improvement of pufem for the numerical solution of high frequency elastic wave scattering on unstructured triangular mesh grids the purpose of this paper which builds on previous work int j numer meth engng 2009 77 1646 1669 is to improve a numerical scheme based on the partition of unity finite element method pufem for the solution of the time harmonic elastic wave equations the approach consists to approximate the displacement field by the standard finite element shape functions enriched locally by superimposing pressure p and shear s plane waves the aim is to accurately model two dimensional elastic wave problems on relatively coarse mesh grids capable of containing many wavelengths per nodal spacing for wide ranges of frequencies this allows us to relax the traditional requirement of about 10 nodal points per s wavelength in this work an exact integration scheme for the linear triangular finite element is developed to evaluate the oscillatory integrals arising from the use of the pufem the main contribution here consists in developing an explicit closed form solution for two dimensional wave based integrals when the phase variation is linear in the local coordinate element system the evaluation of the element mass matrix is performed from appropriate edge integrals all other element matrices obtained by adequate splitting of the element stress tensor matrix are simply deduced from the element mass matrix entries the results show clearly that the proposed integration scheme evaluates accurately the entries of the global matrix with drastic reduction of the computational time numerical tests dealing with the scattering of s elastic plane waves by a circular rigid body show that for the same discretization level it is possible to improve the accuracy by using large elements associated with high numbers of approximating plane waves rather than using small elements with less plane waves however this increases the conditioning and the fill in of the global matrix at high frequency it is even possible to push the number of degrees of freedom per s wavelength under 2 and still achieve good accuracy finally some remarks on the choice of the numbers of p and s plane waves leading to better accuracy and conditioning are discussed copyright 2010 john wiley sons ltd

data record size requirements for adaptive space time ds cdma signal detection we investigate the data record size requirements of sample matrix inversion based minimum variance distortionless response and maximum signal to interference plus noise ratio adaptive algorithms to meet a given performance objective in joint space time signal detection problems for direct sequence code division multiple access systems we derive closed form expressions that provide the data record size that is necessary to achieve a given performance confidence level in a neighborhood of the optimal performance point as well as expressions that identify the performance level that can be reached for a given data record size this is done by using close approximations of the involved probability density functions the practical significance of the derived expressions lies in the fact that the expressions are functions of the number of antenna elements the number of multipaths and the system spreading gain only while they depend neither on the ideal input covariance matrix which is not known in most realistic applications nor on the exact ideal performance value

validity of the limp model for porous materials a criterion based on the biot theory the validity of using the limp model for porous materials is addressed in this paper the limp model is derived from the poroelastic biot model assuming that the frame has no bulk stiffness being an equivalent fluid model accounting for the motion of the frame it has fewer limitations than the usual equivalent fluid model assuming a rigid frame a criterion is proposed to identify the porous materials for which the limp model can be used it relies on a new parameter the frame stiffness influence fsi based on porous material properties the critical values of fsi under which the limp model can be used are determined using a one dimensional analytical modeling for two boundary sets absorption of a porous layer backed by a rigid wall and radiation of a vibrating plate covered by a porous layer compared with other criteria the criterion associated with fsi provides information in a wider frequency range and can be used for configurations that include vibrating plates

investigation of the convergence of the mixed displacement pressure formulation for three dimensional poroelastic materials using hierarchical elements recently a mixed pressure displacement u p formulation based on biot s poroelasticity equations has been presented for porous materials this model leads to a reduction of the number of degrees of freedom required for the modeling of three dimensional porous media in comparison to classical displacement displacement u u formulations in this paper an extension of the u p formulation based on hierarchical elements is presented first a variant of the weak integral form of the u p formulation is presented and its numerical implementation using hierarchical elements is detailed together with the application of boundary and loading conditions numerical results are presented to show the accuracy and performance of the present approach in particular the importance of correctly capturing the coupling effects between the two phases is highlighted

performances of the partition of unity finite element method for the analysis of two dimensional interior sound fields with absorbing materials the paper deals with the numerical simulation of the acoustic field in two dimensional cavities in which absorbing materials are present though finite element method fem could be employed for this purpose the discretization level required for achieving reasonable accuracy renders the method impractical in the mid frequency range to alleviate this limitation the partition of unity finite element method pufem using plane wave functions has been shown to be very effective for solving short wave helmholtz problems in the present work the method is extended to the computation of the pressure wave field within the absorbing media which is modeled as a bulk reacting material characterized by a complex valued and frequency dependent mean density and dynamic compressibility lagrange multipliers are used to enforce the transmission conditions at the air material interface performances of the pufem are compared with a standard fem in several examples of practical interests it is shown that the technique is a good candidate for solving noise control problems at high frequency

