multimodality image registration by maximization of mutual information a new approach to the problem of multimodality medical image registration is proposed using a basic concept from information theory mutual information mi or relative entropy as a new matching criterion the method presented in this paper applies mi to measure the statistical dependence or information redundancy between the image intensities of corresponding voxels in both images which is assumed to be maximal if the images are geometrically aligned maximization of mi is a very general and powerful criterion because no assumptions are made regarding the nature of this dependence and no limiting constraints are imposed on the image content of the modalities involved the accuracy of the mi criterion is validated for rigid body registration of computed tomography ct magnetic resonance mr and photon emission tomography pet images by comparison with the stereotactic registration solution while robustness is evaluated with respect to implementation issues such as interpolation and optimization and image content including partial overlap and image degradation our results demonstrate that subvoxel accuracy with respect to the stereotactic reference solution can be achieved completely automatically and without any prior segmentation feature extraction or other preprocessing steps which makes this method very well suited for clinical applications

a projection regularized newton method for nonlinear ill posed problems and its application to parameter identification problems with finite element discretization this paper is concerned with nonlinear ill posed operator equations f a y e g parameter identification problems and their approximate solution by a newton type method that is regularized by projecting the linearized equation in each newton step onto a finite dimensional space e g a finite element space and by stopping the newton iteration at an appropriate index we prove convergence as the iteration index n goes to infinity in the noise free case and convergence as the data noise level delta goes to zero in the case of noisy data as well as convergence rates under certain additional conditions

iterative regularization of a parameter identification problem occurring in polymer crystallization this paper is devoted to the mathematical analysis and regularization of an identification problem related to nonisothermal crystallization of polymers which can be modeled by an initial boundary value problem for a coupled system of parabolic and hyperbolic partial differential equations the identification problem consists of estimating a material function of temperature which appears as a nonlinearity in the equations existence and uniqueness of a solution of the direct problem is shown as well as its stability with respect to the parameter furthermore we develop algorithms for the application of various iterative regularization methods to this particular problem their use is justified by verifying the fr echet differentiability of the parameter to output map which is needed for their realization the numerical performance of the iterative methods is compared with respect to speed of convergence stability and efficiency

variational geometric and statistical methods for modeling brain anatomy and function we survey the recent activities of the odyssee laboratory in the area of the application of mathematics to the design of models for studying brain anatomy and function we start with the problem of reconstructing sources in meg and eeg and discuss the variational approach we have developed for solving these inverse problems this motivates the need for geometric models of the head we present a method for automatically and accurately extracting surface meshes of several tissues of the head from anatomical magnetic resonance mr images anatomical connectivity can be extracted from diffusion tensor magnetic resonance images but in the current state of the technology it must be preceded by a robust estimation and regularization stage we discuss our work based on variational principles and show how the results can be used to track fibers in the white matter wm as geodesics in some riemannian space we then go to the statistical modeling of functional magnetic resonance imaging fmri signals from the viewpoint of their decomposition in a pseudo deterministic and stochastic part that we then use to perform clustering of voxels in a way that is inspired by the theory of support vector machines and in a way that is grounded in information theory multimodal image matching is discussed next in the framework of image statistics and partial differential equations pdes with an eye on registering fmri to the anatomy the paper ends with a discussion of a new theory of random shapes that may prove useful in building anatomical and functional atlases

computing optical flow via variational techniques defined as the apparent motion in a sequence of images the optical flow is very important in the computer vision community where its accurate estimation is necessary for many applications it is o

fast algorithms for low level vision a recursive filtering structure is proposed that drastically reduces the computational effort required for smoothing performing the first and second directional derivatives and carrying out the laplacian of an image these operations are done with a fixed number of multiplications and additions per output point independently of the size of the neighborhood considered the key to the approach is first the use of an exponentially based filter family and second the use of the recursive filtering applications to edge detection problems and multiresolution techniques are considered and an edge detector allowing the extraction of zero crossings of an image with only 14 operations per output element at any resolution is proposed various experimental results are shown

variational methods for multimodal image matching matching images of different modalities can be achieved by the maximization of suitable statistical similarity measures within a given class of geometric transformations handling complex nonrigid deformations in this context turns out to be particularly difficult and has attracted much attention in the last few years the thrust of this paper is that many of the existing methods for nonrigid monomodal registration that use simple criteria for comparing the intensities e g ssd can be extended to the multimodal case where more complex intensity similarity measures are necessary to this end we perform a formal computation of the variational gradient of a hierarchy of statistical similarity measures and use the results to generalize a recently proposed and very effective optical flow algorithm l alvarez j weickert and j sanchez 2000 technical report and ijcv 39 1 41 56 to the case of multimodal image registration our method readily extends to the case of locally computed similarity measures thus providing the flexibility to cope with spatial non stationarities in the way the intensities in the two images are related the well posedness of the resulting equations is proved in a complementary work o d faugeras and g hermosillo 2001 technical report 4235 inria using well established techniques in functional analysis we briefly describe our numerical implementation of these equations and show results on real and synthetic data

efficient iteration schemes for anisotropic hyperelasto plasticity numerical issues arising when integrating hyperelasto plastic constitutive equations with elastic anisotropy stemming from anisotropic damage and plastic anisotropy as represented by kinematic hardening are discussed in particular solution algorithms for the corresponding non linear system of equations due to implicit integration algorithms are addressed it is shown that algorithms like staggered iteration and quasi newton techniques are superior to a pure newton technique when the cpu time is compared however the drawback of the staggered and the quasi newton technique is that rather small time steps must be taken to ensure convergence which can be of importance when applying complex constitutive models in a finite element programme copyright 2005 john wiley sons ltd

application of the mesh independence principle to mesh refinement the mesh independence principle mip for a newton iteration applied to an operator equation and its discretization for different stepsizes h states for a fixed starting point the number of iterations of newton s method to obtain a fixed tolerance is eventually independent of h this mip is used to formulate an efficient strategy for the solution of nonlinear equations amounting to the work equivalent of two or three newton iterates for the smallest h examples are given

