structural instability analyses based on generalised path following this paper describes how quasi static conservative instability problems can be completely described using generalised path following procedures for augmented equilibrium formulations in particul

c1 continuous stress recovery in finite element analysis abstract a penalized discrete least squares pdls variational principle is employed to recover c 1 continuous smooth stress fields from finite element stresses the error functional involves discrete least squares with a penalty constraint to enforce c 1 continuity of the recovered stresses the recovery procedure uses a smoothing element analysis sea with element based interpolation functions to minimize the error functional sea pdls recovers a superconvergent stress field of higher accuracy and continuity than the underlying consistent finite element stress field general and specialized formulations of the functional are given and an appropriate discretization strategy for the sea is discussed numerical results for both one and two dimensional stress fields are presented and compared with the corresponding solutions for the superconvergent patch recovery spr method of zienkiewicz and zhu the results demonstrate that in addition to achieving a higher degree of continuity sea pdls produces generally more accurate stresses than spr although an additional global analysis is required results indicate that two coarse mesh analyses finite element and smoothing produce solutions comparable to a single finite element analysis with a much greater degree of refinement and more computational effort the procedure is unique in that the recovered stress field is essentially c 1 continuous the results are shown to be insensitive to the value of the penalty parameter above a threshold and hence uncertainty in the choice of an appropriate penalty value is eliminated

hierarchical bases give conjugate gradient type methods a multigrid speed of convergence the interesting properties of the discretization matrices arising in the finite element solution of plane elliptic boundary value problems when using hierarchical bases are described the condition numbers of these discretization matrices grow only quadratically in the number of refinement levels contrary to the exponential growth found with nodal bases furthermore it is easily possible to compute the product of such a discretization matrix with a given coefficient vector we show how these results can be used to solve the discretized problem in o n log n computer operations where n is the number of unknowns special emphasis is layed on the refinement structures used in r e bank s pltmg package which have not been treated in the author s previous papers

a short characterization of relative entropy we prove characterization theorems for relative entropy also known as kullback leibler divergence q logarithmic entropy also known as tsallis entropy and q logarithmic relative entropy all three have been characterized axiomatically before but we show that earlier proofs can be simplified considerably at the same time relaxing some of the hypotheses

models algorithms and error estimation for computational viscoelasticity this article reviews numerical algorithms for problems in solid polymer viscoelasticity in both small and large deformation for the linear small strain case we review both the quasistatic and the dynamic problem and give recent results on a posteriori error estimation for the large strain case we focus on the formulation and computational modelling of constrained membrane inflation the application of which is to the thermoforming process

computational methods for multiphase flow and reactive transport problems arising in subsurface contaminant remediation a mathematical formulation and some numerical approximation techniques are described for a system of coupled partial differential and algebraic equations describing multiphase flow transport and interactions of chemical species in the subsurface a parallel simulator parsim has been developed based on these approximation techniques and is being used to study contaminant remediation strategies numerical results for a highly complex geochemistry problem involving strontium disposal in a pit at oak ridge national laboratory are presented

manifold regularization a geometric framework for learning from labeled and unlabeled examples we propose a family of learning algorithms based on a new form of regularization that allows us to exploit the geometry of the marginal distribution we focus on a semi supervised framework that incorporates labeled and unlabeled data in a general purpose learner some transductive graph learning algorithms and standard methods including support vector machines and regularized least squares can be obtained as special cases we use properties of reproducing kernel hilbert spaces to prove new representer theorems that provide theoretical basis for the algorithms as a result in contrast to purely graph based approaches we obtain a natural out of sample extension to novel examples and so are able to handle both transductive and truly semi supervised settings we present experimental evidence suggesting that our semi supervised algorithms are able to use unlabeled data effectively finally we have a brief discussion of unsupervised and fully supervised learning within our general framework

the generalized finite element method for helmholtz equation theory computation and open problems in this paper we address the generalized finite element method for the helmholtz equation we obtain our method by employing the finite element method on cartesian meshes which may overlap the boundaries of the problem domain and by enriching the approximation by plane waves pasted into the finite element basis at each mesh vertex by the partition of unity method here we address the q convergence of the method where q is the number of plane waves added at each vertex for the class of smooth analytic solutions for which we get better than exponential convergence for sufficiently small h depending on p an important observation is that we can monitor the accuracy in any computed solution quantity of interest at negligible cost by using q extrapolation our results assume exact integration of all the employed integrals further studies are needed to analyze the effects of the numerical integrations and also the effect of the roundoff errors

low rank matrix factorization with adaptive graph regularizer in this paper we present a novel low rank matrix factorization algorithm with adaptive graph regularizer lmfagr we extend the recently proposed low rank matrix with manifold regularization mmf method with an adaptive regularizer different from mmf which constructs an affinity graph in advance lmfagr can simultaneously seek graph weight matrix and low dimensional representations of data that is graph construction and low rank matrix factorization are incorporated into a unified framework which results in an automatically updated graph rather than a predefined one the experimental results on some data sets demonstrate that the proposed algorithm outperforms the state of the art low rank matrix factorization methods

fast nonnegative matrix factorization an active set like method and comparisons nonnegative matrix factorization nmf is a dimension reduction method that has been widely used for numerous applications including text mining computer vision pattern discovery and bioinformatics a mathematical formulation for nmf appears as a nonconvex optimization problem and various types of algorithms have been devised to solve the problem the alternating nonnegative least squares anls framework is a block coordinate descent approach for solving nmf which was recently shown to be theoretically sound and empirically efficient in this paper we present a novel algorithm for nmf based on the anls framework our new algorithm builds upon the block principal pivoting method for the nonnegativity constrained least squares problem that overcomes a limitation of the active set method we introduce ideas that efficiently extend the block principal pivoting method within the context of nmf computation our algorithm inherits the convergence property of the anls framework and can easily be extended to other constrained nmf formulations extensive computational comparisons using data sets that are from real life applications as well as those artificially generated show that the proposed algorithm provides state of the art performance in terms of computational speed

a new bem fem coupling strategy for two dimensional fluid solid interaction problems we present a numerical method to solve a fluid solid interaction problem posed in the plane in this scheme we use a finite element method to approximate the solid vibrations and the near wave field the far field effects are taken into account by means of boundary integral equations posed on an artificial interface that contains the obstacle the boundary unknown involved in our formulation is approximated by a spectral method we obtain a fully discrete galerkin procedure whose main advantage is the simplicity of the quadratures used to approximate the weakly singular boundary integrals we provide numerical results that illustrate the accuracy of our method and the stability of the algorithm used to solve the linear systems of equations that arise from this discretization technique

