conjugate gradient projection subspace tracking in this correspondence we develop a new subspace tracking algorithm called the conjugate gradient projection subspace tracker cgpst the algorithm is based on a recently introduced rls like subspace cost function which we recursively minimize using conjugate gradient iterations subspace averaging concepts are used to produce an o r sup 2 m algorithm that updates an r dimensional subspace of c sup m the algorithm is parallelizable rapidly convergent numerically stable and computationally efficient simulation studies test the algorithm s performance and show it to compare favorably with other subspace trackers

estimating the covariance matrix by signal subspace averaging an efficient algorithm is presented for estimating a covariance matrix consisting of a low rank signal term and a full rank noise term known apart from a scalar factor for each sample of the vector of sensor outputs the algorithm approximates in the least squares sense a rank one update of the covariance matrix under the side condition that the rank of the signal term remains bounded if the model noise is spatially colored the least squares approximation is preceded by spatial prewhitening it is shown that if the rank of the signal term is small compared to the number of sensors then the proposed algorithm requires substantially less computational work than conventional averaging some simulation results are included indicating that the proposed algorithm reduces the variance of some commonly used spectral estimators in off target directions without impairing their detection and resolution properties

stable cell centered finite volume discretization for biot equations in this paper we discuss a new discretization for the biot equations the discretization treats the coupled system of deformation and flow directly as opposed to combining discretizations for the two separate subproblems the coupled discretization has the following key properties the combination of which is novel 1 the variables for the pressure and displacement are co located and are as sparse as possible e g one displacement vector and one scalar pressure per cell center 2 with locally computable restrictions on grid types the discretization is stable with respect to the limits of incompressible fluid and small time steps 3 no artificial stabilization term has been introduced furthermore due to the finite volume structure embedded in the discretization explicit local expressions for both momentum balancing forces and mass conservative fluid fluxes are available we prove stability of the proposed method with respect to all relevant limits together with consistency this proves conve

a linear quadratic control problem for the stochastic heat equation driven by q wiener processes abstract we consider a control problem for the stochastic heat equation with neumann boundary condition where controls and noise terms are defined inside the domain as well as on the boundary the noise terms are given by independent q wiener processes under some assumptions we derive necessary and sufficient optimality conditions stochastic controls have to satisfy using these optimality conditions we establish explicit formulas with the result that stochastic optimal controls are given by feedback controls this is an important conclusion to ensure that the controls are adapted to a certain filtration therefore the state is an adapted process as well

diffusion in poro elastic media existence uniqueness and regularity theory is developed for a general initial boundary value problem for a system of partial differential equations which describes the biot consolidation model in poro elasticity as well as a coupled quasi static problem in thermoelasticity additional effects of secondary consolidation and pore fluid exposure on the boundary are included this quasi static system is resolved as an application of the theory of linear degenerate evolution equations in hilbert space and this leads to a precise description of the dynamics of the system

an lq problem for the heat equation on the halfline with dirichlet boundary control and noise we study a linear quadratic problem for a system governed by the heat equation on a halfline with boundary control and dirichlet boundary noise we show that this problem can be reformulated as a stochastic evolution equation in a certain weighted l 2 space an appropriate choice of weight allows us to prove a stronger regularity for the boundary terms appearing in the infinite dimensional state equation the direct solution of the riccati equation related to the associated nonstochastic problem is used to find the solution of the problem in feedback form and to write the value function of the problem

gauss markov processes on hilbert spaces k it o characterised in 16 zero mean stationary gauss markov processes evolving on a class of innite dimension al spaces in this work we extend the work of it o in the case of hilbert spaces gauss markov families that are time homogenous are identied as solutions to linear stochastic dierential equations with singular coecients choosing an appropriate locally convex topology on the space of weakly sequentially continuous functions we also characterize the transition semigroup the generator and its core thus providing an innite dimension al extension of the classical result of courr ege 4 in the case of gauss markov semigroups

a multipoint flux mixed finite element method we develop a mixed finite element method for single phase flow in porous media that reduces to cell centered finite differences on quadrilateral and simplicial grids and performs well for discontinuous full tensor coefficients motivated by the multipoint flux approximation method where subedge fluxes are introduced we consider the lowest order brezzi douglas marini bdm mixed finite element method a special quadrature rule is employed that allows for local velocity elimination and leads to a symmetric and positive definite cell centered system for the pressures theoretical and numerical results indicate second order convergence for pressures at the cell centers and first order convergence for subedge fluxes second order convergence for edge fluxes is also observed computationally if the grids are sufficiently regular

