an iterative reweighted method for tucker decomposition of incomplete tensors we consider the problem of low rank decomposition of incomplete tensors since many real world data lie on an intrinsically low dimensional subspace tensor low rank decomposition with missing entries has applications in many data analysis problems such as recommender systems and image inpainting in this paper we focus on tucker decomposition which represents an n th order tensor in terms of n factor matrices and a core tensor via multilinear operations to exploit the underlying multilinear low rank structure in high dimensional datasets we propose a group based log sum penalty functional to place structural sparsity over the core tensor which leads to a compact representation with smallest core tensor the proposed method is developed by iteratively minimizing a surrogate function that majorizes the original objective function this iterative optimization leads to an iteratively reweighted least squares algorithm in addition to reduce the computational complexity an over relaxed monotone fast iterative shrinkage thresholding technique is adapted and embedded in the iterative reweighted process the proposed method is able to determine the model complexity i e multilinear rank in an automatic way simulation results show that the proposed algorithm offers competitive performance compared with other existing algorithms

on stabilized finite element methods based on the scott zhang projector circumventing the inf sup condition for the stokes problem abstract in this work we propose a stabilized finite element method that permits us to circumvent discrete inf sup conditions e g allowing equal order interpolation the type of method we propose belongs to the family of symmetric stabilization techniques which are based on the introduction of additional terms that penalize the difference between some quantities i e the pressure gradient in the stokes problem and their finite element projections the key feature of the formulation we propose is the definition of the projection to be used a non standard scott zhang projector that is well defined for l 1 functions the resulting method has some appealing features the projector is local and nested meshes or enriched spaces are not required

stability and convergence of two level iterative methods for the stationary incompressible magnetohydrodynamics with different reynolds numbers abstract in the paper we develop some two level finite element iterative methods and use these methods to solve the stationary incompressible magnetohydrodynamics mhd with different reynolds numbers under some different uniqueness conditions firstly we use the stokes type iterative method newton type iterative method and oseen type iterative method of m times on a coarse mesh with mesh size h and then solve a linear problem with the stokes type newton type and oseen type correction of one time on a fine grid with mesh sizes h h furthermore we analyze the uniform stability and convergence of these methods with respect to reynolds numbers mesh sizes h and h and iterative times m finally the stationary incompressible mhd equations with large reynolds number are researched by the one level finite element method based on the oseen type iteration on a fine mesh under a weak uniqueness condition

a unified convergence analysis of block successive minimization methods for nonsmooth optimization the block coordinate descent bcd method is widely used for minimizing a continuous function f of several block variables at each iteration of this method a single block of variables is optimized while the remaining variables are held fixed to ensure the convergence of the bcd method the subproblem of each block variable needs to be solved to its unique global optimal unfortunately this requirement is often too restrictive for many practical scenarios in this paper we study an alternative inexact bcd approach which updates the variable blocks by successively minimizing a sequence of approximations of f which are either locally tight upper bounds of f or strictly convex local approximations of f the main contributions of this work include the characterizations of the convergence conditions for a fairly wide class of such methods especially for the cases where the objective functions are either nondifferentiable or nonconvex our results unify and extend the existing convergence results

a multistage representation of the wiener filter based on orthogonal projections the wiener filter is analyzed for stationary complex gaussian signals from an information theoretic point of view a dual port analysis of the wiener filter leads to a decomposition based on orthogonal projections and results in a new multistage method for implementing the wiener filter using a nested chain of scalar wiener filters this new representation of the wiener filter provides the capability to perform an information theoretic analysis of previous basis dependent reduced rank wiener filters this analysis demonstrates that the cross spectral metric is optimal in the sense that it maximizes mutual information between the observed and desired processes a new reduced rank wiener filter is developed based on this new structure which evolves a basis using successive projections of the desired signal onto orthogonal lower dimensional subspaces the performance is evaluated using a comparative computer analysis model and it is demonstrated that the low complexity multistage reduced rank wiener filter is capable of outperforming the more complex eigendecomposition based methods

hp adaptive finite elements in electromagnetics a model problem for the steady state form of maxwell s equations is considered the problem is formulated in a weak form using a lagrange multiplier laying down a foundation for a general class of novel hp adaptive fe approximations a convergence proof for curvilinear elements is presented the proposed method is illustrated and verified by a series of 2d experiments which include elements with curved boundaries and nonhomogeneous media

subspace learning and imputation for streaming big data matrices and tensors extracting latent low dimensional structure from high dimensional data is of paramount importance in timely inference tasks encountered with big data analytics however increasingly noisy heterogeneous and incomplete datasets as well as the need for real time processing of streaming data pose major challenges to this end in this context the present paper permeates benefits from rank minimization to scalable imputation of missing data via tracking low dimensional subspaces and unraveling latent possibly multi way structure from incomplete streaming data for low rank matrix data a subspace estimator is proposed based on an exponentially weighted least squares criterion regularized with the nuclear norm after recasting the nonseparable nuclear norm into a form amenable to online optimization real time algorithms with complementary strengths are developed and their convergence is established under simplifying technical assumptions in a stationary setting the asymptotic estimates obtained offer the well documented performance guarantees of the batch nuclear norm regularized estimator under the same unifying framework a novel online adaptive algorithm is developed to obtain multi way decompositions of low rank tensors with missing entries and perform imputation as a byproduct simulated tests with both synthetic as well as real internet and cardiac magnetic resonance imagery mri data confirm the efficacy of the proposed algorithms and their superior performance relative to state of the art alternatives