a self optimizing single step algorithm for the numerical integration of parabolic equations abstract an unconditionally stable single step time marching algorithm for parabolic equations is presented in this algorithm time stepping parameters are chosen according to an error condition such that large time step accuracy is achieved and the solution is also free from oscillations it is different from conventional algorithms such as the crank nicolson scheme in that it uses a matrix of time stepping parameters rather than a single scalar value these parameters can be approximated inexpensively this algorithm is easily programmed and comparisons are made with other methods for different cases of a heat conduction problem it is found that the algorithm gives a more accurate solution for all degrees of freedom for the cases considered it is therefore advantageous over the conventional variably weighted euler method which has a constraint that the same value must be used for all degrees of freedom and that values have to be changed by trial and error for different time step sizes and mesh refinements in order to achieve best results

an improved variational method for finite element stress recovery and a posteriori error estimation abstract a new variational formulation is presented which serves as a foundation for an improved finite element stress recovery and a posteriori error estimation in the case of stress predictions interelement discontinuous stress fields from finite element solutions are transformed into a c 1 continuous stress field with c 0 continuous stress gradients these enhanced results are ideally suited for error estimation since the stress gradients can be used to assess equilibrium satisfaction the approach is employed as a post processing step in finite element analysis the variational statement used herein combines discrete least squares penalty constraint and curvature control functionals thus enabling automated recovery of smooth stresses and stress gradients the paper describes the mathematical foundation of the method and presents numerical examples including stress recovery in two dimensional structures and built up aircraft components and error estimation for adaptive mesh refinement procedures

wavelet based ilu preconditioners for the numerical solution by pufem of high frequency elastic wave scattering daubechies family of wavelets combined to the incomplete lower upper ilu factorization are considered as preconditioners for a block sparse linear system arising from the approximation of the time harmonic elastic wave equations by the partition of unity finite element method pufem after applying the discrete wavelet transform dwt to each dense block in the final matrix and the known right hand side due to the local enrichment by pressure p and shear s plane waves the resulting linear system is solved by the restarted generalized minimum residual method gmres with ilu preconditioners allowing fill in elements in the l and u matrix factors a reordering algorithm of the vertices based on gibbs method is also introduced it leads to a significant reduction of the bandwidth of the wave based finite element fe matrix and enables the ilu preconditioners to be more effective to study the performance of the proposed preconditioners a problem of a horizontal s plane wave scattered by a rigid circular body in an infinite elastic medium is considered the numerical tests show the good performance of the dwt based ilu preconditioners in improving the rate of convergence of gmres for high numbers of approximating p and s plane waves on coarse mesh grids containing multi wavelength sized elements moreover the haar dwt enhances the scalability with respect to the problem size when the number of the nodal points increases of the ilu preconditioner which uses the threshold strategy in the control of the fill in elements despite the high level of the conditioning a good accuracy may be achieved for a discretization level of around 1 9 degrees of freedom per s wavelength which is far below the rule of thumb of 10 nodal points per wavelength adopted for the conventional fe

a comparison of nrbcs for pufem in 2d helmholtz problems at high wave numbers in this work exact and approximate non reflecting boundary conditions nrbcs are implemented with the partition of unity finite element method pufem to solve short wave scattering problems governed by the helmholtz equation in two dimensions by short wave problems we mean situations in which the wavelength is a small fraction of the characteristic dimension of the scatterer various nrbcs are implemented and a comparison of their performance is carried out based on the accuracy of the results ease of implementation and computational cost the aim is to accurately model such problems in a reduced computational domain around the scatterer with fewer elements and without refining the mesh at each wave number

graph regularized restricted boltzmann machine the restricted boltzmann machine rbm has received an increasing amount of interest in recent years it determines good mapping weights that capture useful latent features in an unsupervised manner the rbm and its generalizations have been successfully applied to a variety of image classification and speech recognition tasks however most of the existing rbm based models disregard the preservation of the data manifold structure in many real applications the data generally reside on a low dimensional manifold embedded in high dimensional ambient space in this brief we propose a novel graph regularized rbm to capture features and learning representations explicitly considering the local manifold structure of the data by imposing manifold based locality that preserves constraints on the hidden layer of the rbm the model ultimately learns sparse and discriminative representations the representations can reflect data distributions while simultaneously preserving the local manifold structure of data we test our model using several benchmark image data sets for unsupervised clustering and supervised classification problem the results demonstrate that the performance of our method exceeds the state of the art alternatives

derivative superconvergence of rectangular finite elements for the reissner mindlin plate abstract the finite element method with rectangular meshes for the reissner mindlin plate is analyzed for a plate with thickness bounded below by a positive constant moderately thick plate derivative superconvergence of the finite element solution at the gaussian points is justified and optimal error estimates for both rotation and displacement are established

a stable bilinear element for the reissner mindlin plate model abstract in this paper we introduce a new quadrilateral element using isoparametric bilinear basis functions for both components of the rotation vector and the deflection the element is a stable modification of the mitc4 element we report on calculations with this new element the original mitc4 and also the bilinear element with selective reduced integration the numerical results are in accordance with the results of the numerical analysis and they show that i the method with reduced integration is highly unreliable and cannot be recommended ii the mitc4 performs rather well but its instability can lead to a decrease in accuracy for the deflection and especially to an inaccurate and oscillating shear force iii the drawbacks of the mitc4 are not present in the modified method

spectral properties of the alignment matrices in manifold learning local methods for manifold learning generate a collection of local parameterizations which is then aligned to produce a global parameterization of the underlying manifold the alignment procedure is carried out through the computation of a partial eigendecomposition of a so called alignment matrix in this paper we present an analysis of the eigenstructure of the alignment matrix giving both necessary and sufficient conditions under which the null space of the alignment matrix recovers the global parameterization we show that the gap in the spectrum of the alignment matrix is proportional to the square of the size the precise definition of the size is given in section sec sp of the overlap of the local parameterizations thus deriving a quantitative measure of how stably the null space can be computed numerically we also give a perturbation analysis of the null space of the alignment matrix when the computation of the local parameterizations is subject to error our analysis provides insights into the behaviors and performance of local manifold learning algorithms

concept factorization with adaptive neighbors for document clustering in this paper a novel concept factorization cf method called cf with adaptive neighbors cfans is proposed the idea of cfan is to integrate an ans regularization constraint into the cf decomposition the goal of cfan is to extract the representation space that maintains geometrical neighborhood structure of the data similar to the existing graph regularized cf cfan builds a neighbor graph weights matrix the key difference is that the cfan performs dimensionality reduction and finds the neighbor graph weights matrix simultaneously an efficient algorithm is also derived to solve the proposed problem we apply the proposed method to the problem of document clustering on the 20 newsgroups reuters 21578 and tdt2 document data sets our experiments demonstrate the effectiveness of the method