a coupled multipoint stress multipoint flux mixed finite element method for the biot system of poroelasticity abstract we present a mixed finite element method for a five field formulation of the biot system of poroelasticity that reduces to a cell centered pressure displacement system on simplicial and quadrilateral grids a mixed stress displacement rotation formulation for elasticity with weak stress symmetry is coupled with a mixed velocity pressure darcy formulation the spatial discretization is based on combining the multipoint stress mixed finite element msmfe method for elasticity and the multipoint flux mixed finite element mfmfe method for darcy flow it uses the lowest order brezzi douglas marini mixed finite element spaces for the poroelastic stress and darcy velocity piecewise constant displacement and pressure and continuous piecewise linear or bilinear rotation a vertex quadrature rule is applied to the velocity stress and stress rotation bilinear forms which block diagonalizes the corresponding matrices and allows for local velocity stress and rotation elimination this leads to a cell centered positive definite system for pressure and displacement at each time step we perform error analysis for the semidiscrete and fully discrete formulations establishing first order convergence for all variables in their natural norms the numerical tests confirm the theoretical convergence rates and illustrate the locking free property of the method

mixed methods for elastodynamics with weak symmetry we analyze the application to elastodynamic problems of mixed finite element meth ods for elasticity with weakly imposed symmetry of stress our approach leads to a semidiscrete method which consists of a system of ordinary differential equations without algebraic constraints our error analysis which is based on a new elliptic projection operator applies to several mixed finite element spaces developed for elastostatics the error estimates we obtain are robust for nearly incompressible materials

gradient type algorithms for partial singular value decomposition it is often desirable to calculate only a few terms of the svd expansion of a matrix corresponding to the largest or smallest singular values two algorithms based on gradient and conjugate gradient search are proposed for this purpose svd is computed term by term in a decreasing or increasing order of singular values the algorithms are simple to implement and are especially advantageous with large matrices

analysis of conjugate gradient algorithms for adaptive filtering the paper presents and analyzes two approaches to the implementation of the conjugate gradient cg algorithm for filtering where several modifications to the original cg method are proposed the convergence rates and misadjustments for the two approaches are compared an analysis in the z domain is used in order to find the asymptotic performance and stability bounds are established the behavior of the algorithms in finite word length computation are described and dynamic range considerations are discussed it is shown that in finite word length computation and close to steady state the algorithms behaviors are similar to the steepest descent algorithm where the stalling phenomenon is observed using 16 bit fixed point number representation our simulations show that the algorithms are numerically stable

a posteriori dual mixed adaptive finite element error control for lame and stokes equations a unified and robust mathematical model for compressible and incompressible linear elasticity can be obtained by rephrasing the herrmann formulation within the hellinger reissner principle this quasi optimally converging extension of peers plane elasticity element with reduced symmetry is called dual mixed hybrid formulation dmh explicit residual based a posteriori error estimates for dmh are introduced and are mathematically shown to be locking free reliable and efficient the estimator serves as a refinement indicator in an adaptive algorithm for effective automatic mesh generation numerical evidence supports that the adaptive scheme leads to optimal convergence for lame and stokes benchmark problems with singularities

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

review and complements on mixed hybrid finite element methods for fluid flows mixed and hybrid finite element methods for the resolution of a wide range of linear and nonlinear boundary value problems linear elasticity stokes problem navier stokes equations boussinesq equations etc have known a great development in the last few years these methods allow simultaneous computation of the original variable and its gradient both of them being equally accurate moreover they have local conservation properties conservation of the mass and the momentum as in the finite volume methods the purpose of this paper is to give a review on some mixed finite elements developed recently for the resolution of stokes and navier stokes equations and the linear elasticity problem further developments for a quasi newtonian flow obeying the power law are presented

inf sup conditions for twofold saddle point problems necessary and sufficient conditions for existence and uniqueness of solutions are developed for twofold saddle point problems which arise in mixed formulations of problems in continuum mechanics this work extends the classical saddle point theory to accommodate nonlinear constitutive relations and the twofold saddle structure application to problems in incompressible fluid mechanics employing symmetric tensor finite elements for the stress approximation is presented

bi iterative least square method for subspace tracking subspace tracking is an adaptive signal processing technique useful for a variety of applications in this paper we introduce a simple bi iterative least square bi ls method which is in contrast to the bi iterative singular value decomposition bi svd method we show that for subspace tracking the bi ls method is easier to simplify than the bi svd method the linear complexity algorithms based on bi ls are computationally more efficient than the existing linear complexity algorithms based on bi svd although both have the same performance for subspace tracking a number of other existing subspace tracking algorithms of similar complexity are also compared with the bi ls algorithms

a dual purpose principal and minor subspace gradient flow the dual purpose principal and minor subspace gradient flow can be used to track principal subspace ps and if altered simply by the sign it can also serve as a minor subspace ms trackor this is of practical significance in the implementations of algorithms in this paper a unified information criterion is proposed and a dual purpose principal and minor subspace gradient flow is derived based on the information criterion in this dual purpose gradient flow the weight matrix length is self stabilizing i e moving towards unit length in each learning step the energy function associated with the dual purpose gradient flow for tracking ps and ms is given and it exhibits a unique global minimum attained if and only if its state matrices span the ps or ms of the autocorrelation matrix of a vector data stream the other stationary points of its energy function are unstable saddle points the proposed dual purpose gradient flow can efficiently track an orthonormal basis of the ps or ms which is illustrated through simulation experiments

