multicolor fourier analysis of the multigrid method for quadratic fem discretizations abstract quadratic finite element methods offer some advantages for the numerical solution of partial differential equations pdes due to their improved approximation properties in comparison to linear approaches the algebraic linear systems arising from the discretization of pdes by this kind of methods require an efficient resolution and multigrid methods provide a good way to solve this problem to design geometric multigrid methods local fourier analysis lfa is a very useful tool however lfa for quadratic finite element discretizations can not be performed in a standard way since the discrete operator is defined by different stencils depending on the location of the points in the grid in this work a multicolor local fourier analysis is presented to analyze multigrid solvers for this type of discretizations with the help of this analysis some point wise and line wise smoothers are analyzed some results showing the good correspondence between the two grid convergence factors predicted by the analysis and the experimentally computed asymptotic convergence factors are presented finally this analysis is applied to design a very efficient multigrid solver for semi structured triangular grids based on a hybrid smoother

chebyshev pseudospectral solution of second order elliptic equations with finite element preconditioning abstract a new chebyshev pseudospectral algorithm for second order elliptic equations using finite element preconditioning is proposed and tested on various problems bilinear and biquadratic lagrange elements are considered as well as bicubic hermite elements the numerical results show that bilinear elements produce spectral accuracy with the minimum computational work l shaped regions are treated by a subdomain approach

algebraic multigrid amg experiences and comparisons algebraic multigrid methods are designed for the solution of sparse linear systems of equations using multigrid principles in contrast to standard multigrid methods amg does not take advantage of the origin of a particular system of equations at hand nor does it exploit any underlying geometrical situation fully automatically and based solely on algebraic information contained in the given matrix amg constructs a sequence of grids and corresponding operators a special amg algorithm will be presented for a wide range of problems including certain problems which do not have a continuous background this algorithm yields an iterative method which exhibits a convergence behavior typical for multigrid methods

an alternative least squares formulation of the navier stokes equations with improved mass conservation the focus of this paper is on incompressible flows in three dimensions modeled by least squares finite element methods lsfem and using a novel reformulation of the navier stokes equations lsfem are attractive because the resulting discrete equations yield symmetric positive definite systems of algebraic equations and the functional provides both a local and global error measure on the other hand it has been documented for existing reformulations that certain types of boundary conditions and high aspect ratio domains can yield very poor mass conservation it has also been documented that improved mass conservation with lsfem can be achieved by strengthening the coupling between the pressure and velocity the new reformulation presented here is demonstrated to provide both improved multigrid convergence rates because it is differentially diagonally dominant and improved mass conservation over existing methods because it increases the pressure velocity coupling along the inflow and outflow boundaries

smoothed aggregation multigrid solvers for high order discontinuous galerkin methods for elliptic problems abstract we develop a smoothed aggregation based algebraic multigrid solver for high order discontinuous galerkin discretizations of the poisson problem algebraic multigrid is a popular and effective method for solving the sparse linear systems that arise from discretizing partial differential equations however high order discontinuous galerkin discretizations have proved challenging for algebraic multigrid the increasing condition number of the matrix and loss of locality in the matrix stencil as p increases in addition to the effect of weakly enforced dirichlet boundary conditions all contribute to the challenging algebraic setting we propose a smoothed aggregation approach that addresses these difficulties in particular the approach effectively coarsens degrees of freedom centered at the same spatial location as well as degrees of freedom at the domain boundary moreover the character of the near null space particularly at the domain boundary is captured by interpolation one classic prolongation smoothing step of weighted jacobi is also shown to be ineffective at high order and a more robust energy minimization approach is used along with block relaxation that more directly utilizes the block diagonal structure of the discontinuous galerkin discretization finally we conclude by examining numerical results in support our proposed method

technical communique comments on finite time stability of time delay systems recently proposed conditions on finite time stability in time delay systems are revisited and it is shown that they are incorrect general comments on possibility of finite time convergence in time delay systems and a necessary condition are given

finite time stability and stabilization of time delay systems finite time stability and stabilization of retarded type functional differential equations are developed first a theoretical result on finite time stability inspired by the theory of differential equations using lyapunov functionals is given as it may appear not easily usable in practice we show how to obtain finite time stabilization of linear systems with delays in the input by using an extension of artstein s model reduction to nonlinear feedback with this approach we give an explicit finite time controller for scalar linear systems and for the chain of integrators with delays in the input

a spectral element least squares formulation for incompressible navier stokes flows using triangular nodal elements we present a least squares formulation for the numerical solution of incompressible flows using high order triangular nodal elements the fekete points of the triangle are used as nodes and numerical integration is performed using tensor product gauss legendre rules in a collapsed coordinate system for the standard triangle a first order system least squares fosls approach based on velocity pressure and vorticity is used to allow the use of practical c 0 element expansions in each triangle the numerical results demonstrate spectral convergence for smooth solutions excellent conservation of mass for steady and unsteady problems of the inflow outflow type and the flexibility of using triangles to partition domains where the use of quadrangles would be cumbersome or inefficient

finite time stabilizability and instabilizability of delayed memristive neural networks with nonlinear discontinuous controller this paper is concerned about the finite time stabilizability and instabilizability for a class of delayed memristive neural networks dmnns through the design of a new nonlinear controller algebraic criteria based on m matrix are established for the finite time stabilizability of dmnns and the upper bound of the settling time for stabilization is estimated in addition finite time instabilizability algebraic criteria are also established by choosing different parameters of the same nonlinear controller the effectiveness and the superiority of the obtained results are supported by numerical simulations

subpixel edge localization and the interpolation of still images in this paper we present a nonlinear interpolation scheme for still image resolution enhancement the algorithm is based on a source model emphasizing the visual integrity of detected edges and incorporates a novel edge fitting operator that has been developed for this application a small neighborhood about each pixel in the low resolution image is first mapped to a best fit continuous space step edge the bilevel approximation serves as a local template on which the higher resolution sampling grid can then be superimposed where disputed values in regions of local window overlap are averaged to smooth errors the result is an image of increased resolution with noticeably sharper edges and in all tried cases lower mean squared reconstruction error than that produced by linear techniques

