on a dimensional reduction method i the optimal selection of basis functions abstract this paper is the first in a series of three which analyze an adaptive approximate approach for solving n 1 dimensional boundary value problems by replacing them with systems of equations in n dimensional space in this approach the unknown functions of n 1 variables are projected onto finite linear combinations of functions of just n variables this paper shows how the coefficients of these linear combinations can be chosen optimally author

adaptive remeshing and h p domain decomposition abstract the h p version of the finite element method combines local mesh refinement with an increase of the shape functions polynomial degree this paper presents a method which uses an h p approximation for a domain decomposition with fully overlapping domains allowing c 0 continuous approximation for geometrically incompatible mesh refinement to be obtained the method is applied to a reaction diffusion problem resulting from semiconductor process simulation in numerical examples it is demonstrated that this approach is well suited for problems with sharp interior layers or shock like behaviour

analysis of three dimensional fracture mechanics problems a two scale approach using coarse generalized fem meshes this paper presents a generalized finite element method gfem based on the solution of interdependent global structural and local crack scale problems the local problems focus on the resolution of fine scale features of the solution in the vicinity of three dimensional cracks while the global problem addresses the macro scale structural behavior the local solutions are embedded into the solution space for the global problem using the partition of unity method the local problems are accurately solved using an hp gfem and thus the proposed method does not rely on analytical solutions the proposed methodology enables accurate modeling of three dimensional cracks on meshes with elements that are orders of magnitude larger than the process zone along crack fronts the boundary conditions for the local problems are provided by the coarse global mesh solution and can be of dirichlet neumann or cauchy type the effect of the type of local boundary conditions on the performance of the proposed gfem is analyzed several three dimensional fracture mechanics problems aimed at investigating the accuracy of the method and its computational performance both in terms of problem size and cpu time are presented copyright 2009 john wiley sons ltd

applying the hp d version of the fem to locally enhance dimensionally reduced models abstract a modification of the hp d method is presented which allows to locally enhance a dimensionally reduced finite element approximation with an ansatz based on a more accurate i e dimensionally higher model the procedure is based on a hierarchical domain decomposition which is applied to couple discretizations of different types of mechanical models like beams plates and solids thereby the error of the underlying mathematical model can be reduced in critical regions by introducing locally a physically more sophisticated model two examples are given to demonstrate the basic properties of the proposed method in the first example the solution of a one dimensional beam model is improved locally by a two dimensional finite element computation in the second example the local enhancement of a reissner mindlin plate by a fully three dimensional continuum approach is considered yielding a significant reduction of the model error

a semi local spectral hp element solver for linear elasticity problems summary we develop an efficient semi local method for speeding up the solution of linear systems arising in spectral hp element discretization of the linear elasticity equations the main idea is to approximate the element wise residual distribution with a localization operator we introduce in this paper and subsequently solve the local linear system additionally we decouple the three directions of displacement in the localization operator hence enabling the use of an efficient low energy preconditioner for the conjugate gradient solver this approach is effective for both nodal and modal bases in the spectral hp element method but here we focus on the modal hierarchical basis in numerical tests we verify that there is no loss of accuracy in the semi local method and we obtain good parallel scalability and substantial speed up compared to the original formulation in particular our tests include both structure only and fluid structure interaction problems with the latter modeling a 3d patient specific brain aneurysm copyright 2014 john wiley sons ltd

high order finite elements for shells in this article the p version finite element method is applied to thin walled structures two different hierarchic element formulations are compared a shell approach as well as a shell like solid formulation both approaches are compared for linear elastic and elastoplastic problems special emphasis is placed on the efficiency as well as on determining the area of application for both formulations

three dimensional stochastic analysis of macrodispersion in aquifers the dispersive mixing resulting from complex flow in three dimensionally heterogeneous porous media is analyzed using stochastic continuum theory stochastic solutions of the perturbed steady flow and solute transport equations are used to construct the macroscopic dispersive flux and evaluate the resulting macrodispersivity tensor in terms of a three dimensional statistically anisotropic input covariance describing the hydraulic conductivity with a statistically isotropic input covariance the longitudinal macrodispersivity is convectively controlled but the transverse macrodispersivity is proportional to the local dispersivity and is several orders of magnitude smaller than the longitudinal term with an arbitrarily oriented anisotropic conductivity covariance all components of the macrodispersivity tensor are convectively controlled and the ratio of transverse to longitudinal dispersivity is of the order of 10 1 in this case the off diagonal components of the dispersivity tensor are significant being numerically larger than the diagonal transverse terms and the transverse dispersion process can be highly anisotropic dispersivities predicted by the stochastic theory are shown to be consistent with controlled field experiments and monte carlo simulations the theory which treats the asymptotic condition of large displacement indicates that a classical gradient transport fickian relationship is valid for large scale displacements