statistics of adaptive nulling and use of the generalized eigenrelation ger for modeling inhomogeneities in adaptive processing this paper examines the integrity of the generalized eigenrelation ger which is an approach to assessing performance in an adaptive processing context involving covariance estimation when the adaptive processors are subject to undernulled interference the ger is a mathematical relation which if satisfied often facilitates closed form analysis of adaptive processors employing estimated covariances subject to inhomogeneities the goal of this paper is to determine what impact this constraint has on the integrity of the adaptive nulling process in order to examine the impact of the ger constraint on adaptive nulling we establish fundamental statistical convergence properties of an adaptive null for the sample covariance based scb minimum variance distortionless response mvdr beamformer novel exact expressions relating the mean and variance of an adaptive null of a homogeneously trained beamformer to the mean and variance of a nonhomogeneous trained beamformer are derived in addition it is shown that the reed et al 1974 result for required sample support can be highly inaccurate under nonhomogeneous conditions indeed the required sample support can at times depend directly on the power of the undernulled interference

performance analysis of the minimum variance beamformer we present an analysis of the signal to interference plus noise ratio sinr at the output of the minimum variance beamformer the analysis is based on the assumption that the signals and noise are gaussian and that the number of samples is large compared to the array size and it yields an explicit expression for the sinr in terms of the different parameters affecting the performance including signal to noise ratio snr interference to noise ratio inr signal to interference ratio sir angular separation between the desired signal and the interference array size and shape correlation between the desired signal and the interference and finite sample size

computation of orthonormal factors for fundamental solution matrices in this work we introduce and analyze two new techniques for obtaining the q factor in the qr factorization of some or all columns of a fundamental solution matrix y of a linear differential system these techniques are based on elementary householder and givens transformations we implement and compare these new techniques with existing approaches on some examples

an exponentially convergent nonpolynomial finite element method for time harmonic scattering from polygons in recent years nonpolynomial finite element methods have received increasing attention for the efficient solution of wave problems as with their close cousin the method of particular solutions high efficiency comes from using solutions to the helmholtz equation as basis functions we present and analyze such a method for the scattering of two dimensional scalar waves from a polygonal domain that achieves exponential convergence purely by increasing the number of basis functions in each element key ingredients are the use of basis functions that capture the singularities at corners and the representation of the scattered field towards infinity by a combination of fundamental solutions the solution is obtained by minimizing a least squares functional which we discretize in such a way that a matrix least squares problem is obtained we give computable exponential bounds on the rate of convergence of the least squares functional that are in very good agreement with the observed numerical convergence challenging numerical examples including a nonconvex polygon with several corner singularities and a cavity domain are solved to around 10 digits of accuracy with a few seconds of cpu time the examples are implemented concisely with mpspack a matlab toolbox for wave computations with nonpolynomial basis functions developed by the authors a code example is included

pdf s confidence regions and relevant statistics for a class of sample covariance based array processors we add to the many results on sample covariance matrix scm dependent array processors by i weakening the traditional assumption of gaussian data and ii providing for a class of array processors additional performance measures that are of value in practice the data matrix is assumed drawn from a class of multivariate elliptically contoured mec distributions the performance measures include the exact probability density functions pdfs confidence regions and moments of the weight vector matrix beam response and beamformer output of certain scm based scb array processors the array processors considered include the scb i maximum likelihood ml signal vector estimator ii linearly constrained minimum variance beamformer lcmv iii minimum variance distortionless response beamformer mvdr and iv generalized sidelobe canceller gsc implementation of the lcmv beamformer it is shown that the exact joint pdfs for the weight vectors matrices of the aforementioned scb array processors are a linear transformation from a complex multivariate extension of the standardized t distribution the scb beam responses are generalized t distributed and the pdfs of the scb beamformer outputs are given by kummer s function all but the beamformer outputs are shown to be completely invariant statistics over the class of mecs considered

