a hybridizable discontinuous galerkin method for stokes flow abstract in this paper we introduce a hybridizable discontinuous galerkin method for stokes flow the method is devised by using the discontinuous galerkin methodology to discretize a velocity pressure gradient formulation of the stokes system with appropriate choices of the numerical fluxes and by applying a hybridization technique to the resulting discretization one of the main features of this approach is that it reduces the globally coupled unknowns to the numerical trace of the velocity and the mean of the pressure on the element boundaries thereby leading to a significant reduction in the size of the resulting matrix moreover by using an augmented lagrangian method the globally coupled unknowns are further reduced to the numerical trace of the velocity only another important feature is that the approximations of the velocity pressure and gradient converge with the optimal order of k 1 in the l 2 norm when polynomials of degree k 0 are used to represent the approximate variables based on the optimal convergence of the hdg method we apply an element by element postprocessing scheme to obtain a new approximate velocity which converges with order k 2 in the l 2 norm for k 1 the postprocessing performed at the element level is less expensive than the solution procedure numerical results are provided to assess the performance of the method

a superconvergent ldg hybridizable galerkin method for second order elliptic problems we identify and study an ldg hybridizable galerkin method which is not an ldg method for second order elliptic problems in several space dimensions with remarkable convergence properties unlike all other known discontinuous galerkin methods using polynomials of degree k 0 for both the potential as well as the flux the order of convergence in l 2 of both unknowns is k 1 moreover both the approximate potential as well as its numerical trace superconverge in l 2 like norms to suitably chosen projections of the potential with order k 2 this allows the application of element by element postprocessing of the approximate solution which provides an approximation of the potential converging with order k 2 in l 2 the method can be thought to be in between the hybridized version of the raviart thomas and that of the brezzi douglas marini mixed methods

unified hybridization of discontinuous galerkin mixed and continuous galerkin methods for second order elliptic problems we introduce a unifying framework for hybridization of finite element methods for second order elliptic problems the methods fitting in the framework are a general class of mixed dual finite element methods including hybridized mixed continuous galerkin nonconforming and a new wide class of hybridizable discontinuous galerkin methods the distinctive feature of the methods in this framework is that the only globally coupled degrees of freedom are those of an approximation of the solution defined only on the boundaries of the elements since the associated matrix is sparse symmetric and positive definite these methods can be efficiently implemented moreover the framework allows in a single implementation the use of different methods in different elements or subdomains of the computational domain which are then automatically coupled finally the framework brings about a new point of view thanks to which it is possible to see how to devise novel methods displaying very localized and simple mortaring techniques as well as methods permitting an even further reduction of the number of globally coupled degrees of freedom

detection of signals by information theoretic criteria a new approach is presented to the problem of detecting the number of signals in a multichannel time series based on the application of the information theoretic criteria for model selection introduced by akaike aic and by schwartz and rissanen mdl unlike the conventional hypothesis testing based approach the new approach does not requite any subjective threshold settings the number of signals is obtained merely by minimizing the aic or the mdl criteria simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented

construction and analysis of fourth order finite difference schemes for the acoustic wave equation in nonhomogeneous media in this article we construct and analyse a family of finite difference schemes for the acoustic wave equation with variable coefficients these schemes are fourth order accurate in space and time in the case of smooth media and are designed to remain stable and optimal for reflection transmission phenomena in the case of discontinuous coefficients together with a detailed mathematical study various numerical results are presented

conditions for superconvergence of hdg methods for stokes flow we provide an a priori error analysis of a wide class of finite element methods for the stokes equations the methods are based on the velocity gradient velocity pressure formulation of the equations and include new and old mixed and hybridizable discontinuous galerkin methods we show how to reduce the error analysis to the verification of some properties of an elementwise defined projection and of the local spaces defining the methods we also show that the projection of the errors only depends on the approximation properties of the projection we then provide sufficient conditions for the superconvergence of the projection of the error in the approximate velocity we give many examples of these methods and show how to systematically construct them from similar methods for the diffusion equation

a hybridizable discontinuous galerkin method for linear elasticity this paper describes the application of the so called hybridizable discontinuous galerkin hdg method to linear elasticity problems the method has three significant features the first is that the only globally coupled degrees of freedom are those of an approximation of the displacement defined solely on the faces of the elements the corresponding stiffness matrix is symmetric positive definite and possesses a block wise sparse structure that allows for a very efficient implementation of the method the second feature is that when polynomials of degree k are used to approximate the displacement and the stress both variables converge with the optimal order of k 1 for any k 0 the third feature is that by using an element by element post processing a new approximate displacement can be obtained that converges at the order of k 2 whenever k 2 numerical experiments are provided to compare the performance of the hdg method with that of the continuous galerkin cg method for problems with smooth solutions and to assess its performance in situations where the cg method is not adequate that is when the material is nearly incompressible and when there is a crack copyright 2009 john wiley sons ltd

