identification of sparse linear operators we consider the problem of identifying a linear deterministic operator from its response to a given probing signal for a large class of linear operators we show that stable identifiability is possible if the total support area of the operator s spreading function satisfies 1 2 this result holds for an arbitrary possibly fragmented support region of the spreading function does not impose limitations on the total extent of the support region and most importantly does not require the support region to be known prior to identification furthermore we prove that stable identifiability of almost all operators is possible if 1 this result is surprising as it says that there is no penalty for not knowing the support region of the spreading function prior to identification algorithms that provably recover all operators with 1 2 and almost all operators with 1 are presented

physics based gmres preconditioner for compressible and incompressible navier stokes equations abstract this paper presents the implementation of a local physics preconditioning mass matrix 8 for an unified approach of 3d compressible and incompressible navier stokes equations using an supg finite element formulation and gmres implicit solver during the last years a lot of effort has been dedicated to finding a unified approach for compressible and incompressible flow in order to treat fluid dynamic problems with a very wide range of mach and reynolds numbers 10 26 37 on the other hand supg finite element formulation and gmres implicit solver is one of the most robust combinations to solve state of the art cfd problems 1 6 9 22 29 30 31 the selection of a good preconditioner and its performance on parallel architecture is another open problem in cfd community the local feature of the preconditioner presented here means that no communication among processors is needed when working on parallel architectures due to these facts we consider that this research can make some contributions towards the development of a unified fluid dynamic model with high rates of convergence for any combination of mach and reynolds numbers being very suitable for massively parallel computations finally it is important to remark that while this kind of preconditioning produces stabilized results in nearly incompressible regimes the standard version exhibits some numerical drawbacks that lead to solutions without physical meaning

time frequency localization operators a geometric phase space approach the author defines a set of operators which localize in both time and frequency these operators are similar to but different from the low pass time limiting operator the singular functions of which are the prolate spheroidal wave functions the author s construction differs from the usual approach in that she treats the time frequency plane as one geometric whole phase space rather than as two separate spaces for disk shaped or ellipse shaped domains in time frequency plane the associated localization operators are remarkably simple their eigenfunctions are hermite functions and the corresponding eigenvalues are given by simple explicit formulas involving the incomplete gamma functions

identification of parametric underspread linear systems and super resolution radar identification of time varying linear systems which introduce both time shifts delays and frequency shifts doppler shifts is a central task in many engineering applications this paper studies the problem of identification of underspread linear systems ulss whose responses lie within a unit area region in the delay doppler space by probing them with a known input signal it is shown that sufficiently underspread parametric linear systems described by a finite set of delays and doppler shifts are identifiable from a single observation as long as the time bandwidth product of the input signal is proportional to the square of the total number of delay doppler pairs in the system in addition an algorithm is developed that enables identification of parametric ulss from an input train of pulses in polynomial time by exploiting recent results on sub nyquist sampling for time delay estimation and classical results on recovery of frequencies from a sum of complex exponentials finally application of these results to super resolution target detection using radar is discussed specifically it is shown that the proposed procedure allows to distinguish between multiple targets with very close proximity in the delay doppler space resulting in a resolution that substantially exceeds that of standard matched filtering based techniques without introducing leakage effects inherent in recently proposed compressed sensing based radar methods

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

time frequency analysis of localization operators abstract we study a class of pseudodifferential operators known as time frequency localization operators anti wick operators gabor toeplitz operators or wave packets given a symbol a and two windows 1 2 we investigate the multilinear mapping from a 1 2 s r 2d s r d s r d to the localization operator aa 1 2 and we give sufficient and necessary conditions for aa 1 2 to be bounded or to belong to a schatten class our results are formulated in terms of time frequency analysis in particular we use modulation spaces as appropriate classes for symbols and windows