an automatic orthonormalization method for solving stiff boundary value problems abstract a new initial value method is described based on a remark by drury for solving stiff linear differential two point cigenvalue and boundary value problems the method is extremely reliable it is especially suitable for high order differential systems and it is capable of accommodating realms of stiffness which other methods cannot reach the key idea behind the method is to decompose the stiff differential operator into two non stiff operators one of which is nonlinear the nonlinear one is specially chosen so that it advances an orthonormal frame indeed the method is essentially a kind of automatic orthonormalization the second is auxiliary but it is needed to determine the required function the usefulness of the method is demonstrated by calculating some eigenfunctions for an orr sommerfeld problem when the reynolds number is as large as 10

the generalized finite element method for helmholtz equation part ii effect of choice of handbook functions error due to absorbing boundary conditions and its assessment abstract in part i t strouboulis i babuska r hidajat the generalized finite element method for helmholtz equation theory computation and open problems comput methods appl mech engrg 195 2006 4711 4731 we introduced the q version of the generalized finite element method gfem for the helmholtz equation and we addressed its a pollution error due to the wave number b exponential q convergence c robustness to perturbations of the mesh the roundoff and numerical quadrature errors and d a posteriori error estimation here we continue the development of the gfem for helmholtz and we address the effects of a alternative handbook functions and mesh types b the error due to the artificial truncation boundary conditions and its assessment the conclusions are 1 the employment of plane wave wave band and vekua handbook functions lead to equivalent results and 2 for high q the most significant component of error may be the one due to the artificial truncation boundary conditions a rather straightforward approach for assessing this error is proposed

componentwise perturbation analyses for the qr factorization this paper gives componentwise perturbation analyses for q and r in the qr factorization a qr q mathrm t q i r upper triangular for a given real m times n matrix a of rank n such specific analyses are important for example when the columns of a are badly scaled first order perturbation bounds are given for both q and r the analyses more accurately reflect the sensitivity of the problem than previous such results the condition number for r is bounded for a fixed n when the standard column pivoting strategy is used this strategy also tends to improve the condition of q so usually the computed q and r will both have higher accuracy when we use the standard column pivoting strategy practical condition estimators are derived the assumptions on the form of the perturbation delta a are explained and extended weaker rigorous bounds are also given

plane wave enriched partition of unity isogeometric analysis puiga for 2d helmholtz problems abstract in general numerical concerns in simulation of time harmonic acoustic waves are mainly due to the dispersion errors and the demands in modeling the problems with higher number of degrees of freedom per wavelength to obtain acceptable results as a remedy plane wave enriched partition of unity finite element method pufem was earlier proposed by melenk and babuska 1996 even though pufem gives accurate results with lesser degrees of freedom and shows exponential convergence it suffers from the approximate representation of geometry and leads to the boundary representation induced errors in this regard plane wave enriched pufem under isogeometric framework named partition of unity isogeometric analysis puiga is proposed for accurate geometry representation and smooth solution approximation which can lead to a better solution several benchmark problems are considered in the present study to illustrate the computational effectiveness of puiga

mixed enrichment for the finite element method in heterogeneous media summary problems of multiple scales of interest or of locally nonsmooth solutions may often involve heterogeneous media these problems are usually very demanding in terms of computations with the conventional finite element method on the other hand different enriched finite element methods such as the partition of unity which proved to be very successful in treating similar problems are developed and studied for homogeneous media in this work we present a new idea to extend the partition of unity finite element method to treat heterogeneous materials the idea is studied in applications to wave scattering and heat transfer problems where significant advantages are noted over the standard finite element method although presented within the partition of unity context the same enrichment idea can also be extended to other enriched methods to deal with heterogeneous materials copyright 2014 john wiley sons ltd

wave interpolation finite elements for helmholtz problems with jumps in the wave speed finite elements for short wave scattering problems have recently been developed by various authors these have almost exclusively dealt with the helmholtz equation the elements have been very successful in terms of drastic reductions of the number of degrees of freedom in the numerical model however most of them are not directly applicable to problems in which the wave speed is not constant but varies with position many important wave problems fall into this latter category this is because short waves are often present in materials whose properties vary in space the present paper demonstrates how the method may be extended so as to deal with problems in which the wave speed is piecewise constant in various regions of the problem domain lagrange multipliers are used to enforce the necessary conditions of compatibility between the different regions the paper gives numerical results for problems for which the analytical solution is known this shows how these methods may be extended in a relatively simple fashion to solve a much larger class of wave problems of great practical interest