an analysis and an affordable regularization technique for the spurious force oscillations in the context of direct forcing immersed boundary methods the framework of this paper is the improvement of direct forcing immersed boundary methods in presence of moving obstacles in particular motivations for the use of the direct forcing df method can be found in the advantage of a fixed computational mesh for fluid structure interaction problems unfortunately the direct forcing approach suffers a serious drawback in case of moving obstacles the well known spurious force oscillations sfos in this paper we strengthen previous analyses of the origin of the sfo through a rigorous numerical evaluation based on taylor expansions we propose a remedy through an easy to implement regularization process regularized df formally this regularization is related to the blending of the navier stokes solver with the interpolation but no modification of the numerical scheme is needed this approach significantly cuts off the sfos without increasing the computational cost the accuracy and the space convergence order of the standard df method are conserved this is illustrated on numerical and physical validation test cases ranging from the taylor couette problem to a cylinder with an imposed sinusoidal motion subjected to a cross flow

lagrangian analysis of transport in heterogeneous formations under transient flow conditions the coupled effects of porous media heterogeneity and flow unsteadiness on transport are investigated we address the problem using a stochastic lagrangian approach the log condictivity is modeled as a space random function however the flow unsteadiness is considered as deterministic and it affects the magnitude and direction of the mean head gradient using a first order solution in terms of the log conductivity variance we developed a three dimensional solution that includes the velocity covariances the macrodispersion coefficients and the displacement tensor all as a function of the media heterogeneity and the unsteady mean flow parameters the model is applied to the case of a periodic variation in the flow direction we show that the effects of unsteadiness on the longitudinal spread are insignificant while it affects strongly the transverse spread in the form of an added constant dispersivity results obtained in previous studies are discussed and are shown to be particular cases of the present results

on a dimensional reduction method ii some approximation theoretic results abstract this paper is the second in a series of three that analyze a method of dimensional reduction it contains some results for approximation of functions on the interval 1 1 with elements from the nullspace of p to the n power n greater than or equal to 1 where p is a second order ordinary differential operator a special case of this is approximation by polynomials the one dimensional results are used as a tool to prove similar versions in several dimensions these multi dimensional results are directly related to the approximate method of dimensional reduction and they lead to statements about the convergence properties of this approach the third paper which analyzes the adaptive aspects of the method is forthcoming

eulerian lagrangian theory of transport in space time nonstationary velocity fields exact nonlocal formalism by conditional moments and weak approximation a unified eulerian lagrangian theory is presented for the transport of a conservative solute in a random velocity field that satisfies locally v x t f x t where f x t is a random function including sources and or the time derivative of head solute concentration satisfies locally the eulerian equation c x t t j x t g x t where j x t is advective solute flux and g x t is a random source independent of f x t we consider the prediction of c x t and j x t by means of their unbiased ensemble moments c x t and j x t conditioned as implied by the subscript on local hydraulic measurements through the use of the latter in obtaining a relatively smooth unbiased estimate x t of v x t these predictors satisfy c x t v t j x t g x t where j x t x t c x t q x t and q x t is a dispersive flux we show that q is given exactly by three space time convolution integrals of conditional lagrangian kernels with q with c and with c for a broad class of v x t fields including fractals this implies that q x t is generally nonlocal and non fickian rendering c x t non gaussian the direct contribution of random variations in f to q depends on c rather than on c we elucidate the nature of the above kernels discuss conditions under which the convolution of and c becomes pseudo fickian with a lagrangian dispersion tensor similar to that derived in 1921 by taylor recall a 1952 result by batchelor which yields an exact expression for c at early time use the latter to conclude that linearizations which predict that c bifurcates at early time when the probability density function of v is unimodal cannot be correct propose instead a weak approximation which leads to a nonlinear integro differential equation for c due to an instantaneous point source and which improves with the quantity and quality of hydraulic data demonstrate that the weak approximation is analogous to the direct interaction closure of turbulence theory offer non fickian and pseudo fickian weak approximations for the second conditional moment of the concentration prediction error demonstrate that it yields the so called two particle covariance as a special case conclude that the conditional variance of c does not become infinite merely as a consequence of disregarding local dispersion and discuss how to estimate explicitly the cumulative release of a contaminant across a compliance surface together with the associated estimation error

