a variational method in image recovery this paper is concerned with a classical denoising and deblurring problem in image recovery our approach is based on a variational method by using the legendre fenchel transform we show how the nonquadratic criterion to be minimized can be split into a sequence of half quadratic problems easier to solve numerically first we prove an existence and uniqueness result and then we describe the algorithm for computing the solution and we give a proof of convergence finally we present some experimental results for synthetic and real images

nonlinear degenerate parabolic equations with measure data abstract in this paper we study the existence of solution to nonlinear degenerate parabolic equations with measure data

the orthogonal decomposition theorems for mimetic finite difference methods accurate discrete analogs of differential operators that satisfy the identities and theorems of vector and tensor calculus provide reliable finite difference methods for approximating the solutions to a wide class of partial differential equations these methods mimic many fundamental properties of the underlying physical problem including conservation laws symmetries in the solution and the nondivergence of particular vector fields i e they are divergence free and should satisfy a discrete version of the orthogonal decomposition theorem this theorem plays a fundamental role in the theory of generalized solutions and in the numerical solution of physical models including the navier stokes equations and in electrodynamics we are deriving mimetic finite difference approximations of the divergence gradient and curl that satisfy discrete analogs of the integral identities satisfied by the differential operators we first define the natural discrete divergence gradient and curl operators based on coordinate invariant definitions such as gauss s theorem for the divergence next we use the formal adjoints of these natural operators to derive compatible divergence gradient and curl operators with complementary domains and ranges of values in this paper we prove that these operators satisfy discrete analogs of the orthogonal decomposition theorem and demonstrate how a discrete vector can be decomposed into two orthogonal vectors in a unique way satisfying a discrete analog of the formula vec a ggrad varphi curl vec b we also present a numerical example to illustrate the numerical procedure and calculate the convergence rate of the method for a spiral vector field

structural image restoration through deformable templates abstract prior knowledge on the space of possible images is given in the form of a function or template in some domain the set of all possible true images is assumed to be formed by a composition of that function with continuous mappings of the domain into itself a prior gaussian distribution is given on the set of continuous mappings the observed image is assumed to be a degradation of the true image with additive noise given the observed image a posterior distribution is then obtained and has the form of a nonlinear perturbation of the gaussian measure on the space of mappings we present simulations of the posterior distribution that lead to structural reconstructions of the true image in the sense that it enables us to determine landmarks and other characteristic features of the image as well as to spot pathologies in it moreover we show that the reconstruction algorithm is relatively robust when the images are degraded by noise that is not necessarily additive

the existence of global attractors for the norm to weak continuous semigroup and application to the nonlinear reaction diffusion equations abstract in this paper first we introduce a new concept called the norm to weak continuous semigroup in a banach space and give a technical theorem to verify this notion of continuity then we establish a general method which is necessary and sufficient to obtain the existence of the global attractor for this kind of semigroup as an application we obtain the existence of the global attractor for a nonlinear reaction diffusion equation with a polynomial growth nonlinearity of arbitrary order and with some weak derivatives in the inhomogeneous term the global attractors are obtained in l p h 0 1 and h 2 h 0 1 respectively a new a priori estimate method called asymptotic a priori estimate has been introduced since the solutions of the equation has no higher regularity and the semigroup associated the solutions is not continuous in l p h 0 1 and h 2 h 0 1 the results in this part are new and appear to be optimal

non linear elliptic and parabolic equations involving measure data in this paper we prove the existence of solutions for equations of the type div a du f in a bounded open set u 0 on where a is a possibly non linear function satisfying some coerciveness and monotonicity assumptions and f is a bounded measure we also consider the equation div a du g u f in u 0 on with f l1 or f m u u 0 and the parabolic equivalent of the first elliptic equation

iterative multigrid regularization techniques for image matching in this paper we consider the problem of matching images i e to find a deformation u which transforms a digital image into another such that the images have nearly equal gray values in every image element the difference of the two images is measured by their l2 difference which should be minimized this yields a nonlinear ill conditioned inverse problem for u so the numerical solution is quite difficult a tikhonov regularization method is considered to rule out discontinuous and irregular solutions to the minimization problem an important problem is a proper choice of the regularization parameter alpha for the practical choice of alpha we use iterative regularization methods based on multigrid techniques to obtain a suitable initial guess we use an approach similar to the full multigrid fmg developed by brandt math comp 31 1977 pp 333 390 the algorithms have optimal complexity the amount of work is proportional to the number of picture elements finally we present some experimental results for synthetic and real images