numerical solution of isospectral flows in this paper we are concerned with the problem of solving numerically isospectral flows these flows are characterized by the differential equation l b l l l 0 l 0 where l 0 is a d x d symmetric matrix b l is a skew symmetric matrix function of l and b l is the lie bracket operator we show that standard runge kutta schemes fail in recovering the main qualitative feature of these flows that is isospectrality since they cannot recover arbitrary cubic conservation laws this failure motivates us to introduce an alternative approach and establish a framework for generation of isospectral methods of arbitrarily high order

plane wave decomposition in the unit disc convergence estimates and computational aspects this paper deals with the numerical simulation of time harmonic wave fields using progressive plane waves it is shown that a plane wave travelling in arbitrary direction can be numerically recovered with an accuracy of the order of the machine precision with a collocation formulation and the square root of the machine precision with a least square formulation however strongly evanescent and nearly singular wave fields cannot be properly recovered with standard double precision floating point arithmetic some of the ideas are applied to the elastic wave equation and a simple optimization algorithm is proposed to find a good compromise between the accuracy and the number of plane waves

approximating lyapunov exponents and sacker sell spectrum for retarded functional differential equations we consider lyapunov exponents and sacker sell spectrum for linear nonautonomous retarded functional differential equations posed on an appropriate hilbert space a numerical method is proposed to approximate such quantities based on the reduction to finite dimension of the evolution family associated to the system to which a classic discrete qr method is then applied the discretization of the evolution family is accomplished by a combination of collocation and generalized fourier projection a rigorous error analysis is developed to bound the difference between the computed stability spectra and the exact stability spectra the efficacy of the results is illustrated with some numerical examples

application of an ultra weak variational formulation of elliptic pdes to the two dimensional helmholtz problem a new technique to solve elliptic linear pdes called ultra weak variational formulation uwvf in this paper is introduced in b despres c r acad sci paris 318 1994 pp 939 944 this paper is devoted to an evaluation of the potentialities of this technique it is applied to a model wave problem the two dimensional helmholtz problem the new method is presented in three parts following the same style of presentation as the classical one of the finite elements method even though they are definitely conceptually different methods the first part is committed to the variational formulation and to the continuous problem the second part defines the discretization process using a galerkin procedure the third part actually studies the efficiency of the technique from the order of convergence point of view this is achieved using theoretical proofs and a series of numerical experiments in particular it is proven and shown the order of convergence is lower bounded by a linear function of the number of degrees of freedom an application to scattering problems is presented in a fourth part

a discontinuous galerkin method with plane waves for sound absorbing materials poro elastic materials are commonly used for passive control of noise and vibration and are key to reducing noise emissions in many engineering applications including the aerospace automotive and energy industries more efficient computational models are required to further optimise the use of such materials in this paper we present a discontinuous galerkin method dgm with plane waves for poro elastic materials using the biot theory solved in the frequency domain this approach offers significant gains in computational efficiency and is simple to implement costly numerical quadratures of highly oscillatory integrals are not needed it is shown that the biot equations can be easily cast as a set of conservation equations suitable for the formulation of the wave based dgm a key contribution is a general formulation of boundary conditions as well as coupling conditions between different propagation media this is particularly important when modelling porous materials as they are generally coupled with other media such as the surround fluid or an elastic structure the validation of the method is described first for a simple wave propagating through a porous material and then for the scattering of an acoustic wave by a porous cylinder the accuracy conditioning and computational cost of the method are assessed and comparison with the standard finite element method is included it is found that the benefits of the wave based dgm are fully realised for the biot equations and that the numerical model is able to accurately capture both the oscillations and the rapid attenuation of the waves in the porous material

the partition of unity finite element method for the simulation of waves in air and poroelastic media recently chazot et al j sound vib 332 1918 1929 2013 applied the partition of unity finite element method for the analysis of interior sound fields with absorbing materials the method was shown to allow a substantial reduction of the number of degrees of freedom compared to the standard finite element method the work is however restricted to a certain class of absorbing materials that react like an equivalent fluid this paper presents an extension of the method to the numerical simulation of biot s waves in poroelastic materials the technique relies mainly on expanding the elastic displacement as well as the fluid phase pressure using sets of plane waves which are solutions to the governing partial differential equations to show the interest of the method for tackling problems of practical interests poroelastic acoustic coupling conditions as well as fixed or sliding edge conditions are presented and numerically tested it is shown that the technique is a good candidate for solving noise control problems at medium and high frequency

