space mapping and defect correction in this paper we show that space mapping optimization can be understood in the framework of defect correction then space mapping algorithms can be seen as special cases of defect correction iteration in order to analyze the properties of space mapping and the space mapping function we introduce the new concept of flexibility of the underlying models the best space mapping results are obtained for so called equally flexible models by introducing an affine operator as a left preconditioner two models can be made equally flexible at least in the neighborhood of a solution this motivates an improved space mapping or manifold mapping algorithm the left preconditioner complements traditional space mapping where only a right preconditioner is used in the last section a few simple examples illustrate some of the phenomena analyzed in this paper

active contours without edges we propose a new model for active contours to detect objects in a given image based on techniques of curve evolution mumford shah 1989 functional for segmentation and level sets our model can detect objects whose boundaries are not necessarily defined by the gradient we minimize an energy which can be seen as a particular case of the minimal partition problem in the level set formulation the problem becomes a mean curvature flow like evolving the active contour which will stop on the desired boundary however the stopping term does not depend on the gradient of the image as in the classical active contour models but is instead related to a particular segmentation of the image we give a numerical algorithm using finite differences finally we present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable also the initial curve can be anywhere in the image and interior contours are automatically detected

on level set regularization for highly ill posed distributed parameter estimation problems the recovery of a distributed parameter function with discontinuities from inverse problems with elliptic forward pdes is fraught with theoretical and practical difficulties better results are obtained for problems where the solution may take on at each point only one of two values thus yielding a shape recovery problem this article considers level set regularization for such problems however rather than explicitly integrating a time embedded pde to steady state which typically requires thousands of iterations methods based on gauss newton are applied more directly one of these can be viewed as damped gauss newton utilized to approximate the steady state equations which in turn are viewed as the necessary conditions of a tikhonov type regularization with a sharpening sub step at each iteration in practice this method is eclipsed however by a special finite time or levenberg marquardt type method which we call dynamic regularization applied to the output least squares formulation our stopping criterion for the iteration does not involve knowledge of the true solution the regularization functional is applied to the smooth level set function rather than to the discontinuous function to be recovered and the second focus of this article is on selecting this functional typical choices may lead to flat level sets that in turn cause ill conditioning we propose a new quartic non local regularization term that penalizes flatness and produces a smooth level set evolution and compare its performance to more usual choices two numerical test cases are considered a potential problem and the classical eit dc resistivity problem

multi level acceleration with manifold mapping of strongly coupled partitioned fluid structure interaction abstract to accelerate the convergence of strongly coupled partitioned fluid structure interaction simulations the manifold mapping algorithm is used which combines a high fidelity model with a low fidelity model a computationally inexpensive low fidelity fluid structure interaction fsi model is combined with a high fidelity fsi model in order to accelerate the convergence of the coupling iterations of the high fidelity fsi model the manifold mapping algorithm is applied to the fluid structure interaction problem in order to minimize the fluid structure interface residual originating from multi fidelity optimization the manifold mapping algorithm is applied for the first time in a simulation context instead of an optimization context the manifold mapping algorithm is applied to an unsteady flow in a one dimensional tube incompressible laminar flow over a fixed cylinder with an attached flexible flap and a wave propagation in a three dimensional elastic tube problem a reduction of approximately 50 in terms of high fidelity iterations is achieved compared to the state of the art interface quasi newton inverse least squares algorithm the convergence of the high fidelity model is accelerated even further when information from previous time steps is reused

high order essentially nonsocillatory schemes for hamilton jacobi equations hamilton jacobi h j equations are frequently encountered in applications e g in control theory and differential games h j equations are closely related to hyperbolic conservation laws in one space dimension the former is simply the integrated version of the latter similarity also exists for the multidimensional case and this is helpful in the design of difference approximations in this paper high order essentially nonoscillatory eno schemes for h j equations are investigated which yield uniform high order accuracy in smooth regions and sharply resolve discontinuities in the derivatives the eno scheme construction procedure is adapted from that for hyperbolic conservation laws the schemes are numerically tested on a variety of one dimensional and two dimensional problems including a problem related to control optimization and high order accuracy in smooth regions good resolution of discontinuities in the derivatives and convergence to viscosity solutions are observed

