hydraulic conductivity estimation in partially saturated soils using the adjoint method abstract an iterative algorithm based on the adjoint method for the estimation of the saturated hydraulic conductivity k in a partially saturated soil q is proposed groundwater flow in q is assumed to be described by richards equation the optimization problem minimizes the l2 error between the pressure head values p k x t calculated as the solution of a direct problem and the measured values of the pressure head at discrete points inside the domain q the exact gradient of the cost functional is obtained by solving an appropriate adjoint problem which is derived from the equations of the g teaux derivatives of the pressure head with respect to the parameter k a finite element procedure is used to obtain approximate solutions of the direct and adjoint problems and the g teaux derivatives a discrete form of the expression of the gradient of the cost functional at the continuous level is used inside a nonlinear conjugate gradient iteration to solve the optimization problem a numerical example showing the implementation of the algorithm to estimate the saturated hydraulic conductivity k x during an hypothetical infiltration experiment in a heterogeneous soil is also presented

stochastic inverse heat conduction using a spectral approach an adjoint based functional optimization technique in conjunction with the spectral stochastic finite element method is proposed for the solution of an inverse heat conduction problem in the presence of uncertainties in material data process conditions and measurement noise the ill posed stochastic inverse problem is restated as a conditionally well posed l 2 optimization problem the gradient of the objective function is obtained in a distributional sense by defining an appropriate stochastic adjoint field the l 2 optimization problem is solved using a conjugate gradient approach accuracy and effectiveness of the proposed approach is appraised with the solution of several stochastic inverse heat conduction problems

physics based gmres preconditioner for compressible and incompressible navier stokes equations abstract this paper presents the implementation of a local physics preconditioning mass matrix 8 for an unified approach of 3d compressible and incompressible navier stokes equations using an supg finite element formulation and gmres implicit solver during the last years a lot of effort has been dedicated to finding a unified approach for compressible and incompressible flow in order to treat fluid dynamic problems with a very wide range of mach and reynolds numbers 10 26 37 on the other hand supg finite element formulation and gmres implicit solver is one of the most robust combinations to solve state of the art cfd problems 1 6 9 22 29 30 31 the selection of a good preconditioner and its performance on parallel architecture is another open problem in cfd community the local feature of the preconditioner presented here means that no communication among processors is needed when working on parallel architectures due to these facts we consider that this research can make some contributions towards the development of a unified fluid dynamic model with high rates of convergence for any combination of mach and reynolds numbers being very suitable for massively parallel computations finally it is important to remark that while this kind of preconditioning produces stabilized results in nearly incompressible regimes the standard version exhibits some numerical drawbacks that lead to solutions without physical meaning

an adjoint method for the inverse design of solidification processes with natural convection this paper presents a finite element algorithm based on the adjoint method for the design of a certain class of solidification processes in particular the paper addresses the design of directional solidification processes for pure materials such that a desired freezing front heat flux and growth velocity are achieved this is the first time that an infinite dimensional continuum adjoint formulation is obtained and implemented for the solution of such inverse design problems with moving boundaries and boussinesq incompressible flow the present design problem belongs to a category of inverse problems in which one is looking for the unknown conditions in part of the boundary while overspecified boundary conditions are supplied in another part of the boundary here the freezing interface the solidification design problem is mathematically posed as a whole time domain optimization problem the gradient of the cost functional is calculated using the solution of an appropriately defined continuous adjoint problem the minimization process is realized by the conjugate gradient method via the solutions of the direct adjoint and sensitivity sub problems the proposed methodology is demonstrated with the solidification of an initially superheated liquid aluminum confined in a square mold the non uniformity in the casting product in the direction of gravity due to the existence of natural convection in the melt is emphasized the inverse design problem is then posed as finding the appropriate spatial temporal variations of the boundary heat flux on the vertical mold walls that can eliminate or reduce the effects of convection on the freezing interface heat fluxes and growth velocity the numerical example demonstrates the accuracy and convergence of the adjoint formulation finally open related research design problems are discussed 1998 john wiley sons ltd

artifact reduction in low bit rate dct based image compression this correspondence presents a scheme for artifact reduction of low bit rate discrete cosine transform compressed dct compressed images first the dc coefficients are calibrated using gradient continuity constraints then an improved huber markov random field based hmrf based smoothing is applied the constrained optimization is implemented by the iterative conditional mode icm final reconstructions of typical images with improvements in both visual quality and peak signal to noise ratio psnr are also shown