global attractors for nonlinear parabolic equations with nonstandard growth and irregular data abstract we investigate the large time behavior of solutions to the following nonlinear parabolic equations u t div u p x 2 u f x u g in r u 0 on r u x 0 u 0 x in where u 0 g l 1 we first provide the existence and uniqueness of an entropy solution for the problem then through some delicate analysis we establish some regularity results on the solution by which we prove the existence of a global attractor for the solution semigroup

a parameter estimation framework for patient specific hemodynamic computations we propose a fully automated parameter estimation framework for performing patient specific hemodynamic computations in arterial models to determine the personalized values of the windkessel models which are used as part of the geometrical multiscale circulation model a parameter estimation problem is formulated clinical measurements of pressure and or flow rate are imposed as constraints to formulate a nonlinear system of equations whose fixed point solution is sought a key feature of the proposed method is a warm start to the optimization procedure with better initial solution for the nonlinear system of equations to reduce the number of iterations needed for the calibration of the geometrical multiscale models to achieve these goals the initial solution computed with a lumped parameter model is adapted before solving the parameter estimation problem for the geometrical multiscale circulation model the resistance and the compliance of the circulation model are estimated and compensated the proposed framework is evaluated on a patient specific aortic model a full body arterial model and multiple idealized anatomical models representing different arterial segments for each case it leads to the best performance in terms of number of iterations required for the computational model to be in close agreement with the clinical measurements

a nonlinear primal dual method for total variation based image restoration we present a new method for solving total variation tv minimization problems in image restoration the main idea is to remove some of the singularity caused by the nondifferentiability of the quantity nabla u in the definition of the tv norm before we apply a linearization technique such as newton s method this is accomplished by introducing an additional variable for the flux quantity appearing in the gradient of the objective function which can be interpreted as the normal vector to the level sets of the image u our method can be viewed as a primal dual method as proposed by conn and overton a primal dual interior point method for minimizing a sum of euclidean norms preprint 1994 and andersen ph d thesis odense university denmark 1995 for the minimization of a sum of euclidean norms in addition to possessing local quadratic convergence experimental results show that the new method seems to be globally convergent

outflow boundary conditions for three dimensional finite element modeling of blood flow and pressure in arteries flow and pressure waves emanate from the heart and travel through the major arteries where they are damped dispersed and reflected due to changes in vessel caliber tissue properties and branch points as a consequence solutions to the governing equations of blood flow in the large arteries are highly dependent on the outflow boundary conditions imposed to represent the vascular bed downstream of the modeled domain the most common outflow boundary conditions for three dimensional simulations of blood flow are prescribed constant pressure or traction and prescribed velocity profiles however in many simulations the flow distribution and pressure field in the modeled domain are unknown and cannot be prescribed at the outflow boundaries an alternative approach is to couple the solution at the outflow boundaries of the modeled domain with lumped parameter or one dimensional models of the downstream domain we previously described a new approach to prescribe outflow boundary conditions for simulations of blood flow based on the dirichlet to neumann and variational multiscale methods this approach termed the coupled multidomain method was successfully applied to solve the non linear one dimensional equations of blood flow with a variety of models of the downstream domain this paper describes the extension of this method to three dimensional finite element modeling of blood flow and pressure in the major arteries outflow boundary conditions are derived for any downstream domain where an explicit relationship of pressure as a function of flow rate or velocities can be obtained at the coupling interface we developed this method in the context of a stabilized semi discrete finite element method flow rate and pressure distributions are shown for different boundary conditions to illustrate the dramatic influence of alternative boundary conditions on these quantities

global attractors for degenerate semilinear parabolic equations abstract let be a smooth bounded domain in r n n 2 we consider the long time behavior of solutions to the following problem u t div x u f u g in r u 0 on r u x 0 u 0 x in where u 0 g l 1 the diffusion coefficient x is measurable nonnegative and is allowed to have a finite number of zeroes at some points we provide the existence and uniqueness results for the problem then we establish some asymptotic regularity results on the solution and consider its long time behavior the existence of a global attractor is obtained in the proper space

