discontinuous galerkin methods for friedrichs systems i general theory this paper presents a unified analysis of discontinuous galerkin methods to approximate friedrichs systems an abstract set of conditions is identified at the continuous level to guarantee existence and uniqueness of the solution in a subspace of the graph of the differential operator then a general discontinuous galerkin method that weakly enforces boundary conditions and mildly penalizes interface jumps is proposed all the design constraints of the method are fully stated and an abstract error analysis in the spirit of strang s second lemma is presented finally the method is formulated locally using element fluxes and links with other formulations are discussed details are given for three examples namely advection reaction equations advection diffusion reaction equations and the maxwell equations in the so called elliptic regime

multigrid acceleration of a high resolution computational aeroacoustics scheme a multigrid method is applied to a fourth order accurate spatially and temporally nite difference runge kutta time marching scheme thisisusedto solvethenonlineareulerequationsfortheef cientprediction ofnoise radiation from turbofan engine inlets this noise prediction approach computes a steady state solution rst and thenasourceisturnedonandtheunsteadysolutioniscomputed thishastheadvantageofusingthesamenumerical scheme to evaluate the residuals of the governing equations in both the steady and unsteady calculations which meansthatthesteady statesolutionissmoothand nonumericalerrorscontaminatetheacousticsolution thehigh

on point covers of c oriented polygons let s be any family of n c oriented polygons of the two dimensional euclidean plane e2 i e bounded intersection of halfplanes whose normal directions of edges belong to a fixed collection of c distinct directions let s denote the packing number of s that is the maximum number of pairwise disjoint objects of s let s be the transversal number of s that is the minimum number of points required so that each object contains at least one of those points we provide linear time algorithms t n c t nc for a fat c oriented polytopes translates or homothets of ed proving that g 2 c o a d g 2 c dd and g 2 c 3d3 2 d respectively

finite difference simulations of transient radiation from a finite length pipe the far field radiation originating from a finite length pipe is well studied especially for steady state conditions however because all physical systems do not begin in steady state these radiation characteristics are only valid after the transient portion of the solution has decayed understanding transient radiation characteristics may be important particularly for systems transmitting very short duration signals as they can differ quite significantly a numerical complication to this problem involves dealing with a sharp corner in the domain of interest while many numerical studies have attempted to couple solutions from the domains inside and outside a pipe the analysis presented in this work treats the computational domain as a single region by expressing the entire physical domain as a map from a simple rectangular domain in generalized curvilinear coordinates this method will be introduced in detail and general results of transient radiation will be presented for an infinitely baffled finite length pipe using the finite difference method expressed in generalized curvilinear coordinates comparison will be made to previous results p stepanishen and r a tougas j acoust soc am 93 3074 3084 1993 that used a semi analytic approach with certain assumptions the far field radiation originating from a finite length pipe is well studied especially for steady state conditions however because all physical systems do not begin in steady state these radiation characteristics are only valid after the transient portion of the solution has decayed understanding transient radiation characteristics may be important particularly for systems transmitting very short duration signals as they can differ quite significantly a numerical complication to this problem involves dealing with a sharp corner in the domain of interest while many numerical studies have attempted to couple solutions from the domains inside and outside a pipe the analysis presented in this work treats the computational domain as a single region by expressing the entire physical domain as a map from a simple rectangular domain in generalized curvilinear coordinates this method will be introduced in detail and general results of transient radiation will be presented for an infinitely baffled f

a time domain numerical modeling of two dimensional wave propagation in porous media with frequency dependent dynamic permeability an explicit finite difference scheme is presented for solving the two dimensional biot equations of poroelasticity across the full range of frequencies the key difficulty is to discretize the johnson koplik dashen jkd model which describes the viscous dissipations in the pores indeed the time domain version of biot jkd model involves order 1 2 fractional derivatives which amount to a time convolution product to avoid storing the past values of the solution a diffusive representation of fractional derivatives is used the convolution kernel is replaced by a finite number of memory variables that satisfy local in time ordinary differential equations the coefficients of the diffusive representation follow from an optimization procedure of the dispersion relation then various methods of scientific computing are applied the propagative part of the equations is discretized using a fourth order finite difference scheme whereas the diffusive part is solved exactly an immersed interface method is implemented to discretize the geometry on a cartesian grid and also to discretize the jump conditions at interfaces numerical experiments are proposed in various realistic configurations

a generalized recursive convolution method for time domain propagation in porous media an efficient numerical method referred to as the auxiliary differential equation ade method is proposed to compute convolutions between relaxation functions and acoustic variables arising in sound propagation equations in porous media for this purpose the relaxation functions are approximated in the frequency domain by rational functions the time variation of the convolution is thus governed by first order differential equations which can be straightforwardly solved the accuracy of the method is first investigated and compared to that of recursive convolution methods it is shown that while recursive convolution methods are first or second order accurate in time the ade method does not introduce any additional error the ade method is then applied for outdoor sound propagation using the equations proposed by wilson et al in the ground 2007 appl acoust 68 173 200 a first one dimensional case is performed showing that only five poles are necessary to accurately approximate the relaxation functions for typical applications finally the ade method is used to compute sound propagation in a three dimensional geometry over an absorbing ground results obtained with wilson s equations are compared to those obtained with zwikker and kosten s equations and with an impedance surface for different flow resistivities

efficient computation of the sound fields above a layered porous ground an efficient computation of sound fields due to a monopole source placed above a porous layer is presented this paper examines an improved scheme whereby the steepest descent path is selected for the numerical evaluation of the sommerfeld integral along the steepest descent path a standard gaussian hermite quadrature can be used to calculate the sound fields effectively the suggested numerical scheme is accurate at all frequencies except in the very near field the proposed method is more numerically efficient than other computational schemes especially at long ranges and high source frequencies

from semidiscrete to fully discrete stability of runge kutta schemes by the energy method the integration of semidiscrete approximations for time dependent problems is encountered in a variety of applications the runge kutta rk methods are widely used to integrate the ode systems which arise in this context resulting in large ode systems called methods of lines these methods of lines are governed by possibly ill conditioned systems with a growing dimension consequently the naive spectral stability analysis based on scalar eigenvalues arguments may be misleading instead we present here a stability analysis of rk methods for well posed semidiscrete approximations based on a general energy method we review the stability question for such rk approximations and highlight its intricate dependence on the growing dimension of the problem in particular we prove the strong stability of general fully discrete rk methods governed by coercive approximations we conclude with two nontrivial examples which demonstrate the versatility of our approach in the context of general systems of convection diffusion equations with variable coefficients a straightforward implementation of our results verify the strong stability of rk methods for local finite difference schemes as well as global spectral approximations since our approach is based on the energy method which is carried in the physical space and since it avoids the von neumann analysis which is carried in the dual fourier space we are able to easily adapt additional extensions due to nonperiodic boundary conditions general geometries etc