a rotational velocity correction projection method for unsteady incompressible magnetohydrodynamics equations abstract this paper provides a rotational velocity correction projection method for the unsteady incompressible magnetohydrodynamics mhd equations in this method the electrical field variable e was eliminated in this way the gauss s law can be conserved the velocity variable u and the pressure field p are solved by a rotational velocity correction projection method the optimal error estimates of the l 2 norm will be given finally we shall present some numerical results to confirm our analysis it shows that our method is effective and can conserve the gauss s law very well

a new approach to collaborative filtering operator estimation with spectral regularization we present a general approach for collaborative filtering cf using spectral regularization to learn linear operators mapping a set of users to a set of possibly desired objects in particular several recent low rank type matrix completion methods for cf are shown to be special cases of our proposed framework unlike existing regularization based cf our approach can be used to incorporate additional information such as attributes of the users objects a feature currently lacking in existing regularization based cf approaches using popular and well known kernel methods we provide novel representer theorems that we use to develop new estimation methods we then provide learning algorithms based on low rank decompositions and test them on a standard cf data set the experiments indicate the advantages of generalizing the existing regularization based cf methods to incorporate related information about users and objects finally we show that certain multi task learning methods can be also seen as special cases of our proposed approach

rank regularization and bayesian inference for tensor completion and extrapolation a novel regularizer of the parafac decomposition factors capturing the tensor s rank is proposed in this paper as the key enabler for completion of three way data arrays with missing entries set in a bayesian framework the tensor completion method incorporates prior information to enhance its smoothing and prediction capabilities this probabilistic approach can naturally accommodate general models for the data distribution lending itself to various fitting criteria that yield optimum estimates in the maximum a posteriori sense in particular two algorithms are devised for gaussian and poisson distributed data that minimize the rank regularized least squares error and kullback leibler divergence respectively the proposed technique is able to recover the ground truth tensor rank when tested on synthetic data and to complete brain imaging and yeast gene expression datasets with 50 and 15 of missing entries respectively resulting in recovery errors at 11 db and 15 db

convergent finite element discretization of the multi fluid nonstationary incompressible magnetohydrodynamics equations we propose a convergent implicit stabilized finite element discretization of the nonstationary incompressible magnetohydrodynamics equations with variable density viscosity and electric conductivity the discretization satisfies a discrete energy law and a discrete maximum principle for the positive density and iterates converge to weak solutions of the limiting problem for vanishing discretization parameters a simple fixed point scheme together with an appropriate stopping criterion is proposed which decouples the computation of density velocity and magnetic field and inherits the above properties provided a mild mesh constraint holds computational studies are provided

a stabilized finite element method for the incompressible magnetohydrodynamic equations we propose and analyze a stabilized finite element method for the incompressible magnetohydrodynamic equations the numerical results that we present show a good behavior of our approximation in experiments which are relevant from an industrial viewpoint we explain in particular in the proof of our convergence theorem why it may be interesting to stabilize the magnetic equation as soon as the hydrodynamic diffusion is small and even if the magnetic diffusion is large this observation is confirmed by our numerical tests

error analysis of a fractional step method for magnetohydrodynamics equations abstract this paper focuses on a fractional step finite element method for the magnetohydrodynamics problems in three dimensional bounded domains it is shown that the proposed fractional step scheme allows for a discrete energy identity a rigorous error analysis is presented we derive the temporal and spatial error estimates of o t h for the velocity and the magnetic field in the discrete space l 2 h 1 l l 2 under the constraint t c h

long term dissipativity of time stepping algorithms for an abstract evolution equation with applications to the incompressible mhd and navier stokes equations abstract this paper examines the long term dissipativity and unconditional non linear stability of time integration algorithms for the incompressible mhd equations the results apply as a particular case to the uncoupled incompressible navier stokes equations the analysis is performed in the setting defined by an abstract evolution equation possessing the same long term dissipative structure as the above physical systems a general class of time stepping schemes is analyzed in this context showing the non linear unconditional stability and long term dissipativity of particular members of this family of algorithms in particular algorithms showing these strong properties which additionally involve the solution of a linear problem at each time step are identified a particular linear algorithm is shown to exhibit optimal long term dissipative properties and to possess an algorithmic global attractor these abstract results apply rigorously to galerkin mixed finite element discretizations of the problem to this end it is shown that such galerkin type projection inherits the dissipative properties of the continuum problem computational aspects involved in the numerical implementation of these methods are addressed and illustrated in representative numerical simulations

thermally coupled magnetohydrodynamics flow abstract this paper deals with the questions of existence and uniqueness of solutions to the equations of stationary incompressible magnetohydrodynamics mhd when bouyancy effects due to temperature differences in the flow cannot be neglected to that effect we couple the mhd equations to the heat equation and employ the well known boussinesq approximation we consider the equations posed on a bounded three dimensional domain we point out that these equations model such phenomena as the cooling of nuclear reactors by electrically conducting fluids continuous metal casting crystal growth and semiconductor manufacture

parallel factor analysis in sensor array processing this paper links multiple invariance sensor array processing mi sap to parallel factor parafac analysis which is a tool rooted in psychometrics and chemometrics parafac is a common name for low rank decomposition of three and higher way arrays this link facilitates the derivation of powerful identifiability results for mi sap shows that the uniqueness of single and multiple invariance esprit stems from uniqueness of low rank decomposition of three way arrays and allows tapping on the available expertise for fitting the parafac model the results are applicable to both data domain and subspace mi sap formulations the paper also includes a constructive uniqueness proof for a special parafac model

elements finis mixtes incompressibles pour l equation de stokes dans ℝ3 we introduce some new families of finite element approximation for the stationary stokes and navier stokes equations in a bounded domain in 3 these elements can used tetahedrons or cubes the approximation satisfie exactly the incompressibility condition