multigrid methods for pde optimization research on multigrid methods for optimization problems is reviewed optimization problems considered include shape design parameter optimization and optimal control problems governed by partial differential equations of elliptic parabolic and hyperbolic type

a multiphase level set framework for image segmentation using the mumford and shah model we propose a new multiphase level set framework for image segmentation using the mumford and shah model for piecewise constant and piecewise smooth optimal approximations the proposed method is also a generalization of an active contour model without edges based 2 phase segmentation developed by the authors earlier in t chan and l vese 1999 in scale space 99 m nilsen et al eds lncs vol 1682 pp 141 151 and t chan and l vese 2001 ieee ip 10 2 266 277 the multiphase level set formulation is new and of interest on its own by construction it automatically avoids the problems of vacuum and overlaps it needs only log n level set functions for n phases in the piecewise constant cases it can represent boundaries with complex topologies including triple junctionss in the piecewise smooth case only two level set functions formally suffice to represent any partition based on the four color theorem finally we validate the proposed models by numerical results for signal and image denoising and segmentation implemented using the osher and sethian level set method

integrated segmentation and interpolation of sparse data we address the two inherently related problems of segmentation and interpolation of 3d and 4d sparse data and propose a new method to integrate these stages in a level set framework the interpolation process uses segmentation information rather than pixel intensities for increased robustness and accuracy the method supports any spatial configurations of sets of 2d slices having arbitrary positions and orientations we achieve this by introducing a new level set scheme based on the interpolation of the level set function by radial basis functions the proposed method is validated quantitatively and or subjectively on artificial data and mri and ct scans and is compared against the traditional sequential approach which interpolates the images first using a state of the art image interpolation method and then segments the interpolated volume in 3d or 4d in our experiments the proposed framework yielded similar segmentation results to the sequential approach but provided a more robust and accurate interpolation in particular the interpolation was more satisfactory in cases of large gaps due to the method taking into account the global shape of the object and it recovered better topologies at the extremities of the shapes where the objects disappear from the image slices as a result the complete integrated framework provided more satisfactory shape reconstructions than the sequential approach

sound wave propagation from a point source over a homogeneous surface and over a surface with an impedance discontinuity the sound field from a point source above an infinite plane with an impedance discontinuity is studied by considering the helmholtz equation with boundary conditions the helmholtz equation is transformed into a singular integral equation and an exact solution formula is given the formula is evaluated for the case when the source and the receiver are close to the boundary many wavelengths from the discontinuity the evaluation gives among other things information on the dependence of the surface wave structure on the impedances and in the case of no surface waves information on the farfield solution if one of the impedances gives a surface wave in the case of a homogeneous boundary then a surface wave appears also in the nonhomogeneous case and is modified depending on the other impedance in the case of no surface waves the rapid decay of the sound field in the homogeneous case does not appear in the nonhomogeneous case since the discontinuity acts as a weak source of slowly decaying waves a numb

aspects of ground effect modeling a recently published one parameter ground model based on darcy s law is here generalized into a two parameter model which depends on an effective flow resistivity and an effective layer depth extensive field measurements of the acoustic impedance of various ground types have been carried out for frequencies in the range from 200 hz to 2 5 khz the model based on darcy s law gives an improved fit to the measurements compared to the delany bazley model it is in addition argued on purely theoretical grounds that the suggested model is preferable in contrast to the delany bazley model it corresponds to a proper causal time domain model this is particularly relevant for extrapolation of the models to lower frequencies and for the recently developed harmonized methods intended for use in the implementation of the european union directive on the assessment and management of environmental noise the harmonized methods include frequencies down to the 25 hz third octave band and have the delany bazley ground

