m psk and m qam ber computation using signal space concepts in this paper we introduce a simple geometric approach that is based on signal space concepts to efficiently evaluate the performance of m ary phase shift keying m psk and m ary quadrature amplitude modulation m qam schemes over an additive white gaussian noise channel in particular new bit error rate approximations are derived and shown to be in excellent agreement with monte carlo simulation results

robust control problems in fluid mechanics abstract in this paper we study a class of robust control problems in fluid mechanics recently proposed by bewley et al physica d 138 3 4 2000 360 using a method of shutyaev russ j numer anal math modell 14 2 1999 137 we provide another proof of the existence and the uniqueness of solutions to the robust control problems under weaker assumptions as compared to those of bewley et al physica d 138 3 4 2000 360 from the numerical point of view the method used in this paper is particularly important since it provides a constructive way to approximate the solutions to these nonlinear control problems

a general framework for robust control in fluid mechanics abstract the application of optimal control theory to complex problems in fluid mechanics has proven to be quite effective when complete state information from high resolution numerical simulations is available p moin t r bewley appl mech rev part 2 47 6 1994 s3 s13 t r bewley p moin r temam j fluid mech 1999 submitted for publication in this approach an iterative optimization algorithm based on the repeated computation of an adjoint field is used to optimize the controls for finite horizon nonlinear flow problems f abergel r temam theoret comput fluid dyn 1 1990 303 325 in order to extend this infinite dimensional optimization approach to control externally disturbed flows in which the controls must be determined based on limited noisy flow measurements alone it is necessary that the controls computed be insensitive to both state disturbances and measurement noise for this reason robust control theory a generalization of optimal control theory has been examined as a technique by which effective control algorithms which are insensitive to a broad class of external disturbances may be developed for a wide variety of infinite dimensional linear and nonlinear problems in fluid mechanics an aim of the present paper is to put such algorithms into a rigorous mathematical framework for it cannot be assumed at the outset that a solution to the infinite dimensional robust control problem even exists in this paper conditions on the initial data the parameters in the cost functional and the regularity of the problem are established such that existence and uniqueness of the solution to the robust control problem can be proven both linear and nonlinear problems are treated and the 2d and 3d nonlinear cases are treated separately in order to get the best possible estimates several generalizations are discussed and an appropriate numerical method is proposed

relation between bit and symbol error probabilities for fsk with ldi detection in m ary gray coded digital communication the bit error probability is usually approximated by the symbol error probability divided by the number of bits in a symbol this approximation is known to be excellent for phase shift keying with coherent detection at high signal to noise ratios and gaussian channel here it is illustrated that this approximation may also be good for m ary frequency shift keying with limiter discriminator integrator detection on gaussian rayleigh and rician channels

the minimal error method for the cauchy problem in linear elasticity numerical implementation for two dimensional homogeneous isotropic linear elasticity abstract in this paper yet another iterative procedure namely the minimal error method mem for solving stably the cauchy problem in linear elasticity is introduced and investigated furthermore this method is compared with another two iterative algorithms i e the conjugate gradient cgm and landweber fridman methods lfm previously proposed by marin et al marin l hao d n lesnic d 2002b conjugate gradient boundary element method for the cauchy problem in elasticity quarterly journal of mechanics and applied mathematics 55 227 247 and marin and lesnic marin l lesnic d 2005 boundary element landweber method for the cauchy problem in linear elasticity ima journal of applied mathematics 18 817 825 respectively in the case of two dimensional homogeneous isotropic linear elasticity the inverse problem analysed in this paper is regularized by providing an efficient stopping criterion that ceases the iterative process in order to retrieve stable numerical solutions the numerical implementation of the aforementioned iterative algorithms is realized by employing the boundary element method bem for two dimensional homogeneous isotropic linear elastic materials