frequency domain prediction of turbofan noise radiation this paper describes a frequency domain numerical method for predicting noise radiation from ducted fans including acoustic treatment and non uniform background flow effects the method solves the euler equations linearized about a mean flow in the frequency domain a pseudo time derivative term is added to the frequency domain equations so that a time marching technique can be employed to drive the acoustic field to steady state explicitly this approach makes distributed parallel computing more viable for equations of this type and will allow for future use of well known convergence acceleration techniques such as multigrid to obtain the solutions efficiently simulations of the jt15d static test inlet are performed including the effects of liners and the results are compared with experimental data a generic engine geometry is used for demonstrating further the prediction capability of the code calculating the attenuation effects of different liner impedances and liner installation locations on the radiated sound fields

deduction of ground impedance from measurements of excess attenuation spectra an efficient numerical method of deducing ground surface impedance from measurements of short range propagation from a point source is proposed the method involves finding the root of a complex equation and uses the fact that the classical approximation for the spherical wave reflection coefficient near grazing incidence is an analytic function of the impedance examples of fitting measured excess attenuation spectra are given methods for ensuring the uniqueness of the resulting impedance fits are discussed subsequent deductions of parameters in a two parameter impedance model are also considered and exemplified

time domain numerical simulation of a flow impedance tube an efficient method has been developed for the application of the surface acoustic impedance condition in time domain solutions of aeroacoustic problems such as the broadband frequency simulation of a flow impedance tube the basis for this method is the standard impedance condition stated in the frequency domain as the particle displacement continuity equation the development of the time domain impedance condition follows the relations among the frequency z and discrete time domains and a rational function representation of the impedance in thez domain the resultant impedance condition consists of finite infinite impulse response type digital filter operations in the time domain which is very suitable to computational aeroacoustics algorithms this paper describes the present approach and discusses the time domain numerical simulations of the nasa langley flow impedance tube with a constant depth ceramic tubular liner both single and broadband frequency simulations are performed excellent agreement is shown with experimental data at various frequencies and flow conditions

surface acoustic impedance and causality several models that are commonly used to calculate the surface acoustic impedance of porous materials are examined in light of the causality requirement in its nonlocal and its approximate local forms strict nonlocal causality requires that the imaginary part of the surface acoustic impedance be the hilbert transform of the real part it is found that the local approximation is not a good test of causality for these models and that even in its general form the equation describing the surface acoustic impedance of these porous materials is not strictly causal at high frequencies

a controllable canonical form implementation of time domain impedance boundary conditions for broadband aeroacoustic computation a new method which can be effectively and efficiently applied in the simulations of broadband noise problems is proposed for time domain impedance boundary condition implementations by using the so called controllable canonical form that is well known in linear system usually the impedance boundary condition can be defined in frequency domain as a rational polynomial function with poles in the negative half of the complex plane to guarantee stability otherwise causality might be violated in the corresponding time domain implementation to address this issue various methodologies have been proposed previously that usually lead to complicated polynomials whose numerical implementations are often indirect and intricate the proposed method with a controllable canonical form on the other hand directly transforms the frequency domain transfer function a quotient of rational polynomials to an equivalent state space model which consists of a series of first order ordinary differential equations that can be numerically implemented in a straightforward way the proposed method is demonstrated by using two benchmark problems a two dimensional gaussian pulse propagating in a uniform flow with a lined wall and the test cases from the nasa langley grazing incidence tube experiments good agreements demonstrate the potential of the proposed computational method

omnidirectional plane wave destruction abstractsteep structures in seismic data may bring directional aliasing thus the plane wave destruction pwd filter cannot obtain an accurate dip estimation we propose to interpret the plane wave construction pwc filter as a line interpolating operator and introduce a novel circle interpolating model the circle interpolating pwc can avoid phase wrapping problems and the related circle interpolating pwd can avoid aliasing problems we design a 2d maxflat fractional delay filter to implement the circle interpolation and we prove that the 2d maxflat filter is separable in each direction using the maxflat fractional delay filter in the circle interpolation we propose omnidirectional plane wave destruction opwd opwd can handle vertical structures and horizontal structures with a synthetic example we show how to obtain an omnidirectional dip estimation using the proposed opwd an application of opwd to a field data set improves the results of predictive painting and event picking as compared to

sound propagation above an inhomogeneous impedance plane abstract boundary integral equation bie methods are described for the prediction of sound propagation in particular from a line source over a flat plane of inhomogeneous impedance approximate methods which satisfy reciprocity for the calculation of the wave field over a two impedance plane are proposed these approximations applied to propagation from a line source give results agreeing well with those of the bie method when they are applied to propagation from a point source agreement with experiment is shown

a numerically stable formulation of the green s function parabolic equation subtracting the surface wave pole the original formulation of the green s function parabolic equation gfpe can have numerical accuracy problems for large normalized surface impedances to solve the accuracy problem an improved form of the gfpe has been developed the improved gfpe formulation is similar to the original formulation but it has the surface wave pole subtracted the improved gfpe is shown to be accurate for surface impedances varying over 2 orders of magnitude with the largest having a magnitude exceeding 1000 also the improved formulation is slightly faster than the original formulation because the surface wave component does not have to be computed separately

computational geometry an introduction from the reviews this book offers a coherent treatment at the graduate textbook level of the field that has come to be known in the last decade or so as computational geometry the book is well organized and lucidly written a timely contribution by two founders of the field it clearly demonstrates that computational geometry in the plane is now a fairly well understood branch of computer science and mathematics it also points the way to the solution of the more challenging problems in dimensions higher than two

boundary conditions for simulations of oscillating bubbles using the non linear acoustic approximation we have developed a new boundary condition for finite volume simulations of oscillating bubbles our method uses an approximation to the motion outside the domain based on the solution at the domain boundary we then use this approximation to apply boundary conditions by defining incoming characteristic waves at the domain boundary our boundary condition is applicable in regions where the motion is close to spherically symmetric we have tested our method on a range of one and two dimensional test cases results show good agreement with previous studies the method allows simulations of oscillating bubbles for long run times 5 10 5 time steps with a cfl number of 0 8 on highly truncated domains in which the boundary condition may be applied within 0 1 of the maximum bubble radius conservation errors due to the boundary conditions are found to be of the order of 0 1 after 105 time steps the method significantly reduces the computational cost of fixed grid finite volume simulations of oscillating bubbles two dimensional results demonstrate that highly asymmetric bubble features such as surface instabilities and the formation of jets may be captured on a small domain using this boundary condition

well posed boundary condition for acoustic liners in straight ducts with flow doi 10 2514 1 j050723 the myers boundary condition for acoustics within flow over an acoustic lining has been shown to be ill posed leading to numerical stability issues in the time domain and mathematical problems with stability analyses this paper gives a modification for flat or cylindrical straight ducts to make the myers boundary condition well posed and indeed more accurate by accounting for a thin inviscid boundary layer over the lining and correctly deriving the boundary condition to first order in the boundary layer thickness the modification involves two integraltermsovertheboundarylayer the firstmaybewrittenintermsofthemass momentum andkinetic energy thicknessesoftheboundarylayer whichareshownto physicallycorrespondtoamodifiedboundarymass modified grazingvelocity andatensionalongtheboundary thesecondintegral termisrelatedtothecriticallayerwithinthe boundary layer a time domain version of the new boundary condition is proposed although not implemented the modified boundary condition is validated against high fidelity numerical solutions of the pridmore brown equation for sheared inviscid flow in a cylinder absolute instability boundaries are given for certain examples though convective instabilities appear to always be present at certain frequencies for any boundary layer thickness