on a dimensional reduction method iii a posteriori error estimation and an adaptive approach abstract this paper analyzes an adaptive approximate approach for solving n 1 dimensional boundary value problems by replacing them with systems of equation in n dimensional space the discussion shows how to find reliable a posteriori estimates for the error and how these can also be used in the design of an adaptive strategy various numerical examples are presented

an efficient multilevel solution scheme for large scale non linear systems we present a new approach for the fast efficient solution of large systems of non linear equations arising from the finite element discretization the proposed non linear solver builds on the advantages of the popular methods of solution that are currently being employed while eliminating most of their undesirable features it combines the well known bfgs method with the fas version of the multigrid method introduced by brandt 1 to form a fast efficient solution method for non linear problems we present numerical performance studies that are indicative of the convergence properties as well as the stability of the new method

pq adaptive solid finite elements for three dimensional plates and shells this article presents a pq adaptive finite element procedure for three dimensional computation of thin walled structures like plates and shells the approach is based on a hexahedral element with high order shape functions the polynomial degree of the shape functions in the three spatial directions of the element is adjusted by means of an adaptive procedure to this end a hierarchical error indicator is applied to automatically control the polynomial degree q in thickness and p in the in plane direction of plate and shell like structures the efficiency and reliability of the proposed adaptive method is demonstrated using two numerical examples

multi level hp adaptivity for cohesive fracture modeling summary discretization induced oscillations in the load displacement curve are a well known problem for simulations of cohesive crack growth with finite elements the problem results from an insufficient resolution of the complex stress state within the cohesive zone ahead of the crack tip this work demonstrates that the hp version of the finite element method is ideally suited to resolve this complex and localized solution characteristic with high accuracy and low computational effort to this end we formulate a local and hierarchic mesh refinement scheme that follows dynamically the propagating crack tip in this way the usually applied static a priori mesh refinement along the complete potential crack path is avoided which significantly reduces the size of the numerical problem studying systematically the influence of h refinement p refinement and hp refinement we demonstrate why the suggested hp formulation allows to capture accurately the complex stress state at the crack front preventing artificial snap through and snap back effects this allows to decrease significantly the number of degrees of freedom and the simulation runtime furthermore we show that by combining this idea with the finite cell method the crack propagation within complex domains can be simulated efficiently without resolving the geometry by the mesh copyright 2016 john wiley sons ltd

macrodispersivity for transport in arbitrary nonuniform flow fields asymptotic and preasymptotic results 1 we use homogenization theory to investigate the asymptotic macrodispersion in arbitrary nonuniform velocity fields which show small scale fluctuations in the first part of the paper a multiple scale expansion analysis is performed to study transport phenomena in the asymptotic limit e 1 where e represents the ratio between typical lengths of the small and large scale in this limit the effects of small scale velocity fluctuations on the transport behavior are described by a macrodispersive term and our analysis provides an additional local equation that allows calculating the macrodispersive tensor for darcian flow fields we show that the macrodispersivity is a fourth rank tensor if dispersion diffusion can be neglected it depends only on the direction of the mean flow with respect to the principal axes of anisotropy of the medium hence the macrodispersivity represents a medium property in the second part of the paper we heuristically extend the theory to finite e effects our results differ from those obtained in the common probabilistic approach employing ensemble averages this demonstrates that standard ensemble averaging does not consistently account for finite scale effects it tends to overestimate the dispersion coefficient in the single realization

homogenization of richards equation in permeability fields with different connectivities 1 large scale modeling of transient flow in the unsaturated zone is important for the estimation of the water budget and solute transport in the vadose zone upscaled flow models need to capture the impact of small scale heterogeneities which are not resolved by the model on large scale flow we perform upscaling of the richards equation in heterogeneous porous media with continuous distributions of the soil hydraulic parameters using homogenization theory and stochastic averaging techniques we restrict the analysis to flow regimes in which the capillary equilibrium assumption holds on the small scale in order to account for effects of capillary entry pressure we apply the brooks corey model for the soil retention and relative permeability curves and consider leverett scaling for the coupling of intrinsic permeability and entry pressure for this model we derive and analyze the ensemble averaged parameter functions for the macroscopic flow equations the effects of a definite entry pressure vanish with increasing variance of the log intrinsic permeability we compare the statistically averaged parameter functions to numerically calculated effective functions for parameter fields with different connectivity properties these results illustrate that soils with well connected coarse materials differ in the relative permeability from those with well connected fine materials or those without particular connectedness