registration and modeling from spaced and misaligned image volumes we address the problem of object modeling from 3d and 3d t data made up of images which contain different parts of an object of interest are separated by large spaces and are misaligned with respect to each other these images have only a limited number of intersections hence making their registration particularly challenging furthermore such data may result from various medical imaging modalities and can therefore present very diverse spatial configurations previous methods perform registration and object modeling segmentation and interpolation sequentially however sequential registration is ill suited for the case of images with few intersections we propose a new methodology which regardless of the spatial configuration of the data performs the three stages of registration segmentation and shape interpolation from spaced and misaligned images simultaneously we integrate these three processes in a level set framework in order to benefit from their synergistic interactions we also propose a new registration method that exploits segmentation information rather than pixel intensities and that accounts for the global shape of the object of interest for increased robustness and accuracy the accuracy of registration is compared against traditional mutual information based methods and the total modeling framework is assessed against traditional sequential processing and validated on artificial ct and mri data

note on a result of morse and bolt abstract a result given without derivation by morse and bolt 1 pertaining to the reflection of a spherical sound wave from an absorbent surface is investigated it is shown that the result as given is not quite accurate

variational b spline level set a linear filtering approach for fast deformable model evolution in the field of image segmentation most level set based active contour approaches take advantage of a discrete representation of the associated implicit function we present in this paper a different formulation where the implicit function is modeled as a continuous parametric function expressed on a b spline basis starting from the active contour energy functional we show that this formulation allows us to compute the solution as a restriction of the variational problem on the space spanned by the b splines as a consequence the minimization of the functional is directly obtained in terms of the b spline coefficients we also show that each step of this minimization may be expressed through a convolution operation because the b spline functions are separable this convolution may in turn be performed as a sequence of simple 1 d convolutions which yields an efficient algorithm as a further consequence each step of the level set evolution may be interpreted as a filtering operation with a b spline kernel such filtering induces an intrinsic smoothing in the algorithm which can be controlled explicitly via the degree and the scale of the chosen b spline kernel we illustrate the behavior of this approach on simulated as well as experimental images from various fields

a note on reflection of spherical waves in 1909 sommerfeld gave an exact solution for the reflection of a spherical wave from a plane surface in terms of an oscillatory integral and also presented an asymptotic solution for the case where both source and receiver are at the boundary weyl 1919 presented an alternative solution and also an asymptotic solution for the case where the source is at the boundary it is known that the general case is solved if a general solution for the case where the source is at the boundary is known here it is demonstrated that it is sufficient to have the general solution for the case where both source and receiver are at the boundary this is mainly of theoretical interest but may have practical applications as an example it is demonstrated that sommerfeld s approximate solution gives ingard s 1951 approximate solution which is valid for arbitrary source and receiver heights

the generalized finite element method this paper describes a pilot design and implementation of the generalized finite element method gfem as a direct extension of the standard finite element method sfem or fem which makes possible the accurate solution of engineering problems in complex domains which may be practically impossible to solve using the fem the development of the gfem is illustrated for the laplacian in two space dimensions in domains which may include several hundreds of voids and or cracks for which the construction of meshes used by the fem is practically impossible the two main capabilities are 1 it can construct the approximation using meshes which may overlap part or all of the domain boundary 2 it can incorporate into the approximation handbook functions which are known analytically or are generated numerically and approximate well the solution of the boundary value problem in the neighborhood of corner points voids cracks etc the main tool is a special integration algorithm which we call the fast remeshing approach which is robust and works for any domain with arbitrary complexity the incorporation of the handbook functions into the gfem is done by employing the partition of unity method pum the presented formulations and implementations can be easily extended to the multi material medium where the voids are replaced by inclusions of various shapes and sizes and to the case of the elasticity problem this work can also be understood as a pilot study for the feasibility and demonstration of the capabilities of the gfem which is needed before analogous implementations are attempted in the three dmensional and nonlinear cases which are the cases of main interest for future work