an adjoint based method for liner impedance eduction validation and numerical investigation abstract an inverse method for liner acoustic impedance eduction in a duct is presented the determination of adjoint equations allows to make explicit the directional derivatives of the objective function needed by the search algorithm direct and adjoint system of equations are spatially discretized by a discontinuous galerkin scheme the propagation model and the eduction process are successfully validated on nasa benchmark data extracted from literature in a no flow configuration objective functions written in terms of acoustic pressure and acoustic velocity are considered successively special attention is given to the possibilities offered by the method such as multiparameter identification with the study of a non homogeneous liner convergence history of the process is also examined revealing interesting properties for the velocity based objective function compared to the pressure based objective function in further developments the method is planned to be used with acoustic velocity fields obtained by laser doppler velocimetry

the complex equivalent source method for sound propagation over an impedance plane the sound field caused by a monopole source above an impedance plane can be calculated by using a superposition of equivalent point sources located along a line in the mirror space below the plane originally such an approach for representing the half space green s function was described by sommerfeld at the beginning of the last century in order to treat half space problems of heat conduction however the representation converges only for masslike impedances and cannot be used for the more important case of reflecting planes with springlike surface impedances the singular part of the line integral can be transformed into a hankel function which shows that surface waves are contained in the whole solution unfortunately this representation suffers from the lack of validity at certain receiver points and from restrictions on wave number and impedance range to ensure the necessary convergence the main idea of the present method is to use also a superposition of equivalent point sources but to allow that these sources can be located at complex source points the corresponding form of the half space green s function is suitable for both masslike and springlike surface impedances and can be used as a cornerstone for a boundary element method

near field computation for sound propagation above ground using complex image theory in this paper a very simple method is introduced for the efficient computation of the sound field in the near region above an impedance ground or an extended reaction ground the procedure is based on complex image theory using prony s method the slowly varying factor in the integrand of the sommerfeld integral is approximated by a short series in terms of complex exponential functions the result can be exactly evaluated by the sommerfeld identity a new closed form approximate expression of the sound field is obtained which is represented as the original source its quasistatic image and several images with complex amplitudes and positions avoiding numerical evaluation of the sommerfeld integral makes these closed form expressions computationally very efficient the representation of the field with complex images makes the formula useful in measurement of ground impedance or in other cases requiring repeated mapping of the sound field numerical results show that these closed form green s functions are very accurate for the computation of the near field

transparent acoustic source condition applied to the euler equations it can be concluded from the present calculations that the transparent source model proposed here is useful to numerically simulate an acoustic source in the computational domain that is located far downstream thus it is possible to simulate a complex acoustic problem such as the reflection and transmission of an incident wave

a simple and accurate complex image interpretation of vertical antennas present in contiguous dielectric half spaces an efficient technique is developed to solve the important problem of vertical antennas located above and penetrating the interface between contiguous dielectric half spaces it begins by deriving the spectral expressions of the vector and scalar potential green functions in terms of the tm wave spectral transmission coefficient the complex image technique is used to derive simple accurate and rapidly convergent expressions of the full wave spatial green functions the spatial green functions are used in the moment method to model vertical thin wire antennas residing above the penetrating the interface separating the contiguous dielectric half spaces with and without loss

acoustic propagation over an impedance plane a new solution is obtained for the acoustic pressure field generated by a point source and scattered by a locally reacting impedance covered plane the new solution is obtained in the form of an asymptotic series which has been shown to agree well with other studies one of the most important features of this solution is that higher order terms can be calculated from preceding terms in the series by the use of recursion formulas comparing data predicted from this solution with that from a numerical integration of the exact expression shows the asymptotic series to be extremely accurate even for relatively low values of the parameter kr not surprisingly the plane wave solution often shows major deviations from the exact integral solution

broadband time domain impedance models the modeling of a set of impedance values given either experimentally or heuristically for implementation as a time domain impedance equivalent boundary condition tdibc is discussed it is shown that impedance as defined by the reflection of plane harmonic waves when extended for broadband time domain applications can correspond to mathematically feasible but physically unacceptable noncausal reflection processes given a set of impedance data on a finite positive and real frequency range it is possible to construct causal time domain models that render efficient implementation of tdibc for broadband reflections however these models defined by measurement of harmonic waves may not be valid for the reflection of impulses for which measurement of transient reflections is warranted

design of broadband time domain impedance boundary conditions using the oscillatory diffusive representation of acoustical models a methodology to design broadband time domain impedance boundary conditions tdibcs from the analysis of acoustical models is presented the derived tdibcs are recast exclusively as first order differential equations well suited for high order numerical simulations broadband approximations are yielded from an elementary linear least squares optimization that is for most models independent of the absorbing material geometry this methodology relies on a mathematical technique referred to as the oscillatory diffusive or poles and cuts representation and is applied to a wide range of acoustical models drawn from duct acoustics and outdoor sound propagation which covers perforates semi infinite ground layers as well as cavities filled with a porous medium it is shown that each of these impedance models leads to a different tdibc comparison with existing numerical models such as multi pole or extended helmholtz resonator provides insights into their suitability additionally the broadly applicable fractional polynomial impedance models are analyzed using fractional calculus

the multidimensional wave equation with generalized acoustic boundary conditions i strong stability we study the wave equation on a domain of mathbb r d d geq 2 with dynamical boundary control applied on a part of the boundary and a dirichlet boundary condition on the remaining part we prove the asymptotic stability and nonuniform stability of the associated semigroup

silhouettes a graphical aid to the interpretation and validation of cluster analysis a new graphical display is proposed for partitioning techniques each cluster is represented by a so called silhouette which is based on the comparison of its tightness and separation this silhouette shows which objects lie well within their cluster and which ones are merely somewhere in between clusters the entire clustering is displayed by combining the silhouettes into a single plot allowing an appreciation of the relative quality of the clusters and an overview of the data configuration the average silhouette width provides an evaluation of clustering validity and might be used to select an appropriate number of clusters

natural continuous extensions of runge kutta methods the present paper develops a theory of natural continuous extensions nces for the discrete approximate solution of an ode given by a runge kutta process these nces are defined in such a way that the continuous solutions furnished by the one step collocation methods are included

