experiments with implicit upwind methods for the euler equations abstract a number of implicit integration schemes for the one dimensional euler equations with conservative upwind spatial differencing are tested on a problem of steady discontinuous flow fastest convergence quadratic for the first order backward euler scheme is obtained with the upwind switching provided by van leer s differentiable split fluxes which easily linearize in time with roe s nondifferentiable split flux differences the iterations may get trapped in a limit cycle this also happens in a second order scheme with split fluxes if the matrix coefficients arising in the implicit time linearization are not properly centered in space the use of second order terms computed from split fluxes degrades the accuracy of the solution especially if these are subjected to a limiter for the sake of monotonicity preservation second order terms computed from the characteristic variables perform best

accurate three dimensional lid driven cavity flow a chebyshev collocation method in space is introduced which allows an accurate calculation of three dimensional lid driven cavity flows the time integration is carried out by an adams bashforth backward euler scheme the accuracy of the method relies on the representation of the solution as a superposition of stationary local asymptotic solutions and a residual flow field this way the most severe discontinuities in the boundary conditions which arise along the lines where moving and stationary walls meet are taken care of analytically and thus do not spoil the numerical part of the solution calculations are carried out for no slip boundary conditions at the cavity end walls as well as for periodic end wall conditions in general the spatial accuracy is better than fifth order for rigid end wall conditions the accuracy is reduced near the end walls to o n 3 2 but recovers in the bulk tabulated data are provided for the most interesting flow properties

two dimensional autoregressive 2 d ar model order estimation much research has been devoted to the area of one dimensional autoregressive 1 d ar and autoregressive moving average arma model order selection the most well known solutions for this problem are the akaike information criterion aic mdl and the minimum eigenvalue mev criteria on the other hand all works in the 2 d case have focused on the problem of parameter estimation in this correspondence we extend the previous criteria to the 2 d ar model order determination the model is assumed causal stable and spatially invariant with p sub 1 spl times p sub 2 quarter plane qp support numerical examples are given to illustrate the effectiveness of each method

a decomposition theorem for singular spaces with trivial canonical class of dimension at most five in this paper we partly extend the beauville bogomolov decomposition theorem to the singular setting we show that any complex projective variety of dimension at most five with canonical singularities and numerically trivial canonical class admits a finite cover etale in codimension one that decomposes as a product of an abelian variety and singular analogues of irreducible calabi yau and irreducible holomorphic symplectic varieties

self similarity of fourier domain mri data abstract this paper presents an overview of our recent research on the self similar properties of magnetic resonance imaging data in the fourier domain the motivation behind our work is to use self similarity as a constraint towards the spatial resolution enhancement of spatially limited magnetic resonance images we describe a fractal based method over complex valued fourier transforms of functions with compact support derived from a fractal based method in the spatial domain we show that our fractal based method can be tailored to perform frequency extrapolation in the frequency domain furthermore we develop a model of the one dimensional mri data that shows local self similarity by drawing a connection to autoregressive modeling finally we present a statistical analysis of two dimensional k space mri data which suggests that mri fourier data can be self similar

an implicit high order hybridizable discontinuous galerkin method for the incompressible navier stokes equations we present an implicit high order hybridizable discontinuous galerkin method for the steady state and time dependent incompressible navier stokes equations the method is devised by using the discontinuous galerkin discretization for a velocity gradient pressure velocity formulation of the incompressible navier stokes equations with a special choice of the numerical traces the method possesses several unique features which distinguish itself from other discontinuous galerkin methods first it reduces the globally coupled unknowns to the approximate trace of the velocity and the mean of the pressure on element boundaries thereby leading to a significant reduction in the degrees of freedom moreover if the augmented lagrangian method is used to solve the linearized system the globally coupled unknowns become the approximate trace of the velocity only second it provides for smooth viscous dominated problems approximations of the velocity pressure and velocity gradient which converge with the optimal order of k 1 in the l2 norm when polynomials of degree k 0 are used for all components of the approximate solution and third it displays superconvergence properties that allow us to use the above mentioned optimal convergence properties to define an element by element postprocessing scheme to compute a new and better approximate velocity indeed this new approximation is exactly divergence free h div conforming and converges with order k 2 for k 1 and with order 1 for k 0 in the l2 norm moreover a novel and systematic way is proposed for imposing boundary conditions for the stress viscous stress vorticity and pressure which are not naturally associated with the weak formulation of the method this can be done on different parts of the boundary and does not result in the degradation of the optimal order of convergence properties of the method extensive numerical results are presented to demonstrate the convergence and accuracy properties of the method for a wide range of reynolds numbers and for various polynomial degrees