dispersion estimation from linear array data in the time frequency plane we consider the problem of estimating the dispersion of a wave field from data recorded by a linear array of geophones the fact that the data we are looking at may contain several propagating waves make this even more challenging in this paper a new algorithm is proposed to solve this issue currently there are two methods for estimating wave dispersion described in the literature the first method estimates the group delay function from the time frequency representation tfr of each sensor separately it is efficient as long as the patterns of the different waves do not overlap in the time frequency plane the second method estimates the dispersion from the two dimensional 2 d fourier transform of the profile or more generally from a velocity frequency representation this assumes that the dispersion is constant along the entire sensor array it is efficient as long as the patterns of the waves do not overlap in the frequency domain our method can be thought of as a hybrid of the above two methods as it is based on the construction of a tfr where the energy of waves that propagate at a selected velocity are amplified the primary advantage of our algorithm is the use of the velocity variable to separate the patterns of the propagating waves in the time frequency plane when applied to both synthetic and real data this new algorithm gives much improved results when compared with other standard methods

a priori estimates for mixed finite element approximations of second order hyperbolic equations with absorbing boundary conditions optimal order l infty in time l 2 in space a priori error estimates are derived for mixed finite element approximations for both displacement and stress for a second order hyperbolic equation with first order absorbing boundary conditions continuous in time explicit in time and implicit in time procedures are formulated and analyzed

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

discontinuous galerkin finite element method for the wave equation the symmetric interior penalty discontinuous galerkin finite element method is presented for the numerical discretization of the second order wave equation the resulting stiffness matrix is symmetric positive definite and the mass matrix is essentially diagonal hence the method is inherently parallel and leads to fully explicit time integration when coupled with an explicit time stepping scheme optimal a priori error bounds are derived in the energy norm and the l 2 norm for the semidiscrete formulation in particular the error in the energy norm is shown to converge with the optimal order cal o h min s ell with respect to the mesh size h the polynomial degree ell and the regularity exponent s of the continuous solution under additional regularity assumptions the l 2 error is shown to converge with the optimal order cal o h min s ell numerical results confirm the expected convergence rates and illustrate the versatility of the method

symplectic hamiltonian hdg methods for wave propagation phenomena abstract we devise the first symplectic hamiltonian hybridizable discontinuous galerkin hdg methods for the acoustic wave equation we discretize in space by using a hamiltonian hdg scheme that is an hdg method which preserves the hamiltonian structure of the wave equation and in time by using symplectic diagonally implicit and explicit partitioned runge kutta methods the fundamental feature of the resulting scheme is that the conservation of a discrete energy which is nothing but a discrete version of the original hamiltonian is guaranteed we present numerical experiments which indicate that the method achieves optimal approximations of order k 1 in the l 2 norm when polynomials of degree k 0 and runge kutta time marching methods of order k 1 are used in addition by means of post processing techniques and by increasing the order of the runge kutta method to k 2 we obtain superconvergent approximations of order k 2 in the l 2 norm for the displacement and the velocity we also present numerical examples that corroborate that the methods conserve energy and that they compare favorably with dissipative hdg schemes of similar accuracy properties for long time simulations

analysis of hdg methods for stokes flow in this paper we analyze a hybridizable discontinuous galerkin method for numerically solving the stokes equations the method uses polynomials of degree k for all the components of the approximate solution of the gradient velocity pressure formulation the novelty of the analysis is the use of a new projection tailored to the very structure of the numerical traces of the method it renders the analysis of the projection of the errors very concise and allows us to see that the projection of the error in the velocity superconverges as a consequence we prove that the approximations of the velocity gradient the velocity and the pressure converge with the optimal order of convergence of k 1 in l 2 for any k 0 moreover taking advantage of the superconvergence properties of the velocity we introduce a new element by element postprocessing to obtain a new velocity approximation which is exactly divergence free h div conforming and converges with order k 2 for k 1 and with order 1 for k 0 numerical experiments are presented which validate the theoretical results

determination of the dimension of a signal subspace from short data records a nested sequence of constant false alarm rate cfar hypothesis tests is presented for rank determination over short data records the procedure is based on the interpretation of sum of squares of singular values as energy in a particular subspace the cfar thresholds are set up based on distributions derived from matrix perturbation ideas expressions for probability of overestimation and underestimation are presented