adaptive method for nonsmooth nonnegative matrix factorization nonnegative matrix factorization nmf is an emerging tool for meaningful low rank matrix representation in nmf explicit constraints are usually required such that nmf generates desired products or factorizations especially when the products have significant sparseness features it is known that the ability of nmf in learning sparse representation can be improved by embedding a smoothness factor between the products motivated by this result we propose an adaptive nonsmooth nmf ans nmf method in this paper in our method the embedded factor is obtained by using a data related approach so it matches well with the underlying products implying a superior faithfulness of the representations besides due to the usage of an adaptive selection scheme to this factor the sparseness of the products can be separately constrained leading to wider applicability and interpretability furthermore since the adaptive selection scheme is processed through solving a series of typical linear programming problems it can be easily implemented simulations using computer generated data and real world data show the advantages of the proposed ans nmf method over the state of the art methods

finite dimensional approximation of bifurcation problems in presence of symmetries we give here a brief summary of the results of 4 14 the aim of our work was not only the finite dimensional approximation of the specific problem studied in 3 but we also wanted to show how to adapt to discrete problems and how to use in this case some classical mathematical tools e g the splitting lemma of gromoll meyer magnus the singularity theory etc such considerations are developed in 5 in particular we prove in 5 that in most cases e g in the examples given in 6 7 9 10 the discrete bifurcation problem behaves as an imperfect bifurcation problem and we improve the methods of 12 another way to use universal unfoldings in the approxima tion of bifurcation problems is suggested by 2

low rank matrix approximation with manifold regularization this paper proposes a new model of low rank matrix factorization that incorporates manifold regularization to the matrix factorization superior to the graph regularized nonnegative matrix factorization this new regularization model has globally optimal and closed form solutions a direct algorithm for data with small number of points and an alternate iterative algorithm with inexact inner iteration for large scale data are proposed to solve the new model a convergence analysis establishes the global convergence of the iterative algorithm the efficiency and precision of the algorithm are demonstrated numerically through applications to six real world datasets on clustering and classification performance comparison with existing algorithms shows the effectiveness of the proposed method for low rank factorization in general

a note on the design of hp adaptive finite element methods for elliptic partial differential equations we introduce an hp adaptive finite element algorithm based on a combination of reliable and efficient residual error indicators and a new hp extension control technique which assesses the local regularity of the underlying analytical solution on the basis of its local legendre series expansion numerical experiments confirm the robustness and reliability of the proposed algorithm

simulation of a free boundary problem using boundary element method and restarted re analysis technique in this work we deal with the numerical approximation of a free boundary problem reformulated as an optimal shape design one the boundary element method is used for the approximation of this problem the iterative method used to solve the discrete problem requires the resolution of intermediate linear systems associated with the successive modification in the design process in many cases one of the main obstacles is the high computational cost involved in the solution of large scale problems to reduce the computational cost a restarted re analysis technique is introduced to solve these systems numerical examples including comparison results are presented to show the efficiency of the proposed approach

the extended domain eigenfunction method for solving elliptic boundary value problems with annular domains standard analytical solutions to elliptic boundary value problems on asymmetric domains are rarely if ever obtainable in this paper we propose a solution technique wherein we embed the original

on principles for the selection of shape functions for the generalized finite element method abstract effective shape functions for the generalized finite element method should reflect the available information on the solution this information is partially fuzzy because the solution is of course unknown and typically the only available information is the solution s inclusion in a variety of function spaces it is desirable to choose shape functions that perform robustly over a family of relevant situations quantitative notions of robustness are introduced and discussed we show in particular that in one dimension polynomials are robust when the available information consists in inclusions in sobolev type spaces that are x independent

numerical analysis of graded mesh methods for a class of second kind integral equations on the real line abstract in this paper we are concerned with the numerical analysis of the collocation method based on graded meshes of second kind integral equations on the real line of the form s s r s t z t t dt s r where l 1 r z l r and bc r the space of bounded continuous complex valued functions on r are assumed known and the function bc r is to be determined we introduce some new graded meshes for the collocation method of the integral equation which are different from those used previously for the wiener hopf integral equation in the case when the solution decays exponentially at infinity and establish optimal local and global l norm error estimates under the condition that the solution decays only polynomially at infinity

the efficient implementation of a finite element multi resolution viscosity method for hyperbolic conservation laws it is well known that the classic galerkin finite element method is unstable when applied to hyperbolic conservation laws such as the euler equations for compressible flows adding a diffusion term to the equations stabilizes the method but sacrifices too much accuracy to be of any practical use an elegant solution developed in the context of spectral methods by eitan tadmor and coworkers is to add diffusion only to the high frequency modes of the solution and can lead to stabilization without sacrificing accuracy we incorporate this idea into the finite element framework by using hierarchical functions as a multi frequency basis the result is a new finite element method for solving hyperbolic conservation laws for this method convergence for a one dimensional scalar conservation law has previously been proved here the method is described in detail several issues connected with its efficient implementation are considered and numerical results for several examples involving one and two dimensional hyperbolic conservation laws are provided several advantageous features of the method are discussed including the ease for which discontinuities can be detected and artificial diffusion can be applied anisotropically and locally in physical as well as frequency space

modeling of convection dominated thermoporomechanics problems using incomplete interior penalty galerkin method abstract in order to obtain converged and accurate numerical solutions in general small time steps are required for time dependent problems for popular continuous finite elements however the use of small time steps often results in oscillatory pressures and temperatures for thermoporomechanics problems with low conductivities moreover convection dominated thermal poromechanics problems often have very sharp temperature fronts that propagate over spatial domains when applied to these problems continuous elements present serious deficiencies in that large error induced in coarse mesh zones will propagate and pollute the solutions in fine mesh zones such oscillatory and polluted solutions are nonphysical and must be precluded we propose discontinuous galerkin methods to be alternatives to handle these challenges this paper focuses on the finite element formulation of the incomplete interior penalty galerkin method on thermoporoelasticity problems with heat convection in this formulation we propose discontinuous spaces for all three field variables to deal with the convection effect an upwinding scheme is simply and elegantly implemented through element interfaces which is favored by the discontinuous galerkin framework in addition the inner pressure boundary conditions important to many engineering problems are also taken into account in our discontinuous galerkin formulation excellent performance of this discontinuous galerkin method on precluding temperature oscillations and on blocking error propagation is demonstrated through solving a convection dominated oil well injection problem