a step size selection strategy for explicit runge kutta methods based on lyapunov exponent theory using a stability result for variable time step runge kutta methods applied to nonautonomous real linear scalar test problem that decays exponentially fast a step size selection algorithm is devised the step size selection algorithm is based partly on stability information obtained by estimating the discrete lyapunov exponent of a runge kutta method applied to a nonautonomous linear scalar problem the utility of the approach is illustrated in numerical experiments that demonstrate how the new algorithm performs against a standard accuracy based step size selection strategy

recursive short data record estimation of av and mmse mvdr linear filters for ds cdma antenna array systems the presence of the desired signal during estimation of the minimum mean square error mmse minimum variance distortionless response mvdr and auxiliary vector av filters under limited data support leads to significant signal to interference plus noise ratio sinr performance degradation we quantify this observation in the context of direct sequence code division multiple access ds cdma communications by deriving close approximations for the mean square filter estimation error the probability density function of the output sinr and the probability density function of the symbol error rate ser of the sample matrix inversion smi receiver evaluated using both a desired signal present and desired signal absent input covariance matrix to avoid such performance degradation we propose a ds cdma receiver that utilizes a simple pilot assisted algorithm that estimates and then subtracts the desired signal component from the received signal prior to filter estimation then to accommodate decision directed operation we develop two recursive algorithms for the on line estimation of the av and mmse mvdr filter and we study their convergence properties finally simulation studies illustrate the ser performance of the overall receiver structures

a discontinuous galerkin method with lagrange multipliers for the solution of helmholtz problems in the mid frequency regime we present a discontinuous galerkin method dgm for the solution of the helmholtz equation in the mid frequency regime our approach is based on the discontinuous enrichment method in which the standard polynomial field is enriched within each finite element by a non conforming field that contains free space solutions of the homogeneous partial differential equation to be solved hence for the helmholtz equation the enrichment field is chosen here as the superposition of plane waves we enforce a weak continuity of these plane waves across the element interfaces by suitable lagrange multipliers preliminary results obtained for two dimensional model problems discretized by uniform meshes reveal that the proposed dgm enables the development of elements that are far more competitive than both the standard linear and the standard quadratic galerkin elements for the discretization of helmholtz problems

a numerical integration scheme for special finite elements for the helmholtz equation the theory for integrating the element matrices for rectangular triangular and quadrilateral finite elements for the solution of the helmholtz equation for very short waves is presented a numerical integration scheme is developed samples of maple and fortran code for the evaluation of integration abscissae and weights are made available the results are compared with those obtained using large numbers of gauss legendre integration points for a range of testing wave problems the results demonstrate that the method gives correct results which gives confidence in the procedures and show that large savings in computation time can be achieved

exponential dichotomy integral separation and diagonalizability of linear systems of ordinary differential equations abstract this paper is concerned with linear systems of ordinary differential equations a criterion for integral separation in terms of exponential dichotomy is given as corollaries we obtain the roughness theorem for integral separation and the new result that an upper triangular system on a half line is integrally separated if and only if the system corresponding to its diagonal is we then show that a diagonal system on a half line is integrally separated if and only if a certain perturbed system is diagonalizable using this result we are able to deduce that the interior of the set of diagonalizable systems on a half line is the set of systems with integral separation and that the interior for the whole line is the set of systems which are integrally separated on both half lines

spline based boundaries a first step towards generic geometric domain descriptions for efficient mid frequency acoustic analysis using the wave based method the application of numerical simulation techniques for the analysis and optimization of the acoustic behavior of all kinds of products has become very important in almost every phase of a design process the large computational burden associated with the finite element method fem limits its applicability to low frequency problems recently the wave based method wbm was proposed as an efficient alternative to the element based methods this method is based on an indirect trefftz approach using an expansion of exact solutions of the governing differential equation to describe the dynamic field variables an important disadvantage of the wbm is the limited geometrical flexibility as compared to the element based techniques this paper aims to alleviate the geometrical restrictions by using b splines for the efficient description of curved edges the introduction of b splines within the wbm requires an adaptation of the numerical integration procedure used to evaluate the weighted residual formulation to this end different types of numerical integration techniques are studied the gauss legendre and the romberg integration procedure a comparative study with the finite element method and the original wbm indicates that the application of b splines and the adapted numerical integration procedure leads to accurate and computationally affordable wb models