explicit finite element methods for symmetric hyperbolic equations a family of explicit space time finite element methods for the initial boundary value problem for linear symmetric hyperbolic systems of equations is described and analyzed the method generalizes the discontinuous galerkin method and as is typical for this method obtains error estimates of order o h n 1 2 for approximations by polynomials of degree le n

estimation of parameters of exponentially damped sinusoids using fast maximum likelihood estimation with application to nmr spectroscopy data we present fast maximum likelihood fml estimation of parameters of multiple exponentially damped sinusoids the fml algorithm was motivated by the desire to analyze data that have many closely spaced components such as the nmr spectroscopy data of human blood plasma the computational efficiency of fml lies in reducing the multidimensional search involved in ml estimation into multiple 1 d searches this is achieved by using our knowledge of the shape of the compressed likelihood function clf in the parameter space the proposed fml algorithm is an iterative method that decomposes the original data into its constituent signal components and estimates the parameters of the individual components efficiently using our knowledge of the shape of the clf the other striking features of the proposed algorithm are that it provides procedures for initialization has a fast converging iteration stage and makes use of the information extracted in preliminary iterations to segment the data suitably to increase the effective signal to noise ratio snr the computational complexity and the performance of the proposed algorithm are compared with other existing methods such as those based on linear prediction kiss iqml alternating projections ap and expectation maximization em

esprit estimation of signal parameters via rotational invariance techniques an approach to the general problem of signal parameter estimation is described the algorithm differs from its predecessor in that a total least squares rather than a standard least squares criterion is used although discussed in the context of direction of arrival estimation esprit can be applied to a wide variety of problems including accurate detection and estimation of sinusoids in noise it exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational invariance structure the technique when applicable manifests significant performance and computational advantages over previous algorithms such as mem capon s mlm and music

mathematica evidence that ramanujan kills baker gammel wills a 1961 conjecture of baker gammel and wills asserts that if a function f is meromorphic in the unit ball and analytic at zero then a subsequence of its diagonal pade approximants converges uniformly in compact subsets omitting poles inasmuch as the denominators of the pade approximants are complex orthogonal polynomials and the convergence of sequences of pade approximants is determined largely by the behaviour of their poles the conjecture deals with distribution of zeros of complex orthogonal polynomials in this paper we present numerical evidence derived using the mathematica package that ramanujan s continued fractionh q z 1 qz 1 q 2z 1 q 3z 1 provides a counterexample provided q is appropriately chosen on the unit circle

a projection based error analysis of hdg methods we introduce a new technique for the error analysis of hybridizable discontinuous galerkin hdg methods the technique relies on the use of a new projection whose design is inspired by the form of the numerical traces of the methods this renders the analysis of the projections of the discretization errors simple and concise by showing that these projections of the errors are bounded in terms of the distance between the solution and its projection our studies of influence of the stabilization parameter are reduced to local analyses of approximation by the projection we illustrate the technique on a specific hdg method applied to a model second order elliptic problem

a new time space domain high order finite difference method for the acoustic wave equation a new unified methodology was proposed in finkelstein and kastner 2007 39 to derive spatial finite difference fd coefficients in the joint time space domain to reduce numerical dispersion the key idea of this method is that the dispersion relation is completely satisfied at several designated frequencies we develop this new time space domain fd method further for 1d 2d and 3d acoustic wave modeling using a plane wave theory and the taylor series expansion new spatial fd coefficients are frequency independent though they lead to a frequency dependent numerical solution we prove that the modeling accuracy is 2nd order when the conventional 2m th order space domain fd and the 2nd order time domain fd stencils are directly used to solve the acoustic wave equation however under the same discretization the new 1d method can reach 2m th order accuracy and is always stable the 2d method can reach 2m th order accuracy along eight directions and has better stability similarly the 3d method can reach 2m th order accuracy along 48 directions and also has better stability than the conventional fd method the advantages of the new method are also demonstrated by the results of dispersion analysis and numerical modeling of acoustic wave equation for homogeneous and inhomogeneous acoustic models in addition we study the influence of the fd stencil length on numerical modeling for 1d inhomogeneous media and derive an optimal fd stencil length required to balance the accuracy and efficiency of modeling a new time space domain high order staggered grid fd method for the 1d acoustic wave equation with variable densities is also developed which has similar advantages demonstrated by dispersion analysis stability analysis and modeling experiments the methodology presented in this paper can be easily extended to solve similar partial difference equations arising in other fields of science and engineering

an analysis of new mixed finite elements for the approximation of wave propagation problems we construct and analyze a new family of rectangular two dimensional or cubic three dimensional mixed finite elements for the approximation of the acoustic wave equations the main advantage of this element is that it permits us to obtain through mass lumping an explicit scheme even in an anisotropic medium nonclassical error estimates are given for this new element