discrete zak transforms polyphase transforms and applications we consider three different versions of the zak 1967 transform zt for discrete time signals namely the discrete time zt the polyphase transform and a cyclic discrete zt in particular we show that the extension of the discrete time zt to the complex z plane results in the polyphase transform an important and well known concept in multirate signal processing and filter bank theory we discuss fundamental properties relations and transform pairs of the three discrete zt versions and we summarize applications of these transforms in particular the discrete time zt and the cyclic discrete zt are important for discrete time gabor 1946 expansion weyl heisenberg frame theory since they diagonalize the weyl heisenberg frame operator for critical sampling and integer oversampling the polyphase representation plays a fundamental role in the theory of filter banks especially dft filter banks simulation results are presented to demonstrate the application of the discrete zt to the efficient calculation of dual gabor windows tight gabor windows and frame bounds

a monolithic approach for interaction of incompressible viscous fluid and an elastic body based on fluid pressure poisson equation this paper describes a new monolithic approach based on the fluid pressure poisson equation ppe to solve an interaction problem of incompressible viscous fluid and an elastic body the ppe is derived so as to be consistent with the coupled equation system for the fluid structure interaction fsi based on this approach we develop two kinds of efficient monolithic methods in both methods the fluid pressure is derived implicitly so as to satisfy the incompressibility constraint and all other unknown variables are derived fully explicitly or partially explicitly the coefficient matrix of the ppe for the fsi becomes symmetric and positive definite and its condition is insensitive to inhomogeneity of material properties the arbitrary lagrangian eulerian ale method is employed for the fluid part in order to take into account the deformable fluid structure interface to demonstrate fundamental performances of the proposed approach the developed two monolithic methods are applied to evaluate the added mass and the added damping of a circular cylinder as well as to simulate the vibration of a rectangular cylinder induced by vortex shedding copyright 2005 john wiley sons ltd

identification of channels with single and multiple inputs and outputs under linear constraints abstract the channel identification problem for multiple input multiple output mimo channels under linear constraints can be formulated as solving a linear system which involves finite dimensional gabor matrices and a pre determined unstructured matrix that represents the linear constraints while matrices of the latter type are fixed a priori by the constraints gabor matrices depend on the choice of their generating windows which is often chosen by the user this is important since even if the matrix associated with the linear constraints is ill conditioned the full system may be solvable if the windows are designed appropriately we prove that linear constraints consisting of a single equation always remove a single degree of freedom in the channel identification problem in the sense that preknowledge of such constraints allows identification of mimo channels with support size one greater than the fundamental limit however we give an explicit example showing that this statement does not generalize to the case of multiple constraints in the single input single output siso case we provide some sufficient conditions on the linear side constraints under which the corresponding siso channels are identifiable

singular values of compact pseudodifferential operators abstract this paper investigates the asymptotic decay of the singular values of compact operators arising from the weyl correspondence the motivating problem is to find sufficient conditions on a symbol which ensure that the corresponding operator has singular values with a prescribed rate of decay the problem is approached by using a gabor frame expansion of the symbol to construct an approximating finite rank operator this establishes a variety of sufficient conditions for the associated operator to be in a particular schatten class in particular an improvement of a sufficient condition of daubechies for an operator to be trace class is obtained in addition a new development and improvement of the calderon vaillancourt theorem in the context of the weyl correspondence is given additional results of this type are then obtained by interpolation

enhanced multi level block ilu preconditioning strategies for general sparse linear systems abstract this paper introduces several strategies to deal with pivot blocks in multi level block incomplete lu factorization bilum preconditioning techniques these techniques are aimed at increasing the robustness and controlling the amount of fill ins of bilum for solving large sparse linear systems when large size blocks are used to form block independent set techniques proposed in this paper include double dropping strategies approximate singular value decomposition variable size blocks and use of an arrowhead block submatrix we point out the advantages and disadvantages of these strategies and discuss their efficient implementations numerical experiments are conducted to show the usefulness of the new techniques in dealing with hard to solve problems arising from computational fluid dynamics in addition we discuss the relation between multi level ilu preconditioning methods and algebraic multi level methods