regularization in model updating this paper presents the theory of sensitivity based model updating with a special focus on the properties of the solution that result from the combination of optimization of the response prediction with a priori information about the uncertain parameters model updating together with the additional regularization criterion is an optimization with two objective functions and must be linearized to obtain the solution structured solutions are obtained based on the generalized singular value decomposition gsvd and specific features of the parameter and response paths as the regularization parameter varies are explored the four different types of spaces that arise in the solution are discussed together with the characteristics of the regularized solution families these concepts are demonstrated on a simulated discrete example and on an experimental case study copyright 2007 john wiley sons ltd

image analysis using multigrid relaxation methods image analysis problems posed mathematically as variational principles or as partial differential equations are amenable to numerical solution by relaxation algorithms that are local iterative and often parallel although they are well suited structurally for implementation on massively parallel locally interconnected computational architectures such distributed algorithms are seriously handi capped by an inherent inefficiency at propagating constraints between widely separated processing elements hence they converge extremely slowly when confronted by the large representations of early vision application of multigrid methods can overcome this drawback as we showed in previous work on 3 d surface reconstruction in this paper we develop multiresolution iterative algorithms for computing lightness shape from shading and optical flow and we examine the efficiency of these algorithms using synthetic image inputs the multigrid methodology that we describe is broadly applicable in early vision notably it is an appealing strategy to use in conjunction with regularization analysis for the efficient solution of a wide range of ill posed image analysis problems

finite and infinite dimensional attractors for porous media equations the fractal dimension of the global attractors of porous media equations in bounded domains is studied the conditions which guarantee this attractor to be finite dimensional are found and the examples of infinite dimensional attractors that do not satisfy these conditions are constructed the upper and lower bounds for the kolmogorov e entropy of infinite dimensional attractors are also obtained

on global attractor for nonlinear parabolic equations of m laplacian type abstract existence and some regularity results of global attractor in l q q 1 for m laplacian type quasilinear parabolic equation with a perturbation like a x u u u u f x with 0 a x 0 are proved for the proofs moser s technique is used extensively

a multilevel method for image registration in this paper we introduce a new framework for image registration our formulation is based on consistent discretization of the optimization problem coupled with a multigrid solution of the linear system which evolves in a gauss newton iteration we show that our discretization is h elliptic independent of parameter choice and therefore a simple multigrid implementation can be used to overcome potential large nonlinearities and to further speed up computation we use a multilevel continuation technique we demonstrate the efficiency of our method on a realistic highly nonlinear registration problem

a more robust multigrid algorithm for diffusion type registration models abstract registration refers to the useful process of aligning two similar but different intensity image functions in order to either track changes or combine information variational models are capable of finding transform maps containing large and non uniform deformations between such a pair of images since finding a transform map is an inverse problem as with all models suitable regularisation is necessary to overcome the non uniqueness of the problem in the case of diffusion type models regularisation terms impose smoothness on the transformation by minimising the gradient of the flow field the diffusion model also coincides with the basic model for optical flow frameworks of horn and schunck 1981 the biggest drawback with variational models is the large computational cost required to solve the highly non linear system of pdes chumchob and chen 2011 developed a non linear multigrid nmg method to address this cost problem however a closer look at the analysis of the nmg scheme highlighted omissions which affected the convergence of the nmg scheme moreover the nmg method proposed by chumchob and chen did not impose any control of non physical folding which invalidates a map this paper has proposed several key ideas first we re evaluate the analysis of the nmg method to show how the omissions in chumchob and chen 2011 have a noticeable impact on the convergence of the nmg method in addition we also provide a way of estimating the convergence rate of a solver on the coarsest grid in order to estimate the number of iterations that will be required to obtain a solution with appropriate accuracy second we propose an extension to the chumchob chen nmg method which controls any folding within the deformation experimental results on the proposed multigrid framework demonstrate improvements in convergence and the accuracy of registrations compared with previous methods