orthogonal and biorthogonal fir hexagonal filter banks with sixfold symmetry recently hexagonal image processing has attracted attention the hexagonal lattice has several advantages in comparison with the rectangular lattice the conventionally used lattice for image sampling and processing for example a hexagonal lattice needs less sampling points it has better consistent connectivity it has higher symmetry and its structure is plausible to human vision systems the multiresolution analysis method has been used for hexagonal image processing since the hexagonal lattice has high degree of symmetry it is desirable that the hexagonal filter banks designed for multiresolution hexagonal image processing also have high order of symmetry which is pertinent to the symmetry structure of the hexagonal lattice the orthogonal or prefect reconstruction pr hexagonal filter banks that are available in the literature have only threefold symmetry in this paper we investigate the construction of orthogonal and pr finite impulse response fir hexagonal filter banks with sixfold symmetry we obtain block structures of 7 size refinement seven channel two dimensional orthogonal and pr fir hexagonal filter banks with sixfold rotational symmetry radic7 refinement orthogonal and biorthogonal wavelets based on these block structures are constructed in this paper we also consider fir hexagonal filter banks with axial line symmetry and we present a block structure of fir hexagonal filter banks with pseudo sixfold axial symmetry

an improved algebraic criterion for global exponential stability of recurrent neural networks with time varying delays this brief paper presents an m matrix based algebraic criterion for the global exponential stability of a class of recurrent neural networks with decreasing time varying delays the criterion improves some previous criteria based on m matrix and is easy to be verified with the connection weights of the recurrent neural networks with decreasing time varying delays in addition the rate of exponential convergence can be estimated via a simple computation based on the criterion herein

a fast motion estimation algorithm based on the block sum pyramid in this correspondence a fast approach to motion estimation is presented the algorithm uses the block sum pyramid to eliminate unnecessary search positions it first constructs the sum pyramid structure of a block successive elimination is then performed hierarchically from the top level to the bottom level of the pyramid many search positions can be skipped from being considered as the best motion vector and thus the search complexity can be reduced the algorithm can achieve the same estimation accuracy as the full search block matching algorithm with much less computation time

a review of algebraic multigrid abstract since the early 1990s there has been a strongly increasing demand for more efficient methods to solve large sparse unstructured linear systems of equations for practically relevant problem sizes classical one level methods had already reached their limits and new hierarchical algorithms had to be developed in order to allow an efficient solution of even larger problems this paper gives a review of the first hierarchical and purely matrix based approach algebraic multigrid amg amg can directly be applied for instance to efficiently solve various types of elliptic partial differential equations discretized on unstructured meshes both in 2d and 3d since amg does not make use of any geometric information it is a plug in solver which can even be applied to problems without any geometric background provided that the underlying matrix has certain properties

fast algorithms for the estimation of motion vectors in this correspondence a fast motion estimation algorithm based on the successive elimination algorithm sea of li and salari 1995 is studied this fast motion estimation algorithm finds the same displacement vectors as the exhaustive search algorithm with a reduced computational load a modified fast motion estimation algorithm introducing negligible distortion into a transform coder but providing for a further computational load reduction is developed implementation issues are also discussed and compared results show that the number of searching operations can be reduced dramatically with the help of fast motion estimation algorithms

fast full search block matching algorithm for motion compensated video compression this paper proposes a fast block matching algorithm that uses three fast matching error measures besides the conventional mean absolute error mae or mean square error mse an incoming reference block in the current frame is compared to candidate blocks within the search window using multiple matching criteria these three fast matching error measures are established on the integral projections having the advantages of being good block features and having simple complexity in measuring matching errors most of the candidate blocks can be rejected only by calculating one or more of the three fast matching error measures the time consuming computations of mse or mae are performed on only a few candidate blocks that first pass all three fast matching criteria simulation results show that a reduction of over 86 in computations is achieved after integrating the three fast matching criteria into the full search algorithm while ensuring optimal accuracy

delay dependent global exponential stability for delayed recurrent neural networks this paper deals with the global exponential stability for delayed recurrent neural networks drnns by constructing an augmented lyapunov krasovskii functional and adopting the reciprocally convex combination approach and wirtinger based integral inequality delay dependent global exponential stability criteria are derived in terms of linear matrix inequalities meanwhile a general and effective method on global exponential stability analysis for drnns is given through a lemma where the exponential convergence rate can be estimated with this lemma some global asymptotic stability criteria of drnns acquired in previous studies can be generalized to global exponential stability ones finally a frequently utilized numerical example is carried out to illustrate the effectiveness and merits of the proposed theoretical results

real time pattern matching using projection kernels a novel approach to pattern matching is presented in which time complexity is reduced by two orders of magnitude compared to traditional approaches the suggested approach uses an efficient projection scheme which bounds the distance between a pattern and an image window using very few operations on average the projection framework is combined with a rejection scheme which allows rapid rejection of image windows that are distant from the pattern experiments show that the approach is effective even under very noisy conditions the approach described here can also be used in classification schemes where the projection values serve as input features that are informative and fast to extract

new algebraic criteria for synchronization stability of chaotic memristive neural networks with time varying delays in this brief we consider the exponential synchronization of chaotic memristive neural networks with time varying delays using the lyapunov functional method and inequality technique the dynamic analysis here employs the theory of differential equations with discontinuous right hand side as introduced by filippov the designing laws in the synchronization of neural networks are proposed via state or output coupling in addition the new proposed algebraic criteria are very easy to verify and they also enrich and improve the earlier publications finally an example is given to show the effectiveness of the obtained results

algebraic multigrid for higher order finite elements two related approaches for solving linear systems that arise from a higher order finite element discretization of elliptic partial differential equations are described the first approach explores direct application of an algebraic based multigrid method amg to iteratively solve the linear systems that result from higher order discretizations while the choice of basis used on the discretization has a significant impact on the performance of the solver results indicate that amg is capable of solving operators from both poisson s equation and a first order system least squares fosls formulation of stoke s equation in a scalable manner nearly independent of basis order p for 3

fast block matching algorithm based on the winner update strategy block matching is a widely used method for stereo vision visual tracking and video compression many fast algorithms for block matching have been proposed in the past but most of them do not guarantee that the match found is the globally optimal match in a search range this paper presents a new fast algorithm based on the winner update strategy which utilizes an ascending lower bound list of the matching error to determine the temporary winner two lower bound lists derived by using partial distance and by using minkowski s inequality are described the basic idea of the winner update strategy is to avoid at each search position the costly computation of the matching error when there exists a lower bound larger than the global minimum matching error the proposed algorithm can significantly speed up the computation of the block matching because 1 computational cost of the lower bound we use is less than that of the matching error itself 2 an element in the ascending lower bound list will be calculated only when its preceding element has already been smaller than the minimum matching error computed so far 3 for many search positions only the first several lower bounds in the list need to be calculated our experiments have shown that when applying to motion vector estimation for several widely used test videos 92 to 98 of operations can be saved while still guaranteeing the global optimality moreover the proposed algorithm can be easily modified either to meet the limited time requirement or to provide an ordered list of best candidate matches

