an optimal dirichlet boundary control problem associated with the two or three dimensional steady state navier stokes equations we prove the convergence of the solutions of the penalized neumann control problem the suboptimality of the limit and the optimality of the limit under further restrictions on the data we describe the numerical algorithm for solving the penalized neumann control problem and report some numerical results

multiple testing of general contrasts powerful improvements are possible for multiple testing procedures when the hypotheses are logically related closed testing with exhaustive tests provides a unifying framework for developing such procedures but can be computationally difficult and can be nonmonotonic in p values royen introduced a truncated closed testing method for the case of all pairwise comparisons in the analysis of variance that is monotonic in p values shaffer developed a similar truncated procedure for more general comparisons but using bonferroni tests rather than exhaustive tests and westfall extended shaffer s method to allow exhaustive tests this article extends royen s method to general contrasts and proves that it is equivalent to the extended shaffer procedure for k contrasts the method generally requires evaluation of o 2k critical values that correspond to subset intersection hypotheses and is computationally infeasible for large k the set of intersections is represented using a tree structure and a

proper orthogonal decomposition for parameter estimation in oscillating biological networks proper orthogonal decomposition pod is frequently applied to estimate parameters of partial differential equations this study examines the application of the pod method in estimating the parameters of an ordinary differential equation ode model of stable oscillating biological networks the mathematical model used to simulate molecular interactions in these oscillating networks is related to the gause lotka volterra equations the findings reveal that pod generates accurate estimates of the parameters even in the presence of experimental noise furthermore extrapolating biologically measured data points to a number of oscillations improves the curve fits c 1 approximations and parameter estimations

finite generation of symmetric ideals let be a commutative noetherian ring and let be the polynomial ring in an infinite collection of indeterminates over let be the group of permutations of the group acts on in a natural way and this in turn gives the structure of a left module over the group ring we prove that all ideals of invariant under the action of are finitely generated as modules the proof involves introducing a certain well quasi ordering on monomials and developing a theory of grobner bases and reduction in this setting we also consider the concept of an invariant chain of ideals for finite dimensional polynomial rings and relate it to the finite generation result mentioned above finally a motivating question from chemistry is presented with the above framework providing a suitable context in which to study it

mathematical and numerical results on the sensitivity of the pod approximation relative to the burgers equation from mathematical and numerical points of view we study the sensitivity with respect to parametric evolutions of the error obtained by approximating a given parametric partial differential equation using a proper orthogonal decomposition pod basis determined once and for all with association to a fixed parameter more precisely we will be considering the one dimensional burgers equation with a source term

trace theorems for three dimensional time dependent solenoidal vector fields and their applications we study trace theorems for three dimensional time dependent solenoidal vector fields the interior function spaces we consider are natural for solving unsteady boundary value problems for the navier stokes system and other systems of partial differential equations we describe the space of restrictions of such vector fields to the boundary of the space time cylinder and construct extension operators from this space of restrictions defined on the boundary into the interior only for two exceptional but useful values of the spatial smoothness index the spaces for which we construct extension operators is narrower than the spaces in which we seek restrictions the trace spaces are characterized by vector fields having different smoothnesses in directions tangential and normal to the boundary this is a consequence of the solenoidal nature of the fields these results are fundamental in the study of inhomogeneous boundary value problems for systems involving solenoidal vector fields in particular we use the trace theorems in a study of inhomogeneous boundary value problems for the navier stokes system of viscous incompressible flows

an improved sequentially rejective bonferroni test procedure complexity these procedures can be used whenever the observed levels of significance are available for all individual tests it is shown that both the holm and shaffer procedures can be improved under the assumption of positive orthant dependence for the test statistics it is noted that this assumption is met in many important practical situations and recommended that in these cases the new procedure be used in place of its predecessors whenever the required observed significance levels are available the methodology is illustrated with a numerical example

an energy space finite element approach for elliptic dirichlet boundary control problems in this paper we present a finite element analysis for a dirichlet boundary control problem where the dirichlet control is considered in a convex closed subspace of the energy space h 1 2 gamma h 1 2 as an equivalent norm in h 1 2 gamma h 1 2 we use the energy norm induced by the so called steklov poincare operator which realizes the dirichlet to neumann map and which can be implemented by using standard finite element methods the presented stability and error analysis of the discretization of the resulting variational inequality is based on the mapping properties of the solution operators related to the primal and adjoint boundary value problems and their finite element approximations some numerical results are given which confirm on one hand the theoretical estimates but on the other hand indicate the differences when modelling the control in l 2 gamma l 2

galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics error estimates for galerkin proper orthogonal decomposition pod methods for nonlinear parabolic systems arising in fluid dynamics are proved for the time integration the backward euler scheme is considered the asymptotic estimates involve the singular values of the pod snapshot set and the grid structure of the time discretization as well as the snapshot locations