conjugate gradient eigenstructure tracking for adaptive spectral estimation a conjugate gradient iteration is derived that converges to the set of r dominant subdominant eigenpairs this iteration is used to construct two eigenstructure tracking algorithms that track the r dimensional dominant or subdominant subspaces of time varying data or data covariance matrices the two eigenstructure tracking algorithms have update complexities o m sup 2 r and the other o mr sup 2 where m is the data dimension the algorithms are customized to solve high resolution temporal and spatial frequency tracking problems they are compared with existing techniques by tying into published simulation based performance tests the algorithms demonstrate rapid convergence and tracking characteristics at a competitive cost

finite volume methods for elasticity with weak symmetry we introduce a new cell centered finite volume discretization for elasticity with weakly enforced symmetry of the stress tensor the method is motivated by the need for robust discretization methods for deformation and flow in porous media and falls in the category of multi point stress approximations mpsa by enforcing symmetry weakly the resulting method has additional flexibility beyond previous mpsa methods this allows for a construction of a method which is applicable to all grid types and in particular the method amends a crucial shortcoming in previous mpsa methods for simplex grids by formulating the method as a discrete variational problem we prove convergence of the new method for a wide range of problems with conditions that can be verified at the time of discretization we present the first set of comprehensive numerical tests for the mpsa methods in three dimensions covering cartesian and simplex grids with both heterogeneous and nearly incompressible media the tests show that the new method consistently is second order convergent in displacement despite being lowest order with a rate that mostly is between 1 and 2 for stresses the results further show that the new method is more robust and computationally cheaper than previous mpsa methods

a discontinuous petrov galerkin method with lagrangian multipliers for second order elliptic problems we present a discontinuous petrov galerkin dpg method for the finite element discretization of second order elliptic boundary value problems the novel approach emanates from a one element weak formulation of the differential problem this procedure which is typical of discontinuous galerkin dg methods is based on introducing variables defined in the interior and on the boundary of the element the interface variables are suitable lagrangian multipliers that enforce interelement continuity of the solution and of its normal derivative thus providing the proper connection between neighboring elements the internal variables can be eliminated in favor of the interface variables using static condensation to end up with a system of reduced size in the sole lagrangian multipliers a stability and convergence analysis of the novel formulation is carried out and its connection with mixed hybrid and dg methods is explored numerical tests on several benchmark problems are included to validate the convergence performance and the flux conservation properties of the dpg method

quadrilateral h div finite elements we consider the approximation properties of quadrilateral finite element spaces of vector fields defined by the piola transform extending results previously obtained for scalar approximation the finite element spaces are constructed starting with a given finite dimensional space of vector fields on a square reference element which is then transformed to a space of vector fields on each convex quadrilateral element via the piola transform associated to a bilinear isomorphism of the square onto the element for affine isomorphisms a necessary and sufficient condition for approximation of order r 1 in l2 is that each component of the given space of functions on the reference element contain all polynomial functions of total degree at most r in the case of bilinear isomorphisms the situation is more complicated and we give a precise characterization of what is needed for optimal order l2 approximation of the function and of its divergence as applications we demonstrate degradation of the convergence order on quadrilateral meshes as compared to rectangular meshes for some standard finite element approximations of h div we also derive new estimates for approximation by quadrilateral raviart thomas elements requiring less regularity and propose a new quadrilateral finite element space which provides optimal order approximation in h div finally we demonstrate the theory with numerical computations of mixed and least squares finite element approximations of the solution of poisson s equation

an updating algorithm for subspace tracking in certain signal processing applications it is required to compute the null space of a matrix whose rows are samples of a signal with p components the usual tool for doing this is the singular value decomposition however the singular value decomposition has the drawback that it requires o p sup 3 operations to recompute when a new sample arrives it is shown that a different decomposition called the urv decomposition is equally effective in exhibiting the null space and can be updated in o p sup 2 time the updating technique can be run on a linear array of p processors in o p time

plane rotation based evd updating schemes for efficient subspace tracking we present new algorithms based on plane rotations for tracking the eigenvalue decomposition evd of a time varying data covariance matrix these algorithms directly produce eigenvectors in orthonormal form and are well suited for the application of subspace methods to nonstationary data after recasting evd tracking as a simplified rank one evd update problem computationally efficient solutions are obtained in two steps first a new kind of parametric perturbation approach is used to express the eigenvector update as an unimodular orthogonal transform which is represented in exponential matrix form in terms of a reduced set of small unconstrained parameters second two approximate decompositions of this exponential matrix into products of plane or givens rotations are derived one of which being previously unknown these decompositions lead to new plane rotation based evd updating schemes proteus whose main feature is the use of plane rotations for updating the eigenvectors thereby preserving orthonormality finally the proteus schemes are used to derive new evd trackers whose convergence and numerical stability are investigated via simulations one algorithm can track all the signal subspace evd components in only o lm operations where l and m respectively denote the data vector and signal subspace dimensions while achieving a performance comparable to an exact evd approach and maintaining perfect orthonormality of the eigenvectors the new algorithms show no signs of error buildup