anisotropic discretization and model error estimation in solid mechanics by local neumann problems first a survey of existing residuum based error estimators and error indicators is given generally residual error estimators which have at least upper bound in contrast to indicators can be locally computed from residua of equilibrium and stress jumps at element interfaces using dirichlet or neumann conditions for element patches or individual elements rem another equivalent method for error estimation can be derived from a posteriori computed improved boundary tractions which provide exact equilibrium of elements they are computed from local neumann problems and yield improved local solution by testing with higher test functions this method is called posterior equilibrium method pem and yields better efficiency indices than rem for the investigated problem even in case of locking also the important feature of model adaptivity via hierarchical error estimation can only be realized by this strategy global neumann type estimators and examples are presented for elastic and elastoplastic deformations controlling equilibrium in tangential space

fixed grid fluid structure interaction in two dimensions based on a partitioned lattice boltzmann and p fem approach over the last decade the lattice boltzmann method which was derived from the kinetic gas theory has matured as an efficient approach for solving navier stokes equations the p fem approach has proved to be highly efficient for a variety of problems in the field of structural mechanics our goal is to investigate the validity and efficiency of coupling the two approaches to simulate transient bidirectional fluid structure interaction problems with geometrically non linear structural deflections a benchmark configuration of self induced large oscillations for a flag attached to a cylinder can be accurately and efficiently reproduced within this setting we describe in detail the force evaluation techniques displacement transfers and the algorithm used to couple these completely different solvers as well as the results and compare them with a benchmark reference solution computed by a monolithic finite element approach copyright 2009 john wiley sons ltd

accelerated staggered coupling schemes for problems of thermoelasticity at finite strains this paper introduces a fully implicit partitioned coupling scheme for problems of thermoelasticity at finite strains utilizing the p version of the finite element method the mechanical and the thermal fields are partitioned into symmetric subproblems where algorithmic decoupling has been obtained by means of an isothermal operator split numerical relaxation methods have been implemented to accelerate the convergence of the algorithm such methods are well known from coupled fluid structure interaction problems leading to highly efficient algorithms having studied the influence of three different strategies polynomial prediction methods numerical relaxation with constant relaxation coefficients its dynamic variant with a residual based relaxation coefficient and a variant of a reduced order model quasi newton method we present several numerical simulations of quasi static problems investigating the performance of accelerated coupling schemes

vector quantization of image subbands a survey subband and wavelet decompositions are powerful tools in image coding because of their decorrelating effects on image pixels the concentration of energy in a few coefficients their multirate multiresolution framework and their frequency splitting which allows for efficient coding matched to the statistics of each frequency band and to the characteristics of the human visual system vector quantization vq provides a means of converting the decomposed signal into bits in a manner that takes advantage of remaining inter and intraband correlation as well as of the more flexible partitions of higher dimensional vector spaces since 1988 a growing body of research has examined the use of vq for subband wavelet transform coefficients we present a survey of these methods

an unfitted hp adaptive finite element method based on hierarchical b splines for interface problems of complex geometry generating finite element discretizations with direct interface parameterizations constitutes a considerable computational expense in case of complex interface geometries the paper at hand introduces a b spline finite element method which circumvents parameterization of interfaces and offers fast and easy meshing irrespective of the geometric complexity involved its core idea is the adaptive approximation of discontinuities by hierarchical grid refinement which adds several levels of local basis functions in the close vicinity of interfaces but unfitted to their exact location so that a simple regular grid of knot span elements can be maintained numerical experiments show that an hp refinement strategy which simultaneously increases the polynomial degree of the b spline basis and the levels of refinement around interfaces achieves exponential rates of convergence despite the presence of discontinuities it is also demonstrated that the hierarchical b spline fem can be used to transfer the recently introduced finite cell concept to geometrically nonlinear problems its computational performance imposition of unfitted boundary conditions and fast hierarchical grid generation are illustrated for a set of benchmark problems in one two and three dimensions and the advantages of the regular grid approach for complex geometries are demonstrated by the geometrically nonlinear simulation of a voxel based foam composite

adaptive hpq finite element methods of hierarchical models for plate and shell like structures abstract a four step adaptive strategy for hpq finite element approximations of hierarchical models of the thin plate and shell like structures is derived based on a priori and a posteriori error estimations this strategy controls three parameters the model level q the mesh size h and the approximation order p so as to produce quasi optimal hierarchical models and finite element meshes numerical results are given supporting the theoretical results

