estimating time evolving partial coherence between signals via multivariate locally stationary wavelet processes we consider the problem of estimating time localized cross dependence in a collection of nonstationary signals to this end we develop the multivariate locally stationary wavelet framework which provides a time scale decomposition of the signals and thus naturally captures the time evolving scale specific cross dependence between components of the signals under the proposed model we rigorously define and estimate two forms of cross dependence measures wavelet coherence and wavelet partial coherence these dependence measures differ in a subtle but important way the former is a broad measure of dependence which may include indirect associations i e dependence between a pair of signals that is driven by another signal conversely wavelet partial coherence measures direct linear association between a pair of signals i e it removes the linear effect of other observed signals our time scale wavelet partial coherence estimation scheme thus provides a mechanism for identifying hidden dynamic relationships within a network of nonstationary signals as we demonstrate on electroencephalograms recorded in a visual motor experiment

implicit high order time marching schemes for the linearized euler equations high order accurate implicit time marching methods are presented for discontinuous galerkin and spectral volume high order accurate spatial discretizations of the linearized euler equations that govern propagation of aeroacoustic disturbances it is found that despite the additional computational time that is required for the solution of the large sparse linear system for the degrees of freedom of high order spectral volume or discontinuous galerkin discretizations implicit methods offer an attractive alternative for practical aeroacoustic computations with these high order methods several explicit and implicit methods for time advancement are tested the advantages of implicit higher order accurate in time methods that involve multiple implicit steps are demonstrated the efficiency and accuracy of time marching methods is evaluated for test problems with exact solutions it is shown that complex domain aeroacoustic predictions can be obtained at a reduced computational cost with the use of high order accurate implicit methods

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

application of dispersion relation preserving theory to develop a two dimensional convection diffusion scheme in this paper a finite difference scheme is developed within the nine point semi discretization framework for the convection diffusion equation the employed pade approximation renders a fourth order temporal accuracy and the spatial approximation of convection terms accommodates the dispersion relation the artificial viscosity introduced in the two dimensional convection diffusion reaction cdr equation for stability reasons is analytically derived constraints on the mesh size and time interval for rendering a monotonic matrix are also rigorously derived to validate the proposed method we investigate several problems that are amenable to the exact solutions the results with good rates of convergence are obtained for the investigated scalar and navier stokes problems

qmr a quasi minimal residual method for non hermitian linear systems the biconjugate gradient bcg method is the natural generalization of the classical conjugate gradient algorithm for hermitian positive definite matrices to general non hermitian linear systems unfortunately the original bcg algorithm is susceptible to possible breakdowns and numerical instabilities in this paper we present a novel bcg like approach the quasi minimal residual qmr method which overcomes the problems of bcg an implementation of qmr based on a look ahead version of the nonsymmetric lanczos algorithm is proposed it is shown how bcg iterates can be recovered stably from the qmr process some further properties of the qmr approach are given and an error bound is presented finally numerical experiments are reported

multidimensional optimization of finite difference schemes for computational aeroacoustics because of the long propagation distances computational aeroacoustics schemes must propagate the waves at the correct wave speeds and lower the isotropy error as much as possible the spatial differencing schemes are most frequently analyzed and optimized for one dimensional test cases therefore in multidimensional problems such optimized schemes may not have isotropic behavior in this work optimized finite difference schemes for multidimensional computational aeroacoustics are derived which are designed to have improved isotropy compared to existing schemes the derivation is performed based on both taylor series expansion and fourier analysis various explicit centered finite difference schemes and the associated boundary stencils have been derived and analyzed the isotropy corrector factor a parameter of the schemes can be determined by minimizing the integrated error between the phase or group velocities on different spatial directions the order of accuracy of the optimized schemes is the same as that of the classical schemes the advantage being in reducing the isotropy error the present schemes are restricted to equally spaced cartesian grids so the generalized curvilinear transformation method and cartesian grid methods are good candidates the optimized schemes are tested by solving various multidimensional problems of aeroacoustics

on the value of information in system identification bounded noise case assuming instantaneous bounds on the noise system parameter identification is formulated as membership set estimation problem sequential algorithms are constructed to estimate the membership sets of the parameters which are consistent with the measurements and the noise constraints the important new feature of the proposed algorithms is their ability to ignore redundant data the efficient data extraction property of the new algorithms is achieved with small computational effort and with improved performance when compared to the least square algorithm the convergence properties and the notion of identifiability in the set theoretic context are also studied