recursive block coding a new approach to transform coding the concept of fast kl transform coding introduced earlier 7 8 for first order markov processes and certain random fields has been extended to higher order autoregressive ar sequences and practical images yielding what we call recursive block coding rbc algorithms in general the rate distortion performance for these algorithms is significantly superior to that of the conventional block kl transform algorithm moreover these algorithms permit the use of small size transforms thereby removing the need for fast transforms and making the hardware implementation of such coders more appealing this improved performance has been verified for practical image data and results in suppression of the block boundary effect commonly observed in traditional transform coding techniques this is illustrated by comparing rbc with cosine transform coding using both one and twodimensional algorithms examples of rbc encoded images at various rates are given

a staggered semi implicit discontinuous galerkin method for the two dimensional incompressible navier stokes equations in this paper we propose a new spatially high order accurate semi implicit discontinuous galerkin dg method for the solution of the two dimensional incompressible navier stokes equations on staggered unstructured curved meshes while the discrete pressure is defined on the primal grid the discrete velocity vector field is defined on an edge based dual grid the flexibility of high order dg methods on curved unstructured meshes allows to discretize even complex physical domains on rather coarse grids formal substitution of the discrete momentum equation into the discrete continuity equation yields one sparse linear equation system with four non zero blocks per element for only one scalar unknown namely the pressure the method is computationally efficient since the resulting system is not only very sparse but also symmetric and positive definite for appropriate boundary conditions furthermore all the volume and surface integrals needed by the scheme presented in this paper depend only on the geometry and the polynomial degree of the basis and test functions and can therefore be precomputed and stored in a preprocessor stage which leads to savings in terms of computational effort for the time evolution part in this way also the extension to a fully curved isoparametric approach becomes natural and affects only the preprocessing step the method is validated for polynomial degrees up to p 3 by solving some typical numerical test problems and comparing the numerical results with available analytical solutions or other numerical and experimental reference data

a rank test based approach to order estimation i 2 d ar models application in system identification and parametric spectral estimation by two dimensional 2 d autoregressive ar and 2 d autoregressive moving average arma models the order selection problem is often required in this correspondence we show that the information of 2 d ar model order is implicitly contained in a correlation matrix an algorithm for 2 d quarter plane ar model order determination is proposed numerical simulations are presented to show the efficiency of the proposed singular value decomposition svd based algorithm

two dimensional linear prediction models part i spectral factorization and realization in this paper we present several results for three different canonical forms of linear prediction on a plane these filters have causal semicausal and noncausal prediction geometries starting from their properties we consider the problem of realization of these filters from a given power spectral density function sdf since it is not possible in general to obtain rational spectral factors of a two dimensional sdf we propose algorithms for obtaining rational approximations which are stable and converge to their limit irrational factors as the order of approximation is increased it is also shown that the normal equations associated with the minimum variance two dimensional prediction filters give a useful algorithm for obtaining rational approximations which are stable and converge to their unique limit filters this result allows design of finite order stable filters by solving a finite number of equations while realizing the given sdf arbitrarily closely

on fano foliations abstract in this paper we address fano foliations on complex projective varieties these are foliations whose anti canonical class k is ample we focus our attention on a special class of fano foliations namely del pezzo foliations on complex projective manifolds we show that these foliations are algebraically integrable with one exceptional case when the ambient space is p n we also provide a classification of del pezzo foliations with mild singularities

kodaira dimension and zeros of holomorphic one forms we show that every holomorphic one form on a smooth complex projective variety of general type must vanish at some point the proof uses generic vanishing theory for hodge modules on abelian varieties