computation of the exact bit error rate of coherent m ary psk with gray code bit mapping the problem of calculating the average bit error probability bep of coherent m ary phase shift keying psk over a gaussian channel has been studied previously in the literature a solution to the problem for systems using a binary reflected gray code brgc to map bits to symbols was first presented by p j lee see ibid vol com 34 p 488 91 1986 we show that the results obtained by lee are incorrect for m spl ges 16 we show that the reason for this is an invalid assumption that the bit error rate ber is independent of the transmitted symbols an assumption which has also propagated to textbooks we give a new expression for the ber of m psk systems using the brgc and compare this with lee s results

computation of the bit error rate of coherent m ary psk with gray code bit mapping efficient computation of the bit error rate ber for the coherent m ary psk signals with gray code bit mapping is considered a closed form expression for the exact ber of 8 ary psk is presented tight upper and lower bounds on ber are also obtained for m ary psk with larger m

an alternative expression for the symbol error probability of mpsk in the presence of i q unbalance this letter provides a new expression for the probability of the phase angle between two vectors perturbed by gaussian noise with in phase quadrature phase i q unbalance in order to simplify the analysis of the error probabilities of m ary phase shift keying mpsk the error probabilities symbol error rates or bit error rates for mpsk with i q balance or unbalance can be presented straightforwardly from the derived expression because the newly derived result is provided in terms of the conventional first order gaussian q function and the joint gaussian q function with a correlation coefficient dependent on m it readily allows rapid evaluation for various cases of practical interest

existence of an optimal solution of a shape control problem for the stationary navier stokes equations this paper is concerned with an optimal shape control problem for the stationary navier stokes system a two dimensional channel flow of an incompressible viscous fluid is examined to determine the shape of a bump on a part of the boundary that minimizes the viscous drag after giving a precise formulation of the extremal problem in a function analytic setting it is shown that optimal solutions exist

retrospective cost adaptive reynolds averaged navier stokes k ω model for data driven unsteady turbulent simulations abstract this paper presents a data driven computational model for simulating unsteady turbulent flows where sparse measurement data is available the model uses the retrospective cost adaptation rca algorithm to automatically adjust the closure coefficients of the reynolds averaged navier stokes rans k turbulence equations to improve agreement between the simulated flow and the measurements the rca rans k model is verified for steady flow using a pipe flow test case and for unsteady flow using a surface mounted cube test case measurements used for adaptation of the verification cases are obtained from baseline simulations with known closure coefficients these verification test cases demonstrate that the rca rans k model can successfully adapt the closure coefficients to improve agreement between the simulated flow field and a set of sparse flow field measurements furthermore the rca rans k model improves agreement between the simulated flow and the baseline flow at locations at which measurements do not exist the rca rans k model is also validated with experimental data from 2 test cases steady pipe flow and unsteady flow past a square cylinder in both test cases the adaptation improves agreement with experimental data in comparison to the results from a non adaptive rans k model that uses the standard values of the k closure coefficients for the steady pipe flow adaptation is driven by mean stream wise velocity measurements at 24 locations along the pipe radius the rca rans k model reduces the average velocity error at these locations by over 35 for the unsteady flow over a square cylinder adaptation is driven by time varying surface pressure measurements at 2 locations on the square cylinder the rca rans k model reduces the average surface pressure error at these locations by 88 8

analysis of lavrentiev finite element methods for data completion problems the variational finite element solution of cauchy s problem expressed in the steklov poincare framework and regularized by the lavrentiev method has been introduced and computationally assessed in azaiez et al inverse probl sci eng 18 1063 1086 2011 the present work concentrates on the numerical analysis of the semi discrete problem we perform the mathematical study of the error to rigorously establish the convergence of the global bias variance error

reduced bases for model updating in structural dynamics based on constitutive relation error abstract this paper deals with the application of a model reduction method to the updating of models of industrial structures with many degrees of freedom the updating method is based on the concept of constitutive relation error this is an iterative method in which each iteration consists of a first step in which the most important errors in the model are localized and a second step in which these errors are corrected the reduction method follows a classical approach in which we introduce a truncated modal basis to which the static responses associated with different excitations are added the efficiency of the method is illustrated on one example of a finite element model containing 10 000 degrees of freedom in the first part we update the mass and stiffness properties of the model based on eigenmodes and eigenfrequencies in the second part the damping properties are updated based on the frequency response functions of the structure