numerical methods for treating problems of viscoelastic isotropic solid deformation mathematical models for treating problems of linear viscoelasticity involving hereditary constitutive relations for compressible solids are discussed and their discretization using finite element methods in space together with quadrature rules in time to treat the hereditary integrals is described the range of applicability of this type of formulation is reviewed in the context of geometric and constitutive linearity nonlinearity and the limitations imposed by the availability of physical data are discussed one of the above models is a volterra integral equation of the second kind in this when the kernel is separable an established technique due to goursat 1933 can be exploited to reformulate the problem as a system of ordinary differential equations this approach will be described for the special case of a linear viscoelastic isotropic homogeneous synchronous constant poisson s ratio solid this method results in a complete decoupling of the space and time dependence in this case the problem can be solved at each time level by solving first a problem of linear elasticity and then a system of ordinary differential equations for each point in the spatial mesh at which the viscoelastic displacements are required the advantages disadvantages and limitations offered by this and various other schemes for solving problems of viscoelasticity as outlined below are discussed

a posteriori error estimates for space time finite element approximation of quasistatic hereditary linear viscoelasticity problems abstract we give a space time galerkin finite element discretisation of the quasistatic compressible linear viscoelasticity problem as described by an elliptic partial differential equation with a fading memory volterra integral the numerical scheme consists of a continuous galerkin approximation in space based on piecewise polynomials of degree p 0 cg p with a discontinuous galerkin piecewise constant dg 0 or linear dg 1 approximation in time a posteriori galerkin error estimates are derived by exploiting the galerkin framework and optimal stability estimates for a related dual backward problem the a posteriori error estimates are quite flexible strong lp energy norms of the errors are estimated using time derivatives of the residual terms when the data are smooth while weak energy norms are used when the data are non smooth in time we also give upper bounds on the dg 0 cg 1 a posteriori error estimates which indicate optimality however a complete analysis is not given

a second order characteristics finite element scheme for natural convection problems in this paper a second order characteristics finite element scheme is applied to the numerical solution of natural convection problems firstly after recalling the mathematical model a second order time discretization of the material time derivative is introduced next fully discretized schemes are proposed by using finite element methods numerical results for the two dimensional problem of buoyancy driven flow in a square cavity with differentially heated side walls are given and compared with a reference solution

a unified formulation of small strain corotational finite elements i theory this paper presents a unified theoretical framework for the corotational cr formulation of finite elements in geometrically nonlinear structural analysis the key assumptions behind cr are i strains from a corotated configuration are small while ii the magnitude of rotations from a base configuration is not restricted following a historical outline the basic steps of the element independent cr formulation are presented the element internal force and consistent tangent stiffness matrix are derived by taking variations of the internal energy with respect to nodal freedoms it is shown that this framework permits the derivation of a set of cr variants through selective simplifications this set includes some previously used by other investigators the different variants are compared with respect to a set of desirable qualities including self equilibrium in the deformed configuration tangent stiffness consistency invariance symmetrizability and element independence we discuss the main benefits of the cr formulation as well as its modeling limitations

analytical solutions for the incompressible viscous flow within a rectangular domain abstract analytical solutions of the velocity pressure and stream function are developed for the slow incompressible viscous fluid in a simple rectangular domain all solutions can be applied to the boundary integral techniques as typical fundamental solutions

an eulerian method for transient nonlinear free surface wave problems abstract an eulerian difference method is developed for the transient potential flow of an incompressible fluid with fully nonlinear free surface conditions the free surface coordinate y x t and the velocity potential x y t on the free surface are recognized as the primary unknowns to be solved as an initial value problem from the pair of nonlinear partial differential equations representing the dynamic and the kinematic conditions of the free surface the continuity relation 2 0 for the velocity potential x y t over the flow field below the free surface is recognized as a subsidiary condition to be enforced at all times the field of computation is transformed into a time invariant cartesian region with the free surface x t represented by a coordinate line or surface the iterative solution for x y t p x y t in this fixed field of computation is facilitated by the use of fast fourier transform fft the iterative process converges rapidly in terms of this converged x y t the free surface location x t and its potential x y t are advanced in time results from two planar examples are illustrated the method is equally applicable to problems in three space dimensions possibly involving interactive matching with neighboring flow fields if the initial free surface potential x y t 0 is unknown difficulties may be encountered in data specification for securing a well posed problem for solution

critical friction for wedged configurations abstract a wedged configuration with coulomb friction is a nontrivial equilibrium state of a linear elastic body in a frictional unilateral contact with a rigid body under vanishing external loads we analyze here the relation between the geometry of the elastic body and the friction coefficient for which wedged configurations exist in a 3 d context the critical friction coefficient w is defined as the infimum of a supremal functional defined on the set of admissible normal displacement and tangential stresses for friction coefficients with w the wedged problem has at least a solution and for the wedged problem is stated in a discrete framework using a mixed finite element approach and the discrete critical friction coefficient h w is introduced as the solution of a global minimization problem involving a non differentiable and non convex functional the existence of h the displacement field of a critical wedged state is proved and a specific numerical method based on a genetic algorithm was developed to compute the critical wedged configurations some techniques to handle the discontinuities of the normal vector on the contact surface are presented and the analysis is illustrated with three numerical simulations

on some recent adventures into improved finite element cfd methods for convective transport abstract the quest continues for computational fluid dynamics cfd algorithms that are accurate and efficient for convection dominated applications including shocks travelling fronts and wall layers the boundary value optimal galerkin weak statement invariably requires manipulation either in the test space or in an augmented form for the conservation law system to handle the disruptive character introduced by the discretized first order convection term an incredible variety of methodologies have been derived and examined to address this issue in particular seeking achievement of accurate and monotone discrete approximate solutions in an efficient implementation the utk cfd research group continues its search on examining the breadth of approaches leading to development of a consistent encompassing theoretical statement exhibiting quality performance included herein are adventures into generalized taylor series lax wendroff methods characteristic euler flux resolutions sub grid embedded high degree lagrange bases with static condensation and assembled stencil fourier analysis optimization for finite element weak statement implementations for appropriate model problems including steady convection diffusion and pure unsteady convection and benchmark navier stokes definitions recent advances have lead to candidate accurate monotone methods with linear basis efficiency this contribution highlights the theoretical developments and presents quantitative documentation of achievable high quality solutions