a unified approach for parameter identification of inelastic material models in the frame of the finite element method this work is concerned with identification of parameters for inelastic material models in order to account for possible non uniformness of stress and strain distributions the identification is performed in the frame of the finite element method in particular linearization procedures are described in a systematic manner for the case of complex material models within a geometric linear theory this unified approach allows one to apply the newton method for solving the associated direct problem and to apply gradient based methods for solving the associated inverse problem which is considered as an optimization problem two numerical examples demonstrate the versatility of our approach firstly we consider cooks membrane problem based on simulated data for re identification of material parameters for a viscoplastic power law furthermore material data for j2 flow theory are determined based on experimental data obtained by a grating method for a compact specimen and we will investigate the results by using different starting values and stochastic perturbation of the experimental data

diffeomorphisms groups and pattern matching in image analysis in a previous paper it was proposed to see the deformations of a common pattern as the action of an infinite dimensional group we show in this paper that this approac h can be applied numerically for pattern matching in image analysis of digital images using lie group ideas we construct a distance between deformations defined through a metric given the cost of infinitesimal deformations then we propose a numerical scheme to solve a variational problem involving this distance and leading to a sub optimal gradient pattern matching its links with fluid models are established

multi view stereo reconstruction and scene flow estimation with a global image based matching score we present a new variational method for multi view stereovision and non rigid three dimensional motion estimation from multiple video sequences our method minimizes the prediction error of the shape and motion estimates both problems then translate into a generic image registration task the latter is entrusted to a global measure of image similarity chosen depending on imaging conditions and scene properties rather than integrating a matching measure computed independently at each surface point our approach computes a global image based matching score between the input images and the predicted images the matching process fully handles projective distortion and partial occlusions neighborhood as well as global intensity information can be exploited to improve the robustness to appearance changes due to non lambertian materials and illumination changes without any approximation of shape motion or visibility moreover our approach results in a simpler more flexible and more efficient implementation than in existing methods the computation time on large datasets does not exceed thirty minutes on a standard workstation finally our method is compliant with a hardware implementation with graphics processor units our stereovision algorithm yields very good results on a variety of datasets including specularities and translucency we have successfully tested our motion estimation algorithm on a very challenging multi view video sequence of a non rigid scene

qmr a quasi minimal residual method for non hermitian linear systems the biconjugate gradient bcg method is the natural generalization of the classical conjugate gradient algorithm for hermitian positive definite matrices to general non hermitian linear systems unfortunately the original bcg algorithm is susceptible to possible breakdowns and numerical instabilities in this paper we present a novel bcg like approach the quasi minimal residual qmr method which overcomes the problems of bcg an implementation of qmr based on a look ahead version of the nonsymmetric lanczos algorithm is proposed it is shown how bcg iterates can be recovered stably from the qmr process some further properties of the qmr approach are given and an error bound is presented finally numerical experiments are reported

classical and enriched finite element formulations for bloch periodic boundary conditions summary in this paper classical and enriched flnite element formulations to impose bloch periodic boundary conditions are proposed bloch periodic boundary conditions arise in the description of wave like phenomena in periodic media we consider the quantum mechanical problem in a crystalline solid and derive the weak formulation and matrix equations for the schrodinger and poisson equations in a parallelepiped unit cell under bloch periodic and periodic boundary conditions respectively for such second order problems these conditions consist of value and derivative periodic parts the value periodic part is enforced as an essential boundary condition by construction of a value periodic basis whereas the derivative periodic part is enforced as a natural boundary condition in the weak formulation we show that the resulting matrix equations can be obtained by suitably specifying the connectivity of element matrices in the assembly of the global matrices or by modifying the neumann

all angle negative refraction and ultra refraction for liquid surface waves in 2d phononic crystals we analyse transport properties of linear liquid waves propagating within arrays of immersed rigid circular cylindrical obstacles fixed to a rough bottom a comparison between multipole and finite element methods is drawn in the case of robin boundary conditions coupled with floquet bloch boundary conditions we find that the first band is concave yet nearly flat associated waves of small negative group velocity and it displays a cut off zero frequency stop band associated with a singular perturbation thanks to this anomalous dispersion in such fluid filled structures we achieve both ultra refraction and negative refraction for waves propagating at their surface potential applications lie in a omnidirective water antenna and a convergent flat water lens the latter one is demonstrated experimentally

green s tensors and lattice sums for electrostatics and elastodynamics we present expressions for the green9s tensors in terms of lattice sums for general two dimensional arrays in both elastostatics and elastodynamics we represent the lattice sums in rapidly convergent forms by fourier transform methods we compare the static lattice sums with recently published highly accurate values for square arrays we also establish rayleigh identities for elastostatic and elastodynamic problems generalizing previous work in electrostatics and electromagnetism the rayleigh identities may be used in studies of phononic band gaps

asymptotic estimates for localized electromagnetic modes in doubly periodic structures with defects the paper presents analytical and numerical models describing localized electromagnetic defect modes in a doubly periodic structure involving closely located inclusions of elliptical and circular shapes two types of localized modes are considered i an axi symmetric mode for the case of transverse electric polarization with an array of metallic inclusions ii a dipole type localized mode that occurs in problems of waveguide modes confined in a defect region of an array of cylindrical fibres and propagating perpendicular to the plane of the array a thin bridge asymptotic analysis is used for case i to establish double sided bounds for the frequencies of localized modes in macro cells with thin bridges for the case ii the electric and magnetic fields independently satisfy helmholtz equations but are coupled through the boundary conditions we show that the model problem associated with localized vibration modes is the dirichlet problem for the helmholtz operator we characterize defect modes by introducing a parameter called the effective diameter we show that for circular inclusions in silica matrix the effective diameter is accurately represented by a linear function of the inclusion radius