c0 discontinuous galerkin methods for a wind driven ocean circulation model two grid algorithm abstract this paper presents a nonconforming finite element method for a streamfunction formulation of the stationary quasi geostrophic equations which describe the large scale wind driven ocean circulation the streamfunction formulation is a fourth order nonlinear pde and the nonconforming method is based on c 0 elements instead of c 1 elements existence and uniqueness of the approximation are proved and optimal error estimates in several norms of interest are demonstrated under a small data assumption two grid algorithms based on picard and newton type linearizations are then presented to efficiently resolve nonlinearities and computational results are given to demonstrate the efficiency of the algorithm the mediterranean sea example is tested with real world coastline data which illustrates the effectiveness of the two grid approach in the wind driven ocean circulation simulation

regularization of the noisy cauchy problem solution approximated by an energy like method summary this paper focuses on the regularization of noisy cauchy data and unknown boundary conditions approximated by the energy like minimization method after providing considerations necessary for the numerical analysis leading to an adequate stopping criterion for the minimization process we describe the denoising procedure proposed numerical experiments involving singular data are presented copyright 2013 john wiley sons ltd

three dimensional recovery of stress intensity factors and energy release rates from surface full field displacements the identification of stress intensity factors sifs from full field displacement measurements by the optic method is accelerating rapidly following the development of precise digital cameras and image correlation algorithms nevertheless as only surface displacements are available most of the identification methods used up to now have been restricted to problems that are invariant with respect to the normal direction of the free surface and must rely on the plane elasticity hypothesis the problem of sifs identification is tackled here in a full three dimensional framework by first deriving a data completion method in elasticity to determine the elastic displacement field inside the solid on the basis of surface displacements the method solves the cauchy problem for the lame operator after which usual numerical methods for computing sifs and energy release rates can be used numerical applications in three dimensional elasticity are described first for a cracked specimen subjected to 3d loadings and secondly for a heterogeneous specimen in a quasi plane situation

global minimax approximations and bounds for the gaussian q function by sums of exponentials this paper presents a novel systematic methodology to obtain new simple and tight approximations lower bounds and upper bounds for the gaussian q function and functions thereof in the form of a weighted sum of exponential functions they are based on minimizing the maximum absolute or relative error resulting in globally uniform error functions with equalized extrema in particular we construct sets of equations that describe the behaviour of the targeted error functions and solve them numerically in order to find the optimized sets of coefficients for the sum of exponentials this also allows for establishing a trade off between absolute and relative error by controlling weights assigned to the error functions extrema we further extend the proposed procedure to derive approximations and bounds for any polynomial of the q function which in turn allows approximating and bounding many functions of the q function that meet the taylor series conditions and consider the integer powers of the q function as a special case in the numerical results other known approximations of the same and different forms as well as those obtained directly from quadrature rules are compared with the proposed approximations and bounds to demonstrate that they achieve increasingly better accuracy in terms of the global error thus requiring significantly lower number of sum terms to achieve the same level of accuracy than any reference approach of the same form

iterative methods for a class of robust control problems in fluid mechanics in this article we consider a class of iterative methods for the numerical solutions of some robust control problems recently studied in t r bewley r temam and m ziane phys d 138 2000 pp 360 392 these methods are based on repeated computations of the state and the adjoint equations using the properties of the control operator we justify these methods and obtain estimates of their convergence rate numerical solutions of a robust control problem related to data assimilation in oceanography using these algorithms are also presented