direct coupling of euler flow equations with plate finite element structures a procedure to compute aeroelasticity by directly coupling the euler equations for fluids and with plate finite element equations for structures is presented the coupled equations are solved using a time integration method the accuracy is maintained using moving grids that conform to aeroelastically deformed shape computed every time step the aeordynamic forces are transferred to structures by using simple lumped load approach and also a more accurate virtual surface approach

reduce and boost recovering arbitrary sets of jointly sparse vectors the rapid developing area of compressed sensing suggests that a sparse vector lying in a high dimensional space can be accurately and efficiently recovered from only a small set of nonadaptive linear measurements under appropriate conditions on the measurement matrix the vector model has been extended both theoretically and practically to a finite set of sparse vectors sharing a common sparsity pattern in this paper we treat a broader framework in which the goal is to recover a possibly infinite set of jointly sparse vectors extending existing algorithms to this model is difficult due to the infinite structure of the sparse vector set instead we prove that the entire infinite set of sparse vectors can be recovered by solving a single reduced size finite dimensional problem corresponding to recovery of a finite set of sparse vectors we then show that the problem can be further reduced to the basic model of a single sparse vector by randomly combining the measurements our approach is exact for both countable and uncountable sets as it does not rely on discretization or heuristic techniques to efficiently find the single sparse vector produced by the last reduction step we suggest an empirical boosting strategy that improves the recovery ability of any given suboptimal method for recovering a sparse vector numerical experiments on random data demonstrate that when applied to infinite sets our strategy outperforms discretization techniques in terms of both run time and empirical recovery rate in the finite model our boosting algorithm has fast run time and much higher recovery rate than known popular methods

an efficient parallel computation of unsteady incompressible viscous flow with elastic moving and compliant boundaries on unstructured grids this paper presents the development and validation of a parallel unstructured grid fluid structure interaction fsi solver for the simulation of unsteady incompressible viscous flow with long elastic moving and compliant boundaries the navier stokes solver on unstructured moving grid using the arbitrary lagrangian eulerian formulation is based on the artificial compressibility approach and a high order characteristics based finite volume scheme both unsteady flow and fsi are calculated with a matrix free implicit dual time stepping scheme a membrane model has been formulated to study fluid flow in a channel with an elastic membrane wall and their interactions this model can be employed to calculate arbitrary wall movement and variable tension along the membrane together with a dynamic mesh method for large deformation of the flow field the parallelization of the fluid structure solver is achieved using the single program multiple data programming paradigm and message passing interface for communication of data the parallel solver is used to simulate fluid flow in a two dimensional channel with and without moving membrane for validation and performance evaluation purposes the speedups and parallel efficiencies obtained by this method are excellent using up to 16 processors on a sgi origin 2000 parallel computer a maximum speedup of 23 14 could be achieved on 16 processors taking advantage of an improved handling of the membrane solver the parallel results obtained are compared with those using serial code and they are found to be identical copyright 2005 john wiley sons ltd

torsional springs for two dimensional dynamic unstructured fluid meshes abstract dynamic fluid grids are commonly used for the solution of flow problems with moving boundaries they are often represented by a network of fictitious lineal springs that can become unreliable when the fluid mesh undergoes large displacements and or deformations in this paper we propose to control the arbitrary motion of two dimensional dynamic unstructured fluid grids with additional torsional springs we show that such springs can be designed to prohibit the interpenetration of neighboring triangles and therefore to provide the method of spring analogy with the robustness needed for enlarging its range of applications we illustrate our new dynamic mesh motion algorithm with several examples that highlight its advantages in terms of robustness quality and performance