unitary integrators and applications to continuous orthonormalization techniques in this paper the issue of integrating matrix differential systems whose solutions are unitary matrices is addressed such systems have skew hermitian coefficient matrices in the linear case and a

computational aspects of the ultra weak variational formulation the ultra weak variational formulation uwvf approach has been proposed as an effective method for solving helmholtz problems with high wave numbers however for coarse meshes the method can suffer from instability in this paper we consider computational aspects of the ultra weak variational formulation for the inhomogeneous helmholtz problem we introduce a method to improve the uwvf scheme and we compare iterative solvers for the resulting linear system computations for the acoustic transmission problem in 2d show that the new approach enables helmholtz problems to be solved on a relatively coarse mesh for a wide range of wave numbers

an alternate derivation of the distribution of the conditioned signal to noise ratio a result in multiple regression analysis is used to derive the probability distribution of the conditioned signal to noise ratio

on the compuation of lyapunov exponents for continuous dynamical systems in this paper we consider discrete and continuous qr algorithms for computing all of the lyapunov exponents of a regular dynamical system we begin by reviewing theoretical results for regular systems and present general perturbation results for lyapunov exponents we then present the algorithms give an error analysis of them and describe their implementation finally we give several numerical examples and some conclusions

on the error in qr integration an important change of variables for a linear time varying system dot x a t x t ge 0 is that induced by the qr factorization of the underlying fundamental matrix solution x qr with q orthogonal and r upper triangular with positive diagonal to find this change of variable one needs to solve a nonlinear matrix differential equation for q practically this means finding a numerical approximation to q by using some appropriate discretization scheme whereby one attempts to control the local error during the integration our contribution in this work is to obtain global error bounds for the numerically computed q these bounds depend on the local error tolerance used to integrate for q and on structural properties of the problem itself but not on the length of the interval over which we integrate this is particularly important since in principle q may need to be found on the half line t ge 0

continuous orthonormalization for boundary value problems abstract continuous orthonormalization describes an initial value method for linear 2 point boundary value problems which provides an orthogonal basis for the solution space at all points of the interval in this paper the equations of continuous orthonormalization are derived with elementary projection arguments to provide geometric insight and motivate some modifications of an earlier algorithm the method is then applied to some oscillatory and stiff boundary value problems to demonstrate that it is simple to use problem independent and as adaptive as the initial value code which is used to integrate the equations of continuous orthonormalization

lyapunov spectral intervals theory and computation different definitions of spectra have been proposed over the years to characterize the asymptotic behavior of nonautonomous linear systems here we consider the spectrum based on exponential dichotomy of sacker and sell j differential equations 7 1978 pp 320 358 and the spectrum defined in terms of upper and lower lyapunov exponents a main goal of ours is to understand to what extent these spectra are computable by using an orthogonal change of variables transforming the system to upper triangular form and the assumption of integral separation for the diagonal of the new triangular system we justify how popular numerical methods the so called continuous qr and svd approaches can be used to approximate these spectra we further discuss how to verify the property of integral separation and hence how to a posteriori infer stability of the attained spectral information finally we discuss the algorithms we have used to approximate the lyapunov and sacker sell spectra and present some numerical results

exponential separation exponential dichotomy and spectral theory for linear systems of ordinary differential equations abstract this paper is concerned with linear nonautonomous systems of ordinary differential equations a criterion for exponential separation in terms of exponential dichotomy is given as corollaries we obtain the roughness theorem for exponential separation and the new result that an upper triangular system on a half line is exponentially separated if and only if the system corresponding to its diagonal is a minimal decomposition into exponentially separated subspaces is defined it turns out that it is in general finer than the sacker sell spectral decomposition but that the two decompositions coincide for almost periodic systems

on the error in computing lyapunov exponents by qr methods we consider the error introduced using qr methods to approximate lyapunov exponents we give a backward error statement for linear non autonomous systems and further discuss nonlinear autonomous problems in particular for linear systems we show that one approximates a nearby discontinuous problem where how nearby is measured in terms of local errors and a measure of non normality for nonlinear problems we use a type of shadowing result