convergence of diagonal pade approximants for functions analytic near 0 for functions analytic in a neighbourhood of 0 we show that at least for a subsequence of the diagonal pade approximants the point 0 attracts a zero proportion of the poles the same is true for every sufficiently dense diagonal subsequence consequently these subsequences have a convergence in capacity type property which is possibly the correct analogue of the nuttallpommerenke theorem in this setting

the convergence of diagonal pade approximants and the pade conjecture questions related to the convergence problem of diagonal pade approximants are discussed a central place is taken by the pade conjecture also known as the baker gammel wills conjecture partial results concerning this conjecture are reviewed and weaker and more special versions of the conjecture are formulated and their plausibility is investigated great emphasis is given to the role of spurious poles of the approximants a conjecture by nuttall 1970 about the number and distribution of such poles is stated and its importance for the pade conjecture is analyzed

a direct approach to convergence of multivariate nonhomogeneous pade approximants we present a direct approach for proving convergence in measure product capacity of multivariate nonhomogeneous pade approximants previous approaches have involved projection onto pade type approximation in one variable and only yielded convergence in lebesgue measure

improving the readability of time frequency and time scale representations by the reassignment method in this paper the use of the reassignment method first applied by kodera gendrin and de villedary 1976 to the spectrogram is generalized to any bilinear time frequency or time scale distribution this method creates a modified version of a representation by moving its values away from where they are computed so as to produce a better localization of the signal components we first propose a new formulation of this method followed by a thorough theoretical study of its characteristics its practical use for a large variety of known time frequency and time scale distributions is then addressed finally some experimental results are reported to demonstrate the performance of this method

superconvergence of discontinuous galerkin and local discontinuous galerkin schemes for linear hyperbolic and convection diffusion equations in one space dimension in this paper we study the superconvergence property for the discontinuous galerkin dg and the local discontinuous galerkin ldg methods for solving one dimensional time dependent linear conservation laws and convection diffusion equations we prove superconvergence towards a particular projection of the exact solution when the upwind flux is used for conservation laws and when the alternating flux is used for convection diffusion equations the order of superconvergence for both cases is proved to be k frac 3 2 when piecewise p k polynomials with k geq1 are used the proof is valid for arbitrary nonuniform regular meshes and for piecewise p k polynomials with arbitrary k geq1 improving upon the results in y cheng and c w shu j comput phys 227 2008 pp 9612 9627 y cheng and c w shu computers and structures 87 2009 pp 630 641 in which the proof based on fourier analysis was given only for uniform meshes with periodic boundary condition and piecewise p 1 polynomials

finite element approximation of the hyperbolic wave equation in mixed form the purpose of this paper is to present a finite element approximation of the scalar hyperbolic wave equation written in mixed form that is introducing an auxiliary vector field to transform the problem into a first order problem in space and time we explain why the standard galerkin method is inappropriate to solve this problem and propose as alternative a stabilized finite element method that can be cast in the variational multiscale framework the unknown is split into its finite element component and a remainder referred to as subscale as original features of our approach we consider the possibility of letting the subscales to be time dependent and orthogonal to the finite element space the formulation depends on algorithmic parameters whose expression is proposed from a heuristic fourier analysis

conditions for superconvergence of hdg methods for second order elliptic problems we provide a projection based analysis of a large class of finite element methods for second order elliptic problems it includes the hybridized version of the main mixed and hybridizable discontinuous galerkin methods the main feature of this unifying approach is that it reduces the main difficulty of the analysis to the verification of some properties of an auxiliary locally defined projection and of the local spaces defining the methods sufficient conditions for the optimal convergence of the approximate flux and the superconvergence of an element by element postprocessing of the scalar variable are obtained new mixed and hybridizable discontinuous galerkin methods with these properties are devised which are defined on squares cubes and prisms

a phase based hybridizable discontinuous galerkin method for the numerical solution of the helmholtz equation we introduce a new hybridizable discontinuous galerkin hdg method for the numerical solution of the helmholtz equation over a wide range of wave frequencies our approach combines the hdg methodology with geometrical optics in a fashion that allows us to take advantage of the strengths of these two methodologies the phase based hdg method is devised as follows first we enrich the local approximation spaces with precomputed phases which are solutions of the eikonal equation in geometrical optics second we propose a novel scheme that combines the hdg method with ray tracing to compute multivalued solution of the eikonal equation third we utilize the proper orthogonal decomposition to remove redundant modes and obtain locally orthogonal basis functions which are then used to construct the global approximation spaces of the phase based hdg method and fourth we propose an appropriate choice of the stabilization parameter to guarantee stability and accuracy for the proposed method numerical experiments presented show that optimal orders of convergence are achieved that the number of degrees of freedom to achieve a given accuracy is independent of the wave number and that the number of unknowns required to achieve a given accuracy with the proposed method is orders of magnitude smaller than that with the standard finite element method