a divergence free condition compensated method for incompressible navier stokes equations the present study aims to develop a new formulation to effectively calculate the incompressible navier stokes solutions in non staggered grids the distinguished feature of the proposed method which avoids directly solving the divergence free equation is to add a rigorously derived source term to the momentum equation to ensure satisfaction of the fluid incompressibility for the sake of numerical accuracy dispersion relation preserving upwind scheme developed within the two dimensional context was employed to approximate the convection terms the validity of the proposed mass preserving navier stokes method is justified by solving two benchmark problems at high reynolds and rayleigh numbers based on the simulated navier stokes solutions the proposed formulation is shown to outperform the conventional segregated method in terms of the reduction of cpu time 2007 elsevier b v all rights reserved

stabilized mixed methods for the stokes problem the solution of the stokes problem is approximated by three stabilized mixed methods one due to hughes balestra and franca and the other two being variants of this procedure in each case the bilinear form associated with the saddle point problem of the standard mixed formulation is modified to become coercive over the finite element space error estimates are derived for each procedure

simulation of improper complex valued sequences an algorithm is proposed for the simulation of improper noncircular complex valued second order stationary stochastic processes having specified second order properties three examples are given generated processes are shown to obey necessary distributional properties

edge stabilization for galerkin approximations of convection diffusion reaction problems n this paper we recall a stabilization technique for finite element methods for convection diffusion reaction equations originally proposed by j douglas jr and t dupont in computing methods in applied sciences second internat sympos versailles 1975 207 216 lecture notes in phys 58 springer berlin 1976 mr0440955 55 13823 the method uses least square stabilization of the gradient jumps across element boundaries we prove that the method is stable in the hyperbolic limit and prove optimal a priori error estimates we address the question of monotonicity of discrete solutions and present some numerical examples illustrating the theoretical results

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

an element by element bicgstab iterative method for three dimensional steady navier stokes equations construction of a stabilized galerkin upwind finite element model for steady and incompressible navier stokes equations in three dimensions is the main theme of this study in the time independent context the weighted residuals statement is kept biased in favor of the upstream flow direction by adding an artificial damping term of physical plausibility to the galerkin framework this upwind approach has significant advantage of seeking solutions free from cross stream diffusion error finite element solutions have been found by mixed formulation implemented in quadratic cubic elements which are characterized as possessing the so called lbb ladyzhenskaya babuska brezzi condition an element by element bicgstab solution solver is intended to alleviate difficulties regarding the asymmetry and indefiniteness arising from the use of a mixed formulation for incompressible fluid flows the developed three dimensional finite element code is first rectified by solving a problem amenable to analytic solution a well known lid driven cavity flow problem in a cubical cavity is also studied

a differentially interpolated direct forcing immersed boundary method for predicting incompressible navier stokes equations in time varying complex geometries a dispersion relation preserving dual compact scheme developed in cartesian grids is applied together with the immersed boundary method to solve the flow equations in irregular and time varying domains the artificial momentum forcing term applied at certain points in cells containing fluid and solid allows an imposition of velocity condition to account for the motion of solid body we develop in this study a differential based interpolation scheme which can be easily extended to three dimensional simulation the results simulated from the proposed immersed boundary method agree well with other numerical and experimental results for the chosen benchmark problems the accuracy and fidelity of the ib flow solver developed to predict flows with irregular boundaries are therefore demonstrated

wavelet coherence for certain nonstationary bivariate processes a previous study considered the estimation of wavelet coherence from jointly stationary time series via time domain smoothing and use of a single morlet wavelet the form of the asymptotic goodman s distribution was derived in this paper we extend this approach to nonstationary time series where the nonstationarity is induced by various types of modulation the model forms of coherence studied include constant over time and scale time varying scale varying and time and scale varying these coherence models are carefully derived from appropriate statistical models for nonstationary processes the portion of the signals used in calculating the coherence at a scale a depends on a provided its size or equivalently the number of degrees of freedom of the estimator is appropriate to the time variation in coherence at that scale good estimation results are achieved moreover goodman s distribution is seen still to be appropriate for the estimator