pairwise comparisons of generally correlated means abstract a commonly occurring statistical inference problem in practice is that of making simultaneous comparisons among three or more treatment means i 1 i k for certain experimental designs one way to do this the t method proposed by tukey 1953 constructs simultaneous confidence intervals for all pairwise differences of the treatment means i j 1 i j k i j the joint confidence level of these confidence intervals however depends in a very complicated fashion on the covariance structure of the treatment mean estimates i and therefore for designs where the covariance structure is not simple the joint confidence level is not readily apparent in general this is the case for any unbalanced design or for designs in which the treatment mean estimates i have unequal correlations tukey conjectured in 1953 that whatever the correlation structure of the treatment mean estimates i the t method would always provide a conservative set of confidence intervals that is that th

a reduced order extrapolated finite difference iterative scheme based on pod method for 2d sobolev equation abstract in this study we devote ourselves to the reduced order extrapolated finite difference iterative roefdi modeling and analysis for the two dimensional 2d sobolev equation to this end we first establish the reduced order extrapolated finite difference iterative roefdi scheme holding sufficiently high accuracy but containing very few degrees of freedom for the 2d sobolev equation via the proper orthogonal decomposition pod technique and then we analyze the stability and convergence of the roefdi solutions finally we use the numerical experiments to verify the feasibility and effectiveness of the roefdi scheme

a parameterized non intrusive reduced order model and error analysis for general time dependent nonlinear partial differential equations and its applications abstract a novel parameterized non intrusive reduced order model p nirom based on proper orthogonal decomposition pod has been developed this p nirom is a generic and efficient approach for model reduction of parameterized partial differential equations p pdes over existing parameterized reduced order models p rom most of them are based on the reduced basis method it is non intrusive and independent on partial differential equations and computational codes during the training process the smolyak sparse grid method is used to select a set of parameters over a specific parameterized space p r p for each selected parameter the reduced basis functions are generated from the snapshots derived from a run of the high fidelity model more generally the snapshots and basis function sets for any parameters over p can be obtained using an interpolation method the p nirom can then be constructed by using our recently developed technique xiao et al 2015 41 42 where either the smolyak or radial basis function rbf methods are used to generate a set of hyper surfaces representing the underlying dynamical system over the reduced space the new p nirom technique has been applied to parameterized navier stokes equations and implemented with an unstructured mesh finite element model the capability of this p nirom has been illustrated numerically by two test cases flow past a cylinder and lock exchange case the prediction capabilities of the p nirom have been evaluated by varying the viscosity initial and boundary conditions the results show that this p nirom has captured the quasi totality of the details of the flow with cpu speedup of three orders of magnitude an error analysis for the p nirom has been carried out

analysis and approximation for linear feedback control for tracking the velocity in navier stokes flows abstract some systematic approaches to the mathematical formulation and numerical resolution of the linear feedback control problem for tracking the velocity in navier stokes flows in a bounded two dimensional domain with bounded distributed control are presented semidiscrete in time and full space time discrete approximations are also studied some computational results are presented and compared with analogous results from optimal control theory

modified sequentially rejective multiple test procedures abstract suppose that n hypotheses h 1 h 2 h n with associated test statistics t 1 t 2 t n are to be tested by a procedure with experimentwise significance level the probability of rejecting one or more true hypotheses smaller than or equal to some specified value a commonly used procedure satisfying this condition is the bonferroni b procedure which consists of rejecting h i for any i iff the associated test statistic t i is significant at the level n holm 1979 introduced a modified bonferroni procedure with greater power than the b procedure under holm s sequentially rejective bonferroni srb procedure if any hypothesis is rejected at the level n the denominator of for the next test is n 1 and the criterion continues to be modified in a stagewise manner with the denominator of reduced by 1 each time a hypothesis is rejected so that tests can be conducted at successively higher significance levels holm proved that the experimentwise significance level

mixed finite element formulation and error estimates based on proper orthogonal decomposition for the nonstationary navier stokes equations in this paper proper orthogonal decomposition pod is used for model reduction of mixed finite element mfe for the nonstationary navier stokes equations and error estimates between a reference solution and the pod solution of reduced mfe formulation are derived the basic idea of this reduction technique is that ensembles of data are first compiled from transient solutions computed equation system derived with the usual mfe method for the nonstationary navier stokes equations or from physics system trajectories by drawing samples of experiments and interpolation or data assimilation and then the basis functions of the usual mfe method are substituted with the pod basis functions reconstructed by the elements of the ensemble to derive the pod reduced mfe formulation for the nonstationary navier stokes equations it is shown by considering numerical simulation results obtained for the illustrating example of cavity flows that the error between pod solution of reduced mfe formulation and the reference solution is consistent with theoretical results moreover it is also shown that this result validates the feasibility and efficiency of the pod method

an improved bonferroni procedure for multiple tests of significance summary a modification of the bonferroni procedure for testing multiple hypotheses is presented the method based on the ordered p values of the individual tests is less conservative than the classical bonferroni procedure but is still simple to apply a simulation study shows that the probability of a type i error of the procedure does not exceed the nominal significance level a for a variety of multivariate normal and multivariate gamma test statistics for independent tests the procedure has type i error probability equal to a the method appears particularly advantageous over the classical bonferroni procedure when several highly correlated test statistics are involved

