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

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

nongaussian density estimation for the classification of acoustic feature vectors in speech recognition a statistical modeling paradigm for automatic machine recognition of speech uses mixtures of nongaussion statistical probability densities which provides improved recognition accuracy speech is modeled by building probability densities from functions of the form exp t 2 for t 0 and 0 mixture components are constructed from different univariate functions the mixture model is used in a maximum likelihood model of speech data

finite difference on grids with nearly uniform cell area and line spacing for the wave equation on complex domains a finite difference time dependent numerical method for the wave equation supported by recently derived novel elliptic grids is analyzed the method is successfully applied to single and multiple two dimensional acoustic scattering problems including soft and hard obstacles with complexly shaped boundaries the new grids have nearly uniform cell area j grids and nearly uniform grid line spacing email protected numerical experiments reveal the positive impact of these two grid properties on the scattered field convergence to its harmonic steady state the restriction imposed by stability conditions on the time step size is relaxed due to the near uniformity cell areas and grid line spacing as a consequence moderately large time steps can be used for relatively fine spatial grids resulting in greater accuracy at a lower computational cost also numerical solutions for wave problems inside annular regions of complex shapes are obtained the use of the new grids results in late time stability in contrast with other classical finite difference time dependent methods

mixture densities maximum likelihood and the em algorithm the problem of estimating the parameters which determine a mixture density has been the subject of a large diverse body of literature spanning nearly ninety years during the last two decades the

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

coupling of dirichlet to neumann boundary condition and finite difference methods in curvilinear coordinates for multiple scattering the applicability of the dirichlet to neumann technique coupled with finite difference methods is enhanced by extending it to multiple scattering from obstacles of arbitrary shape the original boundary value problem bvp for the multiple scattering problem is reformulated as an interface bvp a heterogenous medium with variable physical properties in the vicinity of the obstacles is considered a rigorous proof of the equivalence between these two problems for smooth interfaces in two and three dimensions for any finite number of obstacles is given the problem is written in terms of generalized curvilinear coordinates inside the computational region then novel elliptic grids conforming to complex geometrical configurations of several two dimensional obstacles are constructed and approximations of the scattered field supported by them are obtained the numerical method developed is validated by comparing the approximate and exact far field patterns for the scattering from two circular obstacles in this case for a second order finite difference scheme a second order convergence of the numerical solution to the exact solution is easily verified

boundary conditions for the numerical solution of elliptic equations in exterior regions elliptic equations in exterior regions frequently require a boundary condition at infinity to ensure the weill posedness of the problem examples of practical applications include the helmholtz equation and laplace s equation computational procedures based on a direct discretization of the elliptic problem require the replacement of the condition at infinity by a boundary condition on a finite artificial surface direct imposition of the condition at infinity along the finite boundary results in large errors a sequence of boundary conditions is developed which provides increasingly accurate approximations to the problem in the infinite domain estimates of the error due to the finite boundary are obtained for several cases computations are presented which demonstrate the increased accuracy that can be obtained by the use of the higher order boundary conditions the examples are based on a finite element formulation but finite difference methods can also be used

time dependent numerical method with boundary conforming curvilinear coordinates applied to wave interactions with prototypical antennas a new unstaggered finite difference time dependent technique to accurately model scattring from prototypical 2d antenna structures is devised the unbounded boundary value problems defining these phenomena are redefined over bounded domains using appropriate radiation operators over finite artificial boundaries generalized curvilinear coordinates are generated such that physical boundaries correspond to coordinate lines a numerical procedure to generate almost orthogonal boundary conforming fine grids over these bounded regions is developed once the governing equations are written in terms of the new curvilinear coordinates a time dependent numerical method is applied to obtain time harmonic steady state solutions to these problems the electric field wave amplitude as well as the wave pattern inside the waveguide and the scattered field from the prototypical antennas are obtained accuracy and computational cost are compared when almost orthogonal and nonorthogonal grids are in use an optical theorem for a flanged waveguide antenna with perfect electrical conductor walls is derived it is verified that the approximate solutions obtained by application of the time dependent numerical method with boundary conforming curvilinear coordinates satisfy the optical theorem