on unique localization of multiple sources by passive sensor arrays necessary and sufficient conditions are derived for the unique localization of narrowband sources having the same known center frequency by passive sensor arrays the conditions specify the maximum number of sources that can be uniquely localized by a general array that satisfies some mild geometric constraints the conditions are expressed in terms of the number of sensors and the rank of the correlation matrix of the sources two different conditions are presented the first guarantees uniqueness for every batch of sampled data the second which is weaker guarantees uniqueness for almost every batch of sampled data with the exception of a set of batches of measure zero it is shown that a condition that is slightly weaker than the second one is also necessary

proper orthogonal decomposition variational multiscale element free galerkin pod vmefg meshless method for solving incompressible navier stokes equation abstract recently because of simplicity of meshless methods they have been employed for solving many partial differential equations one of the meshless methods is element free galerkin technique the element free galerkin is very similar to the finite element method with this difference that the test and trial spaces of efg procedure are shape functions of moving least squares approximation using the mentioned shape functions solving a problem on a complex domain is very simple some researchers proposed several modifications and enriched approaches for improving the element free galerkin method that one of them is variational multiscale element free galerkin procedure up to the best of authors knowledge the element free galerkin method based on the shape functions of moving least squares approximation needs more cpu time than the element free galerkin method based on the shape functions of moving kriging interpolation thus in the current paper we employ the variational multiscale element free galerkin based on the shape functions of moving kriging interpolation also for reducing the cpu time of the presented numerical scheme we use the proper orthogonal decomposition pod approach therefore in the current paper we propose the proper orthogonal decomposition variational multiscale element free galerkin pod vmefg method for solving time dependent incompressible navier stokes equation moreover several test problems are given that show the acceptable accuracy and efficiency of the proposed scheme

arbitrary lagrangian eulerian formulation for fluid rigid body interaction a new formulation for two dimensional fluid rigid body interaction problems is developed in particular vortex induced oscillations of a rigid body in viscous incompressible flow are studied the incompressible navier stokes equations are used to describe the motion of the fluid while it is assumed that the rigid body is mounted on a system consisting of a spring and a dashpot an arbitrary lagrangian eulerian formulation ale is used in order to account for large boundary motion a general formulation for the coupled problem is obtained by uncoupling the translation motion of the body from its rotational motion and developing a specific algorithm to efficiently handle the nonlinear dependence of the rotations this general formulation can be easily applied to multi body problems two numerical examples involving either translations and rotations are presented as an illustration of the proposed methodologies for fluid rigid body interaction

weighted zak transforms and the dual tiling condition abstract for t 0 and a periodic complex valued sequence c we introduce the weighted zak transform z c t and study its properties as our main result we give characterizations for mapping properties and unitarity of z c t l 2 r l 2 s where functions in the image are understood as restrictions to a set s r 2 in particular we show that for almost every choice of l periodic sequences c the mapping properties of z c t l 2 r l 2 s simplify to statements on the geometry of s they involve a dual tiling condition on s with respect to the lattices t z z and l t z l z where 1 l t

structural analysis of a queueing system with multiclasses of correlated arrivals and blocking in assemble to order production systems and others of a similar flavor it is often the case that orders for components of various types are placed simultaneously but that these components are manufactured or assembled at separate facilities t he order process introduces correlation among the jobs at separate facilities the purpose of this paper is to study the effect of this correlation on a variety of system performance measures consider a system that consists of s parallel servers where e ach server has a finite buffer and is dedicated to a separate job type multiple classes of customer orders arrive to the system where each class is composed of one or more unique job types upon the arrival of an order each job in the order is separately routed to its designated buffer if the buffer is full that job is blocked and lost otherwise it enters the buffer and is served according to the fcfs discipline under markovian assumptions we systematically examine the impact of arrival correlati ons on system based performance measures such as the queue length vector and the workload vector and class based performance measures such as the waiting time vector and the order response time among other things we establish several stochastic orders between performance vectors with different degrees of arrival correlations we also show that greater arrival correlation can stochastically improve the worst component in a performance vector e g the longest queue the heaviest workload reduce the expected sum of the j longest queues 1 j s and for any given order type increase its entering probability and reduce its order response time our results can also be extended to the compound poisson arrival process where each order contains multiple units of several job types