reduced order modeling of the upper tropical pacific ocean model using proper orthogonal decomposition the proper orthogonal decomposition pod is shown to be an efficient model reduction technique for simulating physical processes governed by partial differential equations in this paper we make an initial effort to investigate problems related to pod reduced modeling of a large scale upper ocean circulation in the tropic pacific domain we construct different pod models with different choices of snapshots and different number of pod basis functions the results from these different pod models are compared with that of the original model the main findings are 1 the large scale seasonal variability of the tropic pacific obtained by the original model is well captured by a low dimensional system of order 22 which is constructed using 20 snapshots and 7 leading pod basis functions 2 the rms errors for the upper ocean layer thickness of the pod model of order 22 are less than 1m that is less than 1 of the average thickness and the correlation between the upper ocean layer thickness with that from the pod model is around 0 99 3 retaining modes that capture 99 energy is necessary in order to construct pod models yielding a high accuracy

a reduced finite volume element formulation and numerical simulations based on pod for parabolic problems a proper orthogonal decomposition pod method is applied to a usual finite volume element fve formulation for parabolic equations such that it is reduced to a pod fve formulation with lower dimensions and high enough accuracy the error estimates between the reduced pod fve solution and the usual fve solution are analyzed it is shown by numerical examples that the results of numerical computation are consistent with theoretical conclusions moreover it is also shown that the reduced pod fve formulation based on pod method is both feasible and highly efficient

second order methods for optimal control of time dependent fluid flow second order methods for open loop optimal control problems governed by the two dimensional instationary navier stokes equations are investigated optimality systems based on a lagrangian formulation and adjoint equations are derived the newton and quasi newton methods as well as various variants of sqp methods are developed for applications to optimal flow control and their complexity in terms of system solves is discussed local convergence and rate of convergence are proved a numerical example illustrates the feasibility of solving optimal control problems for two dimensional instationary navier stokes equations by second order numerical methods in a standard workstation environment

boundary velocity control of incompressible flow with an application to viscous drag reduction an optimal boundary control problem for the navier stokes equations is presented the control is the velocity on the boundary which is constrained to lie in a closed convex subset of h 1 2 of the boundary a necessary condition for optimality is derived computations are done when the control set is actually finite dimensional resulting in an application to viscous drag reduction

a reduced order extrapolation central difference scheme based on pod for two dimensional fourth order hyperbolic equations the reduced order extrapolating fd schemes are just developed by luo s research team since 2013 see 47 52 and a very new technique the reduced order extrapolation central difference scheme based on pod for two dimensional fourth order hyperbolic equations is first built by us we provide theoretical analysis and examples to show the advantage of our method this paper is concerned with establishing the reduced order extrapolation central difference roecd scheme based on proper orthogonal decomposition pod for two dimensional 2d fourth order hyperbolic equations for this purpose we first develop the classical central difference cd scheme for the 2d fourth order hyperbolic equations and analyze its stability and convergence then by making use of the pod method we build the roecd scheme with fewer degrees of freedom and sufficiently high accuracy and furnish the error estimates of the roecd solutions and the algorithm procedure for solving the roecd scheme finally we employ some numerical examples to confirm the correctness of theoretical conclusions this implies that roecd scheme is feasible and efficient for seeking the numerical solutions of the 2d fourth order hyperbolic equations

a stagewise rejective multiple test procedure based on a modified bonferroni test summary simes 1986 has proposed a modified bonferroni procedure for the test of an overall hypothesis which is the combination of n individual hypotheses in contrast to the classical bonferroni procedure it is not obvious how statements about individual hypotheses are to be made for this procedure in the present paper a multiple test procedure allowing statements on individual hypotheses is proposed it is based on the principle of closed test procedures marcus peritz gabriel 1976 and controls the multiple level a

shortcuts for locally consonant closed test procedures the closed testing principle provides a general and simple framework to construct powerful multiple test procedures for k elementary null hypotheses while controlling the familywise error rate in the strong sense however the closed testing principle has the disadvantage of leading to the evaluation of o 2k intersection hypotheses multiple test procedures based on the closed testing principle may thus require substantial computational efforts consonant closed test procedures for unrestricted hypotheses have the advantage of rejecting at least one elementary null hypothesis whenever the global null hypothesis is rejected and thus admit shortcuts of size k if the elementary null hypotheses are restricted by logical constraints the closure of common tests such as max t or min p tests may not be consonant in the usual sense in this article we introduce a weaker consonance property denoted as local consonance and show that many closed test procedures with restricted hypotheses satisfy this condition

a fast reduced order model for radial integral boundary element method based on proper orthogonal decomposition in nonlinear transient heat conduction problems abstract in order to efficiently solve nonlinear transient heat conduction problem a method combining the radial integration boundary element method ribem and the proper orthogonal decomposition pod is proposed to establish the nonlinear reduced order model and the implementation of the reduced order model makes fast numerical simulation possible in engineering field transient heat conduction problems with temperature dependent and temperature independent thermal conductivity are firstly solved by the ribem respectively and two types of snapshots are composed of these solved transient temperature fields subsequently the pod is applied in the analysis of the snapshots and then a set of optimal orthogonal basis can be obtained in the procedure of establishing the reduced order model we need to redistribute the nonlinear equations the strategy is to separate the boundary nodes defined as dirichlet condition and then the orthogonal basis is used to derive a reduced order expression for the remaining unknowns therefore the degree of freedom that needs to be solved can be greatly reduced numerical examples show that different reduced order models based on nonlinear basis and linear basis are all consistent with the full order model what is more the computational efficiency is greatly improved due to the introduction of the reduced order model