a posteriori modeling error estimation for hierarchic plate models hierarchic plate models are dimensional reductions obtained by semidiscretization of the three dimensional plate problem in the transverse direction and energy projection we derive computable a posteriori estimators for the modeling error thus incurred under the assumption that the resulting two dimensional plate models are solved exactly the estimators are valid for homogeneous monoclinic materials for plates with unsmooth midsurfaces and for a wide class of variational edge conditions computable a posteriori bounds on the effectivity indices are also derived and sufficient conditions for the asymptotic i e as the plate thickness tends to zero and the spectral i e as the order of the plate model tends to infinity exactness of the estimators are given numerical examples are presented

high order thin walled solid finite elements applied to elastic spring back computations in this paper we present a new approach for computing elastic spring back based on a strictly three dimensional high order solid finite element formulation for curved thin walled structures allowing for an anisotropic discretization in combination with appropriate mesh design the p version yields an exponential rate of convergence in the error in energy norm in contrast to low order elements which yield only an algebraic rate of convergence anisotropic ansatz spaces based on high order elements lead to very efficient discretizations the structural behavior of three dimensional thin walled continua can be predicted with a similar number of degrees of freedom as in the two dimensional case yet significantly more accurately because of the three dimensional model we also introduce an approach for the efficient computation of the relevant geometrically nonlinear problem furthermore the paper describes the necessary model conversion from a low order deep drawing simulation to a spring back computation based on the p version of the fem

the p version of the finite element method for three dimensional curved thin walled structures in this paper we present an implementation of a three dimensional p version for structural problems of solids with almost arbitrarily curved surfaces applying the blending function method complex structures can often be modelled by a few p elements being the basis for a higher order approximation numerical examples will demonstrate that the p version with anisotropic ansatz spaces allows to predict the structural behaviour of three dimensional plates and shells with approximately the same amount of degrees of freedom as in the two dimensional case yet significantly more accurate due to the three dimensional model furthermore it is advantageous to compute complex structures exclusively with three dimensional discretizations as no special elements are needed to model the transition from dimensionally reduced formulations like plates or shells to fully three dimensional solid elements using the p version with anisotropic ansatz spaces the whole structure can be efficiently discretized with solid elements even if the aspect ratio of the elements becomes very large copyright 2001 john wiley sons ltd

the hp d adaptive finite cell method for geometrically nonlinear problems of solid mechanics summary the finite cell method fcm combines the fictitious domain approach with the p version of the finite element method and adaptive integration for problems of linear elasticity it offers high convergence rates and simple mesh generation irrespective of the geometric complexity involved this article presents the integration of the fcm into the framework of nonlinear finite element technology however the penalty parameter of the fictitious domain is restricted to a few orders of magnitude in order to maintain local uniqueness of the deformation map as a consequence of the weak penalization nonlinear strain measures provoke excessive stress oscillations in the cells cut by geometric boundaries leading to a low algebraic rate of convergence therefore the fcm approach is complemented by a local overlay of linear hierarchical basis functions in the sense of the hp d method which synergetically uses the h adaptivity of the integration scheme numerical experiments show that the hp d overlay effectively reduces oscillations and permits stronger penalization of the fictitious domain by stabilizing the deformation map the hp d adaptive fcm is thus able to restore high convergence rates for the geometrically nonlinear case while preserving the easy meshing property of the original fcm accuracy and performance of the present scheme are demonstrated by several benchmark problems in one two and three dimensions and the nonlinear simulation of a complex foam sample copyright 2011 john wiley sons ltd

an iterative bayesian algorithm for sparse component analysis in presence of noise we present a bayesian approach for sparse component analysis sca in the noisy case the algorithm is essentially a method for obtaining sufficiently sparse solutions of underdetermined systems of linear equations with additive gaussian noise in general an underdetermined system of linear equations has infinitely many solutions however it has been shown that sufficiently sparse solutions can be uniquely identified our main objective is to find this unique solution our method is based on a novel estimation of source parameters and maximum a posteriori map estimation of sources to tackle the great complexity of the map algorithm when the number of sources and mixtures become large we propose an iterative bayesian algorithm iba this iba algorithm is based on the map estimation of sources too but optimized with a steepest ascent method the convergence analysis of the iba algorithm and its convergence to true global maximum are also proved simulation results show that the performance achieved by the iba algorithm is among the best while its complexity is rather high in comparison to other algorithms simulation results also show the low sensitivity of the iba algorithm to its simulation parameters