data assimilation and modelling of patient specific single ventricle physiology with and without valve regurgitation a closed loop lumped parameter model of blood circulation is considered for single ventricle shunt physiology its parameters are estimated by an inverse problem based on patient specific haemodynamics measurements as opposed to a black box approach maximizing the number of parameters that are related to physically measurable quantities motivates the present model heart chambers are described by a single fibre mechanics model and valve function is modelled with smooth opening and closure a model for valve prolapse leading to valve regurgitation is proposed the method of data assimilation in particular the unscented kalman filter is used to estimate the model parameters from time varying clinical measurements this method takes into account both the uncertainty in prior knowledge related to the parameters and the uncertainty associated with the clinical measurements two patient specific cases one without regurgitation and one with atrioventricular valve regurgitation are presented pulmonary and systemic circulation parameters are successfully estimated without assumptions on their relationships parameters governing the behaviour of heart chambers and valves are either fixed based on biomechanics or estimated results of the inverse problem are validated qualitatively through clinical measurements or clinical estimates that were not included in the parameter estimation procedure the model and the estimation method are shown to successfully capture patient specific clinical observations even with regurgitation such as the double peaked nature of valvular flows and anomalies in electrocardiogram readings lastly biomechanical implications of the results are discussed

a nonlinear variational problem for image matching minimizing a nonlinear functional is presented as a way of obtaining a planar mapping that matches two similar images a smoothing term is added to the nonlinear functional to penalize discontinuous and irregular solutions one option for the smoothing term is a quadratic form generated by a linear differential operator the functional is then minimized using the fourier representation of the planar mapping with this representation the quadratic form is diagonalized another option is a quadratic form generated via a basis of compactly supported wavelets in both cases a natural approximation scheme is described both quadratic forms are shown to impose the same smoothing however in terms of the finite dimensional approximations it is easier to accommodate local deformations using the wavelet basis

analysis of discrete ill posed problems by means of the l curve when discrete ill posed problems are analyzed and solved by various numerical regularization techniques a very convenient way to display information about the regularized solution is to plot the norm or seminorm of the solution versus the norm of the residual vector in particular the graph associated with tikhonov regularization plays a central role the main purpose of this paper is to advocate the use of this graph in the numerical treatment of discrete ill posed problems the graph is characterized quantitatively and several important relations between regularized solutions and the graph are derived it is also demonstrated that several methods for choosing the regularization parameter are related to locating a characteristic l shaped corner of the graph

a variational approach to nonrigid morphological image registration a variational method for nonrigid registration of multimodal image data is presented a suitable deformation will be determined via the minimization of a morphological i e contrast invariant matching functional along with an appropriate regularization energy the aim is to correlate the morphologies of a template and a reference image under the deformation mathematically the morphology of images can be described by the entity of level sets of the image and hence by its gauss map a class of morphological matching functionals is presented which measure the defect of the template gauss map in the deformed state with respect to the deformed gauss map of the reference image the problem is regularized by considering a nonlinear elastic regularization energy existence of homeomorphic minimizing deformation is proved under assumptions on the class of admissible deformations with respect to actual medical applications suitable generalizations of the matching energies and the boundary conditions are pre

a hyperelastic regularization energy for image registration image registration is one of the most challenging problems in image processing where ill posedness arises due to noisy data as well as nonuniqueness and hence the choice of regularization is crucial this paper presents hyperelasticity as a regularizer and introduces a new and stable numerical implementation on one hand hyperelastic registration is an appropriate model for large and highly nonlinear deformations for which a linear elastic model needs to fail on the other hand the hyperelastic regularizer yields very regular and diffeomorphic transformations while hyperelasticity might be considered as just an additional outstanding regularization option for some applications it becomes inevitable for applications involving higher order distance measures like mass preserving registration the paper gives a short introduction to image registration and hyperelasticity the hyperelastic image registration problem is phrased in a variational setting and an existence proof is provided the focus of th

global attractors for weighted p laplacian equations with boundary degeneracy using a new a priori estimate method which is introduced by zhong et al j differ equations 223 2 367 2006 10 1016 j jde 2005 06 008 we establish the existence of a global attractor in l2 and lq q 2 respectively for weighted p laplacian equations with boundary degeneracy and without any restriction on the growing order of the nonlinearity