some probability inequalities for ordered rm mtp sb 2 random variables a proof of the simes conjecture some new probability inequalities involving the ordered components of an mtp 2 random vector are derived which provide an analytical proof of an important conjecture in the field of multiple hypothesis testing this conjecture has been mostly validated so far using simulation

existence of optimal controls for viscous flow problems a class of optimal control problems in viscous flow is studied main result is the existence theorem for optimal control three typical flow control problems are formulated within this general class

first order sufficient optimality conditions for navier stokes flow dual feedback controls the navier stokes system of partial differential equations with navier boundary condition that models the evolution of viscous incompressible flows is studied as a controllable system and the optimal cost functional with respect to that control is invstigated a dual dynamic programming approach is proposed and sufficient optimality conditions in terms of verification theorem are proved the essential novelty of the paper is that all equations under consideration are treated in weak form dual feedback controls are proposed for the problem under study

stability enhancement by boundary control in 2 d channel flow in this paper we stabilize the parabolic equilibrium profile in a two dimensional 2 d channel flow using actuators and sensors only at the wall the control of channel flow was previously considered by speyer and coworkers and bewley and coworkers who derived feedback laws based on linear optimal control and implemented by wall normal actuation with an objective to achieve global lyapunov stabilization we arrive at a feedback law using tangential actuation using teamed pairs of synthetic jets or rotating disks and only local measurements of wall shear stress allowing to embed the feedback in microelectromechanical systems mems hardware without need for wiring this feedback is shown to guarantee global stability in at least h sup 2 norm which by sobolev s embedding theorem implies continuity in space and time of both the flow field and the control as well as their convergence to the desired steady state the theoretical results are limited to low values of reynolds number however we present simulations that demonstrate the effectiveness of the proposed feedback for values five order of magnitude higher

a reduced finite difference scheme based on singular value decomposition and proper orthogonal decomposition for burgers equation in this article a reduced optimizing finite difference scheme fds based on singular value decomposition svd and proper orthogonal decomposition pod for burgers equation is presented also the error estimates between the usual finite difference solution and the pod solution of reduced optimizing fds are analyzed it is shown by considering the results obtained for numerical simulations of cavity flows that the error between the pod solution of reduced optimizing fds and the solution of the usual fds is consistent with theoretical results moreover it is also shown that the reduced optimizing fds is feasible and efficient

a parabolic inverse convection diffusion reaction problem solved using space time localization and adaptivity this paper investigates the solution of a parabolic inverse problem based upon the convection diffusion reaction equation which can be used to estimate both water and air pollution we will consider both known and unknown source location while in the first case the problem is solved using a projected damped gauss newton pdgn in the second one it is ill posed and an adaptive parametrization with space time localization will be adopted to regularize it

analysis and finite element approximation of optimal control problems for the stationary navier stokes equations with distributed and neumann controls we examine certain analytic and numerical aspects of optimal control problems for the stationary navier stokes equations the controls considered may be of either the distributed or neumann type the functionals minimized are either the viscous dissipation or the l4 distance of candidate flows to some desired flow we show the existence of optimal solutions and justify the use of lagrange multiplier techniques to derive a system of partial differential equations from which optimal solutions may be deduced we study the regularity of solutions of this system then we consider the approximation by finite element methods of solutions of the optimality system and derive optimal error estimates

solving inverse problems involving the navier stokes equations discretized by a lagrange galerkin method abstract in this article we are investigating the numerical approximation of an inverse problem involving the evolution of a newtonian viscous incompressible fluid described by the navier stokes equations in 2d this system is discretized using a low order finite element in space coupled with a lagrange galerkin scheme for the nonlinear advection operator we introduce a full discrete linearized scheme that is used to compute the gradient of a given cost function by ensuring its consistency using gradient based optimization algorithms we are able to deal with two fluid flow inverse problems the drag reduction around a moving cylinder and the identification of a far field velocity using the knowledge of the fluid load on a rectangular bluff body for both fixed and prescribed moving configurations

two level discretizations of nonlinear closure models for proper orthogonal decomposition proper orthogonal decomposition has been successfully used in the reduced order modeling of complex systems its original promise of computationally efficient yet accurate approximation of coherent structures in high reynolds number turbulent flows however still remains to be fulfilled to balance the low computational cost required by reduced order modeling and the complexity of the targeted flows appropriate closure modeling strategies need to be employed since modern closure models for turbulent flows are generally nonlinear their efficient numerical discretization within a proper orthogonal decomposition framework is challenging this paper proposes a two level method for an efficient and accurate numerical discretization of general nonlinear closure models for proper orthogonal decomposition reduced order models the two level method computes the nonlinear terms of the reduced order model on a coarse mesh compared with a brute force computational approach in which the nonlinear terms are evaluated on the fine mesh at each time step the two level method attains the same level of accuracy while dramatically reducing the computational cost we numerically illustrate these improvements in the two level method by using it in three settings the one dimensional burgers equation with a small diffusion parameter n 10 3 the two dimensional flow past a cylinder at reynolds number re 200 and the three dimensional flow past a cylinder at reynolds number re 1000