fundamental problems with the model of uniform flow over acoustic linings abstract the walls of ducts containing flow are often acoustically lined in order to reduce sound many simple models of acoustic linings assume the lining to be linear and locally reacting examples considered here include the three parameter mass spring damper helmholtz resonator and enhanced helmholtz resonator models all of these models have been found to have stability issues with uniform mean grazing flow and there has been some confusion over the existence of hydrodynamic instability surface waves over such linings mathematically the standard proven briggs bers stability analysis is not applicable computationally the hydrodynamic modes are routinely ignored in the frequency domain and instabilities filtered out in the time domain this confusion also causes significant problems for mode matching green functions and scattering analyses in this paper it is shown that any situation not capable of being analysed using the briggs bers criterion is illposed and that this is the root cause of the confusion over hydrodynamic instabilities a large class of lining models including all those mentioned above are shown to be illposed with uniform mean flow an explanation is given of the effects of this illposedness in practice and it is argued that illposed models should not be used an alternative stability criterion to briggs bers has been occasionally used in the literature this alternative criterion involving analytic continuation to purely imaginary frequencies was recently christened the crighton leppington stability criterion however this stability criterion is incorrect and several counter examples are given here

impedance boundary condition for truncated open spaces the propagation of waves governed by hyperbolic systems at a surface is in general reflective the numerical solution of many problems in mechanics necessitates the truncation of an open space to a finite domain the reflectivity of the boundary of a truncated domain can be effectively characterized by a few parameters and implemented as a time domain impedance boundary condition it is shown that the concept of a time domain impedance boundary condition affords a simple and effective treatment of waves allowing them to exit the surfaces of a truncated domain as a causal local space time continuation rather than a global boundary confinement we presentanddiscusstheopen spaceimpedancesofradiativeandconvective fields theirmodeling analyticstructures implementation and solution effectiveness as an open space impedance boundary condition we further propose a generalmethodologyfornumericaldefinitionofopen spaceimpedanceanditsapplicationwithinexistingschemesto reduce truncated domains and computational resources

an extension of complex modes for the resolution of finite element poroelastic problems a new modal synthesis technique inspired from complex modes is presented in this paper the purpose of this method is to find an alternative to the weakness of usual modal techniques in order to improve resolution of finite element poroelastic problems firstly the construction of modes and the synthesis for a general forcing is explained secondly the approach is applied to a one dimensional poroelastic problem finally the approach is numerically tested and its performance is investigated by comparison with solutions obtained with a direct resolution of the system

time domain impedance boundary conditions for computational aeroacoustics it is an accepted practice in aeroacoustics to characterize the properties of an acoustically treated surface by a quantity known as impedance impedance is a complex quantity as such it is designed primarily for frequency domain analysis time domain boundary conditions that are the equivalent of the frequency domain impedance boundary condition are proposed both single frequency and model broadband time domain impedance boundary conditions are provided it is shown that the proposed boundary conditions together with the linearized euler equations form well posed initial boundary value problems unlike ill posed problems they are free from spurious instabilities that would render time marching computational solutions impossible

parallel computation of forward radiated noise of ducted fans with acoustic treatment forward radiated noise of ducted fans is computed numerically on parallel processors solving the three dimensional time dependent euler equations in body conformed coordinates with a fourth order accurate finite difference runge kutta time integration scheme sound attenuation effects of inlet wall acoustic treatment are included in computations employing a time discrete form of the standard impedance condition a distributed computing approach with domain decomposition is used for integrating the equations in parallel using the message passing interface library routines the abilities of the method are demonstrated with hard and soft wall simulations of the jt15d inlet including flow effects

an efficient realization of frequency dependent boundary conditions in an acoustic finite difference time domain model abstract the finite difference time domain fdtd method provides a simple and accurate way of solving initial boundary value problems however most acoustic problems involve frequency dependent boundary conditions and it is not easy to include such boundary conditions in an fdtd model although solutions to this problem exist most of them have high computational costs and stability cannot always be ensured in this work a solution is proposed based on mixing modelling strategies this involves separating the fdtd mesh and the boundary conditions a digital filter representation of the impedance and combining them into a global solution this solution is based on an interaction model that involves wave digital filters the proposed method is validated with several test cases

runge kutta methods for parabolic equations and convolution quadrature we study the approximation properties of runge kutta time discretizations of linear and semilinear parabolic equations including incompressible navier stokes equations we derive asymptotically sharp error bounds and relate the temporal order of convergence which is generally noninteger to spatial regularity and the type of boundary conditions the analysis relies on an interpretation of runge kutta methods as convolution quadratures in a different context these can be used as efficient computational methods for the approximation of convolution integrals and integral equations they use the laplace transform of the confolution kernal via a discrete operational calculus 23 refs 2 tabs

wave equation stabilization by delays equal to even multiples of the wave propagation time for a string equation with time delays in the output feedback loop we study stability and show that the system is a riesz spectral system and prove that the spectrum determined growth condition holds for all delays when the delay is equal to the even multiples of the wave propagation time we develop the necessary and sufficient conditions for the feedback gain and time delay which guarantee the exponential stability of the closed loop system in particular we show that as the delay of even multiples is increasing to infinity the stability bound on the feedback gain decays to zero we also show that whenever the delay is an odd multiple of the wave propagation time the closed loop system is unstable the lack of robustness to a small perturbation in time delay is specifically discussed for the delay equal to two a numerical simulation for the case of the delay equal to two is presented to illustrate the convergence finally an alternative stability analysis is conducted within the framework of well posed infinite dimensional systems

high order accurate thin layer approximations for time domain electromagnetics part i general metal backed coatings we present a family of high order accurate thin layer approximations for time domain electromagnetics the thin layer approximations are valid for metal backed coatings of general isotropic materials and certain classes of anisotropic materials on smooth curvilinear backgrounds both dielectric and magnetic materials can be considered these models are non trivial and we discuss their properties and implementation in the context of discontinuous galerkin methods which are particularly well suited for these models the range of validity accuracy and stability of the resulting schemes is demonstrated through one and two dimensional examples

low dispersion finite difference methods for acoustic waves in a pipe a new algorithm for computing one dimensional acoustic waves in a pipe is demonstrated by solving the acoustic equations as an initial boundary value problem conventional dissipation free second order finite difference methods suffer severe phase distortion for grids with less that about ten mesh points per wavelength using the signal generated by a piston in a duct as an example transient acoustic computations are presented using a new compact three point algorithm which allows about 60 fewer mesh points per wave length both pulse and harmonic excitation are considered coupling of the acoustic signal with the pipe resonant modes are shown to generate a complex transient wave with rich harmonic content

implicit high order compact algorithm for computational acoustics accurate solution of the linearized multidimensional euler equations for aeroacoustics as a system of simple wave equations is demonstrated if organized this system has unambiguous easily implemented boundary conditions allowing waves of same group speeds to pass through numerical boundaries or comply with wall conditions thus the task of designing a complex multidimensional scheme with approximate boundary conditions reduces to the design of accurate schemes for the simple wave equation in particular an implicit compact finite difference scheme and a characteristically exact but numerically nth order accurate boundary condition are used this low dispersion scheme has a third order spatial accuracy for various types of nonuniform meshes fourth order accuracy on uniform meshes and by choice a temporal accuracy of second order for algorithmic simplicity as the crank nicolson scheme the robustness and accuracy of the scheme and the validity of the system decoupling are demonstrated through a series of numerical experiments and comparisons with published results including the recent institute for computer applications in science and engineering nasa langley research center benchmark problems of acoustic and convective wave propagation in cartesian and cylindrical domains and reflection at stationary and or moving boundaries