weighted least squares finite elements based on particle imaging velocimetry data the solution of the navier stokes equations requires that data about the solution is available along the boundary in some situations such as particle imaging velocimetry there is additional data available along a single plane within the domain and there is a desire to also incorporate this data into the approximate solution of the navier stokes equation the question that we seek to answer in this paper is whether two dimensional velocity data containing noise can be incorporated into a full three dimensional solution of the navier stokes equations in an appropriate and meaningful way for addressing this problem we examine the potential of least squares finite element methods lsfem because of their flexibility in the enforcement of various boundary conditions further by weighting the boundary conditions in a manner that properly reflects the accuracy with which the boundary values are known we develop the weighted lsfem the potential of weighted lsfem is explored for three different test problems the first uses randomly generated gaussian noise to create artificial experimental data in a controlled manner and the second and third use particle imaging velocimetry data in all test problems weighted lsfem produces accurate results even for cases where there is significant noise in the experimental data

global exponential periodicity and stability of a class of memristor based recurrent neural networks with multiple delays the paper presents theoretical results on the global exponential periodicity and stability of a class of memristor based recurrent neural networks with multiple delays the dynamic analysis in the paper employs the theory of differential equations with discontinuous right hand side as introduced by filippov by using the inequality techniques and a useful lyapunov functional some new testable algebraic criteria are obtained for ensuring the existence and global exponential stability of periodic solution of the system the model based on the memristor widens the application scope for the design of neural networks and the new effective results also enrich the toolbox for the qualitative analysis of neural networks

a multilevel successive elimination algorithm for block matching motion estimation an efficient algorithm is proposed to reduce the computation cost of block matching algorithms for motion estimation in video coding based on a new insight in block matching algorithms we extend the successive elimination algorithm to a multilevel case by using the sum norms of the blocks and the subblocks tighter and tighter decision boundaries can be obtained for eliminating the search positions the efficiency of the proposed algorithm combined with the full search algorithm and several fast search algorithms is verified by simulation results

an overlapping schwarz method for spectral element solution of the incompressible navier stokes equations efficient solution of the navier stokes equations in complex domains is dependent upon the availability of fast solvers for sparse linear systems for unsteady incompressible flows the pressure operator is the leading contributor to stiffness as the characteristic propagation speed is infinite in the context of operator splitting formulations it is the pressure solve which is the most computationally challenging despite its elliptic origins we examine several preconditioners for the consistent l2poisson operator arising in the pn pn 2spectral element formulation of the incompressible navier stokes equations we develop a finite element based additive schwarz preconditioner using overlapping subdomains plus a coarse grid projection operator which is applied directly to the pressure on the interior gauss points for large two dimensional problems this approach can yield as much as a fivefold reduction in simulation time over previously employed methods based upon deflation

fast algorithm for robust template matching with m estimators we propose a fast algorithm for speeding up the process of template matching that uses m estimators for dealing with outliers we propose a particular image hierarchy called the p pyramid that can be exploited to generate a list of ascending lower bounds of the minimal matching errors when a nondecreasing robust error measure is adopted then the set of lower bounds can be used to prune the search of the p pyramid and a fast algorithm is thereby developed in this paper this fast algorithm ensures finding the global minimum of the robust template matching problem in which a nondecreasing m estimator serves as an error measure experimental results demonstrate the effectiveness of our method

schwarz analysis of iterative substructuring algorithms for elliptic problems in three dimensions domain decomposition methods provide powerful preconditioners for the iterative solution of the large systems of algebraic equations that arise in finite element or finite difference approximations

mean square stability of two classes of theta methods for numerical computation and simulation of delayed stochastic hopfield neural networks abstract recently the investigation on the stability of the numerical solutions to delayed stochastic differential equations has received an increasing attention but there has been little work on the stability analysis of the numerical solutions to delayed stochastic hopfield neural networks dshnns so far the aim in this paper is to study the mean square exponential stability of the split step theta sst method and the stochastic linear theta slt method for the underlying model it is proved that for any 0 1 2 there exists a constant 0 depending on such that the numerical schemes produced by the sst method and the slt method are mean square exponentially stable for 0 under the same assumptions as those to guarantee the mean square exponential stability of the underlying continuous model for the case 1 2 1 we show the same stability conclusion for all 0 to carry out the required conclusion a novel technique for the stability analysis of discrete numerical schemes with multi time delays namely the weighted sum lyapunov functional method is proposed finally a numerical example is given to illustrate the application of the suggested methods and to verify the stability conclusions obtained

detail enhanced exposure fusion in a typical processing chain of image enhancement an exposure fusion scheme can be used to synthesize a more detailed low dynamic range ldr image directly from a set of differently exposed ldr images without generation of an intermediate high dynamic range image in this brief we introduce a new quadratic optimization based method to extract fine details from a vector field the new method extracts fine details from a set of differently exposed ldr images simultaneously the extracted fine details are then added to an intermediate ldr image which is fused by simply using an existing exposure fusion scheme with this the proposed scheme can enhance fine details to produce sharper images

an efficient computation constrained block based motion estimation algorithm for low bit rate video coding we present an efficient computation constrained block based motion vector estimation algorithm for low bit rate video coding that yields good tradeoffs between motion estimation distortion and number of computations a reliable predictor determines the search origin localizing the search process an efficient search pattern exploits structural constraints within the motion field a flexible cost measure used to terminate the search allows simultaneous control of the motion estimation distortion and the computational cost experimental results demonstrate the viability of the proposed algorithm in low bit rate video coding applications the resulting low bit rate video encoder yields essentially the same levels of rate distortion performance and subjective quality achieved by the ubc h 263 video coding reference software however the proposed motion estimation algorithm provides substantially higher encoding speed as well as graceful computational degradation capabilities

on global dissipativity of nonautonomous neural networks with multiple proportional delays this brief addresses the problem of global dissipativity analysis of nonautonomous neural networks with multiple proportional delays by using a novel constructive approach based on some comparison techniques for differential inequalities new explicit delay independent conditions are derived using m matrix theory to ensure the existence of generalized exponential attracting sets and the global dissipativity of the system the method presented in this brief is also utilized to derive a generalized exponential estimate for a class of halanay type inequalities with proportional delays finally three numerical examples are given to illustrate the effectiveness and improvement of the obtained results

a polylogarithmic bound for an iterative substructuring method for spectral elements in three dimensions iterative substructuring methods form an important family of domain decomposition algorithms for elliptic finite element problems a p version finite element method based on continuous piecewise q p functions is considered for second order elliptic problems in three dimensions this special method can also be viewed as a conforming spectral element method an iterative method is designed for which the condition number of the relevant operator grows only in proportion to 1 log p 2 this bound is independent of jumps in the coefficient of the elliptic problem across the interfaces between the subregions numerical results are also reported which support the theory