a velocity stream function method for three dimensional incompressible fluid flow abstract we describe a velocity stream function method for computing incompressible fluid flow extending earlier work in two to three dimensions we present a strictly divergence free finite element in primitive variables in 3d as the curl of a generalized hermite vector potential element with velocity degrees of freedom and show a method for its derivation this linear velocity element is defined on a reference cube with 8 nodes each node having 3 vector potential stream function and 3 velocity degrees of freedom the method and element are applied to the lid driven cavity problem and open duct flow in three dimensions

enhancing low rank subspace clustering by manifold regularization recently low rank representation lrr method has achieved great success in subspace clustering sc which aims to cluster the data points that lie in a union of low dimensional subspace given a set of data points lrr seeks the lowest rank representation among the many possible linear combinations of the bases in a given dictionary or in terms of the data itself however lrr only considers the global euclidean structure while the local manifold structure which is often important for many real applications is ignored in this paper to exploit the local manifold structure of the data a manifold regularization characterized by a laplacian graph has been incorporated into lrr leading to our proposed laplacian regularized lrr laplrr an efficient optimization procedure which is based on alternating direction method of multipliers admm is developed for laplrr experimental results on synthetic and real data sets are presented to demonstrate that the performance of lrr has been enhanced by using the manifold regularization

interior superconvergence in mortar and non mortar mixed finite element methods on non matching grids we establish interior velocity superconvergence estimates for mixed finite element approximations of second order elliptic problems on non matching rectangular and quadrilateral grids both mortar and non mortar methods for imposing the interface conditions are considered in both cases it is shown that a discrete l 2 error in the velocity in a compactly contained subdomain away from the interfaces con1 2 higher than the error in the whole domain for the non mortar method we also establish pressure superconvergence which is needed in the velocity analysis numerical results are presented in confirmation of the theory

predicting ct image from mri data through feature matching with learned nonlinear local descriptors attenuation correction for positron emission tomography pet magnetic resonance mr hybrid imaging systems and dose planning for mr based radiation therapy remain challenging due to insufficient high energy photon attenuation information we present a novel approach that uses the learned nonlinear local descriptors and feature matching to predict pseudo computed tomography pct images from t1 weighted and t2 weighted magnetic resonance imaging mri data the nonlinear local descriptors are obtained by projecting the linear descriptors into the nonlinear high dimensional space using an explicit feature map and low rank approximation with supervised manifold regularization the nearest neighbors of each local descriptor in the input mr images are searched in a constrained spatial range of the mr images among the training dataset then the pct patches are estimated through k nearest neighbor regression the proposed method for pct prediction is quantitatively analyzed on a dataset consisting of paired brain mri and ct images from 13 subjects our method generates pct images with a mean absolute error mae of 75 25 18 05 hounsfield units a peak signal to noise ratio of 30 87 1 15 db a relative mae of 1 56 0 5 in pet attenuation correction and a dose relative structure volume difference of 0 055 0 107 in d 98 as compared with true ct the experimental results also show that our method outperforms four state of the art methods

a priori and a posteriori error analysis for a large scale ocean circulation finite element model we consider the finite element solution of the stream function vorticity formulation for a large scale ocean circulation model first we study existence and uniqueness of solution for the continuous and discrete problems under appropriate regularity assumptions we prove that the stream function can be computed with an error of order h in h1 seminorm second we introduce and analyze an h adaptive mesh refinement strategy to reduce the spurious oscillations and poor resolution which arise when convective terms are dominant we propose an a posteriori anisotropic error indicator based on the recovery of the hessian from the finite element solution which allows us to obtain well adapted meshes the numerical experiments show an optimal order of convergence of the adaptive scheme furthermore this strategy is efficient to eliminate the oscillations around the boundary layer

ensemble manifold regularized sparse low rank approximation for multiview feature embedding in computer vision and pattern recognition researches the studied objects are often characterized by multiple feature representations with high dimensionality thus it is essential to encode that multiview feature into a unified and discriminative embedding that is optimal for a given task to address this challenge this paper proposes an ensemble manifold regularized sparse low rank approximation emr slra algorithm for multiview feature embedding the emr slra algorithm is based on the framework of least squares component analysis in particular the low dimensional feature representation and the projection matrix are obtained by the low rank approximation of the concatenated multiview feature matrix by considering the complementary property among multiple features emr slra simultaneously enforces the ensemble manifold regularization on the output feature embedding in order to further enhance its robustness against the noise the group sparsity is introduced into the objective formulation to impose direct noise reduction on the input multiview feature matrix since there is no closed form solution for emr slra this paper provides an efficient emr slra optimization procedure to obtain the output feature embedding experiments on the pattern recognition applications confirm the effectiveness of the emr slra algorithm compare with some other multiview feature dimensionality reduction approaches highlightsthis paper proposes a novel emr slra algorithm for multiview feature embedding the least squares component analysis is generalized to multiview version the ensemble manifold regularization is enforced to explore the complementarity the group sparsity is introduced to promote the robustness against the noise an efficient iterative procedure is developed to solve emr slra

descriptor learning via supervised manifold regularization for multioutput regression multioutput regression has recently shown great ability to solve challenging problems in both computer vision and medical image analysis however due to the huge image variability and ambiguity it is fundamentally challenging to handle the highly complex input target relationship of multioutput regression especially with indiscriminate high dimensional representations in this paper we propose a novel supervised descriptor learning sdl algorithm for multioutput regression which can establish discriminative and compact feature representations to improve the multivariate estimation performance the sdl is formulated as generalized low rank approximations of matrices with a supervised manifold regularization the sdl is able to simultaneously extract discriminative features closely related to multivariate targets and remove irrelevant and redundant information by transforming raw features into a new low dimensional space aligned to targets the achieved discriminative while compact descriptor largely reduces the variability and ambiguity for multioutput regression which enables more accurate and efficient multivariate estimation we conduct extensive evaluation of the proposed sdl on both synthetic data and real world multioutput regression tasks for both computer vision and medical image analysis experimental results have shown that the proposed sdl can achieve high multivariate estimation accuracy on all tasks and largely outperforms the algorithms in the state of the arts our method establishes a novel sdl framework for multioutput regression which can be widely used to boost the performance in different applications

equilibrium subsets for multi parametric structural analysis the paper discusses multi parametric formulations for structural equilibrium problems by seeking subsets of equilibrium states which also fulfil extra conditions more detailed information on structural behaviour can be obtained these conditions can be related to analyses of e g critical behaviour imperfections or optimisation the paper shows a general problem setting and some interesting augmentations a solution method for the special case of one dimensional equilibrium subsets is described the algorithm is a generalisation of a path following algorithm where new methods are developed for the evaluation of the path tangent and for the isolation of special solution points examples are used to show the properties and the possibilities of the ideas