a projection approach for robust adaptive beamforming it is well known that calibration errors can seriously degrade performance in adaptive arrays particularly when the input signal to noise ratio is large the effect is caused by the perturbation of the presumed steering vector from its optimal value although it is not as widely known similar degradation occurs in sampled matrix inversion processing when the covariance matrix is estimated while the desired signal is present in the snapshot data under these conditions performance loss is due to errors in the estimated covariance matrix and occurs even when the steering vector is known exactly in the paper a new method based of modification of the steering vector is proposed to overcome both the problems of perturbation and of sample covariance errors the method involves projection of the presumed steering vector onto the observed signal plus interference subspace an analysis is also presented illustrating that the sample covariance errors can be viewed as a particular type of perturbation error and a simple approximation is derived for the expected beamformer performance as a function of the number of data snapshots both analytical and experimental results are presented that illustrate the advantages of the proposed method

identifying the wavenumber for the inverse helmholtz problem using an enriched finite element formulation abstract we investigate the inverse problem of identifying the wavenumber for the helmholtz equation the problem solution is based on measurements taken at few points from inside the computational domain or on its boundary a novel iterative approach is proposed based on coupling the secant and the descent methods with the partition of unity method starting from an initial guess for the unknown wavenumber the forward problem is solved using the partition of unity method then the secant descent methods are used to improve the initial guess by minimizing a predefined objective function based on the difference between the solution and a set of data points in the next round of iterations the improved wavenumber estimate is used for the forward problem solution and the partition of unity approximation is improved by adding more enrichment functions the iterative process is terminated when the objective function has converged and a set of two predefined tolerances are met to evaluate the estimate accuracy we propose to utilize extra data points to validate the approach and test its efficiency two wave applications with known analytical solutions are studied the results show that the proposed approach can achieve high accuracy for the studied applications even when the considered data is contaminated with noise despite the clear advantages that were previously shown in the literature for solving the forward helmholtz problem this work presents a first attempt to solve the inverse helmholtz problem with an enriched finite element approach

design and analysis of supervised and decision directed estimators of the mmse lcmv filter in data limited environments we consider sample matrix inversion smi type estimates of the minimum mean square error mmse and the linearly constrained minimum variance lcmv linear filters obtained from data records of limited size we quantify theoretically the detrimental effect of the desired signal energy level on the mean square ms filter estimation error and the normalized output signal to interference plus noise ratio sinr by deriving a new exact analytical expression and a lower bound respectively for cases where accumulation of pure disturbance observations is not possible we show theoretically how certain intuitive pilot assisted and decision directed adaptive filter implementations that utilize desired signal present data observations perform close to their desired signal absent counterparts simulation studies illustrate our theoretical developments in the context of spread spectrum communications over multipath fading channels under perfect and nonperfect synchronization

adaptive convergence of linearly constrained beamformers based on the sample covariance matrix a statistical analysis of the adaptive convergence behavior of linearly constrained beamformers is given assuming the sample covariance estimator is used to estimate the covariance matrix the sensor data are assumed to be gaussian distributed and independent from data vector to data vector the output power and mean squared error in the absence of the desired signal are shown to be multiples of chi squared random variables the presence of the desired signal results in an excess mean squared error that is beta distributed and depends only on the signal power number of data vectors and number of adaptive degrees of freedom the expected value of the excess mean squared error resulting from the signal presence is directly proportional to the signal power and number of adaptive degrees of freedom but is inversely proportional to the number of data vectors

a class of intrinsic schemes for orthogonal integration numerical integration of odes on the orthogonal stiefel manifold is considered points on this manifold are represented as n k matrices with orthonormal columns of particular interest is the case when n gg k mainly two requirements are imposed on the integration schemes first they should have arithmetic complexity of order nk2 second they should be intrinsic in the sense that they require only the ode vector field to be defined on the stiefel manifold as opposed to for instance projection methods the design of the methods makes use of retractions maps two algorithms are proposed one where the retraction map is based on the qr decomposition of a matrix and one where it is based on the polar decomposition numerical experiments show that the new methods are superior to standard lie group methods with respect to arithmetic complexity and may be more reliable than projection methods owing to their intrinsic nature