a pressure correction scheme for convection dominated incompressible flows with discontinuous velocity and continuous pressure in this work we present a pressure correction scheme for the incompressible navier stokes equations combining a discontinuous galerkin approximation for the velocity and a standard continuous galerkin approximation for the pressure the main interest of pressure correction algorithms is the reduced computational cost compared to monolithic strategies in this work we show how a proper discretization of the decoupled momentum equation can render this method suitable to simulate high reynolds regimes the proposed spatial velocity pressure approximation is lbb stable for equal polynomial orders and it allows adaptive p refinement for velocity and global p refinement for pressure the method is validated against a large set of classical two and three dimensional test cases covering a wide range of reynolds numbers in which it proves effective both in terms of accuracy and computational cost

digital image restoration using spatial interaction models this paper is concerned with developing fast nonrecursive algorithms for the minimum mean squared error restoration of degraded images the degradation is assumed to be due to a space invariant periodic nonseparable known point spread function and additive white noise our basic approach is to represent the images by a class of spatial interaction models namely the simultaneous autoregressve models and the conditional markov models defined on toroidal lattices and develop minimum mean squared error restoration algorithms using these models the restoration algorithms are optimal if the parameters characterizing the interaction models are exactly known however in practice the parameters are estimated from the images by using spatial interaction models we develop restoration algorithms that do not require the availability of the original image or its prototype the specific structure of the underlying lattice enables the implementation of the filters using fast fourier transform fft computations several restoration examples are given

a full plane block kalman filter for image restoration a two dimensional method which uses a full plane image model to generate a more accurate filtered estimate of an image that has been corrupted by additive noise and full plane blur is presented causality is maintained within the filtering process by using multiple concurrent block estimators in addition true state dynamics are preserved resulting in an accurate kalman gain matrix simulation results on a test image corrupted by additive white gaussian noise are presented for various image models and compared to those of the previous block kalman filtering methods

high re solutions for incompressible flow using the navier stokes equations and a multigrid method the vorticity stream function formulation of the two dimensional incompressible navierstokes equations is used to study the effectiveness of the coupled strongly implicit multigrid csi mg method in the determination of high re fine mesh flow solutions the driven flow in a square cavity is used as the model problem solutions are obtained for configurations with reynolds number as high as 10 000 and meshes consisting of as many as 257 x 257 points for re 1000 the 129 x 129 grid solution required 1 5 minutes of cpu time on the amdahl 470 v 6 computer because of the appearance of one or more secondary vortices in the flow field uniform mesh refinement was preferred to the use of one dimensional gridclustering coordinate transformations the past decade has witnessed a great deal of progress in the area of computational fluid dynamics developments in computer technology hardware as well as in advanced numerical algorithms have enabled attempts to be made towards analysis and numerical solution of highly complex flow problems for some of these applications the use of simple iterative techniques to solve the navier stokes equations leads to a rather slow convergence rate for the solutions the solution convergence rate can be seriously affected if the coupling among the various governing differential equations is not properly honored either in the interior of the solution domain or at its boundaries the rate of convergence is also generally strongly dependent on such problem parameters as the reynolds number the mesh size and the total number of computational points this has led several researchers to examine carefully the recently emerging multigrid mg technique as a useful means for enhancing the convergence rate of iterative numerical methods for solving discretized equations at a number of computational grid points so large as to be considered impractical previously

hybridizable discontinuous galerkin projection methods for navier stokes and boussinesq equations schemes for the incompressible navier stokes and boussinesq equations are formulated and derived combining the novel hybridizable discontinuous galerkin hdg method a projection method and implicit explicit runge kutta imex rk time integration schemes we employ an incremental pressure correction and develop the corresponding hdg finite element discretization including consistent edge space fluxes for the velocity predictor and pressure correction we then derive the proper forms of the element local and hdg edge space final corrections for both velocity and pressure including the hdg rotational correction we also find and explain a consistency relation between the hdg stability parameters of the pressure correction and velocity predictor we discuss and illustrate the effects of the time splitting error we then detail how to incorporate the hdg projection method time split within standard imex rk time stepping schemes our high order hdg projection schemes are implemented for arbitrary mixed element unstructured grids with both straight sided and curved meshes in particular we provide a quadrature free integration method for a nodal basis that is consistent with the hdg method to prevent numerical oscillations we develop a selective nodal limiting approach its applications show that it can stabilize high order schemes while retaining high order accuracy in regions where the solution is sufficiently smooth we perform spatial and temporal convergence studies to evaluate the properties of our integration and selective limiting schemes and to verify that our solvers are properly formulated and implemented to complete these studies and to illustrate a range of properties for our new schemes we employ an unsteady tracer advection benchmark a manufactured solution for the steady diffusion and stokes equations and a standard lock exchange boussinesq problem