an effective explicit pressure gradient scheme implemented in the two level non staggered grids for incompressible navier stokes equations in this paper an improved two level method is presented for effectively solving the incompressible navier stokes equations this proposed method solves a smaller system of nonlinear navier stokes equations on the coarse mesh and needs to solve the oseen type linearized equations of motion only once on the fine mesh level within the proposed two level framework a prolongation operator which is required to linearize the convective terms at the fine mesh level using the convergent navier stokes solutions computed at the coarse mesh level is rigorously derived to increase the prediction accuracy this indispensable prolongation operator can properly communicate the flow velocities between the two mesh levels because it is locally analytic solution convergence can therefore be accelerated for the sake of numerical accuracy momentum equations are discretized by employing the general solution for the two dimensional convection diffusion reaction model equation the convective instability problem can be simultaneously eliminated thanks to the proper treatment of convective terms the converged solution is thus very high in accuracy as well as in yielding a quadratic spatial rate of convergence for the sake of programming simplicity and computational efficiency pressure gradient terms are rigorously discretized within the explicit framework in the non staggered grid system the proposed analytical prolongation operator for the mapping of solutions from the coarse to fine meshes and the explicit pressure gradient discretization scheme which accommodates the dispersion relation preserving property have been both rigorously justified from the predicted navier stokes solutions

element by element parallel computation of incompressible navier stokes equations in three dimensions development of a stable finite element model for solving steady incompressible viscous fluid flows in three dimensions is the main theme of the present study for stability reasons weighting functions are designed in favor of field variables on the upstream side for accuracy reasons it is required that weighting functions be equipped with the streamline operator so that false diffusion errors can be largely suppressed in the steady state analysis of navier stokes equations we adopt the mixed formulation to preserve mass conservation on quadratic elements which accommodate the ladyzhenskaya babuska brezzi lbb stability condition to resolve difficulties arising from asymmetry and indefiniteness in the resulting large size matrix equations we abandon the elimination like solution solver because the storage demand exceeds the ability of our hardware to solve for three dimensional problems a modern iteration solver known as the biconjugate gradiant stabilized bicgstab solution solver is thus implemented in an element by element fashion to effectively alleviate the problem for performance reasons the finite element code developed here should be implemented in a hardware environment which is suited to the use of an iterative solver to this end our analysis is implemented in shared memory parallel architectures cray c 90 and j 90 we benchmark the parallel computing performance through a lid driven cavity flow problem and a problem amenable to analytic solution

trivariate spline approximations of 3d navier stokes equations we present numerical approximations of the 3d steady state navier stokes equations in velocity pressure formulation using trivariate splines of arbitrary degree d and arbitrary smoothness r with r d using functional arguments we derive the discrete navier stokes equations in terms of b coefficients of trivariate splines over a tetrahedral partition of any given polygonal domain smoothness conditions boundary conditions and the divergence free condition are enforced through lagrange multipliers the pressure is computed by solving a poisson equation with neumann boundary conditions we have implemented this approach in matlab and present numerical evidence of the convergence rate as well as experiments on the lid driven cavity flow problem

analysis of central and upwind compact schemes central and upwind compact schemes for spatial discretization have been analyzed with respect to accuracy in spectral space numerical stability and dispersion relation preservation a von neumann matrix spectral analysis is developed here to analyze spatial discretization schemes for any explicit and implicit schemes to investigate the full domain simultaneously this allows one to evaluate various boundary closures and their effects on the domain interior the same method can be used for stability analysis performed for the semi discrete initial boundary value problems ibvp this analysis tells one about the stability for every resolved length scale some well known compact schemes that were found to be g k s and time stable are shown here to be unstable for selective length scales by this analysis this is attributed to boundary closure and we suggest special boundary treatment to remove this shortcoming to demonstrate the asymptotic stability of the resultant schemes numerical solution of the wave equation is compared with analytical solution furthermore some of these schemes are used to solve two dimensional navier stokes equation and a computational acoustic problem to check their ability to solve problems for long time it is found that those schemes that were found unstable for the wave equation are unsuitable for solving incompressible navier stokes equation in contrast the proposed compact schemes with improved boundary closure and an explicit higher order upwind scheme produced correct results the numerical solution for the acoustic problem is compared with the exact solution and the quality of the match shows that the used compact scheme has the requisite drp property