newton multigrid least squares fem for the v v p formulation of the navier stokes equations we solve the v v p vorticity velocity pressure formulation of the stationary incompressible navier stokes equations based on the least squares finite element method for the discrete systems we use a conjugate gradient cg solver accelerated with a geometric multigrid preconditioner for the complete system in addition we employ a krylov space smoother inside of the multigrid which allows a parameter free smoothing combining this linear solver with the newton linearization we construct a very robust and efficient solver we use biquadratic finite elements to enhance the mass conservation of the least squares method for the inflow outflow problems and to obtain highly accurate results we demonstrate the advantages of using the higher order finite elements and the grid independent solver behavior through the solution of three stationary laminar flow problems of benchmarking character the comparisons show excellent agreement between our results and those of the galerkin mixed finite element method as well as available reference solutions

a novel two phase hilbert scan based search algorithm for block motion estimation using ctf data structure motion estimation is one of the kernel issues in mpeg series in this correspondence a novel two phase hilbert scan based search algorithm for block motion estimation is presented first in the intra phase a segmentation of the hilbert curve is applied to the current block then a novel coarse to fine data structure is developed to eliminate the impossible reference blocks in the search window of the reference frame in the inter phase a new prediction scheme for estimating the initial motion vector of the current block is presented experimental results reveal that when compared to the gapd algorithm our proposed algorithm has better execution time and estimation accuracy performance under the same estimation accuracy our proposed algorithm has better execution time performance when compared to the fs algorithm in addition when comparing with the tss algorithm our proposed algorithm has better estimation accuracy performance but has worse execution time performance

full search equivalent pattern matching with incremental dissimilarity approximations this paper proposes a novel method for fast pattern matching based on dissimilarity functions derived from the lp norm such as the sum of squared differences ssd and the sum of absolute differences sad the proposed method is full search equivalent i e it yields the same results as the full search fs algorithm in order to pursue computational savings the method deploys a succession of increasingly tighter lower bounds of the adopted lp norm based dissimilarity function such bounding functions allow for establishing a hierarchy of pruning conditions aimed at skipping rapidly those candidates that cannot satisfy the matching criterion the paper includes an experimental comparison between the proposed method and other full search equivalent approaches known in literature which proves the remarkable computational efficiency of our proposal

fast template matching based on normalized cross correlation with adaptive multilevel winner update in this paper we propose a fast pattern matching algorithm based on the normalized cross correlation ncc criterion by combining adaptive multilevel partition with the winner update scheme to achieve very efficient search this winner update scheme is applied in conjunction with an upper bound for the cross correlation derived from cauchy schwarz inequality to apply the winner update scheme in an efficient way we partition the summation of cross correlation into different levels with the partition order determined by the gradient energies of the partitioned regions in the template thus this winner update scheme in conjunction with the upper bound for ncc can be employed to skip unnecessary calculation experimental results show the proposed algorithm is very efficient for image matching under different lighting conditions

first order system least squares fosls for coupled fluid elastic problems mathematical models for the mechanical coupling between a moving fluid and an elastic solid are inherently nonlinear because the shape of the eulerian fluid domain is not known a priori it is at least partially determined by the displacement of the elastic solid in this paper a first order system least squares finite element formulation is used to solve the nonlinear system of model equations using different iteration techniques including an approach where the equations are fully coupled and two other approaches in which the equations are decoupled the discrete linear system of equations is solved using an algebraic multigrid solver as a preconditioner for a conjugate gradient iteration the numerical results show that the approach is optimal in the sense that computational cost is proportional to the degrees of freedom the results also show that the choice of iteration method from fully coupled to fully decoupled does not significantly effect computational cost but it does influence the error in the solution

on mass conserving least squares methods least squares variational methods have several practical and theoretical advantages for solving elliptic partial differential equations including symmetric positive definite discrete operators and a sharp error measure one of the potential drawbacks especially in three dimensions is that mass conservation is achieved only in a least squares sense and underresolved solutions are especially vulnerable to poor conservation for the stationary navier stokes equations which are typically rewritten as a larger system of first order equations the loss of mass in the approximate solution is strongly dependent upon the boundary conditions used a new first order system reformulation of the navier stokes equations is presented that admits a wider range of mass conserving boundary conditions this new formulation is shown to provide both excellent mass conservation and excellent algebraic multigrid performance for three different problems a square channel backward facing step and branching tubes with two generations of bifurcations

a least squares based 2 d filtering scheme for stereo image compression a two dimensional 2 d least squares ls based filtering scheme for high fidelity stereo image compression applications is introduced in this correspondence this method removes the effects of mismatching in a stereo image pair by applying the left image as the reference input to a 2 d transversal filter while the right image is used as the desired output the weights of the filter are computed using a block based ls method a reduced order filtering scheme is also introduced to find the optimum number of filter coefficients the principal coefficients and the disparity vectors are used together with left image to reconstruct the right image at the receiver the proposed schemes are examined on a real stereo image pair for 3d tv applications and the results were benchmarked against those of the block matching method

two level domain decomposition preconditioning for the p version finite element method in three dimensions this paper presents a flexible approach to domain decomposition preconditioning for problems expressed in terms of local stiffness matrices of subdomains evaluation of the preconditioner requires fully parallelizable local computations and the solution of a global auxiliary problem with few variables per subdomain convergence factors can be bounded using properties of the local stiffness matrices only the method is applied to the p version finite element method for three dimensional elasticity we treat each element as a subdomain and compute explicit convergence bounds

finite time stability and stabilization of a class of nonlinear time delay systems this paper investigates the finite time stability fts and stabilization for a class of nonlinear time delay systems and proposes some new results first an equivalent form is presented for the systems by a coordinate transformation and a criterion on the fts is obtained for nonlinear time delay systems via the razumikhin approach r approach then based on the criterion and the equivalent form some delay independent and delay dependent conditions on the fts are derived for this class of systems by constructing a new lyapunov function third we use the obtained fts results to investigate the finite time stabilization problem and present a control design procedure for the time delay systems it is shown that our method can avoid solving nonlinear matrix inequalities by transferring them into the form of linear matrix inequalities which can be easily solved with the lmi toolbox of matlab finally study of illustrative examples shows that the results obtained in this paper work very well in the ft

robustness analysis of global exponential stability of recurrent neural networks in the presence of time delays and random disturbances in recent years the global stability of recurrent neural networks rnns has been investigated extensively it is well known that time delays and external disturbances can derail the stability of rnns in this paper we analyze the robustness of global stability of rnns subject to time delays and random disturbances given a globally exponentially stable neural network the problem to be addressed here is how much time delay and noise the rnn can withstand to be globally exponentially stable in the presence of delay and noise the upper bounds of the time delay and noise intensity are characterized by using transcendental equations for the rnns to sustain global exponential stability moreover we prove theoretically that for any globally exponentially stable rnns if additive noises and time delays are smaller than the derived lower bounds arrived at here then the perturbed rnns are guaranteed to also be globally exponentially stable three numerical examples are provided to substantiate the theoretical results