classification of unique mappings for 8psk based on bit wise distance spectra the performance of bit interleaved coded modulation bicm with or without iterative decoding id is significantly influenced by the mapping of bits to the symbol constellation our main objective in this paper is to develop a systematic design approach for bicm id schemes ensuring the best possible performance with iterative decoding although useful mappings for bicm id have been found based on various search strategies no attempt has been made to systematically enumerate and classify all unique mappers for a given constellation as the basis for a systematic enumeration and classification we define the average bit wise distance spectrum for a mapping from bits to symbols different bit wise distance spectra are derived assuming no prior information or full prior information respectively the bit wise distance spectra determine corresponding bit wise error probability and bit wise mutual information the latter allows us to use the classification of mappings with unique bit wise distance spectra to also classify mappings with unique extremal points in the corresponding extrinsic information transfer exit curves as an example of our approach we classify 8psk mappings into 86 classes of unique mappings according to bit wise distance spectra the classification can be used to significantly reduce the complexity of the search for suitable mappers for bicm id for 8psk and a given encoder only 86 different mappings need to be investigated as examples of the systematic design approach the best 8psk mappings for minimizing the convergence threshold are found for concatenation with the rate 1 2 5 7 8 and 133 171 8 convolutional codes and the rate 1 2 umts turbo code with identical constituent convolutional codes 15 13 8

matrix free methods for the stability and control of boundary layers this paper presents matrix free methods for the stability analysis and control design of high dimensional systems arising from the discretized linearized navier stokes equations the methods are ap

performances of ds ssma communications with mpsk signaling and complex signature sequences we study a direct sequence spread spectrum multiple access ds ssma communication system with m ary phase shift keyed mpsk signaling users in the system employ complex signature sequences which are modeled as deterministic sequences we present upper and lower bounds for the probability of bit error p b e of a reference transmission first the conditional p b e given the multiple user interference mui is obtained then the conditioning is removed by averaging over the discretized probability density function p d f of the mui the result is an upper or lower bound when the discretized p d f is a shifted high or shifted low version of a sectioned p d f this process requires the two dimensional p d f of the mui which is derived arbitrarily tight bounds can be obtained at the cost of increased computation numerical results are presented for complex fzc and near optimal 4 phase sequences as well as real binary gold sequences for bpsk 4 psk and 8 psk gray code bit mapping is assumed although the analysis can be applied to other bit mappings results show that complex sequences can yield better performance than binary sequences in mpsk signaling using complex sequences the number of available signature sequences is greatly enlarged

error estimate procedure in the finite element method and applications statically and kinematically admissible fields are explicitly derived from the finite element solution of the primal form of linear models the error on constitutive law for these fields yields an expression of the finite element error moreover the contribution of each element to this error allows to implement an automatic mesh refinement procedure leading to a uniform distribution of a given accuracy

optimal control problems with state constraint governed by navier stokes equations abstract this work deals with the existence of optimal solution and the maximum principle for optimal control problem governed by navier stokes equations with state constraint of pointwise type in 3d strong results in 2d are also given

space shift keying ssk mimo with practical channel estimates in this paper we study the performance of space modulation for multiple input multiple output mimo wireless systems with imperfect channel knowledge at the receiver we focus our attention on two transmission technologies which are the building blocks of space modulation i space shift keying ssk modulation and ii time orthogonal signal design tosd ssk modulation which is an improved version of ssk modulation providing transmit diversity we develop a single integral closed form analytical framework to compute the average bit error probability abep of a mismatched detector for both ssk and tosd ssk modulations the framework exploits the theory of quadratic forms in conditional complex gaussian random variables rvs along with the gil pelaez inversion theorem the analytical model is very general and can be used for arbitrary transmit and receive antennas fading distributions fading spatial correlations and training pilots the analytical derivation is substantiated through monte carlo simulations and it is shown over independent and identically distributed i i d rayleigh fading channels that ssk modulation is as robust as single antenna systems to imperfect channel knowledge and that tosd ssk modulation is more robust to channel estimation errors than the alamouti scheme furthermore it is pointed out that only few training pilots are needed to get reliable enough channel estimates for data detection and that transmit and receive diversity of ssk and tosd ssk modulations are preserved even with imperfect channel knowledge