an implicit high order hybridizable discontinuous galerkin method for nonlinear convection diffusion equations in this paper we present hybridizable discontinuous galerkin methods for the numerical solution of steady and time dependent nonlinear convection diffusion equations the methods are devised by expressing the approximate scalar variable and corresponding flux in terms of an approximate trace of the scalar variable and then explicitly enforcing the jump condition of the numerical fluxes across the element boundary applying the newton raphson procedure and the hybridization technique we obtain a global equation system solely in terms of the approximate trace of the scalar variable at every newton iteration the high number of globally coupled degrees of freedom in the discontinuous galerkin approximation is therefore significantly reduced we then extend the method to time dependent problems by approximating the time derivative by means of backward difference formulae when the time marching method is p 1 th order accurate and when polynomials of degree p 0 are used to represent the scalar variable each component of the flux and the approximate trace we observe that the approximations for the scalar variable and the flux converge with the optimal order of p 1 in the l 2 norm finally we apply element by element postprocessing schemes to obtain new approximations of the flux and the scalar variable the new approximate flux which has a continuous interelement normal component is shown to converge with order p 1 in the l 2 norm the new approximate scalar variable is shown to converge with order p 2 in the l 2 norm the postprocessing is performed at the element level and is thus much less expensive than the solution procedure for the time dependent case the postprocessing does not need to be applied at each time step but only at the times for which an enhanced solution is required extensive numerical results are provided to demonstrate the performance of the present method

superconvergent discontinuous galerkin methods for second order elliptic problems we identify discontinuous galerkin methods for second order elliptic problems in several space dimensions having superconvergence properties similar to those of the raviart thomas and the brezzi douglas marini mixed methods these methods use polynomials of degree k 0 for both the potential as well as the flux we show that the approximate flux converges in l2 with the optimal order of k 1 and that the approximate potential and its numerical trace superconverge in l2 like norms to suitably chosen projections of the potential with order k 2 we also apply element by element postprocessing of the approximate solution to obtain new approximations of the flux and the potential the new approximate flux is proven to have normal components continuous across inter element boundaries to converge in l2 with order k 1 and to have a divergence converging in l2 also with order k 1 the new approximate potential is proven to converge with order k 2 in l2 numerical experiments validating these theoretical results are presented

high order implicit hybridizable discontinuous galerkin methods for acoustics and elastodynamics we present a class of hybridizable discontinuous galerkin hdg methods for the numerical simulation of wave phenomena in acoustics and elastodynamics the methods are fully implicit and high order accurate in both space and time yet computationally attractive owing to their following distinctive features first they reduce the globally coupled unknowns to the approximate trace of the velocity which is defined on the element faces and single valued thereby leading to a significant saving in the computational cost in addition all the approximate variables including the approximate velocity and gradient converge with the optimal order of k 1 in the l 2 norm when polynomials of degree k 0 are used to represent the numerical solution and when the time stepping method is accurate with order k 1 when the time stepping method is of order k 2 superconvergence properties allows us by means of local postprocessing to obtain better yet inexpensive approximations of the displacement and velocity at any time levels for which an enhanced accuracy is required in particular the new approximations converge with order k 2 in the l 2 norm when k 1 for both acoustics and elastodynamics extensive numerical results are provided to illustrate these distinctive features

numerical solution of the acoustic wave equation using raviart thomas elements in this paper we discuss the numerical approximation of the displacement form of the acoustic wave equation using mixed finite elements the mixed formulation allows for approximation of both displacement and pressure at each time step without the need for post processing lowest order and next to lowest order raviart thomas elements are used for the spatial discretization and centered finite differences are used to advance in time use of these raviart thomas elements results in a diagonal mass matrix for resolution of pressure and a mass matrix for the displacement variable that is sparse with a simple structure convergence results for a model problem are provided as are numerical results for a two dimensional problem with a point source

on svd for estimating generalized eigenvalues of singular matrix pencil in noise several algorithms for estimating generalized eigenvalues ges of singular matrix pencils perturbed by noise are reviewed the singular value decomposition svd is explored as the common structure in the three basic algorithms direct matrix pencil algorithm pro esprit and tls esprit it is shown that several svd based steps inherent in the algorithms are equivalent to the first order approximation in particular the pro esprit and its variant tls pro esprit are shown to be equivalent and the tls esprit and its earlier version ls esprit are shown to be asymptotically equivalent to the first order approximation for the problem of estimating superimposed complex exponential signals the state space algorithm is shown to be also equivalent to the previous matrix pencil algorithms to the first order approximation the second order perturbation and the threshold phenomenon are illustrated by simulation results based on a damped sinusoidal signal an improved state space algorithm is found to be the most robust to noise