analysis of parallel finite element algorithm based on three linearization methods for the steady incompressible mhd flow abstract based on full domain partition parallel finite element algorithm based on three linearizations is designed to solve the stationary incompressible magnetohydrodynamics mhd in every algorithm each processor is in charge of a subproblem which is linearized by three options stokes type newton s and picard s iterations each subproblem is defined in the whole domain with vast majority of the degrees of freedom associated with the particular subdomain the error estimates of these proposed algorithms with respect to iterative step and small mesh sizes are analyzed finally some numerical experiments are provided to show the validity and high efficiency of our algorithms

block preconditioners for stable mixed nodal and edge finite element representations of incompressible resistive mhd the scalable iterative solution of strongly coupled three dimensional incompressible resistive magnetohydrodynamics mhd equations is very challenging because disparate time scales arise from the electromagnetics the hydrodynamics as well as the coupling between these systems this study considers a mixed finite element discretization of a dual saddle point formulation of the incompressible resistive mhd equations using a stable nodal q2 q1 discretization for the hydrodynamics and a stable edge node discretization of a reduced form of the maxwell equations this paper presents new approximate block factorization preconditioners for this system which reduce the system to approximate schur complement systems that can be solved using algebraic multilevel methods these preconditioners include a new augmentation based approximation for the magnetic induction saddle point system as well as efficient approximations of the schur complements that arise from the complex coupling between the navier stokes eq

the arrow hurwicz iterative finite element method for the stationary magnetohydrodynamics flow abstract in this paper we propose and analyze an arrow hurwicz iterative finite element method for solving the stationary incompressible magnetohydrodynamics mhd equations discretized by mixed element methods comparing with the other iterative methods the significant feature of this iterative method is that it does not need to solve any saddle point system at each iteration step except for determination of the initial functions under several reasonable conditions it is proved that the solution solved by the proposed iterative method is uniformly bounded with respect to the mesh width h and the iteration number n and the method converges geometrically with a contraction number independent of the finite element mesh width h ample numerical experiments are performed to validate the accuracy and the efficiency of the numerical scheme

stability and convergence of semi implicit time stepping algorithm for stationary incompressible magnetohydrodynamics abstract for the stationary incompressible magnetohydrodynamics mhd equations we provide a new uniqueness assumption a0 and show the exponential stability of the solution then the semi implicit time stepping algorithm is used to solve the stationary mhd equations the algorithm is proved to be unconditionally stable the discrete velocity and magnetic field are bounded in l 0 l for any space and time step sizes the error estimates for the algorithm are deduced under the uniqueness conditions finally numerical experiments are performed to testify our theoretical analysis

singularities of electromagnetic fields in polyhedral domains in this paper we investigate the singular solutions of time harmonic maxwell equations in a domain which has edges and polyhedral corners it is now well known that in the presence of non convex edges the solution fields have no square integrable gradients in general and that the main singularities are the gradients of singular functions of the laplace operator 4 5 we show how this type of result can be derived from the classical mellin analysis and how this analysis leads to sharper results concerning the singular parts which belong to h 1 for the singular functions we exhibit simple and explicit formulas based on generalized dirichlet and neumann singularities for the laplace operator these formulas are more explicit than the results announced in our note 10

vector potential finite element formulations for two dimensional resistive magnetohydrodynamics abstract vector potential formulations are attractive for electromagnetic problems in two dimensions since they reduce both the number and complexity of equations particularly in coupled systems such as magnetohydrodynamics mhd in this paper we consider the finite element formulation of a vector potential model of two dimensional resistive mhd existence and uniqueness are considered separately for the continuum nonlinear equations and the discretized and linearized form that arises from newton s method applied to a modified system under some conditions we prove that the solutions of the original and modified weak forms are the same allowing us to prove convergence of the discretization and well posedness of the nonlinear iteration near a solution

mixed finite element methods for stationary incompressible magneto hydrodynamics a new mixed variational formulation of the equations of stationary incompressible magneto hydrodynamics is introduced and analyzed the formulation is based on curl conforming sobolev spaces for the magnetic variables and is shown to be well posed in possibly non convex lipschitz polyhedra a finite element approximation is proposed where the hydrodynamic unknowns are discretized by standard inf sup stable velocity pressure space pairs and the magnetic ones by a mixed approach using nedelec s elements of the first kind an error analysis is carried out that shows that the proposed finite element approximation leads to quasi optimal error bounds in the mesh size

modeling of electromagnetic absorption scattering problems using hp adaptive finite elements a model problem for the steady state form of maxwell s equations is considered the problem is formulated in a weak form using a lagrange multiplier laying down a foundation for a general class of novel hp adaptive fe approximations a convergence proof for affine elements is presented the proposed method is illustrated and verified with a series of 2d experiments including elements with curved boundaries and nonhomogeneous media

on an efficient second order backward difference newton scheme for mhd system abstract for the 2d 3d time dependent magnetohydrodynamics mhd system we propose a new second order backward difference formula newton scheme sbdfn which is a combination of second order backward difference approximation of the time derivative terms and newton treatment of the nonlinear terms meanwhile the finite element method is applied as spatial discretization firstly the optimal convergence of spatially semi discrete form is deduced secondly the stability and well posedness of sbdfn scheme are provided under c where c is independent of h based on these results optimal error estimates of the scheme in time are proved by negative norm technique finally numerical experiments are carried out to validate the theoretical analysis