robustness and scalability of algebraic multigrid algebraic multigrid amg is currently undergoing a resurgence in popularity due in part to the dramatic increase in the need to solve physical problems posed on very large unstructured grids while amg has proved its usefulness on various problem types it is not commonly understood how wide a range of applicability the method has in this study we demonstrate that range of applicability while describing some of the recent advances in amg technology moreover in light of the imperatives of modern computer environments we also examine amg in terms of algorithmic scalability finally we show some of the situations in which standard amg does not work well and indicate the current directions taken by amg researchers to alleviate these difficulties

multi p preconditioners a class of algebraic multi p methods for solving the p version of the finite element equations is first presented and discussed it is then shown how these multi p methods can be used as preconditioners for the conjugate gradient cg method in particular it is shown that given any preconditioner mp to cg a multi p preconditioner bp based on mp can be constructed which leads to a smaller condition number and hence faster convergence numerical experiments on representative problems indicate that the condition numbers after multi p preconditionings are in fact independent of p the numerical results also show greater efficiency for the preconditioned conjugate gradient pcg method with the multi p preconditioners in terms of number of iterations and cpu time when compared with two sophisticated linear equation solvers 1 a direct frontal solver specially designed for the p version of the finite element analysis 2 a highly tuned pcg code in itpack2c http www netlib org itpack 1994 preliminary comparisons of the number of iterations are also made with rockits solvers international inc boulder co 1994 a new commercial code used for the p version

algebraic multigrid for moderate order finite elements we investigate the use of algebraic multigrid amg methods for the solution of large sparse linear systems arising from the discretization of scalar elliptic partial differential equations with lagrangian finite elements of order at most 4 the resulting system matrices do not have the m matrix property that is required by standard analyses of classical amg and aggregation based amg methods a unified approach is presented that allows us to extend these analyses it uses an intermediate m matrix and highlights the role of the spectral equivalence constant that relates this matrix to the original system matrix this constant is shown to be bounded independently of the problem size and jumps in the coefficients of the partial differential equations provided that jumps are located at elements boundaries for two dimensional problems it is further shown to be uniformly bounded if the angles in the triangulation also satisfy a uniform bound this analysis validates the application of the amg methods to the

multiscale hybrid linear models for lossy image representation in this paper we introduce a simple and efficient representation for natural images we view an image in either the spatial domain or the wavelet domain as a collection of vectors in a high dimensional space we then fit a piece wise linear model i e a union of affine subspaces to the vectors at each downsampling scale we call this a multiscale hybrid linear model for the image the model can be effectively estimated via a new algebraic method known as generalized principal component analysis gpca the hybrid and hierarchical structure of this model allows us to effectively extract and exploit multimodal correlations among the imagery data at different scales it conceptually and computationally remedies limitations of many existing image representation methods that are based on either a fixed linear transformation e g dct wavelets or an adaptive uni modal linear transformation e g pca or a multimodal model that uses only cluster means e g vq we will justify both quantitatively and experimentally why and how such a simple multiscale hybrid model is able to reduce simultaneously the model complexity and computational cost despite a small overhead of the model our careful and extensive experimental results show that this new model gives more compact representations for a wide variety of natural images under a wide range of signal to noise ratios than many existing methods including wavelets we also briefly address how the same hybrid linear modeling paradigm can be extended to be potentially useful for other applications such as image segmentation

passivity and passification of memristor based recurrent neural networks with additive time varying delays this paper presents a new design scheme for the passivity and passification of a class of memristor based recurrent neural networks mrnns with additive time varying delays the predictable assumptions on the boundedness and lipschitz continuity of activation functions are formulated the systems considered here are based on a different time delay model suggested recently which includes additive time varying delay components in the state the connection between the time varying delay and its upper bound is considered when estimating the upper bound of the derivative of lyapunov functional it is recognized that the passivity condition can be expressed in a linear matrix inequality lmi format and by using characteristic function method for state feedback passification it is verified that it is apathetic to use immediate or delayed state feedback by constructing a lyapunov krasovskii functional and employing jensen s inequality and reciprocal convex combination technique together with a tighter estimation of the upper bound of the cross product terms derived from the derivatives of the lyapunov functional less conventional delay dependent passivity criteria are established in terms of lmis moreover second order reciprocally convex approach is employed for deriving the upper bound for terms with inverses of squared convex parameters the model based on the memristor with additive time varying delays widens the application scope for the design of neural networks finally pertinent examples are given to show the advantages of the derived passivity criteria and the significant improvement of the theoretical approaches

multigrid solver for the inner problem in domain decomposition methods for p fem from the literature it is known that the conjugate gradient method with domain decomposition preconditioners is one of the most efficient methods for solving systems of linear algebraic equations resulting from p version finite element discretizations of elliptic boundary value problems the ingredients of such a preconditioner are a preconditioner for the schur complement a preconditioner related to the dirichlet problems in the subdomains and an extension operator from the boundaries of the subdomains into their interior in the case of poisson s equation we propose a preconditioner for the problems in the subdomains which can be interpreted as the stiffness matrix resulting from an h version finite element discretization of a degenerate operator for solving the corresponding systems of finite element equations a multigrid algorithm with a special line smoother is used we prove that the convergence rate of the multigrid method is independent of the discretization parameter the proof is based on the strengthened cauchy inequality the theoretical result is confirmed by numerical examples

an efficient search strategy for block motion estimation using image features block motion estimation using the exhaustive full search is computationally intensive fast search algorithms offered in the past tend to reduce the amount of computation by limiting the number of locations to be searched nearly all of these algorithms rely on this assumption the mean absolute difference mad distortion function increases monotonically as the search location moves away from the global minimum essentially this assumption requires that the mad error surface be unimodal over the search window unfortunately this is usually not true in real world video signals however we can reasonably assume that it is monotonic in a small neighborhood around the global minimum consequently one simple strategy but perhaps the most efficient and reliable is to place the checking point as close as possible to the global minimum in this paper some image features are suggested to locate the initial search points such a guided scheme is based on the location of certain feature points after applying a feature detecting process to each frame to extract a set of feature points as matching primitives we have extensively studied the statistical behavior of these matching primitives and found that they are highly correlated with the mad error surface of real world motion vectors these correlation characteristics are extremely useful for fast search algorithms the results are robust and the implementation could be very efficient a beautiful point of our approach is that the proposed search algorithm can work together with other block motion estimation algorithms results of our experiment on applying the present approach to the block based gradient descent search algorithm bbgds the diamond search algorithm ds and our previously proposed edge oriented block motion estimation show that the proposed search strategy is able to strengthen these searching algorithms as compared to the conventional approach the new algorithm through the extraction of image features is more robust produces smaller motion compensation errors and has a simple computational complexity