analysis of elastic band structures for oblique incidence we propose a canonical basis that is used in the expansion of eigensolutions for a problem of oblique incidence of elastic waves on a doubly periodic array of cylindrical channels we apply a multipole method to study the spectral properties of waves in such a structure dispersion diagrams constructed on the basis of an analytical solution show the presence of a full phononic band gap when the angle of oblique incidence exceeds certain critical value explicit asymptotic formulae are presented for the effective refractive index associated with shear waves in oblique incidence

strong localized perturbations of eigenvalue problems this paper considers the effect of three types of perturbations of large magnitude but small extent on a class of linear eigenvalue problems for elliptic partial differential equations in bounded o

consistent tangent operators for rate independent elastoplasticity abstract it is shown that for problems involving rate constitutive equations such as rate independent elastoplasticity the notion of consistency between the tangent stiffness operator and the integration algorithm employed in the solution of the incremental problem plays a crucial role in preserving the quadratic rate of asymptotic convergence of iterative solution schemes based upon newton s method within the framework of closest point projection algorithms a methodology is presented whereby tangent operators consistent with this class of algorithms may be systematically developed to wit associative j 2 flow rules with general nonlinear kinematic and isotropic hardening rules as well as a class of non associative flow rules are considered the resulting iterative solution scheme preserves the asymptotic quadratic convergence characteristic of newton s method whereas use of the socalled elastoplastic tangent in conjunction with a radial return integration algorithm a procedure often employed results in newton type of algorithms with suboptimal rate of convergence application is made to a set of numerical examples which include saturation hardening laws of exponential type

analytical and numerical analysis of lensing effect for linear surface water waves through a square array of nearly touching rigid square cylinders this paper describes transport properties of linear water waves propagating within a square array of fixed square cylinders the main focus is on achieving the conditions for all angle negative refraction aanr thanks to anomalous dispersion in fluid filled periodic structures of particular interest are two limit cases when either the edges or the vertices of the cylinders come close to touching in the former case the array can be approximated by a lattice of thin water channels for which dispersion curves are given in closed form and thus frequencies at which aanr occurs whereas in the latter case the array behaves as a checkerboard with cells consisting either of water tanks or rigid cylinders for which standing modes are given in closed form the tools of choice for the present analysis are on the one hand the finite element method which solves numerically spectral problems in periodic media and on the other hand a two scale asymptotic method which provides estimates of dispersion curves and associated eigenfields through a lattice approximation namely thin water channels between rigid cylinders simple duality correspondences are found based on fourfold symmetry of square water checkerboards that allow us to get some insight into their spectra last some numerical evidence is provided for water waves focusing with no astigmatism through such arrays when they are of finite extent

generalized parameter identification for finite viscoelasticity elastomeric and other rubber like materials are often simultaneously exposed to short and long time loads within engineering applications when aiming at establishing a general simulation tool for viscoelastic media over these different time scales a suitable material model and its corresponding material parameters can only be determined if an appropriate number of experimental data is taken into account in this work we present an algorithm for the identification of material parameters for large strain viscoelasticity in which data of multiple experiments are considered based on this method the experimental loading intervals for long time experiments can be shortened in time and the parameter identification procedure is now referred to experimental data of tests under short and long time loads without separating the parameters due to these different time scales the employed viscoelastic material law is based on a nonlinear evolution law and valid far from thermodynamic equilibrium the identification is carried out by minimizing a least squares functional comparing inhomogeneous displacement fields from experiments and fem simulations at given measured force loads within this optimization procedure all material parameters are identified simultaneously by means of a gradient based method for which a semi analytical sensitivity analysis is calculated a representative numerical example is referred to measured data based on short time and long time tests of a non cellular polyurethane as an advantage the developed identification scheme renders solely one single set of material parameters

adaptivity for parameter identification of incompressible hyperelastic materials using stabilized tetrahedral elements abstract this work is concerned with the identification of material parameters for isotropic incompressible hyperelastic material models besides the principal stretch based strain energy function by ogden an invariant based strain energy function by rivlin saunders is considered for which parameter sensitivities are derived the identification is formulated as a least squares minimization problem based on the finite element method to account for inhomogeneous states of stresses and strains in the experimental data which is obtained by optical measurements for the finite element method low order tetrahedral elements in a mixed displacement pressure formulation with stabilization are considered special attention is payed to an adaptive mesh refinement based on a goal oriented a posteriori error indicator to gain reliable material parameters to approximate error terms an element wise recovery technique based on enhanced gradients is introduced

lattice sums for the helmholtz equation a survey of different representations for lattice sums for the helmholtz equation is made these sums arise naturally when dealing with wave scattering by periodic structures one of the main objectives is to show how the various forms depend on the dimension d of the underlying space and the lattice dimension d lambda lattice sums are related to and can be calculated from the quasi periodic green s function and this object serves as the starting point of the analysis

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

adaptive finite element methods for optimal control of partial differential equations basic concept a new approach to error control and mesh adaptivity is described for the discretization of optimal control problems governed by elliptic partial differential equations the lagrangian formalism yields the first order necessary optimality condition in form of an indefinite boundary value problem which is approximated by an adaptive galerkin finite element method the mesh design in the resulting reduced models is controlled by residual based a posteriori error estimates these are derived by duality arguments employing the cost functional of the optimization problem for controlling the discretization error in this case the computed state and costate variables can be used as sensitivity factors multiplying the local cell residuals in the error estimators this results in a generic and simple algorithm for mesh adaptation within the optimization process this method is developed and tested for simple boundary control problems in semiconductor models

a strategy for input estimation with sensitivity analysis the estimation of unknown excitation or input signals from measured response is essentially the solution of an optimization problem a function representing the input is sought such that the discrepancy between measured and simulated response is minimized from the view of optimization it is convenient to consider the general situation where the governing differential equations may be time variant and non linear moreover the choice of parameterization for the sought input sampling instances of measurement data and discretization of the state problem are all decoupled in contrast to standard methods such as dynamic programming in this paper the optimization problem is solved by seeking a stationary point of the pertinent lagrangian functional resulting in a newton type iterative algorithm moreover the sensitivity of the solution with respect to measurement noise may also be estimated from a perturbation analysis of the optimality conditions two numerical examples show that the approach produces results in agreement with those of standard methods however with the additional advantage the numerical properties of the considered problem may be investigated in particular such knowledge may be used for choosing a proper amount of regularization copyright 2006 john wiley sons ltd