multidimensional stochastic ordering and associated random variables this paper presents several relationships between the concept of associated random variables rvs and notions of stochastic ordering the question that provides the impetus for this work is whether the association of the valued rvs x1 xn implies a possible stochastic ordering between the n valued rv x x1 xn and its independent version xi xi 1 xi n this leads to results on how multidimensional probability distributions are determined by conditions on their one dimensional marginal distributions in the event of comparison under the stochastic orderings st c1 cv d and k such results have direct implications for the comparison of bounds for fork join queues and for the structure of monotone functions of several variables

sampling and reconstruction of operators we study the recovery of operators with a bandlimited kohn nirenberg symbol from the action of such operators on a weighted impulse train a procedure we refer to as sampling of operators kailath bello and later kozek and the authors have shown that the sampling of operators is possible if the symbol of the operator is bandlimited to a set with area less than one in this paper we develop the theory of the sampling of operators in analogy with the classical theory of sampling of bandlimited functions we define the notions of sampling set and sampling rate for operators and give necessary and sufficient conditions on the sampling rate that depend on the size and geometry of the bandlimiting set we develop explicit reconstruction formulas for operator sampling that generalize reconstruction formulas for bandlimited functions we give necessary and sufficient conditions on the bandlimiting set under which sampling of operators is possible by their action on a given periodically weighted delta train we show that under mild geometric conditions on the bandlimiting set classes of operators are bandlimited to an unknown set of area less than one half permit sampling and reconstruction we generalize two results of the heckel and bolcskei concerning sampling of operators with area not greater than one half and less than one respectively by finding a larger class of operators to which they apply operators with bandlimited symbols have been used to model doubly dispersive communication channels with slowly time varying impulse response the results in this paper are rooted in work by bello and kailath in the 1960s

majorization of weighted trees a new tool to study correlated stochastic systems stochastic models with simultaneous arrivals arise naturally in the areas such as synchronized communication networks flexible manufacturing systems production inventory systems reliability modeling in random environment etc with a wide variety of interpretations simultaneous arrivals introduce dependence among various components of the system and make the explicit solutions of joint system performance measures either computationally intensive or intractable this calls for structural analysis of dependence natures of such systems so that the insight gained from the analysis can suggest plausible approaches to develop tight bounds and efficient approximations to key system performance measures the usual majorization order on a totally ordered index set and schur convexity are powerful tools for establishing inequalities in particular for stochastic systems however the investigation on stochastic systems with simultaneous arrivals leads naturally to the comparison of distributions of parameter values on a tree structured index set in this paper we introduce the notion ofmajorization with respect to weighted trees the fundamental strength of tree majorization lies in its ability to make versatile comparisons over two parameter sets defined on a partially ordered index set we identify several classes of transformations that provide simple characterizations of tree majorization orders finally we apply the new notion to an assemble to order system and to a shock model with simultaneous subsystem failures and study the dependence structure of these systems our results show that tree majorization and its interplay with various notions of stochastic orders are useful tools to study the dependency of stochastic systems with multivariate synchronized input processes

estimation of ambiguity functions with limited spread in this correspondence we propose a class of estimators of the ambiguity function of a discrete time process using thresholding to this purpose the distributional and moment properties of the empirical ambiguity function for a realization of an analytic random process are derived and the moments for the special cases of stationary uniformly modulated and deterministic signals immersed in noise processes are determined suitable thresholds are chosen based on the distributional properties of the empirical ambiguity function and the procedure is tested on simulated data