a reduced order extrapolation technique for solution coefficient vectors in the mixed finite element method for the 2d nonlinear rosenau equation abstract this study focuses mainly on a reduced order method for the coefficient vectors in the crank nicolson mixed finite element cnmfe solutions for the two dimensional nonlinear rosenau equation we first provide a cnmfe method for the rosenau equation and give relative theoretical results as well as rewrite the cnmfe method in matrix form we then produce two sets of proper orthogonal decomposition pod bases by means of the first few coefficient vectors of the cnmfe solutions and set up a reduced order extrapolating cnmfe roecnmfe model with the pod bases as well as discuss the existence and stability as well as errors of the roecnmfe solutions by means of the matrix tool resulting in the theoretical analysis becoming very succinct lastly we present some numerical experiments to validate the correctness of the theoretical results finding that the superiority of the roecnmfe method is further verified

the partitioning principle a powerful tool in multiple decision theory a first general principle and nowadays state of the art for the construction of powerful multiple test procedures controlling a multiple level a is the so called closure principle in this article we introduce another powerful tool for the construction of multiple decision procedures especially for the construction of multiple test procedures and selection procedures this tool is based on a partition of the parameter space and will be called partitioning principle pp in the first part of the paper we review basic concepts of multiple hypotheses testing and discuss a slight generalization of the current theory in the second part we present various variants of the pp for the construction of multiple test procedures these are a general pp gpp a weak pp wpp and a strong pp spp it will be shown that depending on the underlying decision problem a pp may lead to more powerful test procedures than a formal application of the closure principle fcp moreover the more complex spp may be more powerful than the wpp based on a duality between testing and selecting pps can also be applied for the construction of more powerful selection procedures in the third part of the paper fcp wpp and spp are applied and compared in some examples

a superconvergent hybridizable discontinuous galerkin method for dirichlet boundary control of elliptic pdes we begin an investigation of hybridizable discontinuous galerkin hdg methods for approximating the solution of dirichlet boundary control problems governed by elliptic pdes these problems can involve atypical variational formulations and often have solutions with low regularity on polyhedral domains these issues can provide challenges for numerical methods and the associated numerical analysis we propose an hdg method for a dirichlet boundary control problem for the poisson equation and obtain optimal a priori error estimates for the control specifically under certain assumptions for a 2d convex polygonal domain we show the control converges at a superlinear rate we present 2d and 3d numerical experiments to demonstrate our theoretical results

an optimal control problem in exterior hydrodynamics in this paper we consider the problem of accelerating an obstacle in an incompressible viscous fluid from rest to a given speed in a given time with minimum energy expenditure an existence theorem for the speed trajectory which corresponds to the absolute minimum is provided the results are valid for arbitrary reynolds numbers

necessary and sufficient conditions for optimal controls in viscous flow problems a class of optimal control problems in viscous flow is studied main results are the pontryagin maximum principle and the verification theorem for the hamilton jacobi bellman equation characterising the feedback problem the maximum principle is established by two quite different methods

stabilized reduced order models for the advection diffusion reaction equation using operator splitting reduced order modeling rom coupled with finite element methods has been used effectively in many disciplines to efficiently solve complex problems however for advection dominated flows numerical simulations often contain spurious nonphysical oscillations which will also be apparent in the rom simulations in this work we consider stabilization methods for rom for the advection diffusion reaction adr equation when it is solved both with and without operator splitting specifically we consider the streamline upwind petrov galerkin supg stabilization method and the spurious oscillations at layers diminishing sold stabilization method we build on these methods by constructing a coherent framework which successfully integrates these model reduction stabilization and operator splitting approaches and we provide numerical examples detailing the application of this framework in the adr setting the stabilized rom results are compared numerically with their corresponding full finite element simulations

control oriented proper orthogonal decomposition models for unsteady flows controller development in the relatively young field of closed loop or feedback flow control is constrained by the lack of proper models for the description of the dynamics and response of flows to a control input actuation if a set of ordinary differential equations could be derived that describes the unsteady flow with sufficient accuracy and that also models the effect of the actuation conventional control theory tools could be employed for controller design in this paper reduced order models based on a galerkin projection of the incompressible navier stokes equations onto a proper orthogonal decomposition modal basis are described the model coefficients can be modified or calibrated to make the model more accurate an error minimization technique is employed to obtain the coefficients that describe how the control input enters the model equations these models work well in the vicinity of the design operating point composite models are constructed by combining modes from different operating points this approach results in more versatile models that are valid for a larger range of operating conditions