multilevel methods for the h p and hp versions of the boundary element method in this paper we give an overview on the definition of finite element spaces for the h p and hp version of the bem along with preconditioners of additive schwarz type we consider screen problems with a hypersingular or a weakly singular integral equation of first kind on an open surface as model problems for the hypersingular integral equation and the h version with piecewise bilinear functions on a coarse and a fine grid we analyze a preconditioner by iterative substructuring based on a non overlapping decomposition of we prove that the condition number of the preconditioned linear system behaves polylogarithmically in h h here h is the size of the subdomains and h is the size of the elements for the hp version and the hypersingular integral equation we comment in detail on an additive schwarz preconditioner which uses piecewise polynomials of high degree on the fine grid and yields also a polylogarithmically growing condition number for the weakly singular integral equation where no continuity of test and trial functions across the element boundaries has to been enforced the method works for nonuniform degree distributions as well numerical results supporting our theory are reported

parallel galerkin domain decomposition procedures based on the streamline diffusion method for convection diffusion problems based upon the streamline diffusion method parallel galerkin domain decomposition procedures for convection diffusion problems are given these procedures use implicit method in the sub domains and simple explicit flux calculations on the inter boundaries of sub domains by integral mean method or extrapolation method to predict the inner boundary conditions thus the parallelism can be achieved by these procedures the explicit nature of the flux calculations induces a time step limitation that is necessary to preserve stability artificial diffusion parameters d are given by analysis optimal order error estimate is derived in a norm which is stronger than l 2 norm for these procedures this error estimate not only includes the optimal h 1 norm error estimate but also includes the error estimate along the streamline direction b u u which cannot be achieved by standard finite element method experimental results are presented to confirm theoretical results

error controlled global sensitivity analysis of ordinary differential equations we propose a novel strategy for global sensitivity analysis of ordinary differential equations it is based on an error controlled solution of the partial differential equation pde that describes the evolution of the probability density function associated with the input uncertainty variability the density yields a more accurate estimate of the output uncertainty variability where not only some observables such as mean and variance but also structural properties e g skewness heavy tails bi modality can be resolved up to a selected accuracy for the adaptive solution of the pde cauchy problem we use the rothe method with multiplicative error correction which was originally developed for the solution of parabolic pdes we show that unlike in parabolic problems conservation properties necessitate a coupling of temporal and spatial accuracy to avoid accumulation of spatial approximation errors over time we provide convergence conditions for the numerical scheme and suggest an implementation using approximate approximations for spatial discretization to efficiently resolve the coupling of temporal and spatial accuracy the performance of the method is studied by means of low dimensional case studies the favorable properties of the spatial discretization technique suggest that this may be the starting point for an error controlled sensitivity analysis in higher dimensions

fem bem coupling for the large body limit in micromagnetics we present and analyze a coupled finite element boundary element method for a model in stationary micromagnetics the finite element part is based on mixed conforming elements for two and three dimensional settings we show well posedness of the discrete problem and present an a priori error analysis for the case of lowest order elements

parallel domain decomposition procedures of improved d d type for parabolic problems two parallel domain decomposition procedures for solving initial boundary value problems of parabolic partial differential equations are proposed one is the extended d d type algorithm which extends the explicit implicit conservative galerkin domain decomposition procedures given in 5 from a rectangle domain and its decomposition that consisted of a stripe of sub rectangles into a general domain and its general decomposition with a net like structure an almost optimal error estimate without the factor h 1 2 given in dawson dupont s error estimate is proved another is the parallel domain decomposition algorithm of improved d d type in which an additional term is introduced to produce an approximation of an optimal error accuracy in l 2 norm

the conditioning of some numerical methods for first kind boundary integral equations we consider the sensitivity of the matrix equations which arise when solving boundary integral equations of negative order specifically in case of the typical example of the operator with logarithmic kernel the sensitivity is expressed using condition numbers and it turns out that the local condition number is a very good indicator in contrast to the ordinary condition number traditionally used

supernatural quad4 a template formulation abstract a universal template for a 4 node quadrilateral in plane stress is constructed using a combination of old and new techniques the use of natural quantities strongly advocated by j h argyris since his continua and discontinua 1965 exposition is further expanded the qualifier supernatural means that all governing equations kinematic constitutive and equilibrium are expressed in both cartesian and natural forms these two sets are used to build different components of the template with timely help from a computer algebra system a template that include all possible quadrilateral elements that pass the individual element test of bergan and hanssen emerges it yields an infinite number of hitherto undiscovered instances that may be customized to fit special needs a striking example is the construction of a two trapezoid macroelement that is bending exact about one direction for any amount of distortion this concludes a five decade search that begins with the formulation of the wing cover rectangular panel in argyris 1954 seminal serial on energy methods and structural analysis

nonnegative ranks decompositions and factorizations of nonnegative matrices the nonnegative rank of a nonnegative matrix is the smallest number of nonnegative rank one matrices into which the matrix can be decomposed additively such decompositions are useful in diverse scientific disciplines we obtain characterizations and bounds and show that the nonnegative rank can be computed exactly over the reals by a finite algorithm

laplacian regularized low rank representation and its applications low rank representation lrr has recently attracted a great deal of attention due to its pleasing efficacy in exploring low dimensional subspace structures embedded in data for a given set of observed data corrupted with sparse errors lrr aims at learning a lowest rank representation of all data jointly lrr has broad applications in pattern recognition computer vision and signal processing in the real world data often reside on low dimensional manifolds embedded in a high dimensional ambient space however the lrr method does not take into account the non linear geometric structures within data thus the locality and similarity information among data may be missing in the learning process to improve lrr in this regard we propose a general laplacian regularized low rank representation framework for data representation where a hypergraph laplacian regularizer can be readily introduced into i e a non negative sparse hyper laplacian regularized lrr model nshlrr by taking advantage of the graph regularizer our proposed method not only can represent the global low dimensional structures but also capture the intrinsic non linear geometric information in data the extensive experimental results on image clustering semi supervised image classification and dimensionality reduction tasks demonstrate the effectiveness of the proposed method

on the fem solution of a coupled contact two phase stefan problem in thermo elasticity coercive case abstract in the paper a semi implicit discretization in time of the weak formulation of the coupled signorini type contact two phase stefan problem is numerically analyzed the problem leads to coupled elliptic variational inequalities which are approximated by the fem

full order convergence of a mixed finite element method for fourth order elliptic equations abstract by using a special interpolation operator and an elaborate element analysis in this paper we improve the classical error estimates to full order for a mixed finite element method for the fourth order elliptic equations on the rectangular mesh therefore we obtain the truly optimal error estimates in view of the interpolation space for the first time