quadtree structured linear prediction models for image sequence processing a summary is presented of a study on two dimensional linear prediction models for image sequence processing and its application to change detection and scene coding the study focused on two dimensional joint process modeling of interframe relationships the derivation of computationally efficient matching algorithms and the implementation of a block adaptive interframe predictor for use in interframe predictive coding and change detection in the approach presented the spatial nonstationarity is handled by an underlying quadtree segmentation structure a maximum likelihood criterion and a simpler minimum variance criterion are discussed as detection and segmentation rules the results of this research indicate that a constrained joint process model involving only a single gain parameter and a shift parameter is the best tradeoff between performance and computational complexity

a discontinuous galerkin method with nonoverlapping domain decomposition for the stokes and navier stokes problems a family of discontinuous galerkin finite element methods is formulated and analyzed for stokes and navier stokes problems an inf sup condition is established as well as optimal energy estimates for the velocity and l 2 estimates for the pressure in addition it is shown that the method can treat a finite number of nonoverlapping domains with nonmatching grids at interfaces

parameter estimation for two dimensional vector models using neural networks this correspondence addresses the problem of two dimensional 2 d vector image model parameter estimation using a new recursive least squares rls based learning method vector autoregressive ar models with various 1 d and 2 d causal and noncausal regions of support ros are considered numerical results are presented which demonstrate the usefulness of the proposed scheme for on line implementation

a hybrid high order method for the incompressible navier stokes equations based on temam s device abstract in this work we propose a novel hybrid high order method for the incompressible navier stokes equations based on a formulation of the convective term including temam s device for stability the proposed method has several advantageous features it supports arbitrary approximation orders on general meshes including polyhedral elements and non matching interfaces it is inf sup stable it is locally conservative it supports both the weak and strong enforcement of velocity boundary conditions it is amenable to efficient computer implementations where a large subset of the unknowns is eliminated by solving local problems inside each element particular care is devoted to the design of the convective trilinear form which mimicks at the discrete level the non dissipation property of the continuous one the possibility to add a convective stabilisation term is also contemplated and a formulation covering various classical options is discussed the proposed method is theoretically analysed and an energy error estimate in h k 1 with h denoting the meshsize is proved under the usual data smallness assumption a thorough numerical validation on two and three dimensional test cases is provided both to confirm the theoretical convergence rates and to assess the method in more physical configurations including in particular the well known two and three dimensional lid driven cavity problems

an artificial compressibility flux for the discontinuous galerkin solution of the incompressible navier stokes equations discontinuous galerkin dg methods have proved to be well suited for the construction of robust high order numerical schemes on unstructured and possibly nonconforming grids for a variety of problems their application to the incompressible navier stokes ins equations has also been recently considered although the subject is far from being fully explored in this work we propose a new approach for the dg numerical solution of the ins equations written in conservation form the inviscid numerical fluxes both in the continuity and in the momentum equation are computed using the values of velocity and pressure provided by the exact solution of the riemann problem associated with a local artificial compressibility perturbation of the equations unlike in most of the existing methods artificial compressibility is here introduced only at the interface flux level therefore resulting in a consistent discretization of the ins equations irrespectively of the amount of artificial compressibility introduced the discretization of the viscous term follows the well established dg scheme named br2 the performance and the accuracy of the method are demonstrated by computing the kovasznay flow and the two dimensional lid driven cavity flow for a wide range of reynolds numbers and for various degrees of polynomial approximation