optimal boundary control for the evolutionary navier stokes system the three dimensional case optimal boundary control problems for the three dimensional evolutionary navier stokes equations in the exterior of a bounded domain are studied control is effected through the dirichlet boundary condition and is sought in a subset of the trace space of velocity fields with almost minimal possible regularity the control objective is to minimize the drag functional the existence of an optimal solution is proved a strong form of an optimality system of equations is derived on the basis of regularity results established in this work for the adjoint oseen equations with regular initial data which do not satisfy the compatibility conditions

proper orthogonal decomposition closure models for turbulent flows a numerical comparison this paper puts forth two new closure models for the proper orthogonal decomposition reduced order modeling of structurally dominated turbulent flows the dynamic subgrid scale model and the variational multiscale model these models which are considered state of the art in large eddy simulation together with the mixing length and the smagorinsky closure models are tested in the numerical simulation of 3d turbulent flow past a circular cylinder at re 1000 five criteria are used to judge the performance of the proper orthogonal decomposition reduced order models the kinetic energy spectrum the mean velocity the reynolds stresses the root mean square values of the velocity fluctuations and the time evolution of the pod coefficients all the numerical results are benchmarked against a direct numerical simulation based on these numerical results we conclude that the dynamic subgrid scale and the variational multiscale models are the most accurate

non linear petrov galerkin methods for reduced order modelling of the navier stokes equations using a mixed finite element pair abstract a new nonlinear petrov galerkin approach has been developed for proper orthogonal decomposition pod reduced order modelling rom of the navier stokes equations the new method is based on the use of the cosine rule between the advection direction in cartesian space time and the direction of the gradient of the solution a finite element pair p 1 dg p 2 which has good balance preserving properties is used here consisting of a mix of discontinuous for velocity components and continuous for pressure basis functions the contribution of the present paper lies in applying this new non linear petrov galerkin method to the reduced order navier stokes equations and thus improving the stability of rom results without tuning parameters the results of numerical tests are presented for a wind driven 2d gyre and the flow past a cylinder which are simulated using the unstructured mesh finite element cfd model in order to illustrate the numerical performance of the method the numerical results obtained show that the newly proposed pod petrov galerkin method can provide more accurate and stable results than the pod bubnov galerkin method

galerkin proper orthogonal decomposition methods for parabolic problems in this work error estimates for galerkin proper orthogonal decomposition pod methods for linear and certain non linear parabolic systems are proved the resulting error bounds depend on the number of pod basis functions and on the time discretization numerical examples are included

a reduced order extrapolation algorithm based on sfve method and pod technique for non stationary stokes equations in this paper a reduced order extrapolation algorithm roea based on proper orthogonal decomposition pod technique and classical stabilized finite volume element sfve method for non stationary stokes equations is established the error estimates between the roea solutions and the classical sfve solutions and the implementation for solving roea are provided some numerical examples are used to verify that the results of numerical computation are consistent with theoretical conclusions moreover it is shown that roea based on sfve formulation and pod method is feasible and efficient for solving non stationary stokes equations

proper general decomposition pgd for the resolution of navier stokes equations in this work the pgd method will be considered for solving some problems of fluid mechanics by looking for the solution as a sum of tensor product functions in the first stage the equations of stokes and burgers will be solved then we will solve the navier stokes problem in the case of the lid driven cavity for different reynolds numbers re 100 1000 and 10 000 finally the pgd method will be compared to the standard resolution technique both in terms of cpu time and accuracy

multiple testing of general contrasts using logical constraints and correlations abstract use of logical constraints among hypotheses and correlations among test statistics can greatly improve the power of step down tests an algorithm for uncovering these logically constrained subsets in a given dataset is described the multiple testing results are summarized using adjusted p values which incorporate the relevant dependence structures and logical constraints these adjusted p values are computed consistently and efficiently using a generalized least squares hybrid of simple and control variate monte carlo methods and the results are compared to alternative stepwise testing procedures

a self contained automated methodology for optimal flow control this paper describes a self contained automated methodology for active flow control which couples the time dependent navier stokes system with an adjoint navier stokes system and optimality conditions from which optimal states i e unsteady flow fields and controls e g actuators may be determined the problem of boundary layer instability suppression through wave cancellation is used as the intital validation case to test the methodology here the objective of control is to match the stress vector along a portion of the boundary to a steady base flow control is effected through the injection or suction of fluid through a single orifice on the boundary the results demonstrate that instability suppression can be achieved without any a priori knowledge of the flow unsteadiness such as frequencies instability type etc the present methodology has been extended to three dimensions and may potentially be applied to separation control relaminarization and turbulence control applications using one to many sensors and actuators

the velocity tracking problem for navier stokes flows with boundary control we present some systematic approaches to the mathematical formulation and numerical approximation of the time dependent optimal control problem of tracking the velocity for navier stokes flows in a bounded two dimensional domain with boundary control we study the existence of optimal solutions and derive an optimality system from which optimal solutions may be determined we also define and analyze semidiscrete in time and full space time discrete approximations of the optimality system and a gradient method for the solution of the fully discrete system the results of some computational experiments are provided