low rank matrix factorization with multiple hypergraph regularizer this paper presents a novel low rank matrix factorization method named multihmmf which incorporates multiple hypergraph manifold regularization to the low rank matrix factorization in order to effectively exploit high order information among the data samples the hypergraph is introduced to model the local structure of the intrinsic manifold specifically multiple hypergraph regularization terms are separately constructed to consider the local invariance the optimal intrinsic manifold is constructed by linearly combining multiple hypergraph manifolds then the regularization term is incorporated into a truncated singular value decomposition framework resulting in a unified objective function so that matrix factorization is changed into an optimization problem alternating optimization is used to solve the optimization problem with the result that the low dimensional representation of data space is obtained the experimental results of image clustering demonstrate that the proposed method outperforms state of the art data representation methods we propose a novel low rank matrix factorization method we incorporate multiple hypergraph manifold regularization to the matrix factorization we adopt alternating optimization to solve the optimization problem

enhanced allman quadrilateral for finite drilling rotations the paper concerns a four node quadrilateral element based on allman shape functions undergoing finite unrestricted drilling rotations and aims at improving its accuracy and facilitating its implementation firstly the classical allman shape functions are valid only for small in plane rotations and must be used with a co rotational frame which embeds finite rotations we derive a new form of allman shape functions which is valid for finite drilling rotations and allows to avoid the use of such a frame secondly the classical allman quadrilateral shows locking in the in plane shear test we study this problem identify its source and remove it by enhancing the element with two additional modes via the enhanced assumed displacement gradient eadg method to accomplish this we extend the original version of the method to mixed functionals including rotations two variational formulations including the drilling rotation via the rotation constraint rc equation are considered one based on the green strain and the other on the relaxed non symmetric right stretch strain numerical tests of the corresponding finite elements show that the improved allman elements are as exact in linear tests as the eadg4 element and perform very well in a severe in plane shear test for one layer of elements undergoing large rotations

graph regularized nonnegative matrix factorization for data representation matrix factorization techniques have been frequently applied in information retrieval computer vision and pattern recognition among them nonnegative matrix factorization nmf has received considerable attention due to its psychological and physiological interpretation of naturally occurring data whose representation may be parts based in the human brain on the other hand from the geometric perspective the data is usually sampled from a low dimensional manifold embedded in a high dimensional ambient space one then hopes to find a compact representation which uncovers the hidden semantics and simultaneously respects the intrinsic geometric structure in this paper we propose a novel algorithm called graph regularized nonnegative matrix factorization gnmf for this purpose in gnmf an affinity graph is constructed to encode the geometrical information and we seek a matrix factorization which respects the graph structure our empirical study shows encouraging results of the proposed algorithm in comparison to the state of the art algorithms on real world problems

bubble functions prompt unusual stabilized finite element methods a second order linear scalar differential equation including a zero th order term is approximated using first the standard galerkin method enriched with bubble functions static condensation of the bubbles suggest an unusual stabilized finite element method for which we establish a convergence study and obtain successful numerical simulations the method is generalized to allow for a convection operator in the equation this work may be employed as a starting point for simulation of nonlinear equations governing turbulence phenomena flows with chemical reactions and other important problems

domain decomposition based mathcal h lu preconditioning hierarchical matrices provide a data sparse way to approximate fully populated matrices the two basic steps in the construction of an mathcal h matrix are a the hierarchical construction of a matrix block partition and b the blockwise approximation of matrix data by low rank matrices in this paper we develop a new approach to construct the necessary partition based on domain decomposition compared to standard geometric bisection based mathcal h matrices this new approach yields mathcal h lu factorizations of finite element stiffness matrices with significantly improved storage and computational complexity requirements these rigorously proven and numerically verified improvements result from an mathcal h matrix block structure which is naturally suited for parallelization and in which large subblocks of the stiffness matrix remain zero in an lu factorization we provide numerical results in which a domain decomposition based mathcal h lu factorization is used as a preconditioner in the iterative solution of the discrete three dimensional convection diffusion equation

parallel galerkin domain decomposition procedures for wave equation parallel galerkin domain decomposition procedures for wave equation are given these procedures use implicit method in the sub domains and simple explicit flux calculation on the inter boundaries of sub domains by integral mean method or extrapolation method thus the parallelism can be achieved by these procedures the explicit nature of the flux prediction induces a time step constraint that is necessary to preserve the stability l 2 norm error estimates are derived for these procedures experimental results are presented to confirm the theoretical results

background foreground modeling based on spatiotemporal sparse subspace clustering background estimation and foreground segmentation are important steps in many high level vision tasks many existing methods estimate background as a low rank component and foreground as a sparse matrix without incorporating the structural information therefore these algorithms exhibit degraded performance in the presence of dynamic backgrounds photometric variations jitter shadows and large occlusions we observe that these backgrounds often span multiple manifolds therefore constraints that ensure continuity on those manifolds will result in better background estimation hence we propose to incorporate the spatial and temporal sparse subspace clustering into the robust principal component analysis rpca framework to that end we compute a spatial and temporal graph for a given sequence using motion aware correlation coefficient the information captured by both graphs is utilized by estimating the proximity matrices using both the normalized euclidean and geodesic distances the low rank component must be able to efficiently partition the spatiotemporal graphs using these laplacian matrices embedded with the rpca objective function these laplacian matrices constrain the background model to be spatially and temporally consistent both on linear and nonlinear manifolds the solution of the proposed objective function is computed by using the linearized alternating direction method with adaptive penalty optimization scheme experiments are performed on challenging sequences from five publicly available datasets and are compared with the 23 existing state of the art methods the results demonstrate excellent performance of the proposed algorithm for both the background estimation and foreground segmentation

a locking free reissner mindlin quadrilateral element on arbitrary regular quadrilaterals a new finite element method for the reissner mindlin plate is proposed where both transverse displacement and rotation are approximated by isoparametric bilinear elements with local bubbles enriching rotation and a local reduction operator is applied to the shear energy term this new method gives optimal error bounds uniform in the thickness of the plate for both transverse displacement and rotation with respect to h1 and l2 norms

a non mortar mixed finite element method for elliptic problems on non matching multiblock grids abstract we consider the approximation of second order elliptic equations on domains that can be described as a union of sub domains or blocks we assume that a grid is defined on each block independently so that the resulting grid over the entire domain need not be conforming i e match across the block boundaries several techniques have been developed to approximate elliptic equations on multiblock grids that utilize a mortar finite element space defined on the block boundary interface itself we define a mixed finite element method that does not use such a mortar space the method has an advantage in the case where adaptive local refinement techniques will be used in that there is no mortar grid to refine as is typical of mixed methods our method is locally conservative element by element it is also globally conservative across the block boundaries theoretical results show that the approximate solution converges at the optimal rate to the true solution we present computational results to illustrate and confirm the theory