an explicit fourth order orthogonal curvilinear staggered grid fdtd method for maxwell s equations the explicit fourth order staggered finite difference time domain scheme previously proposed for a cartesian grid is extended to maxwell s equations in an orthogonal curvilinear coordinate system and applied to electromagnetic wave problems a simple technique is also presented for generating orthogonal curvilinear grids that conform to the material boundaries and interfaces of the problem numerical experiments are presented to illustrate the efficiency and accuracy of the method

generation of boundary conforming grids around wing body configurations using transfinite interpolation a computational procedure for generating three dimensional nonorthogonal surface fitted mesh systems around wing fuselage configurations is presented the method is based on the concept of transfinite interpolation which has been extended to handle very general mapping function specifications at the boundaries thereby making it possible to generate single block mappings with geometry data specified only at the outer boundaries of the computational domain since it is a direct algebraic mapping technique the method is very inexpensive in terms of computer cost different types of possible mappings are compared with respect to resolution and economy of nodal points a procedure for a novel type of mapping designated type o o is described and several plots of generated grids demonstrate the capabilities of the method the singular lines inherent in every three dimensional mesh for this type of surface geometry are also discussed

the enhancement of an elliptic grid using appropriate control functions three dimensional structured grid generation methodology based on elliptic partial differential equation pde method is reviewed it will be shown that the quality of a grid depends on how to treat the second normal derivative terms involved in control functions a 7 point finite analytic scheme based on one dimensional analytic solution will be introduced to discretize the governing equations of the elliptic grid generation

the stability of numerical boundary treatments for compact high order finite difference schemes the stability characteristics of various compact fourth and sixth order spatial operators are assessed with the theory of gustafsson kreiss and sundstrom g k s for the semidiscrete initial boundary value problem these results are generalized to the fully discrete case with a recently developed theory of kreiss and wu in all cases favorable comparisons are obtained between g k s theory eigenvalue determination and numerical simulation the conventional definition of stability then is sharpened to include only those spatial discretizations that are asymptotically stable bounded left half plane eigenvalues many of the higher order schemes that are g k s stable are not asymptotically stable a series of compact fourth and sixth order schemes that are both asymptotically and g k s stable for the scalar case are then developed

high order unstructured curved mesh generation using the winslow equations we propose a method to generate high order unstructured curved meshes using the classical winslow equations we start with an initial straight sided mesh in a reference domain and fix the position of the nodes on the boundary on the true curved geometry in the interior of the domain we solve the winslow equations using a new continuous galerkin finite element discretization this formulation appears to produce high quality curved elements which are highly resistant to inversion in addition the corresponding nonlinear equations can be solved efficiently using picard iterations even for highly stretched boundary layer meshes compared to several previously proposed techniques such as optimization and approaches based on elasticity analogies this can significantly reduce the computational cost while producing curved elements of similar quality we show a number of examples in both two and three space dimensions including complex geometries and stretched boundary layers and demonstrate the high quality of the generated meshes and the performance of the nonlinear solver

numerical solution of the quasilinear poisson equation in a nonuniform triangle mesh a finite difference method using a nonuniform triangle mesh is described for the numerical solution of the nonlinear two dimensional poisson equation s 0 where is a function of or its derivatives sis a function of position and or its normal derivative is specified on the boundary the finite difference equations are solved by successive overrelaxation the triangle mesh which is constructed numerically by solving laplace s equation is easily adapted to nonrectangular boundaries and interfaces examples of numerical results are given for the magnetostatic problem with iron and other possible applications are mentioned

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

finite difference time domain modeling of curved surfaces em scattering the finite difference time domain fdtd method is generalized to include the accurate modeling of curved surfaces this generalization the contour path cp method accurately models the illumination of bodies with curved surfaces yet retains the ability to model corners and edges cp modeling of two dimensional electromagnetic wave scattering from objects of various shapes and compositions is presented

gaussian mixture density modeling decomposition and applications we present a new approach to the modeling and decomposition of gaussian mixtures by using robust statistical methods the mixture distribution is viewed as a contaminated gaussian density using this model and the model fitting mf estimator we propose a recursive algorithm called the gaussian mixture density decomposition gmdd algorithm for successively identifying each gaussian component in the mixture the proposed decomposition scheme has advantages that are desirable but lacking in most existing techniques in the gmdd algorithm the number of components does not need to be specified a priori the proportion of noisy data in the mixture can be large the parameter estimation of each component is virtually initial independent and the variability in the shape and size of the component densities in the mixture is taken into account gaussian mixture density modeling and decomposition has been widely applied in a variety of disciplines that require signal or waveform characterization for classification and recognition we apply the proposed gmdd algorithm to the identification and extraction of clusters and the estimation of unknown probability densities probability density estimation by identifying a decomposition using the gmdd algorithm that is a superposition of normal distributions is successfully applied to automated cell classification computer experiments using both real data and simulated data demonstrate the validity and power of the gmdd algorithm for various models and different noise assumptions