existence and uniqueness for a degenerate parabolic equation with l1 data in this paper we study existence and uniqueness of solutions for the boundary value problem with initial datum in l1 ut div a x du in 0 u a u on 0 u x 0 u0 x in where a is a caratheodory function satisfying the classical leray lions hypothesis a is the neumann boundary operator associated to a du the gradient of u and is a maximal monotone graph in r r with 0 0

multiscale joint segmentation and registration of image morphology multimodal image registration significantly benefits from previous denoising and structure segmentation and vice versa in particular combined information of different image modalities makes segmentation significantly more robust indeed fundamental tasks in image processing are highly interdependent a variational approach is presented which combines the detection of corresponding edges an edge preserving denoising and the morphological registration via a nonrigid deformation for a pair of images with structural correspondence the morphology of an image function is split into a singular part consisting of the edge set and a regular part represented by the field of normals on the ensemble of level sets a mumford shah type free discontinuity problem is applied to treat the singular morphology and the matching of corresponding edges under the deformation the matching of the regular morphology is quantified by a second contribution which compares deformed normals and normals at deformed positions finally a nonlinear elastic energy controls the deformation itself and ensures smoothness and injectivity a multiscale approach that is based on a phase field approximation leads to an effective and efficient algorithm numerical experiments underline the robustness of the presented approach and show applications on medical images

multimodal image registration using a variational approach this paper presents an approach to obtain a deformation which matches two images acquired from different medical imaging modalities this problem arises in the investigation of human brains two distance functionals for the images are proposed with different pros and cons these functionals are to be minimized we add a smoothing term to the minimization problem which retains certain desired elastic features in the solution at each minimization step an approximate solution for the linearized problem is computed with a multigrid method as an inner iteration furthermore we use a multiresolution minimization approach to obtain a suitable initial guess finally we present some experimental results for registration problems of synthetic images and for a real computer tomography ct magnetic resonance imaging mri registration

adjoint based inverse analysis of windkessel parameters for patient specific vascular models a human circulatory system is composed of more than 50 000 miles of blood vessels such a huge network of vessels is responsible for the elevated pressure values within large arteries as such modeling of large blood arteries requires a full modeling of circulatory system this in turn is computationally not affordable thus a multiscale modeling of the arterial network is a necessity the multiscale approach is achieved through first modeling the arterial regions of interest with 3d models and the rest of the circulatory network with reduced dimensional reduced d models then coupling the multiscale domains together though reduced d models can well reproduce physiology calibrating them to fit 3d patient specific fluid structure interaction fsi geometries has received little attention for this reason this work develops calibration methods for reduced d models using adjoint based methods we also propose a reduced modeling complexity rmc approach that reduces the calibration cost of expensive fsi models using pure fluid modeling finally all of the developed calibration techniques are tested on patient specific arterial geometries showing the power and stability of the proposed calibration methods

variational optical flow computation in real time this paper investigates the usefulness of bidirectional multigrid methods for variational optical flow computations although these numerical schemes are among the fastest methods for solving equation systems they are rarely applied in the field of computer vision we demonstrate how to employ those numerical methods for the treatment of variational optical flow formulations and show that the efficiency of this approach even allows for real time performance on standard pcs as a representative for variational optic flow methods we consider the recently introduced combined local global method it can be considered as a noise robust generalization of the horn and schunck technique we present a decoupled as well as a coupled version of the classical gau spl szlig seidel solver and we develop several multigrid implementations based on a discretization coarse grid approximation in contrast with standard bidirectional multigrid algorithms we take advantage of intergrid transfer operators that allow for nondyadic grid hierarchies as a consequence no restrictions concerning the image size or the number of traversed levels have to be imposed in the experimental section we juxtapose the developed multigrid schemes and demonstrate their superior performance when compared to unidirectional multigrid methods and nonhierachical solvers for the well known 316 spl times 252 yosemite sequence we succeeded in computing the complete set of dense flow fields in three quarters of a second on a 3 06 ghz pentium4 pc this corresponds to a frame rate of 18 flow fields per second which outperforms the widely used gau spl szlig seidel method by almost three orders of magnitude