a theoretical framework for convex regularizers in pde based computation of image motion many differential methods for the recovery of the optic flow field from an image sequence can be expressed in terms of a variational problem where the optic flow minimizes some energy typically these energy functionals consist of two terms a data term which requires e g that a brightness constancy assumption holds and a regularizer that encourages global or piecewise smoothness of the flow field in this paper we present a systematic classification of rotation invariant convex regularizers by exploring their connection to diffusion filters for multichannel images this taxonomy provides a unifying framework for data driven and flow driven isotropic and anisotropic as well as spatial and spatio temporal regularizers while some of these techniques are classic methods from the literature others are derived here for the first time we prove that all these methods are well posed they posses a unique solution that depends in a continuous way on the initial data an interesting structural relation between isotropic and anisotropic flow driven regularizers is identified and a design criterion is proposed for constructing anisotropic flow driven regularizers in a simple and direct way from isotropic ones its use is illustrated by several examples

a return mapping algorithm for plane stress elastoplasticity an unconditionally stable algorithm for plane stress elastoplasticity is developed based upon the notion of elastic predictor return mapping plastic corrector enforcement of the consistency condition is shown to reduce to the solution of a simple nonlinear equation consistent elastoplastic tangent moduli are obtained by exact linearization of the algorithm use of these moduli is essential in order to preserve the asymptotic rate of quadratic convergence of newton methods the accuracy of the algorithm is assessed by means of iso error maps the excellent performance of the algorithm for large time steps is illustrated in numerical experiments

reliable estimation of dense optical flow fields with large displacements in this paper we show that a classic optical flow technique by nagel and enkelmann 1986 ieee trans pattern anal mach intell vol 8 pp 565 593 can be regarded as an early anisotropic diffusion method with a diffusion tensor we introduce three improvements into the model formulation that i avoid inconsistencies caused by centering the brightness term and the smoothness term in different images ii use a linear scale space focusing strategy from coarse to fine scales for avoiding convergence to physically irrelevant local minima and iii create an energy functional that is invariant under linear brightness changes applying a gradient descent method to the resulting energy functional leads to a system of diffusion reaction equations we prove that this system has a unique solution under realistic assumptions on the initial data and we present an efficient linear implicit numerical scheme in detail our method creates flow fields with 100 density over the entire image domain it is robust under a large range of parameter variations and it can recover displacement fields that are far beyond the typical one pixel limits which are characteristic for many differential methods for determining optical flow we show that it performs better than the optical flow methods with 100 density that are evaluated by barron et al 1994 int j comput vision vol 12 pp 43 47 our software is available from the internet

a robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry abstract this paper proposes a robust approach to image matching by exploiting the only available geometric constraint namely the epipolar constraint the images are uncalibrated namely the motion between them and the camera parameters are not known thus the images can be taken by different cameras or a single camera at different time instants if we make an exhaustive search for the epipolar geometry the complexity is prohibitively high the idea underlying our approach is to use classical techniques correlation and relaxation methods in our particular implementation to find an initial set of matches and then use a robust technique the least median of squares lmeds to discard false matches in this set the epipolar geometry can then be accurately estimated using a meaningful image criterion more matches are eventually found as in stereo matching by using the recovered epipolar geometry a large number of experiments have been carried out and very good results have been obtained regarding the relaxation technique we define a new measure of matching support which allows a higher tolerance to deformation with respect to rigid transformations in the image plane and a smaller contribution for distant matches than for nearby ones a new strategy for updating matches is developed which only selects those matches having both high matching support and low matching ambiguity the update strategy is different from the classical winner take all which is easily stuck at a local minimum and also from loser take nothing which is usually very slow the proposed algorithm has been widely tested and works remarkably well in a scene with many repetitive patterns

regularizing newton kaczmarz methods for nonlinear ill posed problems we introduce a class of stabilizing newton kaczmarz methods for nonlinear ill posed problems and analyze their convergence and regularization behavior as usual for iterative methods for solving nonlinear ill posed problems conditions on the nonlinearity or the derivatives have to be imposed in order to obtain convergence as we shall discuss in general and in some specific examples the nonlinearity conditions obtained for the newton kaczmarz methods are less restrictive than those for previously existing iteration methods and can be verified for several practical applications we also discuss the discretization and efficient numerical solution of the linear problems arising in each step of a newton kaczmarz method and we carry out numerical experiments for two model problems

modelling of electromagnetic waves in periodic media with finite elements edge elements have been previously used to study electromagnetic waves conically propagating through a finite stack of arrays of fibres ieee trans magn 38 2 2002 this paper presents a new extension of this technique to the analysis of the propagation of such waves in a doubly periodic array of fibres in the proposed approach only the unit cell of the periodic material has to be meshed thanks to floquet bloch theory

four phase checkerboard composites two dimensional periodic rectangular checkerboard media are considered in the situation where mean fluxes are prescribed across the structure the closed form solution is obtained in the general case where the checkerboard is constructed using four rectangular cells each having a different constant resistivity this four cell structure then repeats doubly periodically to cover the whole plane this general solution is then used to calculate the effective properties thus this four phase checkerboard encapsulates many limiting and special cases as a starting point we develop a concise closed form solution to a basic problem involving four joined quarter planes each of a different resistivity subsequent manipulations yield solutions to problems posed in increasingly convoluted domains while retaining the essentially simple structure found for joined quarter planes

