corner treatments for high order local absorbing boundary conditions in high frequency acoustic scattering this paper deals with the design and validation of accurate local absorbing boundary conditions set on convex polygonal computational domains for the finite element solution of high frequency acoustic scattering problems while high order absorbing boundary conditions habcs are accurate for smooth fictitious boundaries the precision of the solution drops in the presence of corners if no specific treatment is applied we present and analyze two strategies to preserve the accuracy of pade type habcs at corners first by using compatibility relations derived for right angle corners and second by regularizing the boundary at the corner we show that the former strategy is well adapted to right corners and efficient for nearly right corners while the later is better for very obtuse corners numerical results are proposed to analyze and compare the approaches for two and three dimensional problems

motion compensation via redundant wavelet multihypothesis multihypothesis motion compensation has been widely used in video coding with previous attention focused on techniques employing predictions that are diverse spatially or temporally in this paper the multihypothesis concept is extended into the transform domain by using a redundant wavelet transform to produce multiple predictions that are diverse in transform phase the corresponding multiple phase inverse transform implicitly combines the phase diverse predictions into a single spatial domain prediction for motion compensation the performance advantage of this redundant wavelet multihypothesis approach is investigated analytically invoking the fact that the multiple phase inverse involves a projection that significantly reduces the power of a dense motion residual modeled as additive noise the analysis shows that redundant wavelet multihypothesis is capable of up to a 7 db reduction in prediction residual variance over an equivalent single phase single hypothesis approach experimental results substantiate the performance advantage for a block based implementation

forced oscillations in quadratically damped systems bayliss 1975 has studied the question whether in the case of linear differential equations the relationship between the stability of the homogeneous equations and the existence of almost periodic solutions to the inhomogeneous equation is preserved by finite difference approximations in the current investigation analogous properties are considered for the case in which the damping is quadratic rather than linear the properties of the considered equation for arbitrary forcing terms are examined and the validity is proved of a theorem concerning the characteristics of the unique solution by using the lipschitz continuity of the mapping and the contracting mapping principle almost periodic solutions can be found for perturbations of the considered equation attention is also given to the lipschitz continuity of the solution operator and the results of numerical tests which have been conducted to test the discussed theory

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

a two way parabolic equation for elastic media the parabolic equation pe method is extended to handle wave propagation and scattering in range dependent elastic waveguides which are approximated by a sequence of range independent regions the two way elastic pe involves an efficient pe based scattering method for computing reflected and transmitted fields at the vertical interfaces separating range independent regions the one way elastic pe is used to propagate the outgoing and incoming fields through the range independent regions with two way range marching in addition to providing the backscattered field the two way pe provides a correction to the outgoing field the self starter is generalized to handle a source in a solid layer

the effect of a thin coating on the scattering of a time harmonic wave for the helmholtz equation a model problem in the scattering of a time harmonic wave by an obstacle coated with a thin penetrable shell is examined in previous studies the contrast coefficients of the thin shell are assumed to tend to infinity in order to compensate for the thickness considered in this paper these coefficients are assumed to remain finite such a treatment leads to a singular perturbation term that creates a typical difficulty for the asymptotic analysis of the problem with respect to the thickness of the coating as a result the asymptotic analysis is essentially based on a suitable handling of the stability of the solution relative to the thickness as a consequence it is shown how effective boundary conditions which can be substituted to the thin shell can then be obtained and analyzed in a simple way

motion compensating prediction with fractional pel accuracy the effect of fractional pel accuracy on the efficiency of motion compensating predictors is studied using various spatial prediction interpolation filters in model calculations the power spectral density of the prediction error is related to the probability density function of the displacement error prediction can be improved both by higher accuracy of motion compensation and by spatial wiener filtering in the predictor beyond a critical accuracy the possibility of further improving prediction by more accurate motion compensation is small experiments with videophone signals and with broadcast tv signals confirm these model calculations sinc interpolation bilinear interpolation and wiener filtering are compared at integer pel 1 2 pel 1 4 pel and 1 8 pel accuracies a three state technique for reliable displacement estimation with fractional pel accuracy is introduced it is based on phase correlation for motion compensation with block size of 16 pels 16 pels 1 4 pel accuracy appears to be sufficient for broadcast tv signals whereas for videophone signals 1 2 pel accuracy is desirable