multiscale computations with a combination of the h and p versions of the finite element method the numerical treatment of structural problems is often difficult if the global system behavior is affected by phenomena on different length scales when simulating multiscale problems it is essential to find a discretization that equally reflects all aspects of the problem with sufficient accuracy the present paper is concerned with the formulation of a finite element procedure which combines the p method to resolve global features of a problem with an h method to resolve local features thus the advantageous properties of both standard procedures can be optimally exploited the implementation provides the further advantage that the numerical treatment of the problems on the different length scales can be done with independent finite element discretizations to solve the overall problem an iteration scheme with an adaptive solution strategy is developed benchmark problems and an example with relevance to soil mechanics are presented

local enrichment of nurbs patches using a non intrusive coupling strategy geometric details local refinement inclusion fracture in this work we apply a non intrusive global local coupling strategy for the modelling of local phenomena in a nurbs patch the idea is to consider the nurbs patch to be enriched as the global model this results in a simple flexible strategy first the global nurbs patch remains unchanged which completely eliminates the need for costly re parametrization procedures even if the local domain is expected to evolve then easy merging of a linear nurbs code with any other existing robust codes suitable for the modelling of complex local behaviour is possible the price to pay is the number of iterations of the non intrusive solver but we show that this can be strongly reduced by means of acceleration techniques the main development for nurbs is to be able to handle non conforming geometries only slight changes in the implementation process including the setting up of suitable quadrature rules for the evaluation of the interface reaction forces are made in response to this issue a range of numerical examples in two dimensional linear elasticity are given to demonstrate the performance of the proposed methodology and its significant potential to treat any case of local enrichment in a nurbs patch simply

mixed spectral hp element formulation for nonlinear elasticity we present a mixed formulation for high order spectral hp element methods and investigate its stability in large strain analysis of nearly incompressible solids specifically we employ the displacement pressure formulation and use a pressure projection method along with general jacobi polynomial bases to derive the discrete equations we first study the convergence of the method for smooth and singular solutions of elastic and hyperelastic problems for various combinations of mixed elements subsequently we investigate numerically the validity of ellipticity and inf sup conditions for various test problems including cases with large deformation we find that the inf sup condition is satisfied even when the pressure interpolation order op is equal to the displacement order ou but to resolve the locking free behavior it is required that op ou 1 and this choice also gives the best convergence rate in large deformation analysis surprisingly the results are more stable for ou op ou k because the ellipticity in kernel is better satisfied with higher k as ou increases compared to the displacement only formulation the mixed formulation seems to have superior accuracy and it is overall more efficient especially for problems with high bulk modulus

macrodispersion in a radially diverging flow field with finite peclet numbers 1 perturbation theory approach we study the transport behavior of a tracer in a radially diverging heterogeneous velocity field making use of homogenization theory we derive effective transport equations these effective transport equations are very similar to those defined on the local scale however the local transport parameters such as local dispersion coefficients are replaced by effective dispersion coefficients for smoothly varying heterogeneous media explicit results for effective radial dispersion coefficients are derived starting with the purely advective transport behavior infinite peclet numbers we extend our calculations to transport with finite peclet numbers we find that the impact of molecular diffusion on the effective dispersivity differs from the impact of local dispersion including local dispersion leads to effective dispersivities which are constant and equivalent to the effective dispersivities found in uniform flow configurations in contrast effective dispersivities including diffusion are not constant but depend on the radial distance we compare the results found by homogenization theory with those derived by neuweiler et al this issue by standard method of moments

a p version finite element approach for two and three dimensional problems of the j2 flow theory with non linear isotropic hardening in this paper an implementation of a two and three dimensional p version approach to the j 2 flow theory with non linear isotropic hardening for small displacements and small strains is presented based on higher order quadrilateral and hexahedral element formulations a newton raphson iteration scheme combined with a radial return algorithm is applied to find approximate solutions for the underlying physically non linear model problem curved boundaries are taken care of with the blending function method allowing an accurate representation of geometry with only a few p elements numerical examples demonstrate that the p version supplies efficient and accurate approximations to this class of physically non linear problems

adaptive global local refinement strategy based on the interior error estimates of the h method an adaptive global local refinement strategy based on the interior error estimates of the h method is proposed adaptive global local refinement strategy is aimed at constructing nearly optimal finite element meshes where the force transfer to the local region of interest is sufficiently accurate so that the local phenomena of interest is resolved with a user specified accuracy numerical examples for linear elasticity problems in two dimensions together with a comparison to the classical adaptive h refinement strategy based on the equidistribution of errors are presented to validate the present formulation