conjugate gradient method for the robin inverse problem associated with the laplace equation this paper studies a non linear inverse problem associated with the laplace equation of identifying the robin coefficient from boundary measurements a variational formulation of the problem is suggested thereby transforming it into an optimization problem mathematical properties relevant to its numerical computation are established the optimization problem is solved using the conjugate gradient method in conjunction with the discrepancy principle and the algorithm is implemented using the boundary element method numerical results are presented for several benchmark problems with both exact and noisy data and the convergence of the algorithm with respect to mesh refinement and decreasing the amount of noise in the data is investigated copyright 2006 john wiley sons ltd

a functional optimization approach to an inverse magneto convection problem a formulation and an fem implementation for the solution of an ill posed inverse design magneto convection problem is proposed in particular an incompressible viscous electrically conducting liquid material occupying a given domain is considered convection is driven by buoyancy effects as well as a lorentz force generated due to the applied magnetic field thermal boundary conditions are only prescribed in the part h0 of the boundary in addition the temperature distribution is also prescribed in the part i of the boundary h1 where the heat flux is known i e i is a boundary with overspecified thermal boundary conditions the inverse magneto convection problem is posed as an optimization problem in l2 i 0 tmax for the calculation of the boundary heat flux qo x t with x t h0 0 tmax the optimization scheme minimizes the discrepancy m x t x t qo l2 i 0 tmax between the temperature x t qo calculated from the solution of a direct problem for each flux qo and the desired or measured temperature m x t on the boundary i the exact l2 gradient of the cost functional is obtained from appropriately defined adjoint fields the adjoint problem is defined from the sensitivity operators obtained by linearization of the equations governing the direct problem the standard supg pspg stabilized fem formulation for incompressible fluid flow simulation is here extended to thermo magnetically driven flows the proposed fem formulation is used for the calculation of the direct adjoint and sensitivity thermal fluid flow and electric potential fields the entire optimization algorithm is solved using the conjugate gradient method finally the method is demonstrated through the solution of a few inverse problems with known results the need for regularization is identified in one of the example problems with uniformly distributed random errors in the temperature data m x t and a h1 regularized formulation is introduced to obtain stable solutions finally the numerical results are elucidated and potential applications are addressed

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

circumventing storage limitations in variational data assimilation studies an application of pontryagin s maximum principle data assimilation is used to blend possibly incomplete or nonuniformly distributed spatio temporal observational data into geophysical models used extensively in engineering control theory applications data assimilation has been introduced relatively recently into meteorological forecasting natural resource recovery modeling and climate dynamics variational data assimilation is a promising assimilation technique in which it is assumed that the optimal state of the system is an extrema of a carefully chosen cost function provided that an adjoint model is available the required model gradient can be computed by integrating the model forward and its adjoint backward the gradient is then used to extremize the cost function with a suitable iterative or conjugate gradient solver the problem addressed in this study is the explosive growth in both on line computer memory and remote storage requirements of computing the gradient by the forward adjoint technique which characterizes large scale assimilation studies storage limitations impose severe limitation on the size of assimilation studies even on the largest computers by using a recursive strategy a schedule can be constructed that enables the forward adjoint model runs to be performed in such a way that storage requirements can be traded for longer computational times this generally applicable strategy enables data assimilation studies on significantly larger domains than would otherwise be possible given the particular hardware constraints without compromising the outcome in any way furthermore it is shown that this tradeoff is indeed viable and that when the schedule is optimized the storage and computational times grow at most logarithmically

growth motion and 1 parameter families of symmetry sets associated to every plane curve there is the locus of centres of circles bitangent to that curve the so called symmetry set of the curve we can view this set as the spine of our curve which can be recovered by taking the envelope of circles of varying radii along this spine varying the symmetry set in some isotopy while keeping the radius function fixed may be viewed as crudely modelling motion of the original curve viewed as a biological object fixing the symmetry set and varying the radius function can be considered to model growth crudely in this paper we shall describe the generic changes in the curves which take place in the process of growth and motion and outline the corresponding results for spheres centred on a space curve we also use the idea of a stratified morse function to describe the generic changes which occur in one parameter families of full bifurcation sets in the plane applying this to the bifurcation set of distance squared functions we find all the transitions of a symmetry set and evolute which occur in a generic isotopy of a plane curve