manifold regularized discriminative nonnegative matrix factorization with fast gradient descent nonnegative matrix factorization nmf has become a popular data representation method and has been widely used in image processing and pattern recognition problems this is because the learned bases can be interpreted as a natural parts based representation of data and this interpretation is consistent with the psychological intuition of combining parts to form a whole for practical classification tasks however nmf ignores both the local geometry of data and the discriminative information of different classes in addition existing research results show that the learned basis is unnecessarily parts based because there is neither explicit nor implicit constraint to ensure the representation parts based in this paper we introduce the manifold regularization and the margin maximization to nmf and obtain the manifold regularized discriminative nmf md nmf to overcome the aforementioned problems the multiplicative update rule mur can be applied to optimizing md nmf but it converges slowly in this paper we propose a fast gradient descent fgd to optimize md nmf fgd contains a newton method that searches the optimal step length and thus fgd converges much faster than mur in addition fgd includes mur as a special case and can be applied to optimizing nmf and its variants for a problem with 165 samples in r1600 fgd converges in 28 s while mur requires 282 s we also apply fgd in a variant of md nmf and experimental results confirm its efficiency experimental results on several face image datasets suggest the effectiveness of md nmf

dual graph regularized latent low rank representation for subspace clustering low rank representation lrr has received considerable attention in subspace segmentation due to its effectiveness in exploring low dimensional subspace structures embedded in data to preserve the intrinsic geometrical structure of data a graph regularizer has been introduced into lrr framework for learning the locality and similarity information within data however it is often the case that not only the high dimensional data reside on a non linear low dimensional manifold in the ambient space but also their features lie on a manifold in feature space in this paper we propose a dual graph regularized lrr model dglrr by enforcing preservation of geometric information in both the ambient space and the feature space the proposed method aims for simultaneously considering the geometric structures of the data manifold and the feature manifold furthermore we extend the dglrr model to include non negative constraint leading to a parts based representation of data experiments are conducted on several image data sets to demonstrate that the proposed method outperforms the state of the art approaches in image clustering

on two dimensional slow viscous flows past obstacles in a half plane we consider a cylinder with arbitrary cross section moving in a viscous incompressible fluid parallel to a plane wall formal asymptotic expansions of the solution for small reynolds numbers are constructed by using boundary integral equations of the first kind in contrast to the problem without a wall we show that there exists a unique solution to the zero th order problem however the problem considered here is still singular in the sense that we find the stokes paradox in the next higher order problem a justification of the formal asymptotic expansion for the first two terms is established rigorously

mr ntd manifold regularization nonnegative tucker decomposition for tensor data dimension reduction and representation with the advancement of data acquisition techniques tensor multidimensional data objects are increasingly accumulated and generated for example multichannel electroencephalographies multiview images and videos in these applications the tensor objects are usually nonnegative since the physical signals are recorded as the dimensionality of tensor objects is often very high a dimension reduction technique becomes an important research topic of tensor data from the perspective of geometry high dimensional objects often reside in a low dimensional submanifold of the ambient space in this paper we propose a new approach to perform the dimension reduction for nonnegative tensor objects our idea is to use nonnegative tucker decomposition ntd to obtain a set of core tensors of smaller sizes by finding a common set of projection matrices for tensor objects to preserve geometric information in tensor data we employ a manifold regularization term for the core tensors constructed in the tucker decomposition an algorithm called manifold regularization ntd mr ntd is developed to solve the common projection matrices and core tensors in an alternating least squares manner the convergence of the proposed algorithm is shown and the computational complexity of the proposed method scales linearly with respect to the number of tensor objects and the size of the tensor objects respectively these theoretical results show that the proposed algorithm can be efficient extensive experimental results have been provided to further demonstrate the effectiveness and efficiency of the proposed mr ntd algorithm

a study of optimal membrane triangles with drilling freedoms abstract this article compares derivation methods for constructing optimal membrane triangles with corner drilling freedoms the term optimal is used in the sense of exact inplane pure bending response of rectangular mesh units of arbitrary aspect ratio following a comparative summary of element formulation approaches the construction of an optimal three node triangle using the andes formulation is presented the construction is based upon techniques developed by 1991 in student term projects but taking advantage of the more general framework of templates developed since the optimal element that fits the andes template is shown to be unique if energy orthogonality constraints are enforced two other formulations are examined and compared with the optimal model retrofitting the conventional linear strain triangle element by midpoint migrating and congruential transformations is shown unable to produce an optimal element while rank deficiency is inevitable use of the quadratic strain field of the 1988 allman triangle or linear filtered versions thereof is also unable to reproduce the optimal element moreover these elements exhibit serious aspect ratio lock these predictions are verified on benchmark examples

a mixed finite element method and solution multiplicity for coulomb frictional contact abstract this paper is concerned with the discrete contact problem governed by coulomb s friction law we propose and study a new technique using mixed finite elements with two multipliers in order to determine numerically critical friction coefficients for which multiple solutions to the friction problem exist the framework is based on eigenvalue problems and it allows to exhibit non uniqueness cases involving an infinity of solutions located on a continuous branch the theory is illustrated with several computations which clearly show the accuracy of the proposed method

principal manifolds and nonlinear dimensionality reduction via tangent space alignment we present a new algorithm for manifold learning and nonlinear dimensionality reduction based on a set of unorganized data points sampled with noise from a parameterized manifold the local geometry of the manifold is learned by constructing an approximation for the tangent space at each data point and those tangent spaces are then aligned to give the global coordinates of the data points with respect to the underlying manifold we also present an error analysis of our algorithm showing that reconstruction errors can be quite small in some cases we illustrate our algorithm using curves and surfaces both in two dimensional three dimensional 2d 3d euclidean spaces and in higher dimensional euclidean spaces we also address several theoretical and algorithmic issues for further research and improvements

strongly elliptic boundary integral equations for electromagnetic transmission problems we study a boundary integral equation method for transmission problems for strongly elliptic differential operators which yields a strongly elliptic system of pseudodifferential operators and which therefore can be used for numerical computations with galerkin s procedure the method is shown to work for the vector helmholtz equation in 3 with electromagnetic transmission conditions we propose a slightly modified system of boundary values in order for the corresponding bilinear form to be coercive over h 1 we analyse the boundary integral equations using the calculus of pseudodifferential operators here the concept of the principal symbol is used to derive existence and regularity results for the solution