bit error probability for coherent m ary psk systems a simple technique for evaluating the bit error probability of coherent m ary phase shift keying psk with any bit mapping is proposed closed form expressions are given in terms of error functions for half and quadrant plane probabilities in the decision space avoiding the numerical evaluation of complicated integrals that occurs in the direct method bit error probability expressions for m ary psk with gray natural binary and folded binary bit mappings are derived

numerical analysis of an energy like minimization method to solve the cauchy problem with noisy data this paper is concerned with solving the cauchy problem for an elliptic equation by minimizing an energy like error functional and by taking into account noisy cauchy data after giving some fundamental results numerical convergence analysis of the energy like minimization method is carried out and leads to adapted stopping criteria for the minimization process depending on the noise rate numerical examples involving smooth and singular data are presented

h control theory of fluid dynamics robust or h control theory has been an expanding subject in recent years because of its wide applications and its close connection to operator theory on hardy spaces we develop an hcontrol theor

sensitivity of inverse advection diffusion reaction to sensor and control a low computational cost tool a two dimensional 2d concentration field may be reconstructed using inverse advection diffusion reaction based on pointwise sensor outputs the studied reconstruction process consists in defining fictitious boundaries and identifying the optimal concentrations on these boundaries that minimize the data misfit the minimization is performed by means of the adjoint method the reconstruction process is observed to fail for some sets of sensor placements therefore in this paper we aim to develop a low computational cost framework that can be used to identify badly placed sensors and to reveal potentially optimal sensor placement from this framework we have derived a sensitivity tool that can predict for a given set of sensors which boundary concentrations are easy or difficult to identify using the inverse method this tool only requires the resolution of an adjoint problem it is compared with the sensitivity to observation method in a 2d water pipe junction with 2000 reynolds number and 1000 peclet number the compared methods do produce similar quantitative and qualitative results

a priori and a posteriori error analysis for a large scale ocean circulation finite element model we consider the finite element solution of the stream function vorticity formulation for a large scale ocean circulation model first we study existence and uniqueness of solution for the continuous and discrete problems under appropriate regularity assumptions we prove that the stream function can be computed with an error of order h in h1 seminorm second we introduce and analyze an h adaptive mesh refinement strategy to reduce the spurious oscillations and poor resolution which arise when convective terms are dominant we propose an a posteriori anisotropic error indicator based on the recovery of the hessian from the finite element solution which allows us to obtain well adapted meshes the numerical experiments show an optimal order of convergence of the adaptive scheme furthermore this strategy is efficient to eliminate the oscillations around the boundary layer

h boundary control with state feedback the hyperbolic case we solve the h control problem with state feedback for infinite dimensional boundary control systems of hyperbolic type with distributed disturbances

a data driven adaptive reynolds averaged navier stokes k ω model for turbulent flow abstract this paper presents a new data driven adaptive computational model for simulating turbulent flow where partial but incomplete measurement data is available the model automatically adjusts the closure coefficients of the reynolds averaged navier stokes rans k turbulence equations to improve agreement between the simulated flow and the measurements this data driven adaptive rans k d dark model is validated with 3 canonical flow geometries pipe flow backward facing step and flow around an airfoil for all test cases the d dark model improves agreement with experimental data in comparison to the results from a non adaptive rans k model that uses standard values of the closure coefficients for the pipe flow adaptation is driven by mean stream wise velocity data from 42 measurement locations along the pipe radius and the d dark model reduces the average error from 5 2 to 1 1 for the 2 dimensional backward facing step adaptation is driven by mean stream wise velocity data from 100 measurement locations at 4 cross sections of the flow in this case d dark reduces the average error from 40 to 12 for the naca 0012 airfoil adaptation is driven by surface pressure data at 25 measurement locations the d dark model reduces the average error in surface pressure coefficients from 45 to 12