distributions of the two dimensional dct coefficients for images for a two dimensional discrete cosine transform dct image coding system there have been different assumptions concerning the distributions of the transform coefficients this paper presents results of distribution tests that indicate that for many images the statistics of the coefficients are best approximated by a gaussian distribution for the dc coefficient and a laplacian distribution for the other coefficients furthermore from a simulation of the dct coding system it is shown that the assumption that the coefficients are laplacian yields a higher actual output signal to noise ratio and a much better agreement between theory and simulation than the gaussian assumption

a medial axis transformation for grayscale pictures blum s medial axis transformation mat for binary pictures yields medial axis points that lie midway between opposite borders of a region or along angle bisectors this note discusses a generalization of the mat in which a score is computed for each point p of a grayscale picture based on the gradient magnitudes at pairs of points that have p as their midpoint these scores are high at points that lie midway between pairs of antiparallel edges or along angle bisectors so that they define a mat like skeleton which we may call the gradmat however this skeleton is rather sensitive to the presence of noise edges or to irregularities in the region edges and it also is subject to artifacts created by pairs of edges belonging to different objects

general choice of the regularization functional in regularized image restoration the determination of the regularization parameter is an important issue in regularized image restoration since it controls the trade off between fidelity to the data and smoothness of the solution a number of approaches have been developed in determining this parameter in this paper a new paradigm is adopted according to which the required prior information is extracted from the available data at the previous iteration step i e the partially restored image at each step we propose the use of a regularization functional instead of a constant regularization parameter the properties such a regularization functional should satisfy are investigated and two specific forms of it are proposed an iterative algorithm is proposed for obtaining a restored image the regularization functional is defined in terms of the restored image at each iteration step therefore allowing for the simultaneous determination of its value and the restoration of the degraded image both proposed iteration adaptive regularization functionals are shown to result in a smoothing functional with a global minimum so that its iterative optimization does not depend on the initial conditions the convergence of the algorithm is established and experimental results are shown

singular improper affine spheres from a given lagrangian submanifold abstract given a lagrangian submanifold l of the affine symplectic 2n space one can canonically and uniquely define a center chord and a special improper affine sphere of dimension 2n both of whose sets of singularities contain l although these improper affine spheres ias always present other singularities away from l the off shell singularities studied in 8 they may also present singularities other than l which are arbitrarily close to l the so called singularities on shell these on shell singularities possess a hidden z 2 symmetry that is absent from the off shell singularities in this paper we study these canonical ias obtained from l and their on shell singularities in arbitrary even dimensions and classify all stable lagrangian legendrian singularities on shell that may occur for these ias when l is a curve or a lagrangian surface

projection based spatially adaptive reconstruction of block transform compressed images at the present time block transform coding is probably the most popular approach for image compression for this approach the compressed images are decoded using only the transmitted transform data we formulate image decoding as an image recovery problem according to this approach the decoded image is reconstructed using not only the transmitted data but in addition the prior knowledge that images before compression do not display between block discontinuities a spatially adaptive image recovery algorithm is proposed based on the theory of projections onto convex sets apart from the data constraint set this algorithm uses another new constraint set that enforces between block smoothness the novelty of this set is that it captures both the local statistical properties of the image and the human perceptual characteristics a simplified spatially adaptive recovery algorithm is also proposed and the analysis of its computational complexity is presented numerical experiments are shown that demonstrate that the proposed algorithms work better than both the jpeg deblocking recommendation and our previous projection based image decoding approach

hallucinating face in the dct domain in this paper we propose a novel learning based face hallucination framework built in the dct domain which can produce a high resolution face image from a single low resolution one the problem is formulated as inferring the dct coefficients in frequency domain instead of estimating pixel intensities in spatial domain our study shows that dc coefficients can be estimated fairly accurately by simple interpolation based methods ac coefficients which contain the information of local features of face image cannot be estimated well using interpolation a simple but effective learning based inference model is proposed to infer the ac coefficients experiments have been conducted to demonstrate the effectiveness of the proposed method in producing high quality hallucinated face images

on the computation of the affine skeletons of planar curves and the detection of skew symmetry abstract in this paper we discuss a new approach to compute discrete skeletons of planar shapes which is based on affine distances being therefore affine invariant the method works with generic curves that may contain concave sections a dynamical interpretation of the affine skeleton construction based on curve evolution is discussed as well we propose an efficient implementation of the method and give examples we also demonstrate how to use this method to detect affine skew symmetry in real images

an approach to the parameterization of structure for fast categorization a decomposition is described which parameterizes the geometry and appearance of contours and regions of gray scale images with the goal of fast categorization to express the contour geometry a contour is transformed into a local global space from which parameters are derived classifying its global geometry arc inflexion or alternating and describing its local aspects degree of curvature edginess symmetry regions are parameterized based on their symmetric axes which are evolved with a wave propagation process enabling to generate the distance map for fragmented contour images the methodology is evaluated on three image sets the caltech 101 set and two sets drawn from the corel collection the performance nearly reaches the one of other categorization systems for unsupervised learning