on uniqueness in candecomp parafac one of the basic issues in the analysis of three way arrays by candecomp parafac cp has been the question of uniqueness of the decomposition kruskal 1977 has proved that uniqueness is guaranteed when the sum of thek ranks of the three component matrices involved is at least twice the rank of the solution plus 2 since then little has been achieved that might further qualify kruskal s sufficient condition attempts to prove that it is also necessary for uniqueness except for rank 1 or 2 have failed but counterexamples to necessity have not been detected the present paper gives a method for generating the class of all solutions or at least a subset of that class given a cp solution that satisfies certain conditions this offers the possibility to examine uniqueness for a great variety of specific cp solutions it will be shown that kruskal s condition is necessary and sufficient when the rank of the solution is three but that uniqueness may hold even if the condition is not satisfied when the rank is four or higher

convergence analysis of three finite element iterative methods for the 2d 3d stationary incompressible magnetohydrodynamics abstract three finite element iterative methods are designed and analyzed for solving 2d 3d stationary incompressible magnetohydrodynamics mhd by a new technique strong uniqueness conditions for both stokes type iterative method iterative method i and newton iterative method iterative method ii are obtained which are weaker than the ones reported in open literature stability and optimal convergence rates for the above two methods are derived where the iterative method ii has an exponential convergent part with respect to iterative step m moreover oseen type iterative method iterative method iii is unconditionally stable and convergent under a uniqueness condition finally performance of the three proposed methods is investigated by numerical experiments

blind parafac receivers for ds cdma systems this paper links the direct sequence code division multiple access ds cdma multiuser separation equalization detection problem to the parallel factor parafac model which is an analysis tool rooted in psychometrics and chemometrics exploiting this link it derives a deterministic blind parafac ds cdma receiver with performance close to non blind minimum mean squared error mmse the proposed parafac receiver capitalizes on code spatial and temporal diversity combining thereby supporting small sample sizes more users than sensors and or less spreading than users interestingly parafac does not require knowledge of spreading codes the specifics of multipath interchip interference doa calibration information finite alphabet constant modulus or statistical independence whiteness to recover the information bearing signals instead parafac relies on a fundamental result regarding the uniqueness of low rank three way array decomposition due to kruskal 1977 1988 and generalized herein to the complex valued case that guarantees identifiability of all relevant signals and propagation parameters these and other issues are also demonstrated in pertinent simulation experiments

a nodal based finite element approximation of the maxwell problem suitable for singular solutions a new mixed finite element approximation of maxwell s problem is proposed its main features being that it is based on a novel augmented formulation of the continuous problem and the introduction of a mesh dependent stabilizing term which yields a very weak control on the divergence of the unknown the method is shown to be stable and convergent in the natural h rm mathbf curl 0 omega norm for this unknown in particular convergence also applies to singular solutions for which classical nodal based interpolations are known to suffer from spurious convergence upon mesh refinement

on finite element approximations of problems having inhomogeneous essential boundary conditions abstract the analysis and implementation of finite element methods for problems with inhomogeneous essential boundary conditions are considered the results are given for linear second order elliptic partial differential equations and for the nonlinear stationary navier stokes equations for certain easily implemented boundary treatments optimal error estimates and numerical examples are provided for problems posed on polyhedral domains

tensor decompositions and applications this survey provides an overview of higher order tensor decompositions their applications and available software a tensor is a multidimensional or n way array decompositions of higher order tensors i e n way arrays with n geq 3 have applications in psycho metrics chemometrics signal processing numerical linear algebra computer vision numerical analysis data mining neuroscience graph analysis and elsewhere two particular tensor decompositions can be considered to be higher order extensions of the matrix singular value decomposition candecomp parafac cp decomposes a tensor as a sum of rank one tensors and the tucker decomposition is a higher order form of principal component analysis there are many other tensor decompositions including indscal parafac2 candelinc dedicom and paratuck2 as well as nonnegative variants of all of the above the n way toolbox tensor toolbox and multilinear engine are examples of software packages for working with tensors

the equations of stationary incompressible magnetohydrodynamics with mixed boundary conditions abstract this paper deals with the questions of existence uniqueness and finite element approximation of solutions to the equations of steady state magnetohydrodynamics with mixed boundary conditions posed on a bounded three dimensional domain the boundary conditions for the velocity equations are of dirichlet neumann and mixed type these boundary conditions are important when considering free boundary value problems problems on artificially truncated domains and control problems which are governed by these equations

existence uniqueness and approximation for generalized saddle point problems extensions of the well known results of brezzi on saddle point problems are presented the class of problems is generalized to include the unsymmetric case and the known stability and approximation results are strengthened and applied to the generalized problem an application to the solution of certain exterior interface problems is indicated

uniformly robust preconditioners for incompressible mhd system abstract in this paper we study efficient schemes and design robust preconditioners for solving incompressible mhd magnetohydrodynamics system we propose the first order and second order symmetric schemes with augmented terms in magnetic equations that are introduced in consideration of designing uniformly robust preconditioners we present optimal error estimates of the proposed time matching scheme further we design block diagonal preconditioners for the schemes and rigorously prove that the condition number of preconditioned system is uniformly bounded by a constant which only depends on the domain finally some numerical experiments including accuracy tests and physical benchmark problems are presented to verify the accuracy of the schemes and the robustness of the preconditioner

on a galerkin lagrange multiplier method for the stationary navier stokes equations a galerkin lagrange multiplier formulation is used for the numerical solution of the stationary navier stokes equations in order to avoid the construction of zero divergence elements the formulation is based on different approximating spaces for the velocity field and the pressure optimal rate of convergence estimates are derived moreover a galerkin newton scheme for the solution of the nonlinear equations is shown to be quadratically locally convergent another scheme is shown to be linearly globally convergent