geometric methods for determining system poles from transient response the problem treated is that of identifying the poles of a finite order system by observing its transient decay after cessation of input for a limited time using possibly multiple observation points and experimental repetition various approaches are studied having the common characteristic that a homogeneous matrix equation must be solved several techniques that have been given scant attention in the literature are consolidated by a geometric treatment together with new results including an analytical treatment of the consequences of assuming an excessively high system order derivation of a statistically unbiased estimate for an intermediate parameter in the solution new theorems on error effects a recipe for effective use of the singular value decomposition and a new method for suppression of extraneous poles

a priori error estimates for mixed finite element approximations of the acoustic wave equation in this paper we derive optimal a priori l infty l 2 error estimates for mixed finite element displacement formulations of the acoustic wave equation the computational complexity of this approach is equivalent to the traditional mixed finite element formulations of the second order hyperbolic equations in which the primary unknowns are pressure and the gradient of pressure however the displacement formulations with the physical variables of interest displacement and pressure requires less regularity on the displacement

hdg methods for elastodynamics abstract we derive and analyze a hybridizable discontinuous galerkin hdg method for approximating weak solutions to the equations of time harmonic linear elasticity on a bounded lipschitz domain in three dimensions the real symmetry of the stress tensor is strongly enforced and its coefficients as well as those of the displacement vector field are approximated simultaneously at optimal convergence with respect to the choice of approximating spaces wavenumber and mesh size sufficient conditions are given so that the system is indeed transferable onto a global hybrid variable that for larger polynomial degrees may be approximated via a smaller dimensional space than the original variables we construct several variants of this method and discuss their advantages and disadvantages and give a systematic approach to the error analysis for these methods we touch briefly on the application of this error analysis to the time dependent problem and finally we examine two different implementations of the method over various polynomial degrees and numerically demonstrate the convergence properties proven herein

signal processing applications of oblique projection operators oblique projection operators are used to project measurements onto a low rank subspace along a direction that is oblique to the subspace they may be used to enhance signals while nulling interferences in the paper the authors give several basic results for oblique projections including formulas for constructing oblique projections with desired range and null space they analyze the algebra and geometry of oblique projections in order to understand their properties they then show how oblique projections can be used to separate signals from structured noise such as impulse noise damped or undamped interfering sinusoids such as power line interference and narrow band noise in some of the problems addressed the oblique projection provides an alternative way to implement an already known solution expressing these solutions as oblique projections brings geometrical insight to the study of the solution the geometry of oblique projections enables one to compute performance in terms of angles between signal and noise subspaces as a special case of removing impulse noise the authors can use oblique projections to interpolate missing data samples in array processing oblique projections can be used to simultaneously steer beams and nulls in communications oblique projections can be used to remove intersymbol interference

broadband dispersion extraction using simultaneous sparse penalization in this paper we propose a broadband method to extract the dispersion curves for multiple overlapping dispersive modes from borehole acoustic data under limited spatial sampling the proposed approach exploits a first order taylor series approximation of the dispersion curve in a band around a given center frequency in terms of the phase and group slowness at that frequency under this approximation the acoustic signal in a given band can be represented as a superposition of broadband propagators each of which is parameterized by the slowness pair above we then formulate a sparsity penalized reconstruction framework as follows these broadband propagators are viewed as elements from an overcomplete dictionary representation and under the assumption that the number of modes is small compared to the size of the dictionary it turns out that an appropriately reshaped support image of the coefficient vector synthesizing the signal using the given dictionary representation exhibits column sparsity our main contribution lies in identifying this feature and proposing a complexity regularized algorithm for support recovery with an l1 type simultaneous sparse penalization note that support recovery in this context amounts to recovery of the broadband propagators comprising the signal and hence extracting the dispersion namely the group and phase slownesses of the modes in this direction we present a novel method to select the regularization parameter based on kolmogorov smirnov ks tests on the distribution of residuals for varying values of the regularization parameter we evaluate the performance of the proposed method on synthetic as well as real data and show its performance in dispersion extraction under presence of heavy noise and strong interference from time overlapped modes

asymptotic wavelet and gabor analysis extraction of instantaneous frequencies the behavior of the continuous wavelet and gabor coefficients in the asymptotic limit using stationary phase approximations are investigated in particular it is shown how under some additional assumptions these coefficients allow the extraction of some characteristics of the analyzed signal such as frequency and amplitude modulation laws applications to spectral line estimations and matched filtering are briefly discussed