robust finite time stabilization of fractional order neural networks with discontinuous and continuous activation functions under uncertainty this paper is concerned with robust finite time stabilization for a class of fractional order neural networks fnns with two types of activation functions i e discontinuous and continuous activation function under uncertainty it is worth noting that there exist few results about fnns with discontinuous activation functions which is mainly because classical solutions and theories of differential equations cannot be applied in this case especially there is no relevant finite time stabilization research for such system and this paper makes up for the gap the existence of global solution under the framework of filippov for such system is guaranteed by limiting discontinuous activation functions according to set valued analysis and kakutani s fixed point theorem we obtain the existence of equilibrium point in particular based on differential inclusion theory and fractional lyapunov stability theory several new sufficient conditions are given to ensure finite time stabilization via a novel discontinuous controller and the upper bound of the settling time for stabilization is estimated in addition we analyze the finite time stabilization of fnns with lipschitz continuous activation functions under uncertainty the results of this paper improve corresponding ones of integer order neural networks with discontinuous and continuous activation functions finally three numerical examples are given to show the effectiveness of the theoretical results

the cross search algorithm for motion estimation image coding a fast block matching algorithm for motion estimation is presented it is based on a logarithmic step where in each search step only four locations are tested for a motion displacement of w pels frame this technique requires 5 4 log sub 2 w computations to locate the best match using sequences of cif standard pictures the interframe motion compensated prediction error with this technique is compared to the other fast methods the computational complexity of this algorithm is also compared against those methods

global exponential stability and global convergence in finite time of delayed neural networks with infinite gain this paper introduces a general class of neural networks with arbitrary constant delays in the neuron interconnections and neuron activations belonging to the set of discontinuous monotone increasing and possibly unbounded functions the discontinuities in the activations are an ideal model of the situation where the gain of the neuron amplifiers is very high and tends to infinity while the delay accounts for the finite switching speed of the neuron amplifiers or the finite signal propagation speed it is known that the delay in combination with high gain nonlinearities is a particularly harmful source of potential instability the goal of this paper is to single out a subclass of the considered discontinuous neural networks for which stability is instead insensitive to the presence of a delay more precisely conditions are given under which there is a unique equilibrium point of the neural network which is globally exponentially stable for the states with a known convergence rate the conditions are easily testable and independent of the delay moreover global convergence in finite time of the state and output is investigated in doing so new interesting dynamical phenomena are highlighted with respect to the case without delay which make the study of convergence in finite time significantly more difficult the obtained results extend previous work on global stability of delayed neural networks with lipschitz continuous neuron activations and neural networks with discontinuous neuron activations but without delays

motion estimation without integer pel search the typical motion estimation me consists of three main steps including spatial temporal prediction integer pel search and fractional pel search the integer pel search which seeks the best matched integer pel position within a search window is considered to be crucial for video encoding it occupies over 50 of the overall encoding time when adopting the full search scheme for software encoders and introduces remarkable area cost memory traffic and power consumption to hardware encoders in this paper we find that video sequences especially high resolution videos can often be encoded effectively and efficiently even without integer pel search such counter intuitive phenomenon is not only because that spatial temporal prediction and fractional pel search are accurate enough for the me of many blocks in fact we observe that when the predicted motion vector is biased from the optimal motion vector mainly for boundary blocks of irregularly moving objects it is also hard for integer pel search to reduce the final rate distortion cost the deviation of reference position could be alleviated with the fractional pel interpolation and rate distortion optimization techniques e g adaptive macroblock mode considering the decreasing proportion of boundary blocks caused by the increasing resolution of videos integer pel search may be rather cost ineffective in the era of high resolution experimental results on 36 typical sequences of different resolutions encoded with x264 which is a widely used video encoder comply with our analysis well for 1080p sequences removing the integer pel search saves 57 9 of the overall h 264 encoding time on average compared to the original x264 with full integer pel search using default parameters while the resultant performance loss is negligible the bit rate is increased by only 0 18 while the peak signal to noise ratio is decreased by only 0 01 db per frame averagely

a new predictive search area approach for fast block motion estimation according to the observation on the distribution of motion differentials among the motion vector of any block and those of its four neighboring blocks from six real video sequences this paper presents a new predictive search area approach for fast block motion estimation employing our proposed simple predictive search area approach into the full search fs algorithm our improved fs algorithm leads to 93 83 average execution time improvement ratio but only has a small estimation accuracy degradation we also investigate the advantages of computation and estimation accuracy of our improved fs algorithm when compared to the edge based search algorithm of chan and siu see ieee trans image processing vol 10 p 1223 1238 aug 2001 experimental results reveal that our improved fs algorithm has 74 33 average execution time improvement ratio and has a higher estimation accuracy finally we further compare the performance among our improved fs algorithm the three step search algorithm and the block based gradient descent search algorithm

controllability method for acoustic scattering with spectral elements we formulate the helmholtz equation as an exact controllability problem for the time dependent wave equation the problem is then discretized in time domain with central finite difference scheme and in space domain with spectral elements this approach leads to high accuracy in spatial discretization moreover the spectral element method results in diagonal mass matrices which makes the time integration of the wave equation highly efficient after discretization the exact controllability problem is reformulated as a least squares problem which is solved by the conjugate gradient method we illustrate the method with some numerical experiments which demonstrate the significant improvements in efficiency due to the higher order spectral elements for a given accuracy the controllability technique with spectral element method requires fewer computational operations than with conventional finite element method in addition by using higher order polynomial basis the influence of the pollution effect is reduced

perceptual evaluation of the mean square error choice of regularization parameter a formal perceptual study shows that the perceptually optimal choice of regularization parameter varies from the minimum mean square error parameter as a function of the original image the point spread function and the signal to noise ratio snr however further studies show that this variation has only a slight effect on the perceived quality of the restoration