the laplacian pyramid as a compact image code we describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions the representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space pixel to pixel correlations are first removed by subtracting a lowpass filtered copy of the image from the image itself the result is a net data compression since the difference or error image has low variance and entropy and the low pass filtered image may represented at reduced sample density further data compression is achieved by quantizing the difference image these steps are then repeated to compress the low pass image iteration of the process at appropriately expanded scales generates a pyramid data structure the encoding process is equivalent to sampling the image with laplacian operators of many scales thus the code tends to enhance salient image features a further advantage of the present code is that it is well suited for many image analysis tasks as well as for image compression fast algorithms are described for coding and decoding

a multiscale method with patch for the solution of stochastic partial differential equations with localized uncertainties abstract we here propose a multiscale numerical method for the solution of stochastic parametric partial differential equations with localized uncertainties described with a finite number of random variables it is based on a multiscale domain decomposition method that exploits the localized side of uncertainties and incidentally improves the conditioning of the problem by operating a separation of scales an efficient iterative algorithm is proposed that requires the solution of a sequence of simple global problems at a macro scale involving a deterministic operator and local problems at a micro scale for which we have the possibility to use fine approximation spaces global and local problems are solved using tensor approximation methods allowing the representation of high dimensional stochastic parametric solutions convergence properties of these tensor based methods which are closely related to spectral decompositions benefit from the separation of scales different types of uncertainties are considered at the micro level they may be associated with some variability in the operator or source terms or even with some geometrical variability in the latter case specific reformulations of local problems using fictitious domain methods are introduced

an integral representation and bounds on the effective diffusivity in passive advection by laminar and turbulent flows precise necessary and sufficient conditions on the velocity statistics for mean field behavior in advection diffusion by a steady incompressible velocity field are developed here under these conditions a rigorous stieltjes integral representation for effective diffusivity in turbulent transport is derived this representation is valid for all peclet numbers and provides a rigorous resummation of the divergent perturbation expansion in powers of the peclet number one consequence of this representation is that convergent upper and lower bounds on effective diffusivity for all peclet numbers can be obtained utilizing a prescribed finite number of terms in the perturbation series explicit rigorous examples of steady incompressible velocity fields are constructed which have effective diffusivities realizing the simplest upper or lower bounds for all peclet numbers a nonlocal variational principle for effective diffusivity is developed along with applications to advection diffusion by random arrays of vortices a new class of rigorous examples is introduced these examples have an explicit stieltjes measure for the effective diffusivity furthermore the effective diffusivity behaves likek0 pe 1 2 in the limit of large peclet numbers wherek0 is the molecular diffusivity formal analogies with the theory of composite materials are exploited systematically

adaptive s method for linear elastostatics abstract a methodology has been developed to simultaneously treat phenomena at several scales the key features of the method are i a detailed error diagnosis which identifies critical regions and ii a feedback procedure which overlays portions of the finite element mesh where unacceptable errors have been identified by local finite element mesh es and then subsequently improves the quality of the solution in the global and local response until the desired level of accuracy is achieved the method can be routinely used as a global local method and or as an adaptive technique which provides a measure of reliability of global and local computations numerical experiments for problems in homogeneous and heterogeneous laminated composites media are presented to validate the present formulation

the multi level hp method for three dimensional problems dynamically changing high order mesh refinement with arbitrary hanging nodes abstract one main challenge of the h p version of the finite element method is the high implementational complexity of the method resulting from the added need of handling hanging nodes appropriately the multi level h p formulation recently introduced for two dimensional applications aims at alleviating these difficulties without compromising the approximation quality this is achieved by changing from the conventional refine by replacement approach to a refine by superposition idea the current work shows that the multi level h p approach can be extended naturally to three dimensional refinement without increasing the complexity of the rule set ensuring linear independence and compatibility of the shape functions in this way a three dimensional h p refinement scheme is formulated in which hanging nodes are avoided by definition this ease of complexity allows for a highly flexible discretization kernel featuring arbitrary irregular meshes and a continuous refinement and coarsening throughout the simulation runtime different numerical examples demonstrate that even in the presence of singularities this novel refinement scheme yields exponential convergence with respect to both the number of unknowns and the computational time it is further shown that the refinement scheme is able to capture complex solution features that demand for three dimensional refinement patterns the dynamic discretization properties of the approach are demonstrated by continuously refining and coarsening the mesh during the simulation runtime to keep the refinement zone local to a moving singularity finally it is shown that the high approximation power of the multi level h p scheme also carries over to curved geometries common in engineering practice without a significant detrimental effect on the conditioning of the stiffness matrix