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

affine plane curve evolution a fully consistent scheme we present an accurate numerical scheme for the affine plane curve evolution and its morphological extension to grey level images this scheme is based on the iteration of a nonlocal fully affine invariant and numerically stable operator which can be exactly computed on polygons the properties of this operator ensure that a few iterations are sufficient to achieve a very good accuracy unlike classical finite difference schemes that generally require a lot of iterations convergence results are provided as well as theoretical examples and experiments

on the limited memory bfgs method for large scale optimization we study the numerical performance of a limited memory quasi newton method for large scale optimization which we call the l bfgs method we compare its performance with that of the method developed by buckley and lenir 1985 which combines cycles of bfgs steps and conjugate direction steps our numerical tests indicate that the l bfgs method is faster than the method of buckley and lenir and is better able to use additional storage to accelerate convergence we show that the l bfgs method can be greatly accelerated by means of a simple scaling we then compare the l bfgs method with the partitioned quasi newton method of griewank and toint 1982a the results show that for some problems the partitioned quasi newton method is clearly superior to the l bfgs method however we find that for other problems the l bfgs method is very competitive due to its low iteration cost we also study the convergence properties of the l bfgs method and prove global convergence on uniformly convex problems

untangling the blum medial axis transform for over 30 years blum s medial axis transform mat has proven to be an intriguing tool for analyzing and computing with form but it is one that is notoriously difficult to apply in a robust and stable way it is well documented how a tiny change to an object s boundary can cause a large change in its mat there has also been great difficulty in using the mat to decompose an object into a hierarchy of parts reflecting the natural parts hierarchy that we perceive this paper argues that the underlying cause of these problems is that medial representations embody both the substance of each part of an object and the connections between adjacent parts a small change in an object s boundary corresponds to a small change in its substance but may involve a large change in its connection information the problems with blum s mat are generated because it does not explicitly represent this dichotomy of information to use the blum mat to it s full potential this paper presents a method for separating the substance and connection information of an object this provides a natural parts hierarchy while eliminating instabilities due to small boundary changes the method also allows for graded fuzzy classifications of object parts to match the ambiguity in human perception of many objects

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

control of a simplified unsteady film cooling flow using gradient based optimization maximization of film cooling effectiveness in an idealized film cooling flow is accomplished using a gradient based control strategy the state equations are the two dimensional unsteady incompressible navier stokes equations and the temperature equation the control is a spatially and temporally varying normal velocity boundary condition subject to a constraint of zero mass and energy flux the control that maximizes the objective function is found using a conjugate gradient method in which the gradient of the objective function with respect to the control variables is obtained from solving a set of adjoint equations the effectiveness of choices for the objective function are examined along with the effect of the event horizon over which the control is obtained by the optimizer drastic improvements in the film cooling effectiveness are obtained for certain choices of the objective function and event horizon although not a specific target of the optimizer one result of the control is that the wall jet remains attached to the wall the numerical issues involved with finding the control are discussed and the features of the resulting control are analyzed with the goal of understanding the mechanisms that affect the film cooling effectiveness

the adjoint method for an inverse design problem in the directional solidification of binary alloys this paper presents a systematic procedure based on the adjoint method for solving a class of inverse directional alloy solidification design problems in which a desired growth velocityvfis achieved under stable growth conditions to the best of our knowledge this is the first time that a continuum adjoint formulation is proposed for the solution of an inverse problem with simultaneous heat and mass transfer thermo solutal convection and phase change in this paper the interfacial stability is considered to imply a sharp solid liquid freezing interface this condition is enforced using the constitutional undercooling criterion in the form of an inequality constraint between the thermal and solute concentration gradients gandgc respectively at the freezing front the main unknowns of the design problem are the heating and or cooling boundary conditions on the mold walls the inverse design problem is formulated as a functional optimization problem the cost functional is defined by the square of thel2norm of the deviation of the freezing interface temperature from the temperature corresponding to thermodynamic equilibrium a continuum adjoint system is derived to calculate the adjoint temperature concentration and velocity fields such that the gradient of the cost functional can be expressed analytically the cost functional minimization process is realized by the conjugate gradient method via the finite element method solutions of the continuum direct sensitivity and adjoint problems the developed formulation is demonstrated with an example of designing the directional solidification of a binary aqueous solution in a rectangular mold such that a stable vertical interface advances from left to right with a desired growth velocity