fingerprint indexing based on minutiae pairs and convex core point an efficient fingerprint indexing which uses ellipse properties is proposed a new fingerprint indexing is proposed using minutiae pairs and convex core point our fingerprint representation is very robust to distortions and noise the proposed fingerprint features are invariant to rotation and translation fingerprint identification is an important issue for identifying fingerprints and plays a key role in the fingerprint recognition systems however performing a fingerprint identification over a large database can be an inefficient task due to the lack of scalability and high computing times of fingerprint matching algorithms fingerprint indexing is a key strategy in automatic fingerprint identification systems afiss which allows us to reduce the number of candidates the search space and the occurrences of false acceptance in large databases in this paper an efficient indexing algorithm is proposed using minutiae pairs and convex core point which employs k means clustering and candidate list reduction criteria to improve the identification performance our proposal can effectively reduce the search space and number of candidates for fingerprint matching and thus achieves higher efficiency and significantly improves the system retrieval performance experimental results over some of the fingerprint verification competition fvc and the national institute of standards and technology nist databases prove the superiority of the proposed approach against some of the well known indexing algorithms

diffusive approximation of a time fractional burger s equation in nonlinear acoustics a fractional time derivative is introduced into burger s equation to model losses of nonlinear waves this term amounts to a time convolution product which greatly penalizes the numerical modeling a diffusive representation of the fractional derivative is adopted here replacing this nonlocal operator by a continuum of memory variables that satisfy local in time ordinary differential equations then a quadrature formula yields a system of local partial differential equations well suited to numerical integration the determination of the quadrature coefficients is crucial to ensure both the well posedness of the system and the computational efficiency of the diffusive approximation for this purpose optimization with constraint is shown to be a very efficient strategy strang splitting is used to solve successively the hyperbolic part by a shock capturing scheme and the diffusive part exactly numerical experiments are proposed to assess the efficiency of the numerical modeling and to illustrate the effect of the fractional attenuation on the wave propagation

an exact laplace transform formulation for a point source above a ground surface an exact analysis is given for a point source in air above a ground surface by representing the plane wave reflection coefficient as the laplace transform of an image source distribution a well behaved image integral instead of the usual sommerfeld integral is obtained the approach is valid for both locally and extended reacting surfaces for a locally reacting ground surface the image integral is an especially simple rapidly convergent integral the integral for local reaction is investigated analytically for a number of limiting cases the resulting analytic solutions are compared with analytic solutions obtained from more standard approaches finally the image integral for local reaction is analyzed numerically and an upper limit on the numerical integration is given it is shown that with realistic values of ground impedance the prescribed integration limit allows the image integral to be easily and accurately computed numerically

broadband impedance boundary conditions for the simulation of sound propagation in the time domain an accurate and practical surface impedance boundary condition in the time domain has been developed for application to broadband frequency simulation in aeroacoustic problems to show the capability of this method two kinds of numerical simulations are performed and compared with the analytical experimental results one is acoustic wave reflection by a monopole source over an impedance surface and the other is acoustic wave propagation in a duct with a finite impedance wall both single frequency and broadband frequency simulations are performed within the framework of linearized euler equations a high order dispersion relation preserving finite difference method and a low dissipation low dispersion runge kutta method are used for spatial discretization and time integration respectively the results show excellent agreement with the analytical experimental results at various frequencies the method accurately predicts both the amplitude and the phase of acoustic pressure and ensures the well posedness of the broadband time domain impedance boundary condition

a time domain method for duct acoustics this paper reports the development of a time accurate method for prediction of acoustics in lined ducts the multi dimensional euler equations are dimensionally split into a system of uni directional simple wave equations which are discretized and solved using an implicit compact high order finite difference scheme the split equations are closed and coupled through the concept of impedance at domain boundaries time domain extensions of the impedance boundary condition and their efficient implementation are introduced for broadband and monotone waves the method is benchmarked by the modal solution of a monopole in the lined duct and used to investigate wall interference on the acoustic fields of realistic sources excellent agreement is found in the comparison with classical solutions and the discrepancy found in the comparison with experiment is ascribable to experimental uncertainty

nonlinear parabolic equation model for finite amplitude sound propagation over porous ground layers the nonlinear parabolic equation npe is a time domain method widely used in underwater sound propagation applications it allows simulation of weakly nonlinear sound propagation within an inhomogeneous medium so that this method can be used for outdoor sound propagation applications it must account for the effects of an absorbing ground surface the npe being formulated in the time domain complex impedances cannot be used and hence the ground layer is included in the computational system with the help of a second npe based on the zwikker kosten model a two way coupling between these two layers air and ground is required for the whole system to behave correctly coupling equations are derived from linearized euler s equations in the frame of a parabolic model this two way coupling only involves spatial derivatives making its numerical implementation straightforward several propagation examples both linear or nonlinear are then presented the method is shown to give satisfactory results for a wide range of ground characteristics finally the problem of including forchheimer s nonlinearities in the two way coupling is addressed and an approximate solution is proposed

sound propagation above an impedance boundary an asymptotic solution of the scalar wave field due to a point source above a locally reacting plane surface is obtained by a modified saddle point method numerical calculation indicates that the relatively simple solution is more accurate than the thomasson asymptotic solution and the chien soroka solution furthermore it is shown that another solution simplified still more is also in good agreement with the exact solution

concerning the cause of instability in time stepping boundary element methods applied to the exterior acoustic problem the boundary element method bem in its simple form when solving the exterior acoustic problem in the frequency domain has difficulties at the frequencies of internal resonances of the closed structure the corresponding time domain form of the exterior problem often exhibits instabilities in the time stepping process the link between these two features is investigated by relating the eigenvalues of the iterating matrix of the time stepping process to damped frequencies numerical evidence from a problem with an analytic solution and from a loudspeaker response are given the suggested link implies that instability comes from numerical errors super imposed on a more fundamental problem and may be best tackled through a time domain technique corresponding to the methods already available in the frequency domain

approximation schemes for covering and packing problems in image processing and vlsi a unified and powerful approach is presented for devising polynomial approximation schemes for many strongly np complete problems such schemes consist of families of approximation algorithms for each desired performance bound on the relative error e o with running time that is polynomial when e is fixed though the polynomiality of these algorithms depends on the degree of approximation e being fixed they cannot be improved owing to a negative result stating that there are no fully polynomial approximation schemes for strongly np complete problems unless np p the unified technique that is introduced here referred to as the shifting strategy is applicable to numerous geometric covering and packing problems the method of using the technique and how it varies with problem parameters are illustrated a similar technique independently devised by b s baker was shown to be applicable for covering and packing problems on planar graphs