an improved surface radiation condition for high frequency acoustic scattering problems a new artificial boundary condition for two dimensional acoustic scattering problems is constructed in this paper it is designed from the principal symbol of the dirichlet to neumann map so that both the propagating and evanescent fields are properly modeled in the high frequency regime the new artificial boundary condition can be used as an on surface radiation condition for efficient approximation of the wave field the accuracy and efficiency of our method are demonstrated in numerical examples

efficiency analysis of multihypothesis motion compensated prediction for video coding overlapped block motion compensation or b frames are examples of multihypothesis motion compensation where several motion compensated signals are superimposed to reduce the bit rate of a video codec this paper extends the wide sense stationary theory of motion compensated prediction mcp for hybrid video codecs to multihypothesis motion compensation the power spectrum of the prediction error is related to the displacement error probability density functions pdfs of an arbitrary number of hypotheses in a closed form expression we then study the influence of motion compensation accuracy on the efficiency of multihypothesis motion compensation as well as the influence of the residual noise level and the gain from optimal combination of n hypotheses for the noise free limiting case doubling the number of equally good hypotheses can yield a gain of up to 1 2 bits sample while doubling the accuracy of motion compensation can additionally reduce the bit rate by up to 1 bit sample independent of n for realistic noise levels it is shown that the introduction of b frames or overlapped block motion compensation can provide larger gains than doubling motion compensation accuracy spatial filtering of the motion compensated candidate signals becomes less important if more hypotheses are combined the critical accuracy beyond which the gain due to more accurate motion compensation is small moves to larger displacement error variances with increasing noise and increasing number of hypotheses n hence sub pel accurate motion compensation becomes less important with multihypothesis mcp the theoretical insights are confirmed by experimental results for overlapped block motion compensation b frames and multiframe motion compensated prediction with up to eight hypotheses from ten previous frames

three dimensional finite element calculations in acoustic scattering using arbitrarily shaped convex artificial boundaries we report on a generalization of the bayliss gunzburger turkel non reflecting boundary conditions to arbitrarily shaped convex artificial boundaries for elongated scatterers such as submarines we show that this generalization can improve significantly the computational efficiency of finite element methods applied to the solution of three dimensional acoustic scattering problems copyright 2001 john wiley sons ltd

a quasi optimal non overlapping domain decomposition method for two dimensional time harmonic elastic wave problems abstract this article presents the construction of a new non overlapping domain decomposition method ddm for two dimensional elastic scattering problems the method relies on a high order transmission boundary condition tbc between sub domains which accurately approximates the exact dirichlet to neumann map first we explain the derivation of this new tbc in the context of a non overlapping ddm next a mode by mode convergence study for a model problem is presented which shows the new method to be quasi optimal i e with an optimal convergence rate for evanescent modes and an improved convergence rate for the other modes compared to the standard low order lysmer kuhlemeyer tbc finally the effectiveness of the new ddm is demonstrated in a finite element context by analyzing the behavior of the method on high frequency elastodynamic simulations

on surface radiation condition for multiple scattering of waves the formulation of the on surface radiation condition osrc is extended to handle wave scattering problems in the presence of multiple obstacles the new multiple osrc simultaneously accounts for the outgoing behavior of the wave fields as well as the multiple wave reflections between the obstacles like boundary integral equations bie this method leads to a reduction in dimensionality from volume to surface of the discretization region however as opposed to bie the proposed technique leads to boundary integral equations with smooth kernels hence these fredholm integral equations can be handled accurately and robustly with standard numerical approaches without the need to remove singularities moreover under weak scattering conditions this approach renders a convergent iterative method which bypasses the need to solve single scattering problems at each iteration inherited from the original osrc the proposed multiple osrc is generally a crude approximate method if accuracy is not satisfactory this approach may serve as a good initial guess or as an inexpensive pre conditioner for krylov iterative solutions of bie