significance linked connected component analysis for wavelet image coding the success in wavelet image coding is mainly attributed to a recognition of the importance of data organization and representation there have been several very competitive wavelet coders developed namely shapiro s 1993 embedded zerotree wavelets ezw servetto et al s 1995 morphological representation of wavelet data mrwd and said and pearlman s see ieee trans circuits syst video technol vol 6 p 245 50 1996 set partitioning in hierarchical trees spiht we develop a novel wavelet image coder called significance linked connected component analysis slcca of wavelet coefficients that extends mrwd by exploiting both within subband clustering of significant coefficients and cross subband dependency in significant fields extensive computer experiments on both natural and texture images show convincingly that the proposed slcca outperforms ezw mrwd and spiht for example for the barbara image at 0 25 b pixel slcca outperforms ezw mrwd and spiht by 1 41 db 0 32 db and 0 60 db in psnr respectively it is also observed that slcca works extremely well for images with a large portion of texture for eight typical 256 spl times 256 grayscale texture images compressed at 0 40 b pixel slcca outperforms spiht by 0 16 db 0 63 db in psnr this performance is achieved without using any optimal bit allocation procedure thus both the encoding and decoding procedures are fast

video block motion estimation based on gray code kernels motion in modern video coders is estimated using a block matching algorithm that calculates the distance and direction of motion on a block by block basis in this paper a novel fast block based motion estimation algorithm is proposed this algorithm uses an efficient projection framework that bounds the distance between a template block and candidate blocks fast projection is performed using a family of highly efficient filter kernels the gray code kernels requiring only 2 operations per pixel per kernel the projection framework is combined with a rejection scheme which allows rapid rejection of candidate blocks that are distant from the template block the tradeoff between computational complexity and quality of results can be easily controlled in the proposed algorithm thus it enables adaptivity to image content to further improve the results experiments show that the proposed adaptive algorithm outperforms other popular fast motion estimation algorithms

first order system least squares for the stokes equations with application to linear elasticity following our earlier work on general second order scalar equations here we develop a least squares functional for the two and three dimensional stokes equations generalized slightly by allowing a pressure term in the continuity equation by introducing a velocity flux variable and associated curl and trace equations we are able to establish ellipticity in an h1 product norm appropriately weighted by the reynolds number this immediately yields optimal discretization error estimates for finite element spaces in this norm and optimal algebraic convergence estimates for multiplicative and additive multigrid methods applied to the resulting discrete systems both estimates are naturally uniform in the reynolds number moreover our pressure perturbed form of the generalized stokes equations allows us to develop an analogous result for the dirichlet problem for linear elasticity where we obtain the more substantive result that the estimates are uniform in the poisson ratio

exponential stabilization of neural networks with various activation functions and mixed time varying delays this paper presents some results on the global exponential stabilization for neural networks with various activation functions and time varying continuously distributed delays based on augmented time varying lyapunov krasovskii functionals new delay dependent conditions for the global exponential stabilization are obtained in terms of linear matrix inequalities a numerical example is given to illustrate the feasibility of our results

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

finite time stability analysis for markovian jump memristive neural networks with partly unknown transition probabilities this paper is concerned with the finite time stochastically stability ftss analysis of markovian jump memristive neural networks with partly unknown transition probabilities in the neural networks there exist a group of modes determined by markov chain and thus the markovian jump was taken into consideration and the concept of ftss is first introduced for the memristive model by introducing a markov switching lyapunov functional and stochastic analysis theory an ftss test procedure is proposed from which we can conclude that the settling time function is a stochastic variable and its expectation is finite the system under consideration is quite general since it contains completely known and completely unknown transition probabilities as two special cases more importantly a nonlinear measure method was introduced to verify the uniqueness of the equilibrium point compared with the fixed point theorem that has been widely used in the existing results this method is more easy to implement besides the delay interval was divided into four subintervals which make full use of the information of the subsystems upper bounds of the time varying delays finally the effectiveness and superiority of the proposed method is demonstrated by two simulation examples

finite time global stabilization by means of time varying distributed delay feedback the paper contains certain results concerning the finite time global stabilization for triangular control systems described by retarded functional differential equations by means of time varying distributed delay feedback these results enable us to present solutions to feedback stabilization problems for systems with delayed input the results are obtained by using the backstepping technique

exponential stability and stabilization of delayed memristive neural networks based on quadratic convex combination method this paper is concerned with the exponential stability and stabilization of memristive neural networks mnns with delays first we present some generalized double integral inequalities which include some existing inequalities as their special cases second combining with quadratic convex combination method these double integral inequalities are employed to formulate a delay dependent stability condition for mnns with delays third a state dependent switching control law is obtained for mnns with delays based on the proposed stability conditions the desired feedback gain matrices are accomplished by solving a set of linear matrix inequalities finally the feasibility and effectiveness of the proposed results are tested by two numerical examples

exponential stabilization of memristive neural networks with time delays in this paper a general class of memristive neural networks with time delays is formulated and studied some sufficient conditions in terms of linear matrix inequalities are obtained in order to achieve exponential stabilization the result can be applied to the closed loop control of memristive systems in particular several succinct criteria are given to ascertain the exponential stabilization of memristive cellular neural networks in addition a simplified and effective algorithm is considered for design of the optimal controller these conditions are the improvement and extension of the existing results in the literature two numerical examples are given to illustrate the theoretical results via computer simulations

video compression of coronary angiograms based on discrete wavelet transform with block classification a new method of video compression for angiographic images has been developed to achieve high compression ratio spl sim 20 1 while eliminating block artifacts which leads to loss of diagnostic accuracy this method adopts motion picture experts group s mpegs motion compensated prediction to takes advantage of frame to frame correlation however in contrast to mpeg the error images arising from mismatches in the motion estimation are encoded by discrete wavelet transform dwt rather than block discrete cosine transform dct furthermore the authors developed a classification scheme which label each block in an image as intra error or background type and encode it accordingly this hybrid coding can significantly improve the compression efficiency in certain eases this method can be generalized for any dynamic image sequences applications sensitive to block artifacts

time harmonic elasticity with controllability and higher order discretization methods the time harmonic solution of the linear elastic wave equation is needed for a variety of applications the typical procedure for solving the time harmonic elastic wave equation leads to difficulties solving large scale indefinite linear systems to avoid these difficulties we consider the original time dependent equation with a method based on an exact controllability formulation the main idea of this approach is to find initial conditions such that after one time period the solution and its time derivative coincide with the initial conditions the wave equation is discretized in the space domain with spectral elements the degrees of freedom associated with the basis functions are situated at the gauss lobatto quadrature points of the elements and the gauss lobatto quadrature rule is used so that the mass matrix becomes diagonal this method is combined with the second order central finite difference or the fourth order runge kutta time discretization as a consequence of these choices only matrix vector products are needed in time dependent simulation this makes the controllability method computationally efficient