efficient implementation of tam and auriault s time domain impedance boundary condition a new and efficient time domain implementation is proposed for the impedance model originally introduced by tam and auriault tam c k w and auriault l time domain impedance boundary conditions for computational aeroacoustics aiaa journal vol 34 no 5 may 1996 pp 917 923 in the frequency domain the pressure can be calculated from the product of the impedance with the normal velocity in the time domain a convolution is needed which may become a costly operation present solutions for this problem involve either a full convolution and storage of a time history of data or a translation of the frequency domain models to time domain formulations involving time derivatives the former approach is very costly in terms of memory and cpu time the latter makes the implementation discretization specific and vulnerable to stability issues a new formulation based on recursive convolution results in an efficient implementation that stores only one accumulator which can be updated at each time step with minimal addition and multiplication it allows for the exact representation of the impedance at a given frequency the formulation is validated by a comparison with the measurement data from the nasa langley grazing flow impedance tube the simulations are performed by introducing a plane wave at a single frequency in the tube and this is done for six frequencies and five different mean flow speeds

towards perfectly absorbing boundary conditions for euler equations in this paper we examine the effectiveness of absorbing layers as non reflecting computational boundaries for the euler equations the absorbing layer equations are simply obtained by splitting the governing equations in the coordinate directions and introducing absorption coefficients in each split equation this methodology is similar to that used by berenger for the numerical solutions of maxwell s equations specifically we apply this methodology to three physical problems shock vortex interactions a plane free shear flow and an axisymmetric jet with emphasis on acoustic wave propagation our numerical results indicate that the use of absorbing layers effectively minimizes numerical reflection in all three problems considered

taylor expansion based fast multipole method for 3 d helmholtz equations in layered media abstract in this paper we develop a taylor expansion te based fast multipole method fmm for low frequency 3d helmholtz green s function in layered media two forms of taylor expansions with either non symmetric or symmetric derivatives of layered media green s functions are used for the implementations of the proposed te fmm in the implementation with non symmetric derivatives an algorithm based on discrete complex image approximations and recurrence formulas is shown to be very efficient and accurate in computing the high order derivatives meanwhile the implementation based on symmetric derivatives is more robust and pre computed tables for the high order derivatives in translation operators are used numerical tests in layered media have validated the accuracy and o n complexity of the proposed algorithms

a space time discretization criterion for a stable time marching solution of the electric field integral equation numerical techniques based on a time domain recursive solution of the electric field integral equation efie may exhibit instability phenomena induced by the joint space time discretization the above problem is addressed with specific reference to the evaluation of electromagnetic scattering from perfectly conducting bodies of arbitrary shape we analyze a particular formulation of the method of moments which relies on a triangular patch geometrical model of the exterior surface of the scattering body and operates according to a marching on in time scheme whereby the surface current distribution at a given time step is recursively evaluated as a function of the current distribution at previous steps a heuristic stability condition is devised which allows us to define a proper time step as well as a geometrical discretization criterion ensuring convergence of the numerical procedure and therefore eliminating insurgence of late time oscillations the stability condition is discussed and validated by means of a few working examples

uniformly best wavenumber approximations by spatial central difference operators we construct accurate central difference stencils for problems involving high frequency waves or multi frequency solutions over long time intervals with a relatively coarse spatial mesh and with an easily obtained bound on the dispersion error this is done by demonstrating that the problem of constructing central difference stencils that have minimal dispersion error in the infinity norm can be recast into a problem of approximating a continuous function from a finite dimensional subspace with a basis forming a chebyshev set in this new formulation characterising and numerically obtaining optimised schemes can be done using established theory

ground parameter information for propagation modeling the relative success of various simplified ground impedance models at fitting data obtained from direct and indirect measurements is reviewed a new two parameter approximation for the normal surface impedance of a nonhard backed layer structure is introduced a two parameter model of this form is shown to have wide success in fitting recent ground impedance and excess attenuation data obtained by a variety of techniques further evidence is produced of the unreliability that would be associated with extrapolation of fits based on the single parameter semiempirical model widely used at present outside the frequency range of the fitted data by refitting classical ground impedance data and tabulating resulting parameters along with those obtained more recently a menu of ground types best fit models associated parameter values and frequency ranges of fits has been compiled

approximation algorithms for the set covering and vertex cover problems we propose a heuristic that delivers in o n 3 steps a solution for the set covering problem the value of which does not exceed the maximum number of sets covering an element times the optimal value

time domain numerical computation of noise reduction by diffraction and finite impedance of barriers a new time domain numerical method is presented for the estimation of noise reduction by the diffraction and finite impedance of barriers high order finite difference schemes conventionally used for computational aeroacoustics and time domain impedance boundary conditions are utilized for the development of the time domain method compared with other methods this method can be applied more easily to the problems related to nonlinear noise propagation such as impulsive noise and broadband noise linearized euler equations in cartesian co ordinates are considered and solved numerically straight and t shaped barriers with and without surface admittance are calculated in order to assess the accuracy of this time domain method comparison with the results of sysnoise software ver 5 3 are made there are very good agreements between the results of the present time domain numerical method and the boundary element method of the sysnoise software

a finite element propagation model for extracting normal incidence impedance in nonprogressive acoustic wave fields a propagation model method for extracting the normal incidence impedance of an acoustic material installed as a finite length segment in a wall of a duct carrying a nonprogressive wave field is presented the method recasts the determination of the unknown impedance as the minimization of the normalized wall pressure error function a finite element propagation model is combined with a coarse fine grid impedance plane search technique to extract the impedance of the material results are presented for three different materials for which the impedance is known for each material the input data required for the prediction scheme were computed from modal theory and then contaminated by random error the finite element method reproduces the known impedance of each material almost exactly for random errors typical of those found in many measurement environments thus the method developed here provides a means for determining the impedance of materials in a nonprogressive wave environment such as that usually encountered in a commercial aircraft engine and in most laboratory settings

treatment of frequency dependent admittance boundary conditions in transient acoustic finite infinite element models the paper addresses the handling of frequency dependent local admittance boundary conditions in acoustic transient finite infinite element models the proposed approach avoids the evaluation of a convolution integral along the related boundary based on a similar technique developed in an aeroacoustic finite difference context the spatially local boundary condition is rewritten in a discrete form that involves normal accelerations and pressure time derivatives at the current time step and few steps before the incorporation of such a discrete in time boundary condition in a finite infinite element context is addressed the infinite element scheme selected for that purpose relies on the conjugated astley leis formulation implementation aspects cover the handling of frequency dependent boundary conditions along both finite and infinite element edges numerical examples waveguide single source in a half space bounded by an impedance plane diffraction by an acoustically treated screen are presented in order to demonstrate the efficiency of the proposed approach