the effect on bending waves by defects in pinned elastic plates abstract this paper presents solutions to a number of problems posed for the out of plane displacement of infinite thin elastic plates that are rigidly pinned in periodic configurations but that possess a finite number of defects we begin by considering a single one dimensional periodic array of pins we derive an analytic solution for the displacement produced by the forced oscillation of the central pin in the array and this solution is shown to be closely connected to the problem of scattering of plane waves by an array when a finite number of pins are removed attention then focuses on doubly periodic rectangular arrays of pinned points possessing defects central to approaching such problems is an understanding of bloch floquet waves in periodic arrays in the absence of defects and a simple method is described for computing the associated dispersion surfaces the solutions to three problems are then sought the trapping of localised waves by a finite number of missing pins trapping of waves by entire rows of missing pins and the wave radiation pattern due to the forcing of a single pin all problems are treated analytically using bounded green s functions for thin elastic plates a discrete fourier transform solution method and simple explicit and rapidly convergent evaluations of the one and two dimensional lattice sums that arise

source neutral green functions for periodic problems in electrostatics and their equivalents in electromagnetism we consider source neutral problems for periodic problems in electrostatics these may be used to derive an identity due to lord rayleigh entirely within the context of the unit cell and without use of reasoning based on contributions from charges at an outer boundary of the periodic system or employing conditionally convergent lattice sums we also consider the equivalent of source free green9functions for the helmholtz equation which are green9functions with their specular parts removed we show that as the wavenumber tends to zero the non specular dynamic green9functions tend with no divergences to the source neutral electrostatic green9function

eigenvalue problems for doubly periodic elastic structures and phononic band gaps we consider the problem of elastic waves propagating in a two dimensional array of circular cavities taking rigorous account of coupling between shear and dilational waves a technique originally due to rayleigh is derived that involves an elegant identity between the singular and non singular components of the stress fields in the array this leads to an infinite linear system which can be truncated and solved in order to determine the complete structure of the propagating modes of particular interest is the possibility of exhibiting phononic band gaps i e domains of frequency for which all propagating vibration in the material is suppressed

sequential quadratic programming for certain parameter identification problems we analyze the method of sequential quadratic programming for equality constrained minimization problems in hilbert spaces of functions and for the discrete approximations of such problems in the context of an elliptic parameter identification problem we show how the discretization can be constructed so as to preserve the convergence behavior of the iterates for the infinite dimensional problem in the finite dimensional approximations we use the structure of the parameter identification problem to reduce the size of the linear system for the sqp step and verify nondegeneracy of the constraints

analytical results for a class of sums involving bessel functions and square arrays we consider a class of sums involving bessel functions summed over the square array the sums involve the length of an arbitrary vector lying within the central unit cell we establish conditions under which the sums reduce to polynomial forms in possibly with a single logarithmic term in addition and show how these polynomials may be conveniently evaluated

alignment by maximization of mutual information a new information theoretic approach is presented for finding the pose of an object in an image the technique does not require information about the surface properties of the object besides its shape and is robust with respect to variations of illumination in our derivation few assumptions are made about the nature of the imaging process as a result the algorithms are quite general and may foreseeably be used in a wide variety of imaging situations experiments are presented that demonstrate the approach registering magnetic resonance mr images aligning a complex 3d object model to real scenes including clutter and occlusion tracking a human head in a video sequence and aligning a view based 2d object model to real images the method is based on a formulation of the mutual information between the model and the image as applied here the technique is intensity based rather than feature based it works well in domains where edge or gradient magnitude based methods have difficulty yet it is more robust than traditional correlation additionally it has an efficient implementation that is based on stochastic approximation

an investigation of smoothness constraints for the estimation of displacement vector fields from image sequences a mapping between one frame from an image sequence and the preceding or following frame can be represented as a displacement vector field in most situations the mere gray value variations do not provide sufficient information in order to estimate such a displacement vector field supplementary constraints are necessary for example the postulate that a displacement vector field varies smoothly as a function of the image position taken as a general requirement this creates difficulties at gray value transitions which correspond to occluding contours nagel therefore introduced the oriented smoothness requirement which restricts variations of the displacement vector field only in directions with small or no variation of gray values this contribution reports results of an investigation about how such an oriented smoothness constraint may be formulated and evaluated

well posedness of two nonrigid multimodal image registration methods image registration methods may be designed as solutions of minimization problems on a set of geometric deformations in the nonrigid case solving these problems often means computing the steady state of a system of evolution equations involving the gradient of the error criterion defined from the euler lagrange equations of the corresponding minimization problem the well posedness of the registration methodrequires showing the existence of a solution to the minimization problem as well as that of a stable solution of the evolution equations derived from it we provide such proofs in the case where the error criterion is derived from two different statistical similarity measures global mutual information and local cross covariance we also describe our numerical implementation for solving the corresponding evolution equations and show examples of registrations of real 2d and 3d images achieved with these algorithms the proofs are quite general and can be applied to most of the known nonrigid image

noncommuting limits in electromagnetic scattering asymptotic analysis for an array of highly conducting inclusions we consider formulations for the helmholtz operator for periodic media containing high contrast inclusions in the limit when the wavelength outside the inclusions tends to infinity applications are to problems of electromagnetism the main focus is on the analysis of the effect of noncommuting limits an effect which indicates that linear boundary value problems of electromagnetism give formally different results for the long wavelength limits in cases where highly conducting inclusions have refractive indices of different orders of magnitude specifically the effective moduli of the homogenized material will depend on the path used to approach the origin in the coordinate space wave number normalized refractive index of the inclusions 1 this mathematical observation gives a physical subtlety which is studied in this paper the dispersion relation for the lowest frequency or acoustic mode is investigated as are the conditions for existence of an acoustic mode cases of both nondispersive and di

calibration of a class of non linear viscoelasticity models with sensitivity assessment based on duality the calibration of constitutive models is based on the solution of an optimization problem whereby the sought parameter values minimize an objective function that measures the discrepancy between experimental observations and the corresponding simulated response by the introduction of an appropriate adjoint problem the resulting formulation becomes well suited for a gradient based optimization scheme a class of viscoelastic models is studied where a discontinuous galerkin method is used to integrate the governing evolution equation in time a practical solution algorithm which utilizes the time flow structure of the underlying evolution equation is presented based on the proposed formulation it is convenient to estimate the sensitivity of the calibrated parameters with respect to measurement noise the sensitivity is computed using a dual method which compares favourably with the conventional primal method the strategy is applied to a viscoelasticity model using experimental data from a uniaxial compression test copyright 2006 john wiley sons ltd