a locally conservative ldg method for the incompressible navier stokes equations in this paper a new local discontinuous galerkin method for the incompressible stationary navier stokes equations is proposed and analyzed four important features render this method unique its stability its local conservativity its high order accuracy and the exact satisfaction of the incompressibility constraint although the method uses completely discontinuous approximations a globally divergence free approximate velocity in h div is obtained by simple element by element post processing optimal error estimates are proven and an iterative procedure used to compute the approximate solution is shown to converge this procedure is nothing but a discrete version of the classical fixed point iteration used to obtain existence and uniqueness of solutions to the incompressible navier stokes equations by solving a sequence of oseen problems numerical results are shown which verify the theoretical rates of convergence they also confirm the independence of the number of fixed point iterations with respect to the discretization parameters finally they show that the method works well for a wide range of reynolds numbers

a high order mimetic method on unstructured polyhedral meshes for the diffusion equation abstract we present a new family of mimetic finite difference schemes for solving elliptic partial differential equations in the primal form on unstructured polyhedral meshes these mimetic discretizations are built to satisfy local consistency and stability conditions the consistency condition is an exactness property i e the mimetic schemes are exact when the solution is a polynomial of an assigned degree the stability condition ensures the well posedness of the method the degrees of freedom are the solution moments on mesh faces and inside mesh cells higher order schemes are built using higher order moments the developed schemes are verified numerically on diffusion problems with constant and spatially variable possibly discontinuous tensorial coefficients

a unified texture model based on a 2 d wold like decomposition a unified texture model that is applicable to a wide variety of texture types found in natural images is presented this model leads to the derivation of texture analysis and synthesis algorithms designed to estimate the texture parameters and to reconstruct the original texture field from these parameters the texture field is assumed to be a realization of a regular homogeneous random field which is characterized in general by a mixed spectral distribution the texture field is orthogonally decomposed into a purely indeterministic component and a deterministic component the deterministic component is further orthogonally decomposed into a harmonic component and a generalized evanescent component both analytical and experimental results show that the deterministic components should be parameterized separately from the purely indeterministic component the model is very efficient in terms of the number of parameters required to faithfully represent textures reconstructed textures are practically indistinguishable from the originals

two dimensional linear prediction model based decorrelation method a unified feature extraction scheme the two dimensional 2 d linear prediction model based decorrelation method is presented by applying 2 d causal linear prediction model to decorrelate a textured image the very heavy computation load required when using a whitening operator to decorrelate the image or the significant information loss when using the gradient operator to approximately whiten the image is avoided the texture model based decorrelation provides three sets of features to perform texture classification the coefficients of the 2 d linear prediction the moments of error residuals and the autocorrelation values an optimum feature selection scheme using modified branch and bound method was introduced to reduce information redundancy after feature selection 100 classification accuracy was achieved for a 20 class texture problem experiments show that this feature extraction scheme is truly information lossless effective and fast

on codimension 1 del pezzo foliations on varieties with mild singularities in this paper we extend to the singular setting the theory of fano foliations developed in our previous paper araujo and druel adv math 238 70 118 2013 a mathbb q fano foliation on a complex projective variety x is a foliation fancyscript f subsetneq t x whose anti canonical class k fancyscript f is an ample mathbb q cartier divisor in the spirit of kobayashi ochiai theorem we prove that under some conditions the index i fancyscript f of a mathbb q fano foliation is bounded by the rank r of fancyscript f and classify the cases in which i fancyscript f r next we consider mathbb q fano foliations fancyscript f for which i fancyscript f r 1 these are called del pezzo foliations we classify codimension 1 del pezzo foliations on mildly singular varieties

discrete functional analysis tools for discontinuous galerkin methods with application to the incompressible navier stokes equations two discrete functional analysis tools are established for spaces of piecewise polynomial functions on general meshes i a discrete counterpart of the continuous sobolev embeddings in both hilbertian and non hilbertian settings ii a compactness result for bounded sequences in a suitable discontinuous galerkin norm together with a weak convergence property for some discrete gradients the proofs rely on techniques inspired by the finite volume literature which differ from those commonly used in finite element analysis the discrete functional analysis tools are used to prove the convergence of discontinuous galerkin approximations of the steady incompressible navier stokes equations two discrete convective trilinear forms are proposed a non conservative one relying on temam s device to control the kinetic energy balance and a conservative one based on a nonstandard modification of the pressure