ranks of mapping tori via the curve complex is generated by nielsen transformations this isequivalent to requiring that our two generating sets for g are related by asequence of the following moves 1 if a6 bare generators replace awith ab 2 if a6 bare generators switch their places in the ordering 3 if ais a generator replace it with a

svms for histogram based image classification traditional classification approaches generalize poorly on image classification tasks because of the high dimensionality of the feature space this paper shows that support vector machines svm can generalize well on difficult image classification problems where the only features are high dimensional histograms heavy tailed rbf kernels of the form k x y e p i x i y i with a 1 and b 2 are evaluated on the classification of images extracted from the corel stock photo collection and shown to far outperform traditional polynomial or gaussian rbf kernels moreover we observed that a simple remapping of the input xi x a i improves the performance of linear svms to such an extend that it makes them for this problem a valid alternative to rbf kernels keywords support vector machines radial basis functions image histogram image classification corel

method and apparatus for constructing continuous parameter fenonic hidden markov models by replacing phonetic models with continous fenonic models a method and apparatus for constructing a hidden markov model comprised of multiple fenones characterized by their duration and a set of acoustic properties the present invention provides a sequence of fenones to model a speech event the sequence may undergo modifications to improve the overall performance of the model

penalized maximum likelihood estimation the baum welch algorithm diagonal balancing of symmetric matrices and applications to training acoustic data we study penalized maximum likelihood estimation methods for nonparametric density estimation and propose their use in training acoustic models for speech recognition several algorithms for the numerical solution of the optimization problems that we encounter are proposed and analyzed

maximum likelihood estimation of a class of non gaussian densities with application to i sub p deconvolution the properties of the maximum likelihood estimator of the generalized p gaussian gpg probability density function from n independent identically distributed samples is investigated especially in the context of the deconvolution problem under gpg white noise specifically the properties in the estimator are first described independently of the application then the solution of the above mentioned deconvolution problem is obtained as the solution of a minimum norm problem in an l sub p normed space it is shown that such minimum norm solution is the maximum likelihood estimate of the system function parameters and that such an estimate is unbiased with the lower bound of the variance of the error equal to the cramer rao lower bound and the upper bound derived from the concept of a generalized inverse the results are illustrated by computer simulations

heegaard genus and rank of augmented link complements we prove that the rank of the fundamental group of an augmented link complement equals its heegaard genus this is achieved by showing that the heegaard genus equals the number of link components a straightforward consequence is that these manifolds satisfy a conjecture of shalen

the dtn nonreflecting boundary condition for multiple scattering problems in the half plane abstract the multiple dirichlet to neumann multiple dtn non reflecting boundary condition is adapted to acoustic scattering from obstacles embedded in the half plane the multiple dtn map is coupled with the method of images as an alternative model for multiple acoustic scattering in the presence of acoustically soft and hard plane boundaries as opposed to the current practice of enclosing all obstacles with a large semicircular artificial boundary that contains portion of the plane boundary the proposed technique uses small artificial circular boundaries that only enclose the immediate vicinity of each obstacle in the half plane the adapted multiple dtn condition is simultaneously imposed in each of the artificial circular boundaries as a result the computational effort is significantly reduced a computationally advantageous boundary value problem is numerically solved with a finite difference method supported on boundary fitted grids approximate solutions to problems involving two scatterers of arbitrary geometry are presented the proposed numerical method is validated by comparing the approximate and exact far field patterns for the scattering from a single and from two circular obstacles in the half plane