adaptive eigensubspace algorithms for direction or frequency estimation and tracking the authors present an adaptive estimator of the complete noise or signal subspace of a sample covariance matrix as well as the estimator s practical implementations the general formulation of the proposed estimator results from an asymptotic argument which shows the signal or noise subspace computation to be equivalent to a constrained gradient search procedure a highly parallel algorithm denoted the inflation method is introduced for the estimation of the noise subspace the simulation results of these adaptive estimators show that the adaptive subspace algorithms perform substantially better than p a thompson s 1980 adaptive version of v f pisarenko s technique 1973 in estimating frequencies or directions of arrival doa of plane waves for tracking nonstationary parameters the simulation results also show that the adaptive subspace algorithms are better than direct eigendecomposition methods for which computational complexity is much higher than the adaptive versions

some history of the conjugate gradient and lanczos methods this paper gives some of the history of the conjugate gradient and lanczos algorithms and an annotated bibliography for the period 1948 1976

stability and monotonicity for some discretizations of the biot s consolidation model abstract we consider finite element discretizations of the biot s consolidation model in poroelasticity with mini and stabilized p1 p1 elements we analyze the convergence of the fully discrete model based on spatial discretization with these types of finite elements and implicit euler method in time we also address the issue related to the presence of non physical oscillations in the pressure approximation for low permeabilities and or small time steps we show that even in 1d a stokes stable finite element pair fails to provide a monotone discretization for the pressure in such regimes we then introduce a stabilization term which removes the oscillations we present numerical results confirming the monotone behavior of the stabilized schemes

a new mixed finite element method for the stokes problem we propose a new mixed formulation of the stokes problem where the extra stress tensor is considered based on such a formulation a mixed finite element is constructed and analyzed this new finite element has properties analogous to the finite volume methods namely the local conservation of the momentum and the mass optimal error estimates are derived for the numerical implementation of this finite element a hybrid form is presented this work is a first step towards the treatment of viscoelastic fluid flows by mixed finite element methods

stabilization of stochastic parabolic equations with boundary noise and boundary control abstract we consider here a state equation of parabolic type on a bounded real interval with neumann boundary conditions consisting in the sum of the control and of a white noise in time we design a simple form easily numerically implementable feedback law that assures the exponential stability in probability of the a given equilibrium solution the form of the feedback involves only the eigenfunctions of the linear operator of the linearized equation

on the existence of optimal controls for spdes with boundary noise and boundary control we consider a stochastic optimal control problem for a heat equation with boundary noise and boundary control under suitable assumptions on the coefficients we prove existence of optimal controls in a strong sense by solving the related stochastic hamiltonian system

a multipoint flux mixed finite element method on distorted quadrilaterals and hexahedra in this paper we develop a new mixed finite element method for elliptic problems on general quadrilateral and hexahedral grids that reduces to a cell centered finite difference scheme a special non symmetric quadrature rule is employed that yields a positive definite cell centered system for the pressure by eliminating local velocities the method is shown to be accurate on highly distorted rough quadrilateral and hexahedral grids including hexahedra with non planar faces theoretical and numerical results indicate first order convergence for the pressure and face fluxes

a least squares mixed finite element method for biot s consolidation problem in porous media a least squares mixed finite element method for the coupled problem of flow and deformation is presented and analyzed in this paper for the analysis we restrict ourselves to fully saturated conditions for the flow process and to a linearly elastic material law for the deformation process this is known in the literature as biot s consolidation problem for simplicity the analysis is presented for the problem in two space dimensions our least squares approach is motivated by the fact that all process variables i e fluid pressure and flux as well as displacement field and stress tensor are approximated directly by suitable finite element spaces ellipticity of the corresponding variational formulation is proven for the stationary case as well as for the subproblems arising at each step of an implicit time discretization in the general time dependent case standard h1 conforming piecewise linear and quadratic finite elements are used for the fluid pressure and for each component of the displacement respectively for the flux and stress components the h div conforming raviart thomas spaces of lowest order are used computational results are presented for some two dimensional test problems

efficient numerically stabilized rank one eigenstructure updating signal processing rank one eigenvalue decomposition evd updating is well suited to the problem of tracking time varying subspaces previously published rank one evd updating algorithms suffer from a linear buildup of roundoff error which makes them impractical for a large number of recursive updates in the present work the authors develop a numerical stabilization technique which eliminates the error buildup problem in a computationally efficient manner and makes the rank one evd update a practical numerical tool for online computation a simplified eigenvalue iteration is also given it reduces the complexity of the algorithm somewhat as well as the computation time simulations are presented to illustrate numerical performance