rational square root approximations for parabolic equation algorithms in this article stable pade approximations to the function 1 z are derived by choosing a branch cut in the negative half plane the pade coefficients are complex and may be derived analytically to arbitrary order from the corresponding real coefficients associated with the principal branch defined by z 1 i z 0 i z denotes the imaginary part of z the characteristics of the corresponding square root approximation are illustrated for various segments of the complex plane in particular for waveguide problems it is shown that an increasingly accurate representation may be obtained of both the evanescent part of the mode spectrum for the acoustic case and the complex mode spectrum for the elastic case an elastic parabolic equation algorithm is used to illustrate the application of the new pade approximations to a realistic ocean environment including elasticity in the ocean bottom

a two way parabolic equation for acoustic backscattering in the ocean the parabolic equation pe method is generalized to handle backscattered acoustic energy in the ocean the two way pe is based on the single scattering approximation and the approach of two way coupled modes in which range dependent environments are approximated by a sequence of range independent regions at the vertical boundaries between regions the solution of the two way pe is required to satisfy two continuity conditions the range derivative in one of the conditions is replaced by a higher order pe depth operator the reflected and transmitted fields that satisfy these conditions are computed with an efficient iteration scheme the outgoing and incoming fields are propagated by two way range marching the two way pe which is presently implemented for two dimensional problems is a practical method for solving large scale reverberation problems the accuracy of the two way pe is demonstrated by comparisons with reference solutions the two way pe is applied to simulate the localization of a source of backscattering using the method of back propagation

formulation and accuracy of on surface radiation conditions for acoustic multiple scattering problems the aim of this paper is 1 to address an extension of the on surface radiation condition osrc method to multiple scattering by a cluster of convex obstacles and 2 to analyze the numerical accuracy of the formulation for some model problems first the acoustic scattering problem is considered and materials about integral equations and osrcs are recalled then an osrc integral equation formulation is developed for the dirichlet multiple scattering problems finally an extensive numerical study of the method is proposed in the special case of the scattering by circular cylinders even if this situation is not completely general it provides an assessment of the accuracy of the approximation with respect to various parameters including thanks to the choice of the osrc operators

a quasi optimal non overlapping domain decomposition algorithm for the helmholtz equation this paper presents a new non overlapping domain decomposition method for the helmholtz equation whose effective convergence is quasi optimal these improved properties result from a combination of an appropriate choice of transmission conditions and a suitable approximation of the dirichlet to neumann operator a convergence theorem of the algorithm is established and numerical results validating the new approach are presented in both two and three dimensions

an approximate boundary condition in acoustics an approximate formula connecting the field and its normal derivative on the surface of a body is derived from comparison with exact results for a sphere and geometrical acoustics for a general obstacle the formula appears to be effective in the middle range of frequencies although it is easy to apply and its structure is simple

composition of pseudo almost periodic functions and semilinear differential equations under the assumption of uniformly continuity we establish a composition theorem of pseudo almost periodic functions in general banach spaces as an application we give some existence theorems of pseudo almost periodic solutions and mild pseudo almost periodic solutions for some differential equations

local absorbing boundary conditions for elliptical shaped boundaries we compare several local absorbing boundary conditions for solving the helmholtz equation by a finite difference or finite element method exterior to a general scatterer these boundary conditions are imposed on an artificial elliptical or prolate spheroid outer surface in order to compare the computational solution with an analytical solution we consider as an example scattering about an ellipse we solve the helmholtz equation with both finite differences and finite elements we also introduce a new boundary condition for an ellipse based on a modal expansion

analytical and numerical investigation of the performance of the bgt2 condition for low frequency acoustic scattering problems a mathematical and numerical analysis is performed to assess the performance of the second order bayliss gunzburger turkel bgt2 condition when applied to solving low frequency acoustic scattering problems in the case of elongated scatterers this investigation suggests that bgt2 retains an acceptable level of accuracy for relatively low wavenumber a damping effect is incorporated to the bgt2 condition in order to extend the range of satisfactory performance this damping procedure consists in adding only a constant imaginary part to the wavenumber the numerical results indicate that the modified version of bgt2 extends the range of satisfactory performance by improving the level of accuracy by up to two orders of magnitude guidelines on the appropriate choice of the damping coefficient are provided