a combined nodal continuous discontinuous finite element formulation for the maxwell problem abstract continuous galerkin formulations are appealing due to their low computational cost whereas discontinuous galerkin formulation facilitate adaptative mesh refinement and are more accurate in regions with jumps of physical parameters since many electromagnetic problems involve materials with different physical properties this last point is very important for this reason in this article we have developed a combined cg dg formulation for maxwell s problem that allows arbitrary finite element spaces with functions continuous in patches of finite elements and discontinuous on the interfaces of these patches in particular the second formulation we propose comes from a novel continuous galerkin formulation that reduces the amount of stabilization introduced in the numerical system in all cases we have performed stability and convergence analyses of the methods the outcome of this work is a new approach that keeps the low cpu cost of recent nodal continuous formulations with the ability to deal with coefficient jumps and adaptivity of discontinuous ones all these methods have been tested using a problem with singular solution and another one with different materials in order to prove that in fact the resulting formulations can properly deal with these problems

global small solutions to an mhd type system the three dimensional case in this paper we consider the global well posedness of a three dimensional incompressible mhd type system with smooth initial data that is close to some nontrivial steady state it is a coupled system between the navier stokes equations and a free transport equation with a universal nonlinear coupling structure the main difficulty of the proof lies in exploring the dissipative mechanism of the system due to the fact that there is a free transport equation of in the coupled equations and only the horizontal derivatives of is dissipative with respect to time to achieve this we first employ anisotropic littlewood paley analysis to establish the key l1 lip 3 estimate to the third component of the velocity field then we prove the global well posedness to this system by the energy method which depends crucially on the divergence free condition of the velocity field 2014 wiley periodicals inc

finite element approximations of the nonstationary navier stokes problem part iv error estimates for second order time discretization this paper provides an error analysis for the crank nicolson method of time discretization applied to spatially discrete galerkin approximations of the nonstationary navier stokes equations second order error estimates are proven locally in time under realistic assumptions about the regularity of the solution for approximations of an exponentially stable solution these local error estimates are extended uniformly in time as text t to infty

error estimates for semidiscrete finite element approximations of linear and semilinear parabolic equations under minimal regularity assumptions semidiscrete finite element error estimates for linear parabolic equations are derived under minimal regularity with the help of l2 projectors then analogous minimal regularity semidiscrete error estimates for semilinear parabolic equations are derived

approximation of the thermally coupled mhd problem using a stabilized finite element method a numerical formulation to solve the mhd problem with thermal coupling is presented in full detail the distinctive feature of the method is the design of the stabilization terms which serve several purposes first convective dominated flows in the navier stokes and the heat equation can be dealt with second there is no restriction in the choice of the interpolation spaces of all the variables and finally flows highly coupled with the magnetic field can be accounted for different aspects related to the design of the final fully discrete and linearized algorithm are also discussed

on the existence uniqueness and finite element approximation of solutions of the equations of stationary incompressible magnetohydrodynamics the authors consider the equations of stationary incompressible magneto hydrodynamics posed in a bounded domain in three dimensions and treat the full coupled system of equations with inhomogeneous boundary conditions under certain conditions on the data they show that the existence and uniqueness of the solution of a weak formulation of the equations can be guaranteed they discuss a finite element discretization of the equations and prove an optimal estimate for the error of the approximate solution

a diffuse interface model and semi implicit energy stable finite element method for two phase magnetohydrodynamic flows abstract in this paper we propose a diffuse interface model and finite element approximation for two phase magnetohydrodynamic mhd flows with different viscosities and electric conductivities an energy stable scheme which is based on the finite element method for the spatial discretization and first order semi implicit scheme combined with convex splitting method for the temporal discretization is proposed to solve this new model the numerical scheme is proved to be mass conservative and energy law preserving by leray schauder fixed point theorem the existence of solutions to the numerical scheme is shown the uniqueness of the numerical solutions is obtained utilizing the stability of the numerical scheme and the compactness method the existence of the weak solutions to the two phase mhd model is established as well furthermore given more regularity on the weak solution the convergence of the numerical scheme is derived finally numerical experiments are provided to verify the theoretical results and validate the proposed model

convergence of a b e based finite element method for mhd models on lipschitz domains abstract we discuss a class of magnetic electric fields based finite element schemes for stationary magnetohydrodynamics mhd systems with two types of boundary conditions we establish a key l 3 estimate for divergence free finite element functions for a new type of boundary conditions with this estimate and a similar one in hu and xu 2018 we rigorously prove the convergence of picard iterations and the finite element schemes with weak regularity assumptions these results demonstrate the convergence of the finite element methods for singular solutions

generalized gaffney inequality and discrete compactness for discrete differential forms we prove generalized gaffney inequalities and the discrete compactness for finite element differential forms on s regular domains including general lipschitz domains in computational electromagnetism special cases of these results have been established for edge elements with weakly imposed divergence free conditions and used in the analysis of nonlinear and eigenvalue problems in this paper we generalize these results to discrete differential forms not necessarily with strongly or weakly imposed constraints the analysis relies on a new hodge mapping and its approximation property as an application we show l p estimates for several finite element approximations of the scalar and vector laplacian problems

overlapping schwarz methods for maxwell s equations in three dimensions two level overlapping schwarz methods are considered for finite element problems of 3d maxwell s equations nedelec elements built on tetrahedra and hexahedra are considered once the relative overlap is fixed the condition number of the additive schwarz method is bounded independently of the diameter of the triangulation and the number of subregions a similar result is obtained for a multiplicative method these bounds are obtained for quasi uniform triangulations in addition for the dirichlet problem the convexity of the domain has to be assumed our work generalizes well known results for conforming finite elements for second order elliptic scalar equations