locking free finite element methods for poroelasticity we propose a new formulation along with a family of finite element schemes for the approximation of the interaction between fluid motion and linear mechanical response of a porous medium known as biot s consolidation problem the steady state version of the system is recast in terms of displacement pressure and volumetric stress and both continuous and discrete formulations are analyzed as compact perturbations of invertible problems employing a fredholm argument in particular the error estimates are derived independently of the lame constants numerical results indicate the satisfactory performance and competitive accuracy of the introduced methods

generalized eigenspace beamformer based on cg lanczos algorithm the generalized eigenspace beamformer geib has been presented as an efficient way to build a beamformer robust to calibration and pointing errors its main drawback is the great computational cost needed to develop the whole structure mainly associated to obtaining the projection matrix in this paper the relation between conjugate gradient and lanczos algorithm is used to modify the conjugate gradient algorithm robust conjugate gradient method rcgm so the eigenstructure of the correlation matrix can be obtained directly the numerical problems associated to the loss of orthogonality in successive gradient vectors have also been overcome via selective orthogonalization so in this way the proposed rcgm is also robust to numerical problems the overall computational cost in the construction of the geib has been reduced from o n sup 3 n sup 2 to o 3n sup 2 by using the rcgm instead of a conventional projection algorithm computer simulations are also presented to demonstrate the merits of the algorithm

a multipoint flux mixed finite element method on hexahedra we develop a mixed finite element method for elliptic problems on hexahedral grids that reduces to cell centered finite differences the paper is an extension of our earlier paper for quadrilateral and simplicial grids m f wheeler and i yotov siam j numer anal 44 2006 pp 2082 2106 the construction is motivated by the multipoint flux approximation method and it is based on an enhancement of the lowest order brezzi douglas duran fortin bddf mixed finite element spaces on hexahedra in particular there are four fluxes per face one associated with each vertex a special quadrature rule is employed that allows for local velocity elimination and leads to a symmetric and positive definite cell centered system for the pressures theoretical and numerical results indicate first order convergence for pressures and subface fluxes on sufficiently regular grids as well as second order convergence for pressures at the cell centers second order convergence for face fluxes is also observed computationally

a unified self stabilizing neural network algorithm for principal and minor components extraction recently many unified learning algorithms have been developed for principal component analysis and minor component analysis these unified algorithms can be used to extract principal components and if altered simply by the sign can also serve as a minor component extractor this is of practical significance in the implementations of algorithms this paper proposes a unified self stabilizing neural network learning algorithm for principal and minor components extraction and studies the stability of the proposed unified algorithm via the fixed point analysis method the proposed unified self stabilizing algorithm for principal and minor components extraction is extended for tracking the principal subspace ps and minor subspace ms the averaging differential equation and the energy function associated with the unified algorithm for tracking ps and ms are given it is shown that the averaging differential equation will globally asymptotically converge to an invariance set and the corresponding energy function exhibit a unique global minimum attained if and only if its state matrices span the ps or ms of the autocorrelation matrix of a vector data stream it is concluded that the proposed unified algorithm for tracking ps and ms can efficiently track an orthonormal basis of the ps or ms simulations are carried out to further illustrate the theoretical results achieved

two families of mixed finite elements for second order elliptic problems two families of mixed finite elements one based on triangles and the other on rectangles are introduced as alternatives to the usual raviart thomas nedelec spaces error estimates inl 2 andh 5 are derived for these elements a hybrid version of the mixed method is also considered and some superconvergence phenomena are discussed

adaptation dynamics of the spherical subspace tracker l ljung s 1977 method for analyzing recursive stochastic algorithms is used to formulate a projection operator ordinary differential equation ode the ode describes the expected convergence dynamics of a noniterative spherical subspace tracker the subspace ode is a riccati equation defined over the manifold of rank r projection matrices in c sup nxn a lyapunov function is defined that is shown to have global maximum and minimum at the signal and noise subspaces respectively by taking a derivative of the lyapunov function along any trajectory it is shown that the dynamics force all trajectories to converge to the signal subspace if the sign of the derivative is changed all trajectories will converge to the noise subspace

efficient high performance subspace tracking for time domain data this paper describes two new algorithms for tracking the subspace spanned by the principal eigenvectors of the correlation matrix associated with time domain i e time series data the algorithms track the d principal n dimensional eigenvectors of the data covariance matrix with a complexity of o nd sup 2 yet they have performance comparable with algorithms having o n sup 2 d complexity the computation reduction is achieved by exploiting the shift invariance property of temporal data covariance matrices experiments are used to compare our algorithms with other well known approaches of similar and or lower complexity our new algorithms are shown to outperform the subset of the general approaches having the same complexity the new algorithms are useful for applications such as subspace based speech enhancement and low rank adaptive filtering