higher order pade approximations for accurate and stable elastic parabolic equations with application to interface wave propagation higher order pade approximations are applied to derive accurate and stable parabolic equations for sound propagation in oceans bounded below by an elastic bottom or bounded above by ice cover accuracy is achieved by placing constraints on the derivatives of the pade approximations at the point corresponding to the reference wave number stability is achieved by requiring that the pade approximations map part of the lower left quadrant of the complex plane into the upper half of the complex plane elastic parabolic equations based on these pade series can handle problems involving compressional shear and interface waves very wide propagation angles and large depth variations and weak range variations in the seismoacoustic parameters a finite difference spectral solution is developed for generating reference solutions and starting fields the rotated elastic parabolic equation is used to investigate the accuracy of the elastic parabolic equation for range dependent problems

anisotropic complex pade hybrid finite difference depth migration standard real valued finite difference fd and fourier finite difference ffd migrations cannot handle evanescent waves correctly which can lead to numerical instabilities in the presence of strong velocity variations a possible solution to these problems is the complex pade approximation which avoids problems with evanescent waves by rotating the branch cut of the complex square root we have applied this approximation to the acoustic wave equation for vertical transversely isotropic media to derive more stable fd and hybrid fd ffd migrations for such media our analysis of the dispersion relation of the new method indicates that it should provide more stable migration results with fewer artifacts and higher accuracy at steep dips our studies lead to the conclusion that the rotation angle of the branch cut that should yield the most stable image is 60 for fd migration as confirmed by numerical impulse responses and work with synthetic data

motion compensated frame interpolation based on multihypothesis motion estimation and texture optimization a novel motion compensated frame interpolation mcfi algorithm to increase video temporal resolutions based on multihypothesis motion estimation and texture optimization is proposed in this paper initially we form multiple motion hypotheses for each pixel by employing different motion estimation parameters i e different block sizes and directions then we determine the best motion hypothesis for each pixel by solving a labeling problem and optimizing the parameters in the labeling problem the cost function is composed of color shape and smoothness terms finally we refine the motion hypothesis field based on the texture optimization technique and blend multiple source pixels to interpolate each pixel in the intermediate frame simulation results demonstrate that the proposed algorithm provides significantly better mcfi performance than conventional algorithms

rate distortion analysis for spatially scalable video coding in this paper we derive the rate distortion lower bounds of spatially scalable video coding techniques the methods we evaluate are subband and pyramid motion compensation where temporal redundancies in the same spatial layer as well as interlayer spatial redundancies are exploited in the enhancement layer encoding the rate distortion bounds are derived from rate distortion theory for stationary gaussian signals where mean square error is used as the distortion criteria assuming that the base layer is encoded by a nonscalable video coder we derive the rate distortion functions for the enhancement layer which depend upon the power spectral density of the input signal the motion prediction error probability density function and the base layer encoding performance we will show that pyramid and subband methods are expected to outperform independently encoding the enhancement layer using motion compensated prediction in terms of rate distortion efficiency when the base layer is encoded at a relatively higher quality or less accurate displacement estimation happens in the enhancement layer

a motion aligned auto regressive model for frame rate up conversion in this paper a motion aligned auto regressive maar model is proposed for frame rate up conversion where each pixel is interpolated as the average of the results generated by one forward maar fw maar model and one backward maar bw maar model in the fw maar model each pixel in the to be interpolated frame is generated as a linear weighted summation of the pixels within a motion aligned square neighborhood in the previous frame to derive more accurate interpolation weights the aligned actual pixels in the following frame are also estimated as a linear weighted summation of the newly interpolated pixels in the to be interpolated frame by the same weights consequently the backward aligned actual pixels in the following frame can be estimated as a weighted summation of the corresponding pixels within an enlarged square neighborhood in the previous frame the bw maar is performed likewise except that it is operated in the reverse direction a damping newton algorithm is then proposed to compute the adaptive interpolation weights for the fw maar and bw maar models extensive experiments demonstrate that the proposed maar model is able to achieve superior performance than the traditional frame interpolation methods such as mci obmc and aobmc and it is even better than star model for the most test sequences with moderate or large motions