generation of curvilinear coordinates on multiply connected regions with boundary singularities a new algorithm to generate smooth two dimensional boundary conforming coordinates with grid lines control on multiply connected regions including boundary singularities is devised the technique fits into the category of elliptic grid generators since it is based on the numerical solution of poisson equations the physical domain d is transformed into a topologically equivalent connected rectangular domain d by defining a branch cut inside d control of the grid line spacing over the multiply connected regions is established by appropriately distributing nodal points on the branch cut and on other boundary curves simple and computationally convenient expressions for the control functions present in the poisson system are obtained from this initial distribution of points thus a natural link between clustering properties and the control functions is created fixing the nodal points on the branch cut causes the convergence of the numerical method about the singular boundary points an iterative smoothing process relocating the branch cut is described as a result smooth grids are obtained grid quality analysis shows that coordinate line orthogonality in the new meshes is superior than in similar grids obtained from a well known commercial software the algorithm is successfully tested over a variety of multiply connected domains the computational advantage of this novel grids is revealed by using them to numerically model the vibrations of complexly shaped annular membranes

exceptional and cosmetic surgeries on knots we show that the bridge distance of a knot determines a lower bound on the genera of essential surfaces and heegaard surfaces in the manifolds that result from non trivial dehn surgeries on the knot in particular knots with high bridge distance do not admit non trivial non hyperbolic surgeries or non trivial cosmetic surgeries we further show that if a knot has bridge distance at least 3 then its bridge number is bounded above by a function of seifert genus or indeed by the genus of almost any essential surface or heegaard surface in the surgered manifold

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

a three dimensional fdtd algorithm in curvilinear coordinates em scattering the finite difference time domain fdtd algorithm for the solution of electromagnetic scattering problems is formulated in numerically defined generalized coordinates in three dimensions and implemented in a code with the lowest order bayliss turkel radiation boundary condition expressed in spherical coordinates it is shown that the algorithm is capable of accurately tracking the progress of a pulse of electromagnetic radiation through the curvilinear mesh generated by a body of revolution the only problems occurring in the vicinity of the rotation axis which represents a coordinate singularity a simple method to deal with this singular line is presented and discussed and its is shown that at least for the test problem this approximation is sufficient the algorithm discussed is useful for the solution of the exterior problem in the presence of conductors and dielectrics with complicated shapes and electrical compositions and for near field problems such as cavity penetration problems the far fields are obtained by replacing the scatterer with a virtual surface enclosing all sources

radiation impedance of tubes with different flanges numerical and experimental investigations end corrections for open ended cylindrical tubes are determined theoretically and experimentally for the zero and low frequencies the wave equation is solved numerically by using a finite difference method for higher frequencies the complex radiation impedance is measured and for circular flanges calculated with the boundary element method for low frequencies the bem links up with the fdm and for higher frequencies fits with experimental results various flanges found in particular in musical instruments are considered circular flanges of various sizes spherical and cylindrical flanges square flanges the normalised flange used for loudspeaker testing short flaring horns and a disk at a certain distance above the open end analytical fit formulas are proposed for each case

support vector machines for histogram based image classification traditional classification approaches generalize poorly on image classification tasks because of the high dimensionality of the feature space this paper shows that support vector machines svm can generalize well on difficult image classification problems where the only features are high dimensional histograms heavy tailed rbf kernels of the form k x y e sup spl rho spl sigma sub i sup xia yia b with a spl les 1 and b spl les 2 are evaluated on the classification of images extracted from the corel stock photo collection and shown to far outperform traditional polynomial or gaussian radial basis function rbf kernels moreover we observed that a simple remapping of the input x sub i spl rarr x sub i sup a improves the performance of linear svm to such an extend that it makes them for this problem a valid alternative to rbf kernels

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

divergence preserving discrete surface integral methods for maxwell s curl equations using non orthogonal unstructured grids abstract several new discrete surface integral methods for solving maxwell s equations in the time domain are presented these methods which allow the use of general non orthogonal mixed polyhedral unstructured grids are direct generalizations of the canonical staggered grid finite difference method these methods are conservative in that they locally preserve divergence or charge employing mixed polyhedral cells hexahedral tetrahedral etc these methods allow more accurate modeling of non rectangular structures and objects because the traditional stair stepped boundary approximations associated with the orthogonal grid based finite difference methods can be avoided numerical results demonstrating the accuracy of these new methods are presented