numerical exploration of flow topology and vortex stability in a curved duct we performed incompressible flow simulation in a square duct with 90 bend and a curvature radius of 2 3 to extend our understanding of the vortical flow development in the bend the solutions for the flow investigated at the reynolds number of re 790 are obtained in a tri quadratic element system where velocities stagger the pressure working variable using the streamline upwind finite element model and the bicgstab iterative solver the simulated results reveal that centrifugal force convects the quickly moving fluid particles towards the outer wall the axial velocity as a result shows twin peaks in the curved channel at about 66 the secondary flow shows three complex pairs of vortices also noteworthy is the formation of a downstream spiralling flow motion to better elucidate the dominating three dimensional flow nature the topological study of limiting streamlines was undertaken insight into the longitudinal flow instability is gained by tracking the formation and diminishing of limiting cycles copyright 2006 john wiley sons ltd

analysis of anisotropy of numerical wave solutions by high accuracy finite difference methods fourier analysis is used to quantitatively assess the resolution and in particular the isotropy of wave solution using finite difference spatial discretization schemes along with fourth order runge kutta temporal scheme aspect ratio of the grid in two dimension along with the angle of wave propagation are the parameters varied to qualitatively and quantitatively assess the anisotropy of the solutions for a a skewed one dimensional wave convecting in two dimensions following the standard convection equation and b a wave propagating following the two dimensional linearized rotating shallow water equations results show the effect of changing the aspect ratio and the propagation angle on the directional nature of the solution as obtained by different methods for the above non dispersive and dispersive wave system

identification of parameter bounds for armax models from records with bounded noise the computation of bounds on the parameters rather than point estimates and covarianccs is considered for autoregressive moving average exogenous armax models the bounds derive from observations affected by bounded noise the influence of noise structure on the performance of the best known parameter bounding algorithm is examined a problem analogous to the bias in least squares estimates when regressors and noise are mutually correlated is also found to arise in parameter bounding an explanation is offered and the possibility of armax parameter bounds being non convex is pointed out

identification and prediction propagation of uncertainty in models with bounded noise abstract the identification of measurement parametric and structural model uncertainty is considered for models from observations with bounded noise a min max estimate for the upper bound of the structural model uncertainty is presented the propa gation of the parametric and structural model uncertainty as a result of the obser vation uncertainty bounds to the model prediction error is examined a simple water quality model is used to illustrate the different steps

brief paper convergence properties of the membership set in this paper we study the convergence properties of the membership set for system identification in the presence of unknown but bounded noise besides the classical pointwise noise model we also analyze the so called window and average models two different scenarios are considered 1 the bound tight or overestimated is known 2 the bound is unknown and has to be estimated from measurement data under some probabilistic assumptions on the noise sequence and with the persistent excitation regressor in the first case we prove that the diameter of the associated membership sets converges to zero with probability one if the noise bound is tight if the bound is overestimated we compute upper bounds for the diameter which are stated in terms of the difference between the true and the over estimated bound in the second case we show that the estimates of the bound converge to the true but unknown noise bound

integral conditions for the pressure in the computation of incompressible viscous flows abstract the problem of finding the correct conditions for the pressure in the time discretized navier stokes equations when the incompressibility constraint is replaced by a poisson equation for the pressure is critically examined it is shown that the pressure conditions required in a nonfractional step scheme to formulate the problem as a system of split second order equations are of an integral character and similar to the previously discovered integral conditions for the vorticity the novel integral conditions for the pressure are used to derive a finite element method which is very similar to that developed by glowinski and pironneau and is the finite element counterpart of the influence matrix method of kleiser and schumann

a transpose free quasi minimal residual algorithm for non hermitian linear systems the biconjugate gradient method bcg for solving general non hermitian linear systems ax b and its transpose free variant the conjugate gradients squared algorithm cgs both typically exhib