density theorems for sampling and interpolation in the bargmann fock space we give a complete description of sampling and interpolation in the bargmann fock space based on a density concept of beurling roughly speaking a discrete set is a set of sampling if and only if its density in every part of the plane is strictly larger than that of the von neumann lattice and similarly a discrete set is a set of interpolation if and only if its density in every part of the plane is strictly smaller than that of the von neumann lattice

on accumulated spectrograms we study the eigenvalues and eigenfunctions of the time frequency localization operator h on a domain of the time frequency plane the eigenfunctions are the appropriate prolate spheroidal functions for an arbitrary domain r indeed in analogy to the classical theory of landau slepianpollak the number of eigenvalues of h in 1 1 is equal to the measure of up to an error term depending on the perimeter of the boundary of our main results show that the spectrograms of the eigenfunctions corresponding to the large eigenvalues which we call the accumulated spectrogram form an approximate partition of unity of the given domain we derive asymptotic non asymptotic and weak l error estimates for the accumulated spectrogram as a consequence the domain can be approximated solely from the spectrograms of eigenfunctions without information about their phase

analysis of fluid structure interaction problems with structural buckling and large domain changes by ale finite element method abstract a 3d finite element analysis program is newly developed for fluid structure interaction problems with structural buckling and large domain changes an arbitrary lagrangian eulerian ale finite element method with automatic mesh updating is formulated for large domain changes in order to cope with the numerical instability caused by the buckling of a thin shell structure a strong coupling strategy is adopted together with some stabilization techniques for fluids and structures a few numerical examples including the simulation of the pulsation of a 2d artifical heart and a 3d simplified model with structural buckling and large domain changes are demonstrated to show the capability of the proposed methods

on the invertibility of rectangular bi infinite matrices and applications in time frequency analysis abstract finite dimensional matrices with more columns than rows have no left inverses while those with more rows than columns have no right inverses we give generalizations of these simple facts to bi infinite matrices our results are then used to obtain density results for p frames of time frequency molecules in modulation spaces and identifiability results for operators with bandlimited kohn nirenberg symbols

measurement of time variant linear channels the goal of channel measurement or operator identification is to obtain complete knowledge of a channel operator by observing the image of a finite number of input signals in this paper it is shown that the spreading support of the operator that is the support of the symplectic fourier transform of the kohn nirenberg symbol of the operator has area less than one then the operator is identifiable if the spreading support is larger than one then the operator is not identifiable the shape of the support region is essentially arbitrary thereby proving a conjecture of bello the input signal considered is a weighted delta train where the weights are the window function of a finite gabor system whose elements satisfy a certain robust completeness property

an efficient parametric technique for doppler delay estimation receiving an output signal that is a weighted sum of doppler and delay shifted versions of an input signal arises in various engineering systems including radar sonar and communications it is often desired to estimate the doppler and delay parameters from noisy measurements of the output signal an estimation algorithm is developed herein for the doppler frequencies delays and amplitudes for a specific choice of the input the algorithm is based on a computationally efficient search free frequency estimation technique for the sum of complex exponentials asymptotic performance bounds are developed for the estimated parameters simulation results show that the variance of the estimation error is close to the bound above a threshold signal to noise ratio indicating that the estimation algorithm is statistically efficient

a computational approach for predicting the hydroelasticity of flexible structures based on the pressure poisson equation this work is concerned with the modeling of the interaction of fluid flow with flexible solid structures the flow under consideration is governed by the navier stokes equations for incompressible viscous fluids and modeled with low order velocity pressure finite elements the motion of the fluid domain is accounted for by the arbitrary lagrangian eulerian formulation the structure is represented by means of an appropriate standard finite element formulation the spring smooth analogy is used to mesh control the time integrating algorithm is based on the predictor multi corrector algorithm an important aspect of the present work is the introduction of a new monolithic approach based on the fluid pressure poisson equation ppe to solve the hydroelasticity problem of an incompressible viscous fluid with an elastic body that is vibrating due to flow excitation the ppe is derived to be consistent with the coupled system equation for the fluid structure interaction fsi based on this approach an efficient monolithic method is adopted to simulate hydroelasticity between the flexible structure and the flow the fluid pressure is implicitly derived to satisfy the incompressibility constraint and the other unknown variables are explicitly derived the coefficient matrix of the ppe for the fsi becomes symmetric and positive definite to demonstrate the performance of the proposed approach two working examples a beam immersed in incompressible fluid and a guide vane of a francis turbine passage were used the results show the validity of the proposed approach copyright 2007 john wiley sons ltd