discretization on unstructured grids for inhomogeneous anisotropic media part i derivation of the methods discretization methods are proposed for control volume formulations on polygonal and triangular grid cells in two space dimensions the methods are applicable for any system of conservation laws where the flow density is defined by a gradient law like darcy s law for porous media flow a strong feature of the methods is the ability to handle media inhomogeneities in combination with full tensor anisotropy this paper gives a derivation of the methods and the relation to previously published methods is also discussed a further discussion of the methods including numerical examples is given in the companion paper part ii siam j sci comput pp 1717 1736

new stabilized discretizations for poroelasticity and the stokes equations in this work we consider the popular p1 rt0 p0 discretization of the three field formulation of biot s consolidation problem since this finite element formulation is not uniformly stable with respect to the physical parameters several issues arise in numerical simulations for example when the permeability is small with respect to the mesh size volumetric locking may occur to alleviate such problems we consider a well known stabilization technique with face bubble functions we then design a perturbation of the bilinear form which allows for local elimination of the bubble functions we further prove that such perturbation is consistent and the resulting scheme has optimal approximation properties for both biot s model as well as the stokes equations for the former the number of degrees of freedom is the same as for the classical p1 rt0 p0 discretization and for the latter stokes equations the number of degrees of freedom is the same as for a p1 p0 discretization we present numerical tests confirming the theoretical results for the poroelastic and the stokes test problems

noniterative subspace tracking a rank one spherical subspace update that is appropriate for subspace based methods like music and minimum norm is introduced this noniterative highly parallel numerically stabilized subspace update is closely related to rank one eigenstructure updating however a rank one subspace update involves less computation than simple rank one correlation accumulation moreover the frequency tracking capabilities of the noniterative subspace update are virtually identical to and in some case more robust than the more computationally expensive eigen based methods

parameter robust discretization and preconditioning of biot s consolidation model biot s consolidation model in poroelasticity has a number of applications in science medicine and engineering the model depends on various parameters and in practical applications these parameters range over several orders of magnitude a current challenge is to design discretization techniques and solution algorithms that are well behaved with respect to these variations the purpose of this paper is to study finite element discretizations of this model and construct block diagonal preconditioners for the discrete biot systems the approach taken here is to consider the stability of the problem in nonstandard or weighted hilbert spaces and employ the operator preconditioning approach we derive preconditioners that are robust with respect to both the variations of the parameters and the mesh refinement the parameters of interest are small time step sizes large bulk and shear moduli and small hydraulic conductivity

a survey of conjugate gradient algorithms for solution of extreme eigen problems of a symmetric matrix a survey of various conjugate gradient cg algorithms is presented for the minimum maximum eigen problems of a fixed symmetric matrix the cg algorithms are compared to a commonly used conventional method found in imsl it is concluded that the cg algorithms are more flexible and efficient than some of the conventional methods used in adaptive spectrum analysis and signal processing

full h div approximation of linear elasticity on quadrilateral meshes based on abf finite elements abstract for meshes of nondegenerate convex quadrilaterals we present a family of stable mixed finite element spaces for the mixed formulation of planar linear elasticity the problem is posed in terms of the stress tensor the displacement vector and the rotation scalar fields with the symmetry of the stress tensor weakly imposed the proposed spaces are based on the arnold boffi falk abf k k 0 elements for the stress and piecewise polynomials for the displacement and the rotation we prove that these finite elements provide full h div approximation of the stress field in the sense that it is approximated to order h k 1 where h is the mesh diameter in the h div norm we show that displacement and rotation are also approximated to order h k 1 in the l 2 norm the convergence is optimal order for k 1 while the lowest order case index k 0 requires special treatment the spaces also apply to both compressible and incompressible isotropic problems i e the poisson ratio may be one half the implementation as a hybrid method is discussed and numerical results are given to illustrate the effectiveness of these finite elements

adaptive spectral estimation by the conjugate gradient method this paper proposes an alternative technique for adaptive spectral estimation the new technique applies the method of conjugate gradient which is used for iteratively finding the generalized eigenvector corresponding to the minimum generalized eigenvalue of a semidefinite hermitian matrix to the adaptive spectral analysis problem computer simulations have been performed to compare the new method to existing ones from the limited examples presented it is seen that the new method is computationally more efficient at the expense of more core storage also this method is effective for small data records and can implement noise correction to yield unbiased spectral estimates if an estimate of the noise covariance matrix is available the technique performs well for both narrow band and wide band signals

error analysis of piecewise constant pressure approximations of darcy s law abstract in this paper we present a short discussion on some finite element formulations for linear elliptic problems for the sake of simplicity we consider the poisson equation p f taking the notation from darcy s law among the zillions of such methods we shall concentrate our attention on fem leading to a final system of linear algebraic equations mp f where each unknown pi represents the constant value of the approximated pressure ph in a single element it is indeed well known that for some applications there is a certain demand for these types of schemes

sliding window adaptive svd algorithms the singular value decomposition svd is an important tool for subspace estimation in adaptive signal processing we are especially interested in tracking the svd of a recursively updated data matrix this paper introduces a new tracking technique that is designed for rectangular sliding window data matrices this approach which is derived from the classical bi orthogonal iteration svd algorithm shows excellent performance in the context of frequency estimation it proves to be very robust to abrupt signal changes due to the use of a sliding window finally an ultra fast tracking algorithm with comparable performance is proposed