constitutive law gap functionals for solving the cauchy problem for linear elliptic pde different numerical methods have been proposed in the literature for solving the cauchy problem for linear elliptic equations modelling different physical phenomena laplace equation for the stationary heat equation lame operator in elasticity etc the aim of this paper is to situate these methods fixed point methods and domain decomposition based techniques in a general variational framework and show the equivalence between them a generalization of the energy gap method proposed by the authors for fourier like boundary conditions is studied then a comparison of these methods by using an analytical example and two numerical problems with complicated geometry or boundary conditions is performed in order to estimate their numerical performances it appeared that no method stood out from the others due to better or worse performance according to the situations the classification of the performances in terms of conditioning an essential factor because the cauchy problem is ill posed or in terms of the capacity to deal with strongly spatially variable data depends on the problem dealt with the issue of regularization is not addressed here because it is method dependent and distorts the appreciation of the basic performance of the different approaches

h_ infty boundary control with state feedback the hyperbolic case necessary and sufficient conditions of existence for the h infty control problem associated with infinite dimensional boundary control systems of hyperbolic type are given

hopf bifurcation of the unsteady regularized driven cavity flow abstract a numerical simulation of the unsteady incompressible flow in the unit cavity is performed by using a chebyshev tau approximation for the space variables the high accuracy of the spectral methods and the condensed distribution of the chebyshev collocation points near the boundary enable us to obtain reliable results for high reynolds numbers with a moderate number of modes it is found that the flow converges to a stationary state for reynolds numbers re up to 10 000 for reynolds numbers larger than a critical value 10 000

a novel dynamic framework for subgrid scale parametrization of mesoscale eddies in quasigeostrophic turbulent flows abstract this paper puts forth a modular dynamic subgrid scale modeling framework for large eddy simulation of quasigeostrophic turbulence based on minimizing the errors between structural and functional subgrid scale models the approximate deconvolution ad procedure is used to estimate the free modeling parameters for the eddy viscosity coefficient parameterized in space and time using the smagorinsky and leith models the novel idea here is to estimate the modeling parameters using the ad method rather than the traditionally used test filtering approach first a priori and a posteriori analyses are presented for solving a canonical homogeneous isotropic decaying turbulence problem the proposed model is then applied to a wind driven quasigeostrophic four gyre ocean circulation problem which is a standard prototype of more realistic ocean dynamics results show that the proposed model captures the quasi stationary ocean dynamics and provides the time averaged four gyre circulation patterns taking locally resolved flow characteristics into account the model dynamically provides higher eddy viscosity values for lower resolutions

the method of fundamental solutions for the cauchy problem in two dimensional linear elasticity in this paper the application of the method of fundamental solutions to the cauchy problem in two dimensional isotropic linear elasticity is investigated the resulting system of linear algebraic equations is ill conditioned and therefore its solution is regularised by employing the first order tikhonov functional while the choice of the regularisation parameter is based on the l curve method numerical results are presented for both smooth and piecewise smooth geometries as well as for constant and linear stress states the convergence and the stability of the method with respect to increasing the number of source points and the distance between the source points and the boundary of the solution domain and decreasing the amount of noise added into the input data respectively are analysed

numerical analysis of an energy like minimization method to solve a parabolic cauchy problem with noisy data this paper is concerned with solving the cauchy problem for the parabolic equation by minimizing an energy like error functional and by taking into account noisy cauchy data after giving some fundamental results numerical convergence analysis of the energy like minimization method is carried out and leads to an adapted stopping criteria depending on noise rate for the minimization process numerical experiments are performed and confirm the theoretical convergence order and the good behavior of the minimization process

an energy error based method for the resolution of the cauchy problem in 3d linear elasticity a new method is described for the problem of expanding known displacement fields at the boundary of a solid together with the surface tractions on it towards the solid interior up to the inaccessible part of the boundary the solid is supposedly linearly elastic with known elastic moduli but not necessarily homogeneous nor isotropic the problem is the cauchy problem for the lame operator a new form of this cauchy problem suited for applications associated with surface tangential fields measurements is also stated and studied the method is based on the splitting of the elastic fields into two separate solutions of wellposed problems the gap between these fields is subsequently minimised with respect to the unknown boundary data in order to produce the desired expanded elastic fields the gap used here is an energy error associated with the elastic energy of the system various 3d applications are given including non linear boundary conditions on the unreachable boundary