order restricted inference for multivariate binary data with application to toxicology in many applications researchers collect multivariate binary response data under two or more naturally ordered experimental conditions in such situations one is often interested in using all binary outcomes simultaneously to detect an ordering among the experimental conditions to make such comparisons we develop a general methodology for testing for the multivariate stochastic order between k 2 multivariate binary distributions our proposed test uses order restricted estimators which according to our simulation study are more efficient than the unrestricted estimators in terms of their mean squared error we compared the power of the proposed test with that of several alternative tests including procedures that combine individual univariate tests for order such as union intersection tests and a bonferroni based test we also compared the proposed test with an unrestricted hotelling t2 type test our simulations suggest that the proposed method competes well with these alternatives the gain i

a theory for sampling signals from a union of subspaces one of the fundamental assumptions in traditional sampling theorems is that the signals to be sampled come from a single vector space e g bandlimited functions however in many cases of practical interest the sampled signals actually live in a union of subspaces examples include piecewise polynomials sparse representations nonuniform splines signals with unknown spectral support overlapping echoes with unknown delay and amplitude and so on for these signals traditional sampling schemes based on the single subspace assumption can be either inapplicable or highly inefficient in this paper we study a general sampling framework where sampled signals come from a known union of subspaces and the sampling operator is linear geometrically the sampling operator can be viewed as projecting sampled signals into a lower dimensional space while still preserving all the information we derive necessary and sufficient conditions for invertible and stable sampling operators in this framework and show that these conditions are applicable in many cases furthermore we find the minimum sampling requirements for several classes of signals which indicates the power of the framework the results in this paper can serve as a guideline for designing new algorithms for various applications in signal processing and inverse problems

parallel multigrid computation of unsteady incompressible viscous flows using a matrix free implicit method and high resolution characteristics based scheme abstract a three dimensional parallel unstructured non nested multigrid solver for solutions of unsteady incompressible viscous flow is developed and validated the finite volume navier stokes solver is based on the artificial compressibility approach with a high resolution method of characteristics based scheme for handling convection terms the unsteady flow is calculated with a matrix free implicit dual time stepping scheme the parallelization of the multigrid solver is achieved by multigrid domain decomposition approach mg dd using single program multiple data spmd and multiple instruction multiple data mimd programming paradigm there are two parallelization strategies proposed in this work first strategy is a one level parallelization strategy using geometric domain decomposition technique alone second strategy is a two level parallelization strategy that consists of a hybrid of both geometric domain decomposition and data decomposition techniques message passing interface mpi and openmp standard are used to communicate data between processors and decompose loop iterations arrays respectively the parallel multigrid code is used to simulate both steady and unsteady incompressible viscous flows over a circular cylinder and a lid driven cavity flow a maximum speedup of 22 5 could be achieved on 32 processors for instance the lid driven cavity flow of re 1000 the results obtained agree well with numerical solutions obtained by other researchers as well as experimental measurements a detailed study of the time step size and number of pseudo sub iterations per time step required for simulating unsteady flow are presented in this paper

sampling of stochastic operators we develop sampling methodology aimed at identifying stochastic operators that satisfy a support size restriction on the autocorrelation of the operators stochastic spreading function the data that we use to reconstruct the operator or in some cases only the autocorrelation of the spreading function is based on the response of the unknown operator to a known deterministic test signal

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100