a dual mixed hybrid formulation for fluid mechanics problems mathematical analysis and application to semiconductor process technology in this paper we propose a dual mixed hybrid formulation capable of treating under a unified framework both compressible and incompressible problems in continuum mechanics a theoretical analysis of the method is carried out and optimal error estimates are derived for both mixed and hybrid variables the potentialities of the novel approach are exploited in the computation of the stress field required in the simulation of the thermal oxidation process in semiconductor technology the numerical formulation is validated both on model problems in continuum mechanics and on a realistic example of the thermal oxidation process in a local oxidation structure

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

a superconvergent hybridisable discontinuous galerkin method for linear elasticity this is the peer reviewed version of the following article sevilla r giacomini m karkoulias a huerta a a superconvergent hybridisable discontinuous galerkin method for linear elasticity international journal for numerical methods in engineering 12 octubre 2018 vol 116 num 2 p 91 116 which has been published in final form at https doi org 10 1002 nme 5916 this article may be used for non commercial purposes in accordance with wiley terms and conditions for self archiving

mixed finite element methods for linear elasticity with weakly imposed symmetry in this paper we construct new finite element methods for the approximation of the equations of linear elasticity in three space dimensions that produce direct approxima tions to both stresses and displacements the methods are based on a modified form of the hellinger reissner variational principle that only weakly imposes the symmetry condition on the stresses although this approach has been previously used by a number of authors a key new ingredient here is a constructive derivation of the elasticity complex starting from the de rham complex by mimicking this construction in the discrete case we derive new mixed finite elements for elasticity in a systematic manner from known discretizations of the de rham complex these elements appear to be simpler than the ones previously derived for example we construct stable discretizations which use only piecewise linear elements to approximate the stress field and piecewise constant functions to approximate the displacement field

a family of mixed finite elements for the elasticity problem a new mixed finite element formulation for the equations of linear elasticity is considered in the formulation the variables approximated are the displacement the unsymmetric stress tensor and the rotation the rotation act as a lagrange multiplier introduced in order to enforce the symmetry of the stress tensor based on this formulation a new family of both two and three dimensional mixed methods is defined optimal error estimates which are valid uniformly with respect to the poisson ratio are derived finally a new postprocessing scheme for improving the displacement is introduced and analyzed

a study of two modes of locking in poroelasticity in this paper we study two modes of locking phenomena in poroelasticity possion locking and pressure oscillations we first study the regularity of the solution of the biot model to gain some insight into the cause of poisson locking and show that the displacement gets into a divergence free state as the lame constant lambda to infty we also examine the cause of pressure oscillations from an algebraic point of view when a three field mixed finite element method is used based on the results of our study on the causes of the two modes of locking we propose a new family of mixed finite elements that are free of both pressure oscillations and poisson locking some numerical results are presented to validate our theoretical studies

fast approximated power iteration subspace tracking this paper introduces a fast implementation of the power iteration method for subspace tracking based on an approximation that is less restrictive than the well known projection approximation this algorithm referred to as the fast approximated power iteration api method guarantees the orthonormality of the subspace weighting matrix at each iteration moreover it outperforms many subspace trackers related to the power iteration method such as past nic np3 and opast while having the same computational complexity the api method is designed for both exponential windows and sliding windows our numerical simulations show that sliding windows offer a faster tracking response to abrupt signal variations

automated goal oriented error control i stationary variational problems this article presents a general and novel approach to the automation of goal oriented error control in the solution of nonlinear stationary finite element variational problems the approach is based on automated linearization to obtain the linearized dual problem automated derivation and evaluation of a posteriori error estimates and automated adaptive mesh refinement to control the error in a given goal functional to within a given tolerance numerical examples representing a variety of different discretizations of linear and nonlinear partial differential equations are presented including poisson s equation a mixed formulation of linear elasticity and the incompressible navier stokes equations 2013 society for industrial and applied mathematics

maximum principle for an optimal control problem associated to a spde with nonlinear boundary conditions abstract we study a control problem where the state equation is a nonlinear partial differential equation of the calculus of variation in a bounded domain perturbed by noise we allow the control to act on the boundary and set boundary conditions which result in a stochastic differential equation for the trace of the solution on the boundary this work provides necessary and sufficient conditions of optimality in the form of a maximum principle we also provide a result of existence for the optimal control in the case where the control acts linearly

robust convergence of multi point flux approximation on rough grids this paper establishes the convergence of a multi point flux approximation control volume method on rough quadrilateral grids by rough grids we refer to a family of refined quadrilateral grids where the cells are not required to approach parallelograms in the asymptotic limit in contrast to previous convergence results for these methods we consider here a version where the flux approximation is derived directly in the physical space and not on a reference cell as a consequence less regular grids are allowed however the extra cost is that the symmetry of the method is lost