tight error bounds for nonuniform signaling over awgn channels we consider a bonferroni type lower bound due to kounias 1968 on the probability of a finite union the bound is expressed in terms of only the individual and pairwise event probabilities however it suffers from requiring an exponentially complex search for its direct implementation we address this problem by presenting a practical algorithm for its evaluation this bound is applied together with two other bounds a recent lower bound the kat bound and a greedy algorithm implementation of an upper bound due to hunter 1976 to examine the symbol error p sub a and bit error p sub b probabilities of an uncoded communication system used in conjunction with m ary phase shift keying psk quadrature amplitude qam psk qam modulations and maximum a posteriori map decoding over additive white gaussian noise awgn channels it is shown that the bounds which can be efficiently computed provide an excellent estimate of the error probabilities over the entire range of the signal to noise ratio snr e sub b n sub 0 the new algorithmic bound and the greedy bound are particularly impressive as they agree with the simulation results even during very severe channel conditions

exact expression for the ber of rectangular qam with arbitrary constellation mapping the exact closed form expression for the bit error rate ber of rectangular quadrature amplitude modulation qam is given the presented formula is independent of the bit mapping and it is thus particularly useful in the design and analysis of modulation schemes employing non gray mapping compared with the so called expurgated bound and the union bound our expression is shown to accurately predict the ber in the low signal to noise ratio range where the bounding techniques fail

a two level finite element discretization of the streamfunction formulation of the stationary quasi geostrophic equations of the ocean in this paper we proposed a two level finite element discretization of the nonlinear stationary quasi geostrophic equations which model the wind driven large scale ocean circulation optimal error estimates for the two level finite element discretization were derived numerical experiments for the two level algorithm with the argyris finite element were also carried out the numerical results verified the theoretical error estimates and showed that for the appropriate scaling between the coarse and fine mesh sizes the two level algorithm significantly decreases the computational time of the standard one level algorithm

a computational framework for the regularization of adjoint analysis in multiscale pde systems this paper examines the regularization opportunities available in the adjoint analysis and optimization of multiscale pde systems regularization may be introduced into such optimization problems by modifying the form of the evolution equation and the forms of the norms and inner products used to frame the adjoint analysis typically l2 brackets are used in the definition of the cost functional the adjoint operator and the cost functional gradient if instead we adopt the more general sobolev brackets the various fields involved in the adjoint analysis may be made smoother and therefore easier to resolve numerically the present paper identifies several relationships which illustrate how the different regularization options fit together to form a general framework the regularization strategies proposed are exemplified using a id kuramoto sivashinsky forecasting problem and computational examples are provided which exhibit their utility a multiscale preconditioning algorithm is also proposed that noticeably accelerates convergence of the optimization procedure application of the proposed regularization strategies to more complex optimization problems of physical and engineering relevance is also discussed

numerical simulations of a two layer quasi geostrophic equation of the ocean our object in this article is to present some numerical schemes for a two layer quasi geostrophic model of the ocean and to study the stability of these schemes we prove the unconditional stability of our numerical schemes numerical results from a wind driven two layer quasi geostrophic model of the ocean using these schemes are also presented

optimal control of thermally convected fluid flows we examine the optimal control of stationary thermally convected fluid flows from the theoretical and numerical point of view we use thermal convection as control mechanism that is control is effected through the temperature on part of the boundary control problems are formulated as constrained minimization problems existence of optimal control is given and a first order necessary condition of optimality from which optimal solutions can be obtained is established we develop numerical methods to solve the necessary condition of optimality and present computational results for control of cavity and channel type flows showing the feasibility of the proposed approach