a stabilization procedure by line search computation for first order approximation strategies in structural optimization the paper is concerned with first order approximation methods to solve non linear optimization problems as they arise in structural optimization a modification of the original method of moving asymptotes mma is presented to prevent oscillation or divergence by incorporating a line search into the global iteration algorithm in this line search a merit function of augmented lagrangian type is decreased by using a backtracking strategy a proof is presented to show the descent property of the proposed merit function for mma numerical examples demonstrate how the new technique stabilizes the iteration process

a class of mixed assumed strain methods and the method of incompatible modes a three field mixed formulation in terms of displacements stresses and an enhanced strain field is presented which encompasses as a particular case the classical method of incompatible modes within this frame work incompatible elements arise as particular compatible mixed approximations of the enhanced strain field the conditions that the stress interpolation contain piece wise constant functions and be l2 ortho gonal to the enhanced strain interpolation ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation the preceding conditions are formulated in a form particularly convenient for element design as an illustration of the methodology three new elements are developed and shown to exhibit good performance a plane 3d elastic plastic quad an axisymmetric element and a thick plate bending quad the formulation described herein is suitable for non linear analysis

analysis of the inexact uzawa algorithm for saddle point problems in this paper we consider the so called inexact uzawa algorithm for iteratively solving linear block saddle point problems such saddle point problems arise for example in finite element and finite difference discretizations of stokes equations the equations of elasticity and mixed finite element discretization of second order problems we consider both the linear and nonlinear variants of the inexact uzawa iteration we show that the linear method always converges as long as the preconditioners defining the algorithm are properly scaled bounds for the rate of convergence are provided in terms of the rate of convergence for the preconditioned uzawa algorithm and the reduction factor corresponding to the preconditioner for the upper left hand block in the case of nonlinear iteration the inexact uzawa algorithm is shown to converge provided that the nonlinear process approximating the inverse of the upper left hand block is of sufficient accuracy bounds for the nonlinear iteration are given in terms of this accuracy parameter and the rate of convergence of the preconditioned linear uzawa algorithm applications to the stokes equations and mixed finite element discretization of second order elliptic problems are discussed and finally the results of numerical experiments involving the algorithms are presented

on the local convergence study for an efficient k step iterative method research was supported in part by programa de apoyo a ia investigacion de ia fundacion seneca agencia de ciencia y tecnologia de la region de murcia 19374 pi 14 by the project of generalitat valenciana prometeo 2016 089 and the projects mtm2015 64382 p mineco feder mtm2014 52016 c2 1 p and mtm2014 52016 c2 2 p of the spanish ministry of science and innovation

bloch waves in periodic multi layered acoustic waveguides the band spectrum and associated floquet bloch eigensolutions arising in acoustic and electromagnetic waveguides which have periodic structure along the guide while remaining of finite width are found homogeneous dirichlet or neumann conditions along the guide walls or an alternation of them are taken importantly in some cases a total stop band at zero frequency is identified providing space for low frequency localized modes geometric defects in the structured waveguide also create these modes numerical and asymptotic techniques identify dispersion curves and trapped modes some cases demonstrate maxima and minima of the spectral edges within the brillouin zone and also allow for ultraslow light or sound imaging applications using anomalous dispersion to generate subwavelength resolution are possible and are demonstrated

quasi newton methods and unconstrained optimal control problems we prove a mesh independence result for the bfgs method in hilbert space and apply it to a class of unconstrained optimal control problems a new fourth order discretization scheme is used in the i

lattice sums and the two dimensional periodic green s function for the helmholtz equation many algorithms that are currently used for the solution of the helmholtz equation in periodic domains require the evaluation of the green s function g x x0 the fact that the natural representat

variational principles surface evolution pdes level set methods and the stereo problem we present a novel geometric approach for solving the stereo problem for an arbitrary number of images spl ges 2 it is based upon the definition of a variational principle that must be satisfied by the surfaces of the objects in the scene and their images the euler lagrange equations that are deduced from the variational principle provide a set of partial differential equations pdes that are used to deform an initial set of surfaces which then move toward the objects to be detected the level set implementation of these pdes potentially provides an efficient and robust way of achieving the surface evolution and to deal automatically with changes in the surface topology during the deformations i e to deal with multiple objects results of an implementation of our theory also dealing with occlusion and visibility are presented on synthetic and real images

group actions homeomorphisms and matching a general framework this paper constructs metrics on the space of images cal i defined as orbits under group actions cal g the groups studied include the finite dimensional matrix groups and their products as well as the infinite dimensional diffeomorphisms examined in trouve 1999 quaterly of applied math and dupuis et al 1998 quaterly of applied math left invariant metrics are defined on the product cal g times cal i thus allowing the generation of transformations of the background geometry as well as the image values examples of the application of such metrics are presented for rigid object matching with and without signature variation curves and volume matching and structural generation in which image values are changed supporting notions such as tissue creation in carrying one image to another

parameter identification for finite deformation elasto plasticity in principal directions this work is concerned with identification of material parameters based on experimental data which represent nonuniform distributions of stresses and deformations within the volume of the specimen both elastic and inelastic material non linearities in the frame of a finite deformation theory are taken into account gradient based descent methods e g gauss newton method quasi newton method are used for minimization of a least squares function to this end a sensitivity analysis is performed and the resulting expressions are presented in a spatial and a material setting in particular the cases of an isotropic hyperelastic model and a multiplicative plasticity model with an exponential type integration scheme both formulated in principal directions are considered two numerical examples based on simulated data and experimental data obtained by a grating method demonstrate the versatility of our approach