the geometric cauchy problem for the hyperbolic hessian one equation abstract we solve the problem of finding all indefinite improper affine spheres passing through a given regular curve of r 3 with a prescribed affine co normal vector field along this curve we prove the problem is well posed when the initial data are non characteristic and show that uniqueness of the solution can fail at characteristic directions as application we classify the indefinite improper affine spheres admitting a geodesic planar curve

a mathematical analysis of the dct coefficient distributions for images over the past two decades there have been various studies on the distributions of the dct coefficients for images however they have concentrated only on fitting the empirical data from some standard pictures with a variety of well known statistical distributions and then comparing their goodness of fit the laplacian distribution is the dominant choice balancing simplicity of the model and fidelity to the empirical data yet to the best of our knowledge there has been no mathematical justification as to what gives rise to this distribution we offer a rigorous mathematical analysis using a doubly stochastic model of the images which not only provides the theoretical explanations necessary but also leads to insights about various other observations from the literature this model also allows us to investigate how certain changes in the image statistics could affect the dct coefficient distributions

simulating the grassfire transform using an active contour model a method for shape description of planar objects that integrates both region and boundary features is presented the method is an implementation of a 2d dynamic grassfire that relies on a distance surface on which elastic contours minimize an energy function the method is based on an active contour model numerous implementation aspects of the shape description method were optimized a euclidean metric was used for optimal accuracy and the active contour model permits bypassing some of the discretization limitations inherent in using a digital grid noise filtering was performed on the basis of both contour feature measures and region measures that is curvature extremum significance and ridge support respectively to obtain robust shape descriptors other improvements and variations of the algorithmic implementation are proposed

analysis of costate discretizations in parameter estimation for linear evolution equations a widely used approach to parameter identification is the output least squares formulation numerical methods for solving the resulting minimization problem almost invariably require the computation of the gradient of the output least squares functional when the identification problem involves time dependent distributed parameter systems or approximations thereof numerical evaluation of the gradient can be extremely time consuming the costate method can greatly reduce the cost of computing these gradients however questions have been raised concerning the accuracy and convergence of costate approximations even when the numerical methods being used are known to converge rapidly on the forward problem in this paper it is shown that the use of time marching schemes that yield high order accuracy on the forward problem does not necessarily lead to high order accurate costate approximations in fact in some cases these approximations do not converge at all however under certain circumstances rapidly converging gradient approximations do result because of rapid weak star type convergence of the costate approximations these issues are treated both theoretically and numerically

fast bayesian jpeg decompression and denoising with tight frame priors jpeg decompression can be understood as an image reconstruction problem similar to denoising or deconvolution such problems can be solved within the bayesian maximum a posteriori probability framework by iterative optimization algorithms prior knowledge about an image is usually described by the l 1 norm of its sparse domain representation for many problems if the sparse domain forms a tight frame optimization by the alternating direction method of multipliers can be very efficient however for jpeg such solution is not straightforward e g due to quantization and subsampling of chrominance channels derivation of such solution is the main contribution of this paper in addition we show that a minor modification of the proposed algorithm solves simultaneously the problem of image denoising in the experimental section we analyze the behavior of the proposed decompression algorithm in a small number of iterations with an interesting conclusion that this mode outperforms full convergence example images demonstrate the visual quality of decompression and quantitative experiments compare the algorithm with other state of the art methods

a functional optimization formulation and implementation of an inverse natural convection problem abstract a formulation and a fem implementation for the solution of an ill posed inverse design natural convection problem is proposed in particular we consider an incompressible viscous liquid material occupying a given domain where convection is driven by buoyancy thermal boundary conditions are only prescribed in the part h 0 of the boundary in addition the temperature distribution is also prescribed in the part i of the boundary h 1 where the heat flux is known i e i is a boundary with over specified thermal boundary conditions the inverse convection problem is posed as an optimization problem in l 2 i 0 t max for the calculation of the boundary heat flux q o x t with x t h 0 0 t max the optimization scheme minimizes the discrepancy m x t x t q o l 2 1 0 t max between the temperature x t q o calculated from the solution of a direct problem for each flux q 0 and the measured or desired temperature m x t at the boundary i the gradient of the cost functional is obtained from the adjoint fields the adjoint problem is defined from the sensitivity operators obtained by linearization of the equations governing the direct problem the conjugate gradient method is employed to perform the optimization process the fem is used for the calculation of the direct adjoint and sensitivity thermal and fluid flow fields finally the method is demonstrated with the solution of some two dimensional inverse problems with known solutions the numerical results are discussed and future work with potential applications is addressed