adjoint based iterative method for robust control problems in fluid mechanics in this article we study the convergence of an adjoint based iterative method recently proposed in t r bewley r temam and m ziane phys d 138 2000 pp 360 392 for the numerical solution of a class of nonlinear robust control problems in fluid mechanics under weaker assumptions than those of t tachim medjo numer funct anal optim 23 2002 pp 849 873 we prove the convergence of the algorithm and we obtain an estimate of the convergence rate numerical solutions of a robust control problem related to data assimilation in oceanography are presented to illustrate the method

constrained optimal control of navier stokes flow by semismooth newton methods abstract we propose and analyze a semismooth newton type method for the solution of a pointwise constrained optimal control problem governed by the time dependent incompressible navier stokes equations the method is based on a reformulation of the optimality system as an equivalent nonsmooth operator equation we analyze the flow control problem and prove q superlinear convergence of the method in the numerical implementation adjoint techniques are combined with a truncated conjugate gradient method numerical results are presented that support our theoretical results and confirm the viability of the approach

relation between bit and symbol error probabilities for dpsk and fsk with differential phase detection in m ary gray coded dpsk and fsk with differential phase detection the bit error probability is usually approximated by the symbol error probability divided by the number of bits in a symbol this approximation is known to be excellent for psk with large signal to noise ratios in a gaussian channel in other cases this approximation may be questionable here we compute the exact values of bit error probability for dpsk and fsk in gaussian rayleigh and rician channels we also compute the relative error involved in this approximation the conclusion is that except for very low values of signal to noise ratio the approximation is good for all channels

optimal control of fluid dynamic systems with state constraint of pointwise type abstract the aim of this work is to obtain the maximum principle by spike perturbation for the optimal control problem with pointwise type state constraint governed by 3 dimensional fluid dynamic systems

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

bounds and approximations for rapid evaluation of coherent mpsk error probabilities the error probability for mpsk detection is expressed here as a sum of a familiar upper bound approximation and a correction term which is well suited for numerical integration an asymptotic expansion of the correction term is derived from which simple and extremely tight upper and lower bounds are obtained relative errors in using these bounds and approximations of them are graphed for cases of practical interest

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

on the optimality of the binary reflected gray code this paper concerns the problem of selecting a binary labeling for the signal constellation in m psk m pam and m qam communication systems gray labelings are discussed and the original work by frank gray is analyzed as is noted the number of distinct gray labelings that result in different bit error probability grows rapidly with increasing constellation size by introducing a recursive gray labeling construction method called expansion the paper answers the natural question of what labeling among all possible constellation labelings will give the lowest possible average probability of bit errors for the considered constellations under certain assumptions on the channel the answer is that the labeling proposed by gray the binary reflected gray code is the optimal labeling for all three constellations which has surprisingly never been proved before

a fundamental limit on the heat flux in the control of incompressible channel flow this paper proves that there are no zero net wall transpiration control strategies that can sustain net heat flux below the laminar level in an incompressible channel flow with constant temperature walls the result represents a fundamental limit on the performance of a controlled nonlinear system as measured by a linear cost function over a broad class of admissible initial conditions and control inputs not a zero sum tradeoff in the frequency domain or time domain both buoyancy effects via the boussinesq approximation and viscous heating effects are accounted for and phenomenological justification for the result is also given the boundedness of solutions of the two way coupled navier stokes energy equations when both buoyancy and viscous heating are accounted for is also discussed and a new proof of existence under an appropriate small data assumption is provided

numerical solution of the cauchy problem for steady state heat transfer in two dimensional functionally graded materials the application of the method of fundamental solutions to the cauchy problem for steady state heat conduction in two dimensional functionally graded materials fgms is investigated the resulting system of linear algebraic equations is ill conditioned and therefore regularization is required in order to solve this system of equations in a stable manner this is achieved by employing the zeroth order tikhonov functional while the choice of the regularization parameter is based on the l curve method numerical results are presented for both smooth and piecewise smooth geometries the convergence and the stability of the method with respect to increasing the number of source points and the distance between the source points and the boundary of the solution domain and decreasing the amount of noise added into the input data respectively are analysed