a robust multigrid approach for variational image registration models variational registration models are non rigid and deformable imaging techniques for accurate registration of two images as with other models for inverse problems using the tikhonov regularization they must have a suitably chosen regularization term as well as a data fitting term one distinct feature of registration models is that their fitting term is always highly nonlinear and this nonlinearity restricts the class of numerical methods that are applicable this paper first reviews the current state of the art numerical methods for such models and observes that the nonlinear fitting term is mostly avoided in developing fast multigrid methods it then proposes a unified approach for designing fixed point type smoothers for multigrid methods the diffusion registration model second order equations and a curvature model fourth order equations are used to illustrate our robust methodology analysis of the proposed smoothers and comparisons to other methods are given as expected of a multigrid method being many orders of magnitude faster than the unilevel gradient descent approach the proposed numerical approach delivers fast and accurate results for a range of synthetic and real test images

lucas kanade meets horn schunck combining local and global optic flow methods differential methods belong to the most widely used techniques for optic flow computation in image sequences they can be classified into local methods such as the lucas kanade technique or bigun s structure tensor method and into global methods such as the horn schunck approach and its extensions often local methods are more robust under noise while global techniques yield dense flow fields the goal of this paper is to contribute to a better understanding and the design of novel differential methods in four ways i we juxtapose the role of smoothing regularisation processes that are required in local and global differential methods for optic flow computation ii this discussion motivates us to describe and evaluate a novel method that combines important advantages of local and global approaches it yields dense flow fields that are robust against noise iii spatiotemporal and nonlinear extensions as well as multiresolution frameworks are presented for this hybrid method iv we propose a simple confidence measure for optic flow methods that minimise energy functionals it allows to sparsify a dense flow field gradually depending on the reliability required for the resulting flow comparisons with experiments from the literature demonstrate the favourable performance of the proposed methods and the confidence measure

on the order of prolongations and restrictions in multigrid procedures abstract it is well known in the world of multigrid that the order of the prolongation and the order of the restriction in a multigrid method should satisfy certain conditions a rule of thumb is that the sum of the orders of the prolongation and of the restriction should at least be equal to the order of the differential equation solved in this note we show the correctness of this rule we notice that we have to distinguish between low frequency and high frequency orders for the transfer operators for the restriction the low frequency order is related with its accuracy whereas for the interpolation operator both orders are related with the accuracy of the result of the interpolation if an interpolation rule leaves all polynomials of degree k 1 invariant then both the low and the high frequency order are equal to k it is the high frequency order that plays a role in the above mentioned rule of thumb

global attractors for the p laplacian equations with nonregular data abstract let be a smooth bounded domain in r n n 3 we consider the long time behavior of solutions to the p laplacian equation u t p u f u g where 2 p n p div u p 2 u is the p laplace operator assume that g and the initial condition u 0 lie in l 1 f r r is of class c 1 and satisfies proper growth conditions firstly we prove the uniqueness of the entropy solution and establish some regularity results then we show the existence of a global attractor a in l r 1 w 0 1 s with s max n p 1 n 1 p r 1 r to obtain the results a decomposition method and a bootstrap technique are used

vectorial total variation based regularization for variational image registration to use interdependence between the primary components of the deformation field for smooth and non smooth registration problems the channel by channel total variation or standard vectorial total variation svtv based regularization has been extended to a more flexible and efficient technique allowing high quality regularization procedures based on this method this paper proposes a fast nonlinear multigrid nmg method for solving the underlying euler lagrange system of two coupled second order nonlinear partial differential equations numerical experiments using both synthetic and realistic images not only confirm that the recommended vtv based regularization yields better registration qualities for a wide range of applications than those of the svtv based regularization but also that the proposed nmg method is fast accurate and reliable in delivering visually pleasing registration results

regularity of random attractors for a degenerate parabolic equations driven by additive noises abstract we study the regularity of random attractors for a class of stochastic degenerate parabolic equations with the leading term involving a diffusion variable which many be non smooth or unbounded without any restrictions on the upper growth order p of the nonlinearity except that p 2 we show that the associated random dynamical system admits a unique compact random attractor in the space d 0 1 2 d n l d n for any 2 2 p 2 where d n is an arbitrary bounded or unbounded domain in r n n 2