a reduced finite element formulation based on pod method for two dimensional solute transport problems abstract a proper orthogonal decomposition pod method is applied to a usual finite element fe formulation for two dimensional solute transport problems with real practical applied background such that it is reduced into a reduced fe formulation with lower dimensions and high enough accuracy the error estimates between the reduced pod fe solutions and the usual fe solutions are provided it is shown by numerical examples that the results of numerical computation are consistent with theoretical conclusions moreover it is also shown that this validates the feasibility and efficiency of pod fe method

discontinuous galerkin multimodel methods for optimal control of aeroacoustics doi 10 2514 1 23798 a new multimodel computational framework for optimal control of aeroacoustic noise is presented using a nearfield compressible navier stokes solver coupled with a far field linearized euler solver both based on a discontinuous galerkin formulation in this approach the coupling of near and far field domains is achieved by weakly enforcing continuity of normal fluxes across a coupling surface that encloses all nonlinearities and noise sources foroptimalcontrol gradientinformationisobtainedbythesolutionofanappropriateadjointproblemthat involves the propagationof adjoint information from the far fieldto the near field thiscomputational framework is applied to study optimal boundary control of blade vortex interaction which is a significant noise source for helicopters on approach to landing in the prototype problem presented here the noise propagated toward the ground is reduced by 12 db demonstrating the potential of an optimization based approach to blade vortexinteraction noise control

the efficiency of simulation based multiple comparisons a frequently encountered problem in practice is that of simultaneous interval estimation of p linear combinations of a parameter beta in the setting of or equivalent to a univariate linear model this problem has been solved adequately only in a few settings when the covariance matrix of the estimator is diagonal in other cases conservative solutions can be obtained by the methods of scheffe bonferroni or sidak 1967 journal of the american statistical association 62 626 633 here we investigate the efficiency of using a simulated critical point for exact intervals which has been suggested before but never put to serious test we find the simulation based method to be completely reliable and essentially exact sample size savings are substantial in our settings 3 19 over the sidak method 4 37 over the bonferroni method and 27 33 over the scheffe method we illustrate the efficiency and flexibility of the simulation based method with case studies in physiology and marine ecology

optimal boundary control of a simplified ericksen leslie system for nematic liquid crystal flows in 2d in this paper we investigate an optimal boundary control problem for a two dimensional simplified ericksen leslie system modelling the incompressible nematic liquid crystal flows the hydrodynamic system consists of the navier stokes equations for the fluid velocity coupled with a convective ginzburg landau type equation for the averaged molecular orientation the fluid velocity is assumed to satisfy a no slip boundary condition while the molecular orientation is subject to a time dependent dirichlet boundary condition that corresponds to the strong anchoring condition for liquid crystals we first establish the existence of optimal boundary controls then we show that the control to state operator is frechet differentiable between appropriate banach spaces and derive first order necessary optimality conditions in terms of a variational inequality involving the adjoint state variables

dynamic programming of the navier stokes equations a class of optimal control problems in viscous flow is studied main results are the pontryagin maximum principle and the verification theorem for the hamilton jacobi bellman equation

controlling the false discovery rate a practical and powerful approach to multiple testing summary the common approach to the multiplicity problem calls for controlling the familywise error rate fwer this approach though has faults and we point out a few a different approach to problems of multiple significance testing is presented it calls for controlling the expected proportion of falsely rejected hypotheses the false discovery rate this error rate is equivalent to the fwer when all hypotheses are true but is smaller otherwise therefore in problems where the control of the false discovery rate rather than that of the fwer is desired there is potential for a gain in power a simple sequential bonferronitype procedure is proved to control the false discovery rate for independent test statistics and a simulation study shows that the gain in power is substantial the use of the new procedure and the appropriateness of the criterion are illustrated with examples

nonlinear model reduction for unsteady discontinuous flows abstract we develop a new nonlinear reduced order model rom based on proper orthogonal decomposition pod which can be used for quantitative simulation of not only smooth flows but also flows with strong discontinuities the new model is derived using a galerkin projection of the fully conservative nonlinear discretized 2 d euler equations onto the pod basis constructed for each conservative variable this approach can be interpreted as a variant of the spectral method with a truncated set of basis functions a system of ordinary differential equations odes derived using this model reduction technique resembles the major nonlinear and conservation properties of the original discretized euler equations the new reduced order model also preserves the stability properties of the discrete full order model equations so that no additional stabilization is required unlike conventional pod based models that are susceptible to numerical instabilities the performance of the new pod rom is evaluated for 2 d compressible unsteady inviscid flows over a wide range of mach numbers including trans and supersonic flows with strong shock waves

h infty feedback boundary stabilization of the two dimensional navier stokes equations we study the robust or h infty exponential stabilization of the linearized navier stokes equations around an unstable stationary solution in a two dimensional domain omega the disturbance is an unknown perturbation in the boundary condition of the fluid flow we determine a feedback boundary control law robust with respect to boundary perturbations by solving a max min linear quadratic control problem next we show that this feedback law locally stabilizes the navier stokes system similar problems have been studied in the literature in the case of distributed controls and disturbances to the authors knowledge it is the first time that the robust stabilization of the navier stokes equations is studied for boundary controls and boundary disturbances