unconditionally stable operator splitting algorithms for the incompressible magnetohydrodynamics system discretized by a stabilized finite element formulation based on projections summary in this article we propose different splitting procedures for the transient incompressible magnetohydrodynamics mhd system that are unconditionally stable we consider two levels of splitting on one side we perform the segregation of the fluid pressure and magnetic pseudo pressure from the vectorial fields computation at the second level the fluid velocity and induction fields are also decoupled this way we transform a fully coupled indefinite multi physics system into a set of smaller definite ones clearly reducing the cpu cost with regard to the finite element approximation we stick to an unconditionally convergent stabilized finite element formulation because it introduces convection stabilization allows to circumvent inf sup conditions clearly simplifying implementation issues and is able to capture non smooth solutions of the magnetic subproblem however residual based finite element formulations are not suitable for segregation because they lose the skew symmetry of the off diagonal blocks therefore in this work we have proposed a novel term by term stabilization of the mhd system based on projections that is still unconditionally convergent copyright 2012 john wiley sons ltd

on kruskal s uniqueness condition for the candecomp parafac decomposition let x be a real valued three way array the candecomp parafac cp decomposition is written as x under bar y under bar 1 y under bar r e where y r are rank 1 arrays and e under bar is a rest term each rank 1 array is defined by the outer product of three vectors a r b r and c r i e y ijk r a i r b j r c k t these vectors make up the r columns of the component matrices a b and c if 2r 2 is less than or equal to the sum of the k ranks of a b and c then the fitted part of the decomposition is unique up to a change in the order of the rank 1 arrays and rescaling counterscaling of each triplet of vectors a r b r c r forming a rank 1 array this classical result was shown by kruskal his proof is however rather inaccessible and does not seem intuitive in order to contribute to a better understanding of cp uniqueness this paper provides an accessible and intuitive proof of kruskal s condition the proof is both self contained and compact and can easily be adapted for the complex valued cp decomposition c 2006 elsevier inc all rights reserved

decoupled schemes for unsteady mhd equations ii finite element spatial discretization and numerical implementation in this article a decoupled fully discrete scheme for solving 2d magnetohydrodynamics mhd equations is proposed the decoupled scheme is used for time discretization and the finite element method is used for spatial discretization firstly the almost unconditional stability t c of this scheme is established then optimal l2 and h1 error estimates of numerical solution are provided finally a numerical example is presented to confirm our theoretical results and show the high efficiency of the decoupled scheme

a least squares finite element method using elsasser variables for magnetohydrodynamic equations abstract there are various different forms of magnetohydrodynamic mhd equations and they have been studied for years due to its complicated coupling between variables this paper proposes to use an equivalently transformed mhd equations with elsasser variables and the least squares finite element method to find the approximation to them introducing new variables by combining fluid velocity and magnetic field yields a navier stokes like system then the first order system least squares method using displacement recasts the transformed mhd equations into a system of first order partial differential equations and the newton s algorithm linearizes the problem an l 2 residual functional is defined to minimize and the unique existence of corresponding weak solution is shown finally the convergence of proposed approximation is analyzed and several numerical examples are presented to verify the theory

on conforming finite element methods for the inhomogeneous stationary navier stokes equations we consider the stationary navier stokes equations written in terms of the primitive variables in the case where both the partial differential equations and boundary conditions are inhomogeneous under certain conditions on the data the existence and uniqueness of the solution of a weak formulation of the equations can be guaranteed a conforming finite element method is presented and optimal estimates for the error of the approximate solution are proved in addition the convergence properties of iterative methods for the solution of the discrete nonlinear algebraic systems resulting from the finite element algorithm are given numerical examples using an efficient choice of finite element spaces are also provided

a new family of mixed finite elements in ir 3 we introduce two families of mixed finite element on conforming inh div and one conforming inh curl these finite elements can be used to approximate the stokes system

iterative methods in penalty finite element discretization for the steady mhd equations this paper characterizes one penalty finite element method for the incompressible mhd equations the method is an interesting combination of the classic iterative schemes stokes newton and oseen iterations with two different finite element pairs p1b p1 p1b and p1 p0 p1 moreover the rigorous analysis of stability and error estimate for the proposed methods are given finally the applicability and effectiveness of the presented schemes are illustrated in several numerical experiments

a robust solver for the finite element approximation of stationary incompressible mhd equations in 3d abstract in this paper we propose a newton krylov solver and a picard krylov solver for finite element discrete problem of stationary incompressible magnetohydrodynamic equations in three dimensions using a mixed finite element method we discretize the velocity and the pressure by h 1 conforming finite elements and discretize the magnetic field by h curl conforming edge elements an efficient preconditioner is proposed to accelerate the convergence of gmres method for solving linearized discrete problems by extensive numerical experiments we demonstrate the robustness of the newton krylov solver for relatively large physical parameters and the optimality with respect to the number of degrees of freedom moreover the numerical experiments show that the newton krylov solver is more robust than the picard krylov solver for large reynolds number

multigrid in h div and h curl summary we consider the solution of systems of linear algebraic equations which arise from the finite element discretization of variational problems posed in the hilbert spaces bf h div and bf h curl in three dimensions we show that if appropriate finite element spaces and appropriate additive or multiplicative schwarz smoothers are used then the multigrid v cycle is an efficient solver and preconditioner for the discrete operator all results are uniform with respect to the mesh size the number of mesh levels and weights on the two terms in the inner products

analysis of a semi implicit structure preserving finite element method for the nonstationary incompressible magnetohydrodynamics equations abstract we revise the structure preserving finite element method in k hu y ma and j xu 2017 stable finite element methods preserving b 0 exactly for mhd models numer math 135 371 396 the revised method is semi implicit in time discretization we prove the linearized scheme preserves the divergence free property for the magnetic field exactly at each time step further we showed the linearized scheme is unconditionally stable and we obtain optimal convergence in the energy norm of the revised method even for solutions with low regularity