controllability method for the helmholtz equation with higher order discretizations we consider a controllability technique for the numerical solution of the helmholtz equation the original time harmonic equation is represented as an exact controllability problem for the time dependent wave equation this problem is then formulated as a least squares optimization problem which is solved by the conjugate gradient method such an approach was first suggested and developed in the 1990s by french researchers and we introduce some improvements to its practical realization we use higher order spectral elements for spatial discretization which leads to high accuracy and lumped mass matrices higher order approximation reduces the pollution effect associated with finite element approximation of time harmonic wave equations and mass lumping makes explicit time stepping schemes for the wave equation very efficient we also derive a new way to compute the gradient of the least squares functional and use algebraic multigrid method for preconditioning the conjugate gradient algorithm numerical results demonstrate the significant improvements in efficiency due to the higher order spectral elements for a given accuracy spectral element method requires fewer computational operations than conventional finite element method in addition by using higher order polynomial basis the influence of the pollution effect is reduced

spectral element methods for large scale parallel navier stokes calculations abstract we analyze the computational complexity of a recently developed two level iteration scheme for spectral element solution of the time dependent incompressible navier stokes equations in complex domains we present several algorithmic advances which significantly enhance the scalability of this approach including implementation of an advanced combine operation for degrees of freedom on subdomain edges parallel solution of the fine grained coarse grid problem and implementation of local low order finite element preconditioners for the find grid problem timings on the 512 node intel delta machine show that the combined improvements lead to a fourfold reduction in navier stokes solution time for the particular case of a three dimensional boundary layer calculation consisting of one million degrees of freedom

finite time stabilization of delayed memristive neural networks discontinuous state feedback and adaptive control approach in this paper a general class of delayed memristive neural networks dmnns system described by functional differential equation with discontinuous right hand side is considered under the extended filippov framework we investigate the finite time stabilization problem for dmnns by using the famous finite time stability theorem and the generalized lyapunov functional method to do so we design two classes of novel controllers including discontinuous state feedback controller and discontinuous adaptive controller without assuming the boundedness and monotonicity of the activation functions several sufficient conditions are given to stabilize the states of this class of dmnns in finite time moreover the upper bounds of the settling time for stabilization are estimated finally numerical examples are provided to demonstrate the effectiveness of the developed method and the theoretical results

finite time stabilization of nonlinear systems with parametric and dynamic uncertainties in this note non smooth finite time stabilization of nonlinear systems with parametric and dynamic uncertainties is investigated to solve this problem the input to state stability property is used to characterize unmeasured dynamic uncertainties a constructive partial state control design is proposed on the basis of involved combined use of lyapunov backstepping and input to state stability techniques under small gain type local conditions a solution for the finite time regulation of a class of uncertain nonlinear systems is obtained

detection of missing data in image sequences bright and dark flashes are typical artifacts in degraded motion picture material the distortion is referred to as dirt and sparkle in the motion picture industry this is caused either by dirt becoming attached to the frames of the film or by the film material being abraded the visual result is random patches of the frames having grey level values totally unrelated to the initial information at those sites to restore the film without causing distortion to areas of the frames that are not affected the locations of the blotches must be identified heuristic and model based methods for the detection of these missing data regions are presented in this paper and their action on simulated and real sequences is compared

projection multilevel methods for quasilinear elliptic partial differential equations theoretical results the goal of this paper is to introduce a new multilevel solver for two dimensional elliptic systems of nonlinear partial differential equations pdes where the nonlinearity is of the type u partial v the incompressible navier stokes equations are an important representative of this class and are the target of this study using a first order system least squares fosls approach and introducing a new variable for partial v for this class of pdes we obtain a formulation in which the nonlinearity appears as a product of two different dependent variables the result is a system that is linear within each variable but nonlinear in the cross terms in this paper we introduce a new multilevel method that treats the nonlinearities directly this approach is based on a projection multilevel pml method s f mccormick multilevel projection methods for partial differential equations siam philadelphia 1992 applied to the fosls functional the implementation of the discretization process relaxation coarse grid correction and cycling strategies is discussed and optimal performance is established numerically a companion paper t a manteuffel s f mccormick and o rohrle siam j numer anal 44 2006 pp 139 152 establishes a two level convergence proof for this new multilevel method

a stable and scalable hybrid solver for rate type non newtonian fluid models we present and analyze hybrid discretization schemes for rate type non newtonian fluids models the method employs higher order conforming approximations for velocity and pressure of the stokes equation and lower order approximations such as piecewise linear or piecewise constant for conformation tensor to reduce the accuracy gap the constitutive equation is discretized on a refined mesh which is obtained by subdividing the mesh for the velocity and pressure the temporal discretization is made by the standard semi lagrangian scheme the fully discrete nonlinear system is shown to be solved iteratively by applying the three steps 1 locating the characteristic feet of fluid particles 2 solving the constitutive equation and 3 solving the momentum and continuity equations stokes type equation to achieve a scalability of the solution process we employ an auxiliary space preconditioning method for the solution to the conforming finite element methods for the stokes equation this method is basically two grid method in which lower order finite element spaces are employed as auxiliary spaces it is shown to not only lead to the mesh independent convergence but also improve robustness and scalability stability analysis shows that if t o h d where d is the dimension of domain then the scheme admits a globally unique solution a number of full 3d test cases are provided to demonstrate the advantages of the proposed numerical techniques in relation to efficiency robustness and weak scalability

on the fly adaptive smoothed aggregation multigrid for markov chains a new adaptive algebraic multigrid scheme is developed for the solution of markov chains where the hierarchy of operators is adapted on the fly in a setup process that is interlaced with the solution process the setup process feeds the solution process with improved operators while the solution process provides the adaptive setup process with better approximations on which to base further improved operators the approach is demonstrated using petrov galerkin smoothed aggregation where only the prolongation operator is smoothed while the restriction remains of low order results show that the on the fly adaptive scheme can improve the performance of multigrid solvers that require extensive setup computations in both serial and parallel environments

semi automatic sparse preconditioners for high order finite element methods on non uniform meshes high order finite elements often have a higher accuracy per degree of freedom than the classical low order finite elements however in the context of implicit time stepping methods high order finite elements present challenges to the construction of efficient simulations due to the high cost of inverting the denser finite element matrix there are many cases where simulations are limited by the memory required to store the matrix and or the algorithmic components of the linear solver we are particularly interested in preconditioned krylov methods for linear systems generated by discretization of elliptic partial differential equations with high order finite elements using a preconditioner like algebraic multigrid can be costly in terms of memory due to the need to store matrix information at the various levels we present a novel method for defining a preconditioner for systems generated by high order finite elements that is based on a much sparser system than the original high order finite element system we investigate the performance for non uniform meshes on a cube and a cubed sphere mesh showing that the sparser preconditioner is more efficient and uses significantly less memory finally we explore new methods to construct the sparse preconditioner and examine their effectiveness for non uniform meshes we compare results to a direct use of algebraic multigrid as a preconditioner and to a two level additive schwarz method