proper orthogonal decomposition approach and error estimation of mixed finite element methods for the tropical pacific ocean reduced gravity model in this paper the tropical pacific ocean reduced gravity model is studied using the proper orthogonal decomposition pod technique of mixed finite element mfe method and an error estimate of pod approximate solution based on mfe method is derived pod is a model reduction technique for the simulation of physical processes governed by partial differential equations e g fluid flows or other complex flow phenomena it is shown by numerical examples that the error between pod approximate solution and reference solution is consistent with theoretical results thus validating the feasibility and efficiency of pod method

numerical solution of a flow control problem vorticity reduction by dynamic boundary action in order to laminarize an unsteady internal flow the vorticity field is minimized in a least squares sense using an optimal control approach the flow model is the navier stokes equation for a viscous incompressible fluid and the flow is controlled by suction and blowing on a part of the boundary a quasi newton method is used for the minimization of a quadratic objective function involving a measure of the vorticity and a regularization term the navier stokes equations are approximated using a finite difference scheme in time and finite element approximations in space accurate expressions for the gradient of the discrete objective function are needed to obtain a satisfactory convergence rate of the minimization algorithm therefore first order necessary conditions for a minimizer of the objective function are derived in the fully discrete case a memory saving device is discussed without which problems of any realistic size especially in three space dimensions would remain computationally intractable the feasibility of the optimal control approach for flow control problems is demonstrated by numerical experiments for a two dimensional flow in a rectangular cavity at a reynolds number high enough for nonlinear effects to be important

boundary value problems and optimal boundary control for the navier stokes system the two dimensional case we study optimal boundary control problems for the two dimensional navier stokes equations in an unbounded domain control is effected through the dirichlet boundary condition and is sought in a subset of the trace space of velocity fields with minimal regularity satisfying the energy estimates an objective of interest is the drag functional we first establish three important results for inhomogeneous boundary value problems for the navier stokes equations namely we identify the trace space for the velocity fields possessing finite energy we prove the existence of a solution for the navier stokes equations with boundary data belonging to the trace space and we identify the space in which the stress vector along the boundary of admissible solutions is well defined then we prove the existence of an optimal solution over the control set finally we justify the use of lagrange multiplier principles derive an optimality system of equations in the weak sense from which optimal states and controls may be determined and prove that the optimality system of equations satisfies in appropriate senses a system of partial differential equations with boundary values

actions of cocommutative hopf algebras abstract let h be a cocommutative hopf algebra acting on an algebra a assuming the base field to be algebraically closed and the h action on a to be integral that is it is given by a coaction of some hopf subalgebra of the finite dual h that is an integral domain we stratify the prime spectrum spec a in terms of the prime spectra of certain commutative algebras for arbitrary h actions in characteristic 0 we show that the largest h stable ideal of a that is contained in a given semiprime ideal of a is semiprime as well

a reduced fve formulation based on pod method and error analysis for two dimensional viscoelastic problem abstract proper orthogonal decomposition pod method has been successfully used in the reduced order modeling of complex systems in this paper we extend the applications of pod method i e combine a classical finite volume element fve method with pod method to establish a reduced fve formulation with lower dimensions and sufficiently high accuracy for two dimensional viscoelastic problem with real practical applied background and analyze the errors between the reduced pod fve solution and the classical fve solution so as to provide scientific theoretic basis for service applications some numerical examples illustrate the fact that the results of numerical computation are consistent with theoretical conclusions moreover it is also shown that the reduced fve formulation based on pod method is feasible and efficient for solving two dimensional viscoelastic problem

reduced order finite difference extrapolation model based on proper orthogonal decomposition for two dimensional shallow water equations including sediment concentration abstract in this study we employ a proper orthogonal decomposition pod method to establish a pod based reduced order finite difference fd extrapolating model with very few degrees of freedom for two dimensional shallow water equations that include the sediment concentration we provide estimates of the error between the accurate solution and classical fd solutions as well as those between the accurate solution and the pod based reduced order fd solutions moreover we present two numerical simulation experiments to demonstrate that the pod based reduced order fd extrapolating model can greatly reduce the computational load thus we validate both the feasibility and efficiency of the pod based reduced order fd extrapolating model

open boundary control problem for navier stokes equations including a free surface data assimilation this paper develops the data assimilation procedure in order to allow for the assimilation of measurements of currents and free surface elevations into an unsteady flow solution governed by the free surface barotropic navier stokes equations the flow is considered in a 2d vertical section in which horizontal and vertical components of velocity are represented as well as the elevation of the free surface since a possible application is to the construction of a coastal limited area circulation model the open boundary control problem is the main scope of the paper the assimilation algorithm is built on the limited memory quasi newton lbfgs method guided by the adjoint sensitivities the analytical step search which is based on the solution of the tangent linear model is used we process the gradients to regularize the solution in numerical experiments we consider different wave patterns with a purpose to specify a set of incomplete measurements which could be sufficient for boundary control identification as a result of these experiments we formulate some important practical conclusions