spatially adaptive high resolution image reconstruction of dct based compressed images the problem of recovering a high resolution image from a sequence of low resolution dct based compressed observations is considered in this paper the introduction of compression complicates the recovery problem we analyze the dct quantization noise and propose to model it in the spatial domain as a colored gaussian process this allows us to estimate the quantization noise at low bit rates without explicit knowledge of the original image frame and we propose a method that simultaneously estimates the quantization noise along with the high resolution data we also incorporate a nonstationary image prior model to address blocking and ringing artifacts while still preserving edges to facilitate the simultaneous estimate we employ a regularization functional to determine the regularization parameter without any prior knowledge of the reconstruction procedure the smoothing functional to be minimized is then formulated to have a global minimizer in spite of its nonlinearity by enforcing convergence and convexity requirements experiments illustrate the benefit of the proposed method when compared to traditional high resolution image reconstruction methods quantitative and qualitative comparisons are provided

finite dimensional approximation of a class of constrained nonlinear optimal control problems an abstract framework for the analysis and approximation of a class of nonlinear optimal control and optimization problems is constructed nonlinearities occur in both the objective functional and the constraints the framework includes an abstract nonlinear optimization problem posed on infinite dimensional spaces an approximate problem posed on finite dimensional spaces together with a number of hypotheses concerning the two problems the framework is used to show that optimal solutions exist to show that lagrange multipliers may be used to enforce the constraints to derive an optimality system from which optimal states and controls may be deduced and to derive existence results and error estimates for solutions of the approximate problem the abstract framework and the results derived from that framework are then applied to three concrete control or optimization problems and their approximation by finite element methods the first involves the von k arm an plate equations of nonlinear elasticity the second the ginzburg landau equations of superconductivity and the third the navier stokes equations for incompressible viscous flows

control of the freezing interface motion in two dimensional solidification processes using the adjoint method the aim of this work is to calculate the optimum history of boundary cooling conditions that in two dimensional conduction driven solidification processes results in a desired history of the freezing interface location motion the freezing front velocity and heat flux on the solid side of the front define the obtained solidification microstructure that can be selected such that desired macroscopic mechanical properties and soundness of the final cast product are achieved the so called two dimensional inverse stefan design problem is formulated as an infinite dimensional minimization problem the adjoint method is developed in conjunction with the conjugate gradient method for the solution of this minimization problem

area based medial axis of planar curves a new definition of affine invariant medial axis of planar closed curves is introduced a point belongs to the affine medial axis if and only if it is equidistant from at least two points of the curve with the distance being a minimum and given by the areas between the curve and its corresponding chords the medial axis is robust eliminating the need for curve denoising in a dynamical interpretation of this affine medial axis the medial axis points are the affine shock positions of the affine erosion of the curve we propose a simple method to compute the medial axis and give examples we also demonstrate how to use this method to detect affine skew symmetry in real images

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

on the solution of an ill posed design solidification problem using minimization techniques in finite and infinite dimensional function spaces this paper provides a comparative study of two alternative methodologies for the solution of an inverse design solidification problem it is the one dimensional solidification problem of calculating the boundary heat flux history that achieves a desired freezing front velocity and desired heat fluxes at the freezing front the front velocity h t and flux history qms t on the solid side of the front control the obtained cast structure as such the potential applications of the proposed methods to the control of casting processes are enormous the first technique utilizes a finite dimensional approximation of the unknown boundary heat flux function q0 t the second technique uses the adjoint method to calculate in l2 the derivative of the cost functional tm t h t t q0 that expresses the square error between the calculated t h t t q0 and the given freezing front temperature tm both steepest descent sdm and conjugate gradient methods cgm are examined a front tracking fem technique is used for the discretization of the state space a detailed numerical analysis of the space and time discretization of the parameter and state spaces of the effect of the end condition of the adjoint problem and of other parameters in the solution are examined

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