the architecture of complex weighted networks networked structures arise in a wide array of different contexts such as technological and transportation infrastructures social phenomena and biological systems these highly interconnected systems have recently been the focus of a great deal of attention that has uncovered and characterized their topological complexity along with a complex topological structure real networks display a large heterogeneity in the capacity and intensity of the connections these features however have mainly not been considered in past studies where links are usually represented as binary states i e either present or absent here we study the scientific collaboration network and the world wide air transportation network which are representative examples of social and large infrastructure systems respectively in both cases it is possible to assign to each edge of the graph a weight proportional to the intensity or capacity of the connections among the various elements of the network we define appropriate metrics combining weighted and topological observables that enable us to characterize the complex statistical properties and heterogeneity of the actual strength of edges and vertices this information allows us to investigate the correlations among weighted quantities and the underlying topological structure of the network these results provide a better description of the hierarchies and organizational principles at the basis of the architecture of weighted networks

optimal control for a stationary mhd system in velocity current formulation an optimal control problem for the equations governing the stationary problem of magnetohydrodynamics mhd is considered control mechanisms by external and injected currents and magnetic fields are treated an optimal control problem is formulated first order necessary and second order sufficient conditions are developed an operator splitting scheme for the numerical solution of the mhd state equations is analyzed

approximation of the inductionless mhd problem using a stabilized finite element method in this work we present a stabilized formulation to solve the inductionless magnetohydrodynamic mhd problem using the finite element fe method the mhd problem couples the navier stokes equations and a darcy type system for the electric potential via lorentz s force in the momentum equation of the navier stokes equations and the currents generated by the moving fluid in ohm s law the key feature of the fe formulation resides in the design of the stabilization terms which serve several purposes first the formulation is suitable for convection dominated flows second there is no need to use interpolation spaces constrained to a compatibility condition in both sub problems and therefore equal order interpolation spaces can be used for all the unknowns finally this formulation leads to a coupled linear system this monolithic approach is effective since the coupling can be dealt by effective preconditioning and iterative solvers that allows to deal with high hartmann numbers

analysis of coupling iterations based on the finite element method for stationary magnetohydrodynamics on a general domain this paper considers finite element approximation and three coupled type iterations of stationary magnetohydrodynamics mhd equations on a general lipschitz domain an additional lagrange multiplier r is introduced related to divergence free of magnetic field b and the b is analyzed in h curl space which is proposed in schotzau 2004 in finite element discretization the hydrodynamic unknowns are approximated by stable finite element pairs and the magnetic unknown is discretized by curl conforming nedelec element spaces the well posedness of this formula and the optimal error estimate are provided based on this for numerical implementation of this scheme we propose and discuss three coupled type iterative methods which are stable and convergent under different conditions specifically iteration i is stable and convergent under strong condition iteration ii is stable and convergent under weaker condition iteration iii is unconditionally stable and convergent under the weakest condition finally some numerical tests confirm our theoretical analysis

an optimal domain decomposition preconditioner for low frequency time harmonic maxwell equations the time harmonic maxwell equations are considered in the low frequency case a finite element domain decomposition approach is proposed for the numerical approximation of the exact solution this leads to an iteration by subdomain procedure which is proven to converge the rate of convergence turns out to be independent of the mesh size showing that the preconditioner implicitly defined by the iterative procedure is optimal for obtaining this convergence result it has been necessary to prove a regularity theorem for dirichlet and neumann harmonic fields

on an unconditionally convergent stabilized finite element approximation of resistive magnetohydrodynamics in this work we propose a new stabilized finite element formulation for the approximation of the resistive magnetohydrodynamics equations the novelty of this formulation is the fact that it always converges to the physical solution even for singular ones a detailed set of numerical experiments have been performed in order to validate our approach

a semi implicit energy conserving finite element method for the dynamical incompressible magnetohydrodynamics equations abstract we present and analyze a semi implicit finite element method fem for the dynamical incompressible magnetohydrodynamics mhd equations the finite element approximation is based on mixed conforming elements where taylor hood type elements are used for the navier stokes equations and nedelec edge elements are used for the magnetic equation the divergence free conditions are weakly satisfied at the discrete level due to the use of nedelec edge element the proposed method is particularly suitable for problems defined on non smooth and multi connected domains for the temporal discretization we use a semi implicit scheme which only needs to solve a linear system at each time step moreover the linearized mixed fem is energy conserving we establish an optimal error estimate under a very low assumption on the exact solutions and domain geometries numerical results are provided to show its effectiveness and verify the theoretical analysis in particular a benchmark lid driven cavity problem is provided to show that the proposed numerical method produces results as good as that of the ones which are divergence free

a centrality measure for communication ability in weighted network abstract this paper proposes a new node centrality measurement in a weighted network the communication centrality which is inspired by hirsch s h index we investigated the properties of the communication centrality and proved that the distribution of the communication centrality has the power law upper tail in weighted scale free networks relevant measures for node and network are discussed as extensions a case study of a scientific collaboration network indicates that the communication centrality is different from other common centrality measures and other h type indexes communication centrality displays moderate correlation with other indexes and contains a well balanced mix of other centrality measures and cannot be replaced by any of them

lobby index in networks abstract we propose a new node centrality measure in networks the lobby index which is inspired by hirsch s h index it is shown that in scale free networks with exponent the distribution of the l index has power tail with exponent 1 properties of the l index and extensions are discussed

weighted regularization of maxwell equations in polyhedral domains we present a new method of regularizing time harmonic maxwell equations by a bf grad div term adapted to the geometry of the domain this method applies to polygonal domains in two dimensions as well as to polyhedral domains in three dimensions in the presence of reentrant corners or edges the usual regularization is known to produce wrong solutions due the non density of smooth fields in the variational space we get rid of this undesirable effect by the introduction of special weights inside the divergence integral standard finite elements can then be used for the approximation of the solution this method proves to be numerically efficient