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

on heegaard decompositions of torus knot exteriors and related seifert fibre spaces the heegaard decompositions of genus 2 oftorus knot exteriors are classified with respect to homeomorphisms it turns out that in general there are three different classes which are also the isotopy classes a similar result is obtained for seifert fibre spaces having a disk as base and two exceptional fibres such as the exteriors of torus knots have or having a sphere as base and three exceptional fibres

a fast higher order solver for scattering by penetrable bodies in three dimensions in this paper we introduce a new fast higher order solver for scattering by inhomogeneous media in three dimensions as in previously existing methods the low complexity of our integral equation method o nlogn operations for an n point discretization is obtained through extensive use of the fast fourier transform fft for the evaluation of convolutions however the present approach obtains significantly higher order accuracy than these previous approaches yielding at worst third order far field accuracy or substantially better for smooth scatterers even for discontinuous and complex refractive index distributions possibly containing severe geometric singularities such as corners and cusps the increased order of convergence of our method results from i a partition of unity decomposition of the green s function into a smooth part with unbounded support and a singular part with compact support and ii replacement of the possibly discontinuous scatterer by an appropriate fourier smoothed scatterer the resulting convolutions can then be computed with higher order accuracy by means of o nlogn ffts we present a parallel implementation of our approach and demonstrate the method s efficiency and accuracy through a variety of computational examples for a very large scatterer considered earlier in the literature with a volume of 3648 l 3 where l is the wavelength using the same number of points per wavelength and in computing times comparable to those required by the previous approach the present algorithm produces far field values whose errors are two orders of magnitude smaller than those reported previously

on the use of higher order finite difference schemes on curvilinear and deforming meshes this study enables the use of very high order finite difference schemes for the solution of conservation laws on stretched curvilinear and deforming meshes to illustrate these procedures we focus on up to 6th order pade type spatial discretizations coupled with up to 10th order low pass filters these are combined with explicit and implicit time integration methods to examine wave propagation and wall bounded flows described by the navier stokes equations it is shown that without the incorporation of the filter application of the high order compact scheme to nonsmooth meshes results in spurious oscillations which inhibit their applicability inclusion of the discriminating low pass high order filter restores the advantages of high order approach even in the presence of large grid discontinuities when three dimensional curvilinear meshes are employed the use of standard metric evaluation procedures significantly degrades accuracy since freestream preservation is violated to overcome this problem a simple technique is adopted which ensures metric cancellation and thus ensures freestream preservation even on highly distorted curvilinear meshes for dynamically deforming grids an effective numerical treatment is described to evaluate expressions containing the time varying transformation metrics with these techniques metric cancellation is guaranteed regardless of the manner in which grid speeds are defined the efficacy of the new procedures is demonstrated by solving several model problems as well as by application to flow past a rapidly pitching airfoil and past a flexible panel

elliptic grid generation based on laplace equations and algebraic transformations abstract an elliptic grid generation method is presented to generate boundary conforming grids in domains in 2d and 3d physical space and on minimal surfaces and parametrized surfaces in 3d physical space the elliptic grid generation method is based on the use of a composite mapping this composite mapping consists of a nonlinear transfinite algebraic transformation and an elliptic transformation the elliptic transformation is based on the laplace equations for domains or on the laplace beltrami equations for surfaces the algebraic transformation maps the computational space one to one onto a parameter space the elliptic transformation maps the parameter space one to one onto the domains or surfaces the composition of these two mappings is a differentiable one to one mapping from computational space onto the domains or surfaces and has a nonvanishing jacobian this composite mapping defines the grid point distribution in the interior of the domains or surfaces for domains and minimal surfaces the composite mapping obeys a nonlinear elliptic poisson system with control functions completely defined by the algebraic transformation the solution of the poisson systems is obtained by picard iteration and black box multigrid solvers for parametrized curved surfaces it is not necessary to define and solve a nonlinear elliptic poisson system instead a linear elliptic system and an inversion problem is solved to generate the grid in the interior of the surface

splittings of knot groups let k be a knot of genus g if k is fibered then it is well known that the knot group pi k splits only over a free group of rank 2g we show that if k is not fibered then pi k splits over non free groups of arbitrarily large rank furthermore if k is not fibered then pi k splits over every free group of rank at least 2g however pi k cannot split over a group of rank less than 2g the last statement is proved using recent results of agol przytycki wise and wise

adaptive solution to two dimensional partial differential equations in curved domains using the monge ampere equation we present a finite difference method for mesh generation and adaptation with application to the solution of partial differential equations in curved domains for mesh generation we construct a ma

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