an extended level set method for shape and topology optimization in this paper the conventional level set methods are extended as an effective approach for shape and topology optimization by the introduction of the radial basis functions rbfs the rbf multiquadric splines are used to construct the implicit level set function with a high level of accuracy and smoothness and to discretize the original initial value problem into an interpolation problem the motion of the dynamic interfaces is thus governed by a system of coupled ordinary differential equations odes and a relatively smooth evolution can be maintained without reinitialization a practical implementation of this method is further developed for solving a class of energy based optimization problems in which approximate solution to the original hamilton jacobi equation may be justified and nucleation of new holes inside the material domain is allowed for furthermore the severe constraints on the temporal and spatial discretizations can be relaxed leading to a rapid convergence to the final design insensitive to initial guesses the normal velocities are chosen to perform steepest gradient based optimization by using shape sensitivity analysis and a bi sectioning algorithm a physically meaningful and efficient extension velocity method is also presented the proposed method is implemented in the framework of minimum compliance design and its efficiency over the existing methods is highlighted numerical examples show its accuracy convergence speed and insensitivity to initial designs in shape and topology optimization of two dimensional 2d problems that have been extensively investigated in the literature

on cost function transformations for the reduction of uncertain model parameters impact towards the optimal solutions uncertainties affect the accuracy of nonlinear static or dynamic optimization and inverse problems the propagation of uncertain model parameters towards the optimal problem solutions can be assessed in a deterministic or stochastic way using monte carlo based techniques and efficient spectral collocation and galerkin projection methods this paper presents cost function transformations for reducing the impact of uncertain model parameters towards the optimal solutions we assess the consistency of the methodology by determining sufficient conditions on the cost function transformations and apply the methodology on several test functions

an exact laplace transform formulation for a point source above a ground surface an exact analysis is given for a point source in air above a ground surface by representing the plane wave reflection coefficient as the laplace transform of an image source distribution a well behaved image integral instead of the usual sommerfeld integral is obtained the approach is valid for both locally and extended reacting surfaces for a locally reacting ground surface the image integral is an especially simple rapidly convergent integral the integral for local reaction is investigated analytically for a number of limiting cases the resulting analytic solutions are compared with analytic solutions obtained from more standard approaches finally the image integral for local reaction is analyzed numerically and an upper limit on the numerical integration is given it is shown that with realistic values of ground impedance the prescribed integration limit allows the image integral to be easily and accurately computed numerically

a markov random field approach for topology preserving registration application to object based tomographic image interpolation this paper proposes a topology preserving multiresolution elastic registration method based on a discrete markov random field of deformations and a block matching procedure the method is applied to the object based interpolation of tomographic slices for that purpose the fidelity of a given deformation to the data is established by a block matching strategy based on intensity and gradient related features the smoothness of the transformation is favored by an appropriate prior on the field and the deformation is guaranteed to maintain the topology by imposing some hard constraints on the local configurations of the field the resulting deformation is defined as the maximum a posteriori configuration additionally the relative influence of the fidelity and smoothness terms is weighted by the unsupervised estimation of the field parameters in order to obtain an unbiased interpolation result the registration is performed both in the forward and backward directions and the resulting transformations are combined by using the local information content of the deformation the method is applied to magnetic resonance and computed tomography acquisitions of the brain and the torso quantitative comparisons offer an overall improvement in performance with respect to related works in the literature additionally the application of the interpolation method to cardiac magnetic resonance images has shown that the removal of any of the main components of the algorithm results in a decrease in performance which has proven to be statistically significant

near field computation for sound propagation above ground using complex image theory in this paper a very simple method is introduced for the efficient computation of the sound field in the near region above an impedance ground or an extended reaction ground the procedure is based on complex image theory using prony s method the slowly varying factor in the integrand of the sommerfeld integral is approximated by a short series in terms of complex exponential functions the result can be exactly evaluated by the sommerfeld identity a new closed form approximate expression of the sound field is obtained which is represented as the original source its quasistatic image and several images with complex amplitudes and positions avoiding numerical evaluation of the sommerfeld integral makes these closed form expressions computationally very efficient the representation of the field with complex images makes the formula useful in measurement of ground impedance or in other cases requiring repeated mapping of the sound field numerical results show that these closed form green s functions are very accurate for the computation of the near field