two level penalty finite element methods for the stationary incompressible magnetohydrodynamics problem in the paper we consider the penalty finite element method for the stationary incompressible magnetohydrodynamics mhd problem with a factor of penalty parameter stability and convergence of numerical solutions are established furthermore two level penalty methods are also developed for the mhd problem our methods consist of solving a nonlinear mhd problem by the usual penalty method on a coarse mesh with mesh size h and then a linearized mhd problem based on the stokes newton and oseen iterations on a fine mesh is solved by the penalty method with mesh size h h h respectively stability and error estimates of numerical solutions in two level penalty methods are presented finally some numerical tests are provided to demonstrate the effectiveness of the developed algorithms

a mixed finite element method with exactly divergence free velocities for incompressible magnetohydrodynamics abstract we introduce and analyze a mixed finite element method for the numerical discretization of a stationary incompressible magnetohydrodynamics problem in two and three dimensions the velocity field is discretized using divergence conforming brezzi douglas marini bdm elements and the magnetic field is approximated by curl conforming nedelec elements the h 1 continuity of the velocity field is enforced by a dg approach a central feature of the method is that it produces exactly divergence free velocity approximations and captures the strongest magnetic singularities we prove that the energy norm error is convergent in the mesh size in general lipschitz polyhedra under minimal regularity assumptions and derive nearly optimal a priori error estimates for the two dimensional case we present a comprehensive set of numerical experiments which indicate optimal convergence of the proposed method for two dimensional as well as three dimensional problems

an efficient two step algorithm for the stationary incompressible magnetohydrodynamic equations a new highly efficient two step algorithm for the stationary incompressible magnetohydrodynamic equations is studied in this paper the algorithm uses a lower order finite element pair i e p 1 b p 1 p 1 to compute an initial approximation that is using the mini element i e p 1 b p 1 to approximate the velocity and pressure and p1 element to approximate the magnetic field then applies a higher order finite element pair i e p 2 p 1 p 2 to solve a linear system on the same mesh furthermore the convergence analyses of standard galerkin finite element method and the two step algorithm are addressed lastly numerical experiments are presented to verify both the theory and the efficiency of the algorithm

performance and analysis of saddle point preconditioners for the discrete steady state navier stokes equations we examine the convergence characteristics of iterative methods based on a new preconditioning operator for solving the linear systems arising from discretization and linearization of the steady state navier stokes equations with a combination of analytic and empirical results we study the effects of fundamental parameters on convergence we demonstrate that the preconditioned problem has an eigenvalue distribution consisting of a tightly clustered set together with a small number of outliers the structure of these distributions is independent of the discretization mesh size but the cardinality of the set of outliers increases slowly as the viscosity becomes smaller these characteristics are directly correlated with the convergence properties of iterative solvers

optimal energy conserving local discontinuous galerkin methods for second order wave equation in heterogeneous media abstract solving wave propagation problems within heterogeneous media has been of great interest and has a wide range of applications in physics and engineering the design of numerical methods for such general wave propagation problems is challenging because the energy conserving property has to be incorporated in the numerical algorithms in order to minimize the phase or shape errors after long time integration in this paper we focus on multi dimensional wave problems and consider linear second order wave equation in heterogeneous media we develop and analyze an ldg method in which numerical fluxes are carefully designed to maintain the energy conserving property and accuracy compatible high order energy conserving time integrators are also proposed the optimal error estimates and the energy conserving property are proved for the semi discrete methods our numerical experiments demonstrate optimal rates of convergence and show that the errors of the numerical solutions do not grow significantly in time due to the energy conserving property

robust preconditioners for incompressible mhd models in this paper we develop two classes of robust preconditioners for the structure preserving discretization of the incompressible magnetohydrodynamics mhd system by studying the well posedness of the discrete system we design block preconditioners for them and carry out rigorous analysis on their performance we prove that such preconditioners are robust with respect to most physical and discretization parameters in our proof we improve the existing estimates of the block triangular preconditioners for saddle point problems by removing the scaling parameters which are usually difficult to choose in practice this new technique is applicable not only to the mhd system but also to other problems moreover we prove that krylov iterative methods with our preconditioners preserve the divergence free condition exactly which complements the structure preserving discretization another feature is that we can directly generalize this technique to other discretizations of the mhd system we also present preliminary numerical results to support the theoretical results and demonstrate the robustness of the proposed preconditioners

a fused cp factorization method for incomplete tensors low rank tensor completion methods have been advanced recently for modeling sparsely observed data with a multimode structure however low rank priors may fail to interpret the model factors of general tensor objects the most common method to address this drawback is to use regularizations together with the low rank priors however due to the complex nature and diverse characteristics of real world multiway data the use of a single or a few regularizations remains far from efficient and there are limited systematic experimental reports on the advantages of these regularizations for tensor completion to fill these gaps we propose a modified cp tensor factorization framework that fuses the l 2 norm constraint sparseness l 1 norm manifold and smooth information simultaneously the factorization problem is addressed through a combination of nesterov s optimal gradient descent method and block coordinate descent here we construct a smooth approximation to the l 1 norm and tv norm regularizations and then the tensor factor is updated using the projected gradient method where the step size is determined by the lipschitz constant extensive experiments on simulation data visual data completion intelligent transportation systems and gps data of user involvement are conducted and the efficiency of our method is confirmed by the results moreover the obtained results reveal the characteristics of these commonly used regularizations for tensor completion in a certain sense and give experimental guidance concerning how to use them