impedance and its time domain extensions the classical concept of impedance as a means to characterize the ree ectivity and absorption of a surface to the incident waves has always been a complex valued quantity akin to plane harmonic waves and the analysis of their ree ections a new look at this classical quantity irrespective of the type of incident waves is presented it points out that a direct operational inversion of impedance into time domain boundary operators will in general lead to an unstable system whereas the inversion of the corresponding ree ection coefe cient will result in stable easily implementable boundary operators for time domain prediction of wave ree ection it reveals the equivalent pulselike causal process of time convoluting the incident wave into the ree ected wave excellent agreement with analytical solutions derived here and from other sources supports the validity of the approach and demonstrates the accuracy of the implementations

frequency dependent fdtd methods using z transforms the frequency dependent finite difference time domain method fd sup 2 td method has been shown to be capable of correctly calculating electromagnetic propagation through media whose dielectric properties are frequency dependent however as researchers search for more elaborate applications the formulation of the fd sup 2 td methods becomes more complex in this work the mathematics of the fd sup 2 td method is developed using z transform theory this has the advantages of presenting a clearer formulation and allowing researchers to draw on the literature of systems analysis and signal processing disciplines

an extension on statistical comparisons of classifiers over multiple data sets for all pairwise comparisons in a recently published paper in jmlr dem sar 2006 recommends a set of non parametric statistical tests and procedures which can be safely used for comparing the performance of classifiers over multiple data sets after studying the paper we realize that the paper correctly introduces the basic procedures and some of the most advanced ones when comparing a control method however it does not deal with some advanced topics in depth regarding these topics we focus on more powerful proposals of statistical procedures for comparing n n classifiers moreover we illustrate an easy way of obtaining adjusted and comparable p values in multiple comparison procedures

numerical prediction of aft radiation of turbofan tones through exhaust jets this paper describes a numerical methodology for calculating tonal noise propagation and radiation through turbomachinery exhaust ducts including non uniform background jet flows the numerical method is based on solution of the linearized euler equations directly in the frequency domain employing a direct sparse matrix solver in parallel acoustic sources are introduced into the computational domain via the perfectly matched layer equations various test cases including propagation through infinite ducts and propagation and radiation through semi infinite ducts with and without liners are solved and results are compared with analytical solutions it is demonstrated that solutions even with thin shear layers separating the exterior and jet streams at reasonably high mach numbers can be obtained quite successfully the method is also validated by simulating the radiated sound waves from two actual engine exhaust cowl geometries and the results are compared with experimental data

optimal runge kutta schemes for discontinuous galerkin space discretizations applied to wave propagation problems we study the performance of methods of lines combining discontinuous galerkin spatial discretizations and explicit runge kutta time integrators with the aim of deriving optimal runge kutta schemes for wave propagation applications we review relevant runge kutta methods from literature and consider schemes of order q from 3 to 4 and number of stages up to q 4 for optimization from a user point of view the problem of the computational efficiency involves the choice of the best combination of mesh and numerical method two scenarios are defined in the first one the element size is totally free and a 8 stage fourth order runge kutta scheme is found to minimize a cost measure depending on both accuracy and stability in the second one the elements are assumed to be constrained to such a small size by geometrical features of the computational domain that accuracy is disregarded we then derive one 7 stage third order scheme and one 8 stage fourth order scheme that maximize the stability limit the performance of the three new schemes is thoroughly analyzed and the benefits are illustrated with two examples for each of these runge kutta methods we provide the coefficients for a 2n storage implementation along with the information needed by the user to employ them optimally

a new efficient algorithm for computational aeroacoustics on parallel processors one of the great challenges in computational physics is the prediction of flow associated noise where the quantities of interest namely the sound waves can be at high frequencies and are usually orders of magnitude smaller in magnitude than the mean quantities in order to numerically resolve such small scales governed by the fluid dynamics equations high resolution schemes are required thus solutions of flow noise problems are computationally intensive an efficient hybrid data parallel computational aeroacoustics algorithm has been developed for the prediction of noise radiation and scattering from three dimensional geometries the algorithm solves the euler navier stokes equations in the interior and nonreflecting boundary conditions on the outer boundaries a moving surface kirchhoff method is coupled to the flow solver for far field predictions the algorithm uses standard time and spatial discretization techniques but utilizes several new optimization strategies that are highly suitable for single zone solutions on data parallel processors one strategy for example enables simultaneous residual evaluations of the interior and far field nonreflecting boundary conditions equations reducing the computational effort spent on them by approximately 60 cpu time savings the algorithms for the flow solver and the kirchhoff method and their coupling are described in this paper and results for some example radiation and scattering problems are presented

transient and multiple frequency sound transmission through perforated plates at high amplitude the transmission of complex periodic and transient acoustic signals through orifice plates at high amplitude and in the absence of mean fluid flow is discussed a simple fluid dynamical model involving a time varying mass end correction is the basis of the theory the equation of motion for the air in the orifice is solved numerically in the time domain for a specific instance an analytical solution in the frequency domain is possible good agreement is noted between experimental and theoretical results in both time and frequency domains

fingerprint indexing based on minutia cylinder code this paper proposes a new hash based indexing method to speed up fingerprint identification in large databases a locality sensitive hashing lsh scheme has been designed relying on minutiae cylinder code mcc which proved to be very effective in mapping a minutiae based representation position angle only into a set of fixed length transformation invariant binary vectors a novel search algorithm has been designed thanks to the derivation of a numerical approximation for the similarity between mcc vectors extensive experimentations have been carried out to compare the proposed approach against 15 existing methods over all the benchmarks typically used for fingerprint indexing in spite of the smaller set of features used top performing methods usually combine more features the new approach outperforms existing ones in almost all of the cases

on the robust flexible and consistent implementation of time domain impedance boundary conditions for compressible flow simulations the accurate simulation of compressible flows requires the appropriate modeling of the reflection of acoustic waves at the boundaries in the present study we discuss time domain impedance boundary conditions tdibc the formulation proposed allows to impose a desired reflection coefficient at the inflow and outflow boundaries our formulation is an extension of the well known navier stokes characteristic boundary conditions the frequency dependent reflections at the boundaries are implemented with a state space model in the time domain we provide a comprehensive discussion on how such state space models can be constructed and interpreted this discussion shows that the state space description allows a robust and flexible implementation it allows to consider complex reflection coefficients and account for non constant cfd time steps in a straight forward manner furthermore we prove analytically and demonstrate numerically that the formulation proposed is consistent i e the formulation ensures that the flow simulation exhibits the reflection coefficient imposed accurately as long as the waves impinging on the boundary are plane and it prohibits drift of the mean flow variables finally the boundary conditions are tested successfully for laminar and turbulent flows

an exact point source starting field for the fourier parabolic equation in outdoor sound propagation a method for exactly representing a point source starting field in a fourier parabolic equation calculation is presented the formulation is based on an exact analytic expression for the field in vertical wave number space k space the field in vertical coordinate space z space is obtained via a fourier transform of the k space field thus one can directly control the fourier components of the starting field so that nonpropagating components are excluded the relation of the exact starting field to the standard gaussian starting field is demonstrated analytically examples of the numerical implementation of the exact starting field are given