algorithms for accelerated convergence of adaptive pca we derive and discuss adaptive algorithms for principal component analysis pca that are shown to converge faster than the traditional pca algorithms due to oja and karhunen 1985 sanger 1989 and xu 1993 it is well known that traditional pca algorithms that are derived by using gradient descent on an objective function are slow to converge furthermore the convergence of these algorithms depends on appropriate choices of the gain sequences since online applications demand faster convergence and an automatic selection of gains we present new adaptive algorithms to solve these problems we first present an unconstrained objective function which can be minimized to obtain the principal components we derive adaptive algorithms from this objective function by using 1 gradient descent 2 steepest descent 3 conjugate direction and 4 newton raphson methods although gradient descent produces xu s lmser algorithm the steepest descent conjugate direction and newton raphson methods produce new adaptive algorithms for pca we also provide a discussion on the landscape of the objective function and present a global convergence proof of the adaptive gradient descent pca algorithm using stochastic approximation theory extensive experiments with stationary and nonstationary multidimensional gaussian sequences show faster convergence of the new algorithms over the traditional gradient descent methods we also compare the steepest descent adaptive algorithm with state of the art methods on stationary and nonstationary sequences

a nonconforming finite element method for the biot s consolidation model in poroelasticity a stable finite element scheme that avoids pressure oscillations for a three field biot s model in poroelasticity is considered the involved variables are the displacements fluid flux darcy velocity and the pore pressure and they are discretized by using the lowest possible approximation order crouzeix raviart finite elements for the displacements lowest order raviart thomas nedelec elements for the darcy velocity and piecewise constant approximation for the pressure mass lumping technique is introduced for the raviart thomas nedelec elements in order to eliminate the darcy velocity and therefore reduce the computational cost we show convergence of the discrete scheme which is implicit in time and use these types of elements in space with and without mass lumping finally numerical experiments illustrate the convergence of the method and show its effectiveness to avoid spurious pressure oscillations when mass lumping for the raviart thomas nedelec elements is used

convergence of a cell centered finite volume discretization for linear elasticity we show convergence of a cell centered finite volume discretization for linear elasticity the discretization termed the mpsa method was recently proposed in the context of geological applications where cell centered variables are often preferred our analysis utilizes a hybrid variational formulation which has previously been used to analyze finite volume discretizations for the scalar diffusion equation the current analysis deviates significantly from the previous in three respects first additional stabilization leads to a more complex saddle point problem second a discrete korn s inequality has to be established for the global discretization finally robustness with respect to the poisson ratio is analyzed the stability and convergence results presented herein provide the first rigorous justification of the applicability of cell centered finite volume methods to problems in linear elasticity

fast subspace decomposition many recent signal processing techniques in various areas e g array signal processing system identification and spectrum estimation require a step of extracting the low dimensional subspace from a large space this step is usually called subspace decomposition which is conventionally accomplished by an eigendecomposition ed since an ed requires o m sup 3 flops for an m spl times m matrix it may represent a barrier to the real time implementation of these algorithms the authors present a fast algorithm for signal subspace decomposition which is termed fsd that exploits the special matrix structure low rank plus identity associated with signal subspace algorithms and requires only o m sup 2 d flops where d often spl lt m denotes the signal subspace dimension unlike most of alternatives the dimension of the signal subspace is not assumed known apriori and is estimated as part of the procedure moreover theoretical analysis has been conducted and its results show the strong consistency of the new detection scheme and the asymptotic equivalence between fsd and ed in estimating the signal subspace their new approach can also exploit other matrix structure common in signal processing areas e g toeplitz or hankel and thus achieve another order of computational reduction moreover it can be easily implemented in parallel to reduce further the computation time to as little as o md using o m simple processors

fast subspace tracking and neural network learning by a novel information criterion we introduce a novel information criterion nic for searching for the optimum weights of a two layer linear neural network nn the nic exhibits a single global maximum attained if and only if the weights span the desired principal subspace of a covariance matrix the other stationary points of the nic are unstable saddle points we develop an adaptive algorithm based on the nic for estimating and tracking the principal subspace of a vector sequence the nic algorithm provides a fast on line learning of the optimum weights for the two layer linear nn we establish the connections between the nic algorithm and the conventional mean square error mse based algorithms such as oja s algorithm oja 1989 lmser past apex and gha the nic algorithm has several key advantages such as faster convergence which is illustrated through analysis and simulation

dual hybrid methods for the elasticity and the stokes problems a unified approach a unified approach to construct finite elements based on a dual hybrid formulation of the linear elasticity problem is given in this formulation the stress tensor is considered but its symmetry is relaxed by a lagrange multiplier which is nothing else than the rotation this construction is linked to the approximations of the stokes problem in the primitive variables and it leads to a new interpretation of known elements and to new finite elements moreover all estimates are valid uniformly with respect to compressibility and apply in the incompressible case which is close to the stokes problem