three dimensional flow in cavity at yaw abstract this study introduces a building block prototype model of three dimensional 3 d flows about protrusions and cavities with an arbitrary angle between the external flow and rigid elements the considered flow in a 3 d cavity has the lid of cavity moving along the lid diagonal case a the proposed case is taken as a typical representative of essentially 3 d highly separated vortical flows having simple single block rectangular geometry of computational domain this 3 d lid driven cavity flow is studied by numerical solution of the 3 d viscous navier stocks equations using fluent software with second order upwind schemes for convective terms computational results are compared to the classical benchmark case where the lid moves in the direction parallel to the cavity side walls case b the volume and plane integrals of momentum in the direction of lid motion and perpendicular to it are introduced to compare cases in a quantitative way the integral momentum of the secondary flow transverse to the lid motion appears to be about an order of magnitude larger than that in case b in the proposed flow the number and strength of secondary vortices depend substantially on the re number of the flow whereas in case b only one pair of secondary vortices appears for arbitrary re number for a rectangular 3 d 3 1 1 cavity the integral momentum of the secondary flow in case a is an order of magnitude larger than that in the case b the flowfield in case a includes a curvilinear separation line and non symmetrical vortices

estimation theory and uncertainty intervals evaluation in presence of unknown but bounded errors linear families of models and estimators the problem of parameter estimation and of the evaluation of related uncertainty intervals is considered in the case that a probabilistic description of noise and errors is not available of suitable but only a bound on them is known in the present paper only linear parametrizations and estimators are considered very simple and computationally feasible algorithms are derived for evaluating two different types of uncertainty intervals estimates uncertainty intervals parameter uncertainty intervals the relationships between the eui s and the pui s are established and the solution to the problem of the minimum uncertainty intervals estimator is given the latter can be obtained by means of a simple linear programming algorithm

a family of low dispersive and low dissipative explicit schemes for flow and noise computations explicit numerical methods for spatial derivation filtering and time integration are proposed they are developed with the aim of computing flow and noise with high accuracy and fidelity all the methods are constructed in the same way by minimizing the dispersion and the dissipation errors in the wavenumber space up to k x 2 corresponding to four points per wavelength they are shown to be more accurate and also more efficient numerically than most of the standard explicit high order methods for uniform and slowly non uniform grids two problems involving long range sound propagation are resolved to illustrate their respective precisions remarks about their practical applications are then made especially about the connection with the boundary conditions finally their relevance for the simulation of turbulent flows is emphasized

a statistical study of temporally smoothed wavelet coherence the use of the wavelet coherence of two series in hypothesis testing relies on some sort of smoothing being carried out in order that the coherence estimator is not simply unity a previous study considered averaging via the use of multiple morse wavelets here we consider time domain smoothing and use of a single morlet wavelet since the morlet wavelet is complex valued we derive analytic results for the case of wavelet coherence calculated from complex valued jointly stationary and gaussian time series the temporally smoothed wavelet coherence can be written in terms of welch s overlapping segment averaging wosa spectrum estimators and by using multitaper equivalent representations for the wosa estimators we show that goodman s distribution is appropriate asymptotically and readily derive the appropriate degrees of freedom the theoretical results are verified via simulations and illustrated using solar physics data

statistical properties for coherence estimators from evolutionary spectra evolutionary spectra were developed by priestley to extend spectral analysis to some nonstationary time series in particular semistationary processes of which the ubiquitous uniformly modulated processes are a subclass coherence is well defined for bivariate semistationary processes and can be estimated from such processes we consider priestley s estimator for the evolutionary spectral density matrix and show that its elements can be written as weighted multitaper estimators with calculable weights and tapers under gaussianity an approximating wishart distribution model follows for the spectral matrix valid for all frequencies except small computable intervals near zero and nyquist moreover the critically important degrees of freedom are known consequently the statistical distribution of the coherence is given by goodman s distribution and the raw coherence estimate can be accurately debiased theoretical results are verified using a model for wind fluctuations simulations give excellent agreement between the mean debiased coherence estimates and true coherence and between the proposed and empirical distributions of coherence

set membership estimation of fiber laser physical parameters from input output power measurements the problem of fiber laser parameters estimation from input output transient power measurements is considered in the paper the proposed procedure is based on a suitable laser model obtained from the rate and propagation equations by proper manipulation of the simplified laser equations the estimation problem is formulated in the bounded error estimation framework where a priori information on physical parameters can be properly taken into account first the so called feasible parameter set is defined then the problem of optimally picking a single model from the set is formulated in terms of central conditional estimation and solved by exploiting recent results by the authors properties of the proposed solution are discussed the proposed algorithm is tested on a set of simulated data obtained from a commercial laser simulator