walking to singular points of fingerprints singular point is an essential global feature in fingerprint images existing methods for singular points detection generally visit each pixel or each small image block to determine the singular point that is to say existing methods require scanning the image to compute a quantity at each pixel or block and hence they are inevitably time consuming we propose a fast algorithm for detecting singular points by walking directly to them instead of scanning the image walking directional fields wdfs are established from the orientation field then following the walking directions on wdfs we can rapidly walk to the singular points the walking algorithm is extremely fast and easily implemented with acceptable accuracy further more its accuracy can also be improved by combining with state of the art methods we can rapidly walk to a candidate singular point then refine its location using existing more accurate method in the local area experimental results on datasets of spd2010 and fvc validate the high efficiency and satisfactory accuracy of the proposed algorithm highlightswe propose a novel fast method for singular point detection we can walk directly to singular points without scanning fingerprint images simplicity of the idea makes the algorithm easy to be implemented our algorithm can be combined with state of the art method to improve performance

time domain implementation of an impedance boundary condition with boundary layer correction a time domain boundary condition is derived that accounts for the acoustic impedance of a thin boundary layer over an impedance boundary based on the asymptotic frequency domain boundary condition of brambley 2011 25 a finite difference reference implementation of this condition is presented and carefully validated against both an analytic solution and a discrete dispersion analysis for a simple test case the discrete dispersion analysis enables the distinction between real physical instabilities and artificial numerical instabilities the cause of the latter is suggested to be a combination of the real physical instabilities present and the aliasing and artificial zero group velocity of finite difference schemes it is suggested that these are general properties of any numerical discretization of an unstable system existing numerical filters are found to be inadequate to remove these artificial instabilities as they have a too wide pass band the properties of numerical filters required to address this issue are discussed and a number of selective filters are presented that may prove useful in general these filters are capable of removing only the artificial numerical instabilities allowing the reference implementation to correctly reproduce the stability properties of the analytic solution

a note on reflection of spherical waves in 1909 sommerfeld gave an exact solution for the reflection of a spherical wave from a plane surface in terms of an oscillatory integral and also presented an asymptotic solution for the case where both source and receiver are at the boundary weyl 1919 presented an alternative solution and also an asymptotic solution for the case where the source is at the boundary it is known that the general case is solved if a general solution for the case where the source is at the boundary is known here it is demonstrated that it is sufficient to have the general solution for the case where both source and receiver are at the boundary this is mainly of theoretical interest but may have practical applications as an example it is demonstrated that sommerfeld s approximate solution gives ingard s 1951 approximate solution which is valid for arbitrary source and receiver heights

stabilization of time domain acoustic boundary element method for the interior problem with impedance boundary conditions the time domain boundary element method bem is associated with numerical instability that typically stems from the time marching scheme in this work a formulation of time domain bem is derived to deal with all types of boundary conditions adopting a multi input multi output infinite impulse response structure the fitted frequency domain impedance data are converted into a time domain expression as a form of an infinite impulse response filter which can also invoke a modeling error in the calculation the response at each time step is projected onto the wave vector space of natural radiation modes which can be obtained from the eigensolutions of the single iterative matrix to stabilize the computation unstable oscillatory modes are nullified and the same decay rate is used for two nonoscillatory modes as a test example a transient sound field within a partially lined parallelepiped box is used within which a point source is excited by an octave band impulse in comparison with the results

invariant representation of orientation fields for fingerprint indexing orientation fields can be used to describe interleaved ridge and valley patterns of fingerprint image providing features useful for fingerprint recognition however for tasks such as fingerprint indexing additional image alignment is often required to avoid confounding effects caused by pose differences in this paper we propose to employ a set of polar complex moments pcms for extraction of rotation invariant fingerprint representation pcms are capable of describing fingerprint ridge flow structures including singular regions and are tolerant to spurious orientations in noisy fingerprints from the orientation fields a set of rotation moment invariants are derived to form a feature vector for comprehensive fingerprint structural description this feature vector gives a compact and rotation invariant representation that is important for pose robust fingerprint indexing a clustering based fingerprint indexing scheme is employed to facilitate efficient and effective retrieval of the most likely candidates from a fingerprint database our experimental results on nist and fvc fingerprint databases indicate that the proposed invariant representation improves the performance of fingerprint indexing as compared to state of the art methods

a stable boundary element method for modeling transient acoustic radiation transient acoustic radiation from a closed axisymmetric three dimensional object is modeled using the time domain boundary element method the widely reported instability problems are overcome by reformulating the integral equation to obtain a burton and miller type equation in the time domain the stability of such an approach is mathematically justified and supported by subsequent numerical results the hypersingular integrals which arise are evaluated using a method valid for any surface discretization numerical results for the radiation of a spherical wave are presented and compared with an exact solution the accuracy and stability of the results are verified for several geometrically different radiating objects

pade approximation in time domain boundary conditions of porous surfaces formulation and implementation of time domain boundary conditions tdbcs at the surface of a reactive porous material are made challenging by the slow decay complexity or noncausal nature of many commonly used models of porous materials in this paper approaches are described that improve computational efficiency and enforce causality one approach involves approximating the known tdbc for the modified zwikker kosten impedance model as a summation of decaying exponential functions a second approach which can be applied to any impedance model involves replacing the characteristic admittance with its pade approximation then approximating fractional derivatives with decaying exponentials a causal and recursive tdbc is formulated

fingerprint reference point detection for image retrieval based on symmetry and variation reference point plays an important role in fingerprint identification systems the reference point is widely used for the fingerprint retrieval in large scale databases this paper proposes a novel algorithm for detecting a convex core point as a unique reference point consistently and accurately for all types of fingerprints in order to detect robust core point candidates a modified complex filter called semi radial symmetry filter is proposed to detect correctly rotational symmetries of core points moreover a vertical orientation variation feature called voriv feature is proposed to remove spurious core points and concave core points therefore the proposed technique computes the variation and symmetry combined energy vscome then the reference point is located by searching the global vscome maximum the experimental results on the public database fvc2004 db1 set a show that the proposed technique exhibits a very high robustness and gets the best performance in comparing with other approaches in literature

energy analysis and discretization of nonlinear impedance boundary conditions for the time domain linearized euler equations time domain impedance boundary conditions tdibcs can be enforced using the impeda nce the admittance or the scattering operator this article demonstrates the computational advantage of the last even for nonlinear tdibcs with the linearized euler equations this is achieved by a systematic semi discrete energy analysis of the weak enforcement of a generic nonlinear tdibc in a discontinuous galerkin finite element method in particular the analysis highlights that the sole definition of a discrete model is not enough to fully define a tdibc to support the analysis an elementary physical nonlinear scattering operator is derived and its computational properties are investigated in an impedance tube then the derivation of time delayed broadband tdibcs from physical reflection coefficient models is carried out for single degree of freedom acoustical liners a high order discretization of the derived time local formulation which consists in composing a set of ordinary differential equations with a transport equation is applied to two flow ducts