matched subspace detectors we formulate a general class of problems for detecting subspace signals in subspace interference and broadband noise we derive the generalized likelihood ratio glr for each problem in the class we then establish the invariances for the glr and argue that these are the natural invariances for the problem in each case the glr is a maximal invariant statistic and the distribution of the maximal invariant statistic is monotone this means that the glr test glrt is the uniformly most powerful invariant detector we illustrate the utility of this finding by solving a number of problems for detecting subspace signals in subspace interference and broadband noise in each case we give the distribution for the detector and compute performance curves

on the complexity of iqml algorithms the authors study the computational complexity of two methods for solving least squares and maximum likelihood modal analysis problems in particular they consider the steiglitz mcbride and iterative quadratic maximum likelihood iqml algorithms j h mcclellan and d lee ibid vol 39 no 2 p 509 12 1991 have shown the iterations of the two methods to be equivalent however they suggest that the steiglitz mcbride algorithm may be computationally preferable a method for reducing the dimension of the matrix inversion required at each iteration of iqml is provided the resulting reduction in the computation makes the computational complexity of iqml commensurate with that of the steiglitz mcbride algorithm

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

a space time discontinuous galerkin method for the solution of the wave equation in the time domain in recent years the focus of research in the field of computational acoustics has shifted to the medium frequency regime and multiscale wave propagation this has led to the development of new concepts including the discontinuous enrichment method its basic principle is the incorporation of features of the governing partial differential equation in the approximation in this contribution this concept is adapted for the simulation of transient problems governed by the wave equation we present a space time discontinuous galerkin method with lagrange multipliers where the shape approximation in space and time is based on solutions of the homogeneous wave equation the use of hierarchical wave like basis functions is enabled by means of a variational formulation that allows for discontinuities in both the spatial and the temporal discretizations numerical examples in one space dimension demonstrate the outstanding performance of the proposed method compared with conventional space time finite element methods copyright 2008 john wiley sons ltd

discontinuous galerkin methods with staggered hybridization for linear elastodynamics abstract in this paper we will develop a new staggered hybridization technique for discontinuous galerkin methods to discretize linear elastodynamic equations the idea of hybridization is used extensively in many discontinuous galerkin methods but the idea of staggered hybridization is new our new approach offers several advantages namely energy conservation high order optimal convergence preservation of symmetry for the stress tensor block diagonal mass matrices as well as low dispersion error the key idea is to use two staggered hybrid variables to enforce the continuity of the velocity and the continuity of the normal component of the stress tensor on a staggered mesh we prove the stability and the convergence of the proposed scheme in both the semi discrete and the fully discrete settings numerical results confirm the optimal rate of convergence and show that the method has a superconvergent property for dispersion furthermore an application of this method to rayleigh wave propagation is presented

an explicit hybridizable discontinuous galerkin method for the acoustic wave equation abstract we present an explicit hybridizable discontinuous galerkin hdg method for numerically solving the acoustic wave equation the method is fully explicit high order accurate in both space and time and coincides with the classic discontinuous galerkin dg method with upwinding fluxes for a particular choice of its stabilization function this means that it has the same computational complexity as other explicit dg methods however just as its implicit version it provides optimal convergence of order k 1 for all the approximate variables including the gradient of the solution and when the time stepping method is of order k 2 it displays a superconvergence property which allow us by means of local postprocessing to obtain new improved approximations of the scalar field variables at any time levels for which an enhanced accuracy is required in particular the new approximations converge with order k 2 in the l 2 norm for k 1 these properties do not hold for all numerical fluxes indeed our results show that when the hdg numerical flux is replaced by the lax friedrichs flux the above mentioned superconvergence properties are lost although some are recovered when the lax friedrichs flux is used only in the interior of the domain finally we extend the explicit hdg method to treat the wave equation with perfectly matched layers we provide numerical examples to demonstrate the performance of the proposed method

5d seismic data completion and denoising using a novel class of tensor decompositions abstractwe have developed a novel strategy for simultaneous interpolation and denoising of prestack seismic data most seismic surveys fail to cover all possible source receiver combinations leading to missing data especially in the midpoint offset domain this undersampling can complicate certain data processing steps such as amplitude variation with offset analysis and migration data interpolation can mitigate the impact of missing traces we considered the prestack data as a 5d multidimensional array or otherwise referred to as a 5d tensor using synthetic data sets we first found that prestack data can be well approximated by a low rank tensor under a recently proposed framework for tensor singular value decomposition tsvd under this low rank assumption we proposed a complexity penalized algorithm for the recovery of missing traces and data denoising in this algorithm the complexity regularization was controlled by tuning a single regularization parameter using a statistical test we tested t