the existence of pseudo almost periodic solutions for some nonlinear differential equations in banach spaces abstract let e be a real banach where x h denotes the limit of the quotient x x t h t as 0 t 0 consider the differential equation d x d t a t x f t where we assume amongst other properties that a is strongly dissipative in the following sense x y a t x a t y p t x y x y where is a function of the type u 0 and p is a function majorized by an almost periodic function with negative mean value first we show that this equation has a unique pseudo almost periodic solution then we apply this result to the class of the following equations d x d t q t x x f t 0 where q is a pseudo almost periodic function with positive mean value

rate distortion analysis of motion side estimation in wyner ziv video coding wyner ziv video coding wzvc has gained considerable interests in the research community in this paper we present a model to examine the wzvc performance and compare it with conventional motion compensated prediction mcp based video coding theoretical results show that although wzvc can achieve as much as 6 db gain over conventional video coding without motion search it still falls 6 db or more behind current best mcp based inter frame video coding we further study the use of subpixel and multireference motion search methods to improve wzvc efficiency the analytical results are confirmed by simulations and experiments

numerical solutions of range dependent benchmark problems in ocean acoustics accurate numerical solutions are presented for benchmark problems associated with propagation in a wedge with different bottom boundary conditions as well as in a plane parallel waveguide with changing profile with range the benchmark problems are solved with three different general purpose numerical codes 1 a coupled mode code providing a full spectrum two way backscatter included solution of the wave equation 2 a finite difference pe code providing a wide angle solution of the one way parabolic approximation of the wave equation and 3 a split step pe code providing a more narrow angle solution of the one way parabolic approximation of the wave equation only the two way coupled mode results can be considered accurate solutions of the benchmark problems

phase reduction models for improving the accuracy of the finite element solution of time harmonic scattering problems i general approach and low order models this paper introduces a new formulation of high frequency time harmonic scattering problems in view of a numerical finite element solution it is well known that pollution error causes inaccuracies in the finite element solution of short wave problems to partially avoid this precision problem the strategy proposed here consists in firstly numerically computing at a low cost an approximate phase of the exact solution through asymptotic propagative models secondly using this approximate phase a slowly varying unknown envelope is introduced and is computed using coarser mesh grids the global procedure is called phase reduction in this first paper the general theoretical procedure is developed and low order propagative models are numerically investigated in detail improved solutions based on higher order models are discussed showing the potential of the method for further developments

motion estimation without integer pel search the typical motion estimation me consists of three main steps including spatial temporal prediction integer pel search and fractional pel search the integer pel search which seeks the best matched integer pel position within a search window is considered to be crucial for video encoding it occupies over 50 of the overall encoding time when adopting the full search scheme for software encoders and introduces remarkable area cost memory traffic and power consumption to hardware encoders in this paper we find that video sequences especially high resolution videos can often be encoded effectively and efficiently even without integer pel search such counter intuitive phenomenon is not only because that spatial temporal prediction and fractional pel search are accurate enough for the me of many blocks in fact we observe that when the predicted motion vector is biased from the optimal motion vector mainly for boundary blocks of irregularly moving objects it is also hard for integer pel search to reduce the final rate distortion cost the deviation of reference position could be alleviated with the fractional pel interpolation and rate distortion optimization techniques e g adaptive macroblock mode considering the decreasing proportion of boundary blocks caused by the increasing resolution of videos integer pel search may be rather cost ineffective in the era of high resolution experimental results on 36 typical sequences of different resolutions encoded with x264 which is a widely used video encoder comply with our analysis well for 1080p sequences removing the integer pel search saves 57 9 of the overall h 264 encoding time on average compared to the original x264 with full integer pel search using default parameters while the resultant performance loss is negligible the bit rate is increased by only 0 18 while the peak signal to noise ratio is decreased by only 0 01 db per frame averagely