truly monolithic algebraic multigrid for fluid structure interaction the coupling of flexible structures to incompressible fluids draws a lot attention during the last decade many different solution schemes have been proposed in this contribution we concentrate on strong coupling fluid structure interaction by means of monolithic solution schemes therein a newton krylov method is applied to the monolithic set of nonlinear equations such schemes require good preconditioning to be efficient we propose two preconditioners that apply algebraic multigrid techniques to the entire fluid structure interaction system of equations the first is based on a standard block gauss seidel approach where approximate inverses of the individual field blocks are based on a algebraic multigrid hierarchy tailored for the type of the underlying physical problem the second is based on a monolithic coarsening scheme for the coupled system that makes use of prolongation and restriction projections constructed for the individual fields the resulting nonsymmetric monolithic algebraic multigrid method therefore involves coupling of the fields on coarse approximations to the problem yielding significantly enhanced performance

a multilevel level set method for optimizing eigenvalues in shape design problems in this paper we consider optimal design problems that involve shape optimization the goal is to determine the shape of a certain structure such that it is either as rigid or as soft as possible to achieve this goal we combine two new ideas for an efficient solution of the problem first we replace the eigenvalue problem with an approximation by using inverse iteration second we use a level set method but rather than propagating the front we use constrained optimization methods combined with multilevel continuation techniques combining these two ideas we obtain a robust and rapid method for the solution of the optimal design problem

a variational problem arising from speech recognition by following the general approach of deformable templates the problem of recognizing a single word independently of the speaker is shown to lead to the computation of the minimum value of some particular functional more precisely this allows us to recover for each possible word in a prespecified set the best matching with the recorded signal by selecting the minimum value the recognition problem can be solved in this paper we are concerned with the detailed study of the variational problem associated with this sort of functional namely the existence of a minimum point and the features of such a minimum finally we discuss the convergence of a discretized finite dimensional approximation suggested by the engineering literature on this subject

a multigrid method for a fourth order diffusion equation with application to image processing in this paper we are concerned with the efficient solution of the elliptic system alpha l nobreak i u nobreak f where l is the biharmonic operator supplemented by higher order boundary conditions this is a core task in image processing arising from the minimization of rotation invariant energy functionals for the purpose of numerical solution we approximate the partial differential equation by finite differences in order to obtain efficient and robust solution methods we discuss how the system can be treated efficiently by multigrid methods finally experimental results are reported that demonstrate the effectiveness of the multigrid approach

long time behavior for quasilinear parabolic equations involving weighted p laplacian operators abstract in this paper we study the first initial boundary value problem for a class of quasilinear degenerate parabolic equations involving weighted p laplacian operators the long time behavior of solutions to that problem is considered via the concept of global attractors for multi valued semiflows

mixed finite elements for elasticity there have been many efforts dating back four decades to develop stable mixed finite elements for the stress displacement formulation of the plane elasticity system this requires the development of a compatible pair of finite element spaces one to discretize the space of symmetric tensors in which the stress field is sought and one to discretize the space of vector fields in which the displacement is sought although there are number of well known mixed finite element pairs known for the analogous problem involving vector fields and scalar fields the symmetry of the stress field is a substantial additional difficulty and the elements presented here are the first ones using polynomial shape functions which are known to be stable we present a family of such pairs of finite element spaces one for each polynomial degree beginning with degree two for the stress and degree one for the displacement and show stability and optimal order approximation we also analyze some obstructions to the construction of such finite element spaces which account for the paucity of elements available

asymptotic regularity for some dissipative equations abstract this paper is devoted to proving some asymptotic regularity for both reaction diffusion equation with a polynomially growing nonlinearity of arbitrary order and strongly damped wave equation with critical nonlinearity which excel the sharp regularity allowed by the corresponding stationary equations equilibrium points based on this regularity the existence of the finite dimensional global and exponential attractors can be obtained easily

on the dynamics of a strongly singular parabolic equation abstract in this paper we study the semiflow defined by a semilinear parabolic equation in which both the diffusion and the reaction term present strong order of singularity at the origin we justify the existence of a global branch of nontrivial equilibrium solutions for subcritical nonlinearities the approach based on the critical caffarelli kohn nirenberg inequality follows the arguments of 21 22