a family of mixed finite elements for the elasticity problem a new mixed finite element formulation for the equations of linear elasticity is considered in the formulation the variables approximated are the displacement the unsymmetric stress tensor and the rotation the rotation act as a lagrange multiplier introduced in order to enforce the symmetry of the stress tensor based on this formulation a new family of both two and three dimensional mixed methods is defined optimal error estimates which are valid uniformly with respect to the poisson ratio are derived finally a new postprocessing scheme for improving the displacement is introduced and analyzed

the application of high order differencing to the scalar wave equation the second order central difference is often used to approximate the derivatives of the wave equation it is demonstrated that gains in computational efficiency can be made by using high order approximations for these derivatives a one dimensional model is used to illustrate the relative accuracy of o t2 x2 o t2 x4 o t4 x4 ando t4 x10 central difference schemes for comparison o t2 ando t4 pseudospectral schemes are used as an additional measure of performance the results indicate that o t4 x10 differencing can achieve similar accuracy as the o t4 spectral scheme for practical illustration a two dimensional form of the o t4 x10 algorithm is used to compute the exploding reflector response of a salt dome model and compared with a fine grid o t2 x4 result transmissive sponge like boundary conditions are also examined and shown to be effective

local time stepping and discontinuous galerkin methods for symmetric first order hyperbolic systems we present a new non conforming space time mesh refinement method for the symmetric first order hyperbolic system this method is based on the one hand on the use of a conservative higher order discontinuous galerkin approximation for space discretization and a finite difference scheme in time on the other hand on appropriate discrete transmission conditions between the grids we use a discrete energy technique to drive the construction of the matching procedure between the grids and guarantee the stability of the method

superconvergent hdg methods on isoparametric elements for second order elliptic problems we propose a projection based a priori error analysis of a wide class of mixed and hybridizable discontinuous galerkin methods for diffusion problems for which the mappings relating the elements to the reference elements are nonlinear we show that if the local spaces on the reference elements satisfy suitable conditions and if the mappings used to define the mesh and global spaces satisfy simple regularity and compatibility conditions the methods provide optimally convergent approximations for both unknowns as well as superconvergent approximations for the scalar variable a crucial feature of the analysis of the methods is the use of two new spaces of traces and two associated suitably defined projections thanks to which the error analysis then becomes almost identical to that obtained by the authors in math comp 81 2012 pp 1327 1353 where the case in which the mappings are affine is considered

a projection based error analysis of hdg methods for timoshenko beams in this paper we give the first a priori error analysis of the hybridizable discontinuous galerkin hdg methods for timoshenko beams the analysis is based on the use of a projection especially designed to fit the structure of the numerical traces of the hdg method this property allows to prove in a very concise manner that the projection of the errors is bounded in terms of the distance between the exact solution and its projection the study of the influence of the stabilization function on the approximation is then reduced to the study of how they affect the approximation properties of the projection in a single element surprisingly and unlike any other discontinuous galerkin method this can be done without assuming any positivity property of the stabilization function of the hdg method we apply this approach to hdg methods using polynomials of degree k 0 in all the unknowns and show that the projection of the error in each of them superconverges with order k 2 when k 1 and converges with order 1 for k 0 as a result we show that the hdg methods converge with optimal order k 1 for all the unknowns and that they are free from shear locking finally we show that all the numerical traces converge with order 2k 1 numerical experiments validating these results are shown

difference approximations of the neumann problem for the second order wave equation stability theory and numerical experiments are presented for a finite difference method that directly discretizes the neumann problem for the second order wave equation complex geometries are discretized using a cartesian embedded boundary technique both second and third order accurate approximations of the boundary conditions are presented away from the boundary the basic second order method can be corrected to achieve fourth order spatial accuracy to integrate in time we present both a second order and a fourth order accurate explicit method the stability of the method is ensured by adding a small fourth order dissipation operator locally modified near the boundary to allow its application at all grid points inside the computational domain numerical experiments demonstrate the accuracy and long time stability of the proposed method

the staggered dg method is the limit of a hybridizable dg method we show in the framework of steady state diffusion boundary value problems that the staggered discontinuous galerkin sdg method siam j numer anal 47 2009 pp 3820 3848 can be obtained from a hybridizable discontinuous galerkin hdg method siam j numer anal 47 2009 pp 1319 1365 by setting its stabilization function to zero at some suitably chosen element faces and by letting it go to infinity at all the remaining others we then show that this point of view allows the sdg method to immediately acquire new properties all inherited from the hdg methods namely their efficient implementation by hybridization their postprocessings and their superconvergence properties