oblique propagation of electromagnetic and elastic waves for an array of cylindrical fibres this paper presents analysis of electromagnetic and elastodynamic waves propagating through a doubly periodic array of cylindrical channels in oblique incidence a new method based on a multipole scattering approach has been proposed to reduce these spectral problems for partial differential equations to certain algebraic problems of the rayleigh type we obtain a formulation in terms of an eigenvalue problem that enables us to construct the high order dispersion curves and to study both photonic and phononic band gap structures in oblique incidence we also address the question of a singular perturbation induced by the conical incidence and discuss some effective properties for ferromagnetic photonic crystal fibres in the long wavelength limit

fully implicit integration and consistent tangent modulus in elasto plasticity this paper deals with the numerical integration of a class of rate independent elasto plastic models the backward euler scheme is used to integrate the rate constitutive relations the non linear equations obtained are solved by the newton method the consistent tangent modulus is obtained by exact linearization of the algorithm in the case of j 2 elastoplasticity with non linear isotropic hardening and non linear kinematic hardening chaboche marquis model explicit formulas are derived without any approximations

parameter identification in constitutive models via optimization with a posteriori error control in this paper we outline a computational technique for the calibration of macroscopic constitutive laws with automatic error control in the most general situation the state variables of the constitutive law as well as the material parameters are spatially non homogeneous the experimental observations are given in space time based on an appropriate dual problem we compute a posteriori the discretization error contributions from approximations of the parameter state and costate elds in space time for an arbitrarily chosen goal oriented error measure of engineering signi cance such a measure can be used in an adaptive strategy not discussed in this paper to meet a prede ned error tolerance an important observation is that the jacobian matrix associated with the resulting newton method is used in principle in solving the dual problem rather than treating the jacobian in a monolithic fashion we utilize a sequential solution strategy whereby the fe topology of the discretized state problem is used repeatedly moreover the proposed solution strategy lends itself naturally to the computation of rst and second order sensitivities which are obtained with little extra computational effort numerical results are given for the prototype model of con ned aquifer ow with spatially non homogeneous permeability the ef ciency of the optimization strategy and the effectivity of the error computation are assessed

slot nozzle design with specified pressure in a given subregion by using embedding method in this paper we study a shape optimization problem connected with controlled pressure in a subregion of a 2d slot nozzle feasible shapes for this problem are characterized only with upper walls this enables us to seek for the optimum in a class of functions and their derivatives instead of a class of shapes the shape optimization problem can be written as an optimal control problem then the resulting distributed control problem is expressed in a measure theoretical form in fact an infinite dimensional linear programming problem the optimal measure representing optimal shape is approximated by the solution of a finite dimensional linear programming problem a brief sensitivity analysis on model parameters is given

analysis of iterative methods for saddle point problems a unified approach in this paper two classes of iterative methods for saddle point problems are considered inexact uzawa algorithms and a class of methods with symmetric preconditioners in both cases the iteration matrix can be transformed to a symmetric matrix by block diagonal matrices a simple but essential observation which allows one to estimate the convergence rate of both classes by studying associated eigenvalue problems the obtained estimates apply for a wider range of situations and are partially sharper than the known estimates in literature a few numerical tests are given which confirm the sharpness of the estimates

acoustic band gaps in arrays of neutral inclusions we analyse numerically the acoustic stop band properties of an array of orthotropic coated cylinders whose elastic parameters are deduced from a geometric transform h chen c t chan acoustic cloaking in three dimensions using acoustic metamaterials appl phys lett 91 2007 183518 we find that whereas a single coated inclusion is acoustically neutral at any frequency an array of them might display some stop bands more precisely an array of freely vibrating coated voids is always neutral whereas an array of clamped coated inclusions might display a zero frequency stop band interestingly an array of radially symmetric coated inclusions behaves as local helmholtz resonators for which the eigenfield within each cloak is obtained in closed form leading to a frequency estimate associated with the lower edge of the low frequency stop band a finite phononic crystal of such coated cylinders behaves either as an invisible material or a reflector depending on the frequency of an acoustic source

convergence theorems for least change secant update methods the purpose of this paper is to present a convergence analysis of least change secant methods in which part of the derivative matrix being approximated is computed by other means the theorems and proofs given here can be viewed as generalizations of those given by broyden dennis more j inst math appl 12 1973 pp 223 246 and by dennis more math comp 28 1974 pp 549 560 the analysis is done in the orthogonal projection setting of dennis schnabel siam rev 21 1980 pp 443 459 and many readers might feel that it is easier to understand the theorems here readily imply local and q superlinear convergence of all the standard methods in addition to proving these results for the first time for the sparse symmetric method of marwil and toint and the nonlinear least squares method of dennis gay welsch

bounds for effective parameters of heterogeneous media by analytic continuation we give a mathematical formulation of a method for obtaining bounds on effective parameters developed by d bergman and g w milton this method in contrast to others used before does not rely on a variational principle but exploits the properties of the effective parameter as an analytic function of the component parameters the method is at present restricted to two component media

projected newton methods for optimization problems with simple constraints we consider the problem min f x x geqq 0 and propose algorithms of the form x k 1 x k alpha k d k nabla f x k where cdot denotes projection on the positive orthant alpha k is a stepsize chosen by an armijo like rule and d k is a positive definite symmetric matrix which is partly diagonal we show that d k can be calculated simply on the basis of second derivatives of f so that the resulting newton like algorithm has a typically superlinear rate of convergence with other choices of d k convergence at a typically linear rate is obtained the algorithms are almost as simple as their unconstrained counterparts they are well suited for problems of large dimension such as those arising in optimal control while being competitive with existing methods for low dimensional problems the effectiveness of the newton like algorithm is demonstrated via computational examples involving as many as 10 000 variables extensions to general linearly constrained pr