adaptive hpq finite element methods for the analysis of 3d based models of complex structures part 1 hierarchical modeling and approximations this is a paper out of a series of three papers devoted to model and hpq adaptive finite element methods assigned for modeling and analysis of complex structures in this paper we focus our attention on hierarchical models and hierarchical approximations while the issues of error estimation and adaptivity control will be presented in the next papers of the series in all the papers we consider the elastic structures of complex mechanical description we apply 3d or 3d based mechanical models hierarchical modeling and hierarchical approximations within our finite element formulation in the proposed approach the mechanical model and discretization parameters such as the size h of the element and the longitudinal and transverse approximation orders p and q can vary locally i e they can be different in each finite element the a posteriori error estimation is based on the residual equilibration methods applied to the assessment of the modeling and approximation errors the error controlled adaptive procedures are derived from a four step strategy with possible iterations on h and p steps

learning the nonlinear geometry of high dimensional data models and algorithms modern information processing relies on the axiom that high dimensional data lie near low dimensional geometric structures this paper revisits the problem of data driven learning of these geometric structures and puts forth two new nonlinear geometric models for data describing related objects phenomena the first one of these models straddles the two extremes of the subspace model and the union of subspaces model and is termed the metric constrained union of subspaces mc uos model the second one of these models suited for data drawn from a mixture of nonlinear manifolds generalizes the kernel subspace model and is termed the metric constrained kernel union of subspaces mc kuos model the main contributions of this paper in this regard include the following first it motivates and formalizes the problems of mc uos and mc kuos learning second it presents algorithms that efficiently learn an mc uos or an mc kuos underlying data of interest third it extends these algorithms to the case when parts of the data are missing last but not least it reports the outcomes of a series of numerical experiments involving both synthetic and real data that demonstrate the superiority of the proposed geometric models and learning algorithms over existing approaches in the literature these experiments also help clarify the connections between this work and the literature on subspace and kernel k means clustering

coupled model and solution adaptivity in the finite element method modeling of elastic thin walled beams plates and shells as id and 2d boundary value problems is valid in undisturbed subdomains disturbances near supports and free edges in the vicinity of concentrated loads and at thickness jumps cannot be described in a sufficient way by 1d and 2d bvps in these disturbed subdomains dimensional d adaptivity and model m adaptivity have to be performed coupled with h and or p adaptivity using hierarchically expanded test spaces in order to guarantee reliable and efficient overall results the expansion strategy is applied for enhancing the spatial dimension and the model which is more efficient and evident for engineers than the reduction method using local residual error estimators of the primal problem in the energy norm by solving dirichlet problems on element patches an efficient integrated adaptive calculation of the discretization and the dimensional error is possible and reasonable demonstrated by examples we also present an error estimator of the dual problem namely a posterior equilibrium method pem for calculation of the interface tractions on local patches with neumann boundary conditions using orthogonality conditions these tractions are equilibrated with respect to the global equilibrium condition of the stress resultants an upper bound error estimator based on differences between the new tractions and the discontinuous tractions calculated from the stresses of the current finite element solution the introduction of new element boundary tractions yields a method which can be regarded as a stepwise hybrid displacement method or as trefftz method for local neumann problems of element patches an important advantage of pem is the coupled computation of local discretization dimensional and model errors by an additive split

compression of color facial images using feature correction two stage vector quantization a feature correction two stage vector quantization fc2vq algorithm was previously developed to compress gray scale photo identification id pictures this algorithm is extended to color images in this work three options are compared which apply the fc2vq algorithm in rgb ycbcr and karhunen loeve transform klt color spaces respectively the rgb fc2vq algorithm is found to yield better image quality than klt fc2vq or ycbcr fc2vq at similar bit rates with the rgb fc2vq algorithm a 128 spl times 128 24 b color id image 49152 bytes can be compressed down to about 500 bytes with satisfactory quality when the codeword indices are further compressed losslessly using a first order huffman coder this size is further reduced to about 450 bytes

low bit rate compression of facial images an efficient approach for face compression is introduced restricting a family of images to frontal facial mug shots enables us to first geometrically deform a given face into a canonical form in which the same facial features are mapped to the same spatial locations next we break the image into tiles and model each image tile in a compact manner modeling the tile content relies on clustering the same tile location at many training images a tree of vector quantization dictionaries is constructed per location and lossy compression is achieved using bit allocation according to the significance of a tile repeating this modeling coding scheme over several scales the resulting multiscale algorithm is demonstrated to compress facial images at very low bit rates while keeping high visual qualities outperforming jpeg 2000 performance significantly