an infinite dimensional convergence theory for reduced sqp methods in hilbert space we develop a general convergence theory for a class of reduced successive quadratic programming sqp methods for infinite dimensional equality constrained optimization problems in hilbert space the methods under consideration approximate second order information of the lagrangian restricted to the null space of h the derivative of the constraints in particular a sufficient condition for two step superlinear convergence will be given and a general result for secant methods will be established which can serve as a tool to prove superlinear convergence in an infinite dimensional framework this result is applied to prove local two step superlinear convergence of reduced sqp methods under the assumption that exact reduced second order information is known up to a compact perturbation to test our convergence theory we consider optimal control problems and we formulate a reduced quasi newton algorithm which presents a new approach to an efficient solution of these problems our main motivation for st

a saddle point variational formulation for projection regularized parameter identification this paper is concerned with the ill posed problem of identifying a parameter in an elliptic equation and its solution applying regularization by projection as the theory has shown the ansatz functions for the parameter have to be sufficiently smooth in this paper we show that these for a practical implementation unrealistic smoothness assumptions can be circumvented by reformulating the problem under consideration as a mixed variational equation we prove convergence as the discretization gets finer in the noise free case and convergence as the data noise level delta goes to zero in the case of noisy data as well as convergence rates under additional smoothness conditions

numerical approximation of an sqp type method for parameter identification this paper deals with the numerical approximation of the levenberg marquardt sqp lmsqp method for parameter identification problems which has been presented and analyzed in m burger and w muhlhuber inverse problems 18 2002 pp 943 969 it is shown that a galerkin type discretization leads to a convergent approximation and that the indefinite system arising from the karush kuhn tucker kkt system is well posed in addition we present a multilevel version of the levenberg marquardt method and discuss the simultaneous solution of the discretized kkt system by preconditioned iteration methods for indefinite problems from a discussion of the numerical effort we conclude that these approaches may lead to a considerable speed up with respect to standard iterative regularization methods that eliminate the underlying state equation the numerical efficiency of the lmsqp method is confirmed by numerical examples

evaluation of phase modulated lattice sums an exact evaluation of two dimensional phase modulated lattice sums of the form exp i g x g 2 is presented in terms of the jacobian theta functions the result generalizes the identity derived by m l glasser j math phys 15 188 1974 to allow for evaluation on nonrectangular lattices the generalized identity is also applied to a problem in vortex dynamics

on an efficient k step iterative method for nonlinear equations this paper is devoted to the construction and analysis of an efficient k step iterative method for nonlinear equations the main advantage of this method is that it does not need to evaluate any high order frechet derivative moreover all the k step have the same matrix in particular only one lu decomposition is required in each iteration we study the convergence order the efficiency and the dynamics in order to motivate the proposed family we prove using some recurrence relations a semilocal convergence result in banach spaces finally a numerical application related to nonlinear conservative systems is presented

propagation of elastic waves through a lattice of cylindrical cavities we consider wave propagation through a doubly periodic array of cavity cylinders in an isotropic elastic medium using the method of matched asymptotic expansions based on the assumptions that the scatterer size is much smaller than both the wavelength and the array periodicity there is no restriction on the wavelength relative to the periodicity and hence the method yields explicit approximations that describe the phenomena associated with periodic media this is illustrated with square and hexagonal lattices

maximum efficiency for a family of newton like methods with frozen derivatives and some applications a generalized k step iterative application of newton s method with frozen derivative is studied and used to solve a system of nonlinear equations the maximum computational efficiency is computed a sequence that approximates the order of convergence is generated for the examples and it numerically confirms the calculation of the order of the method and computational efficiency this type of method appears in many applications where the authors have heuristically chosen a given number of steps with frozen derivatives an example is shown in which the total variation tv minimization model is approximated using the schemes described in this paper

global convergence of trust region interior point algorithms for infinite dimensional nonconvex minimization subject to pointwise bounds a class of interior point trust region algorithms for infinite dimensional nonlinear optimization subject to pointwise bounds in l p banach spaces 2 le p le infty is formulated and analyzed the problem formulation is motivated by optimal control problems with l p controls and pointwise control constraints the interior point trust region algorithms are generalizations of those recently introduced by coleman and li siam j optim 6 1996 pp 418 445 for finite dimensional problems many of the generalizations derived in this paper are also important in the finite dimensional context all first and second order global convergence results known for trust region methods in the finite dimensional setting are extended to the infinite dimensional framework of this paper

duality relation for the maxwell system this paper is intended to establish a link between the vector maxwell system for three dimensional 3d and 2d finite photonic crystals in the low frequency limit for this we generalize the classical results of keller and dykhne chessboard problem to periodic media described by piecewise continuous permittivity profiles our theorem enlights the result of mendelson polycrystalline and multiphase media in the framework of homogenization theory of elliptic operators in fine we give illustrative examples by using both integral equation and variational approaches via the so called method of fictitious charges and finite element method

newton s method for a class of optimal shape design problems a class of optimal shape design problems is considered where a part of the boundary of the domain represents the free parameter the variable domain is parametrized by a class of functions in such a way that the optimal design problem results in an optimal control problem on a fixed domain the functions for the parametrization of the domain are used as controls and the corresponding states are then given by the solution of an elliptic boundary value problem on a fixed domain discretizing this control problem normally leads to a large scale optimization problem where the corresponding solution methods are characterized by the requirement of solving many boundary value problems in spite of this interesting numerical challenge until now little work has been done to derive more efficient algorithms by taking advantage of the specific structure of this kind of problem in this report newton s method in function space is derived resulting in an efficient algorithm for the discretized optimization problems by using the specific structure of these optimal shape design problems an efficient implementation of the numerical algorithm is introduced the properties of this algorithm are compared with those of the gradient method using illustrative numerical examples

stereo matching with nonlinear diffusion one of the central problems in stereo matching and other image registration tasks is the selection of optimal window sizes for comparing image regions this paper addresses this problem with some novel algorithms based on iteratively diffusing support at different disparity hypotheses and locally controlling the amount of diffusion based on the current quality of the disparity estimate it also develops a novel bayesian estimation technique which significantly outperforms techniques based on area based matching ssd and regular diffusion we provide experimental results on both synthetic and real stereo image pairs