local solutions to high frequency 2d scattering problems we consider the solution of high frequency scattering problems in two dimensions modeled by an integral equation on the boundary of a smooth scattering object we devise a numerical method to obtain solutions on only parts of the boundary with little computational effort the method incorporates asymptotic properties of the solution and can therefore attain particularly good results for high frequencies we show that the integral equation in this approach reduces to an ordinary differential equation

optimal temporal interpolation filter for motion compensated frame rate up conversion frame rate up conversion fruc methods that employ motion have been proven to provide better image quality compared to nonmotion based methods while motion based methods improve the quality of interpolation artifacts are introduced in the presence of incorrect motion vectors in this paper we study the design problem of optimal temporal interpolation filter for motion compensated fruc mc fruc the optimal filter is obtained by minimizing the prediction error variance between the original frame and the interpolated frame in fruc applications the original frame that is skipped is not available at the decoder so models for the power spectral density of the original signal and prediction error are used to formulate the problem the closed form solution for the filter is obtained by lagrange multipliers and statistical motion vector error modeling the effect of motion vector errors on resulting optimal filters and prediction error is analyzed the performance of the optimal filter is compared to nonadaptive temporal averaging filters by using two different motion vector reliability measures the results confirm that to improve the quality of temporal interpolation in mc the interpolation filter should be designed based on the reliability of motion vectors and the statistics of the mc prediction error

spatial sparsity induced prediction sip for images and video a simple way to reject structured interference we propose a prediction technique that is geared toward forming successful estimates of a signal based on a correlated anchor signal that is contaminated with complex interference the corruption in the anchor signal involves intensity modulations linear distortions structured interference clutter and noise just to name a few the proposed setup reflects nontrivial prediction scenarios involving images and video frames where statistically related data is rendered ineffective for traditional methods due to cross fades blends clutter brightness variations focus changes and other complex transitions rather than trying to solve a difficult estimation problem involving nonstationary signal statistics we obtain simple predictors in linear transform domain where the underlying signals are assumed to be sparse we show that these simple predictors achieve surprisingly good performance and seamlessly allow successful predictions even under complicated cases none of the interference parameters are estimated as our algorithm provides completely blind and automated operation we provide a general formulation that allows for nonlinearities in the prediction loop and we consider prediction optimal decompositions beyond an extensive set of results on prediction and registration the proposed method is also implemented to operate inside a state of the art compression codec and results show significant improvements on scenes that are difficult to encode using traditional prediction techniques

motion compensated coding and frame rate up conversion models and analysis block based motion estimation me and motion compensation mc techniques are widely used in modern video processing algorithms and compression systems the great variety of video applications and devices results in diverse compression specifications such as frame rates and bit rates in this paper we study the effect of frame rate and compression bit rate on block based me and mc as commonly utilized in inter frame coding and frame rate up conversion fruc this joint examination yields a theoretical foundation for comparing mc procedures in coding and fruc first the video signal is locally modeled as a noisy translational motion of an image then we theoretically model the motion compensated prediction of available and absent frames as in coding and fruc applications respectively the theoretic mc prediction error is studied further and its autocorrelation function is calculated yielding useful separable simplifications for the coding application we argue that a linear relation exists between the variance of the mc prediction error and temporal distance while the relevant distance in mc coding is between the predicted and reference frames mc fruc is affected by the distance between the frames available for interpolation we compare our estimates with experimental results and show that the theory explains qualitatively the empirical behavior then we use the models proposed to analyze a system for improving of video coding at low bit rates using a spatio temporal scaling although this concept is practically employed in various forms so far it lacked a theoretical justification we here harness the proposed mc models and present a comprehensive analysis of the system to qualitatively predict the experimental results

existence uniqueness and attractiveness of a pseudo almost automorphic solutions for some dissipative differential equations in banach spaces abstract we give sufficient conditions ensuring the existence uniqueness and global attractiveness of a pseudo compact almost automorphic solution of the following differential equation x t f t x t in a banach space e where f r e e is a pseudo almost automorphic function with respect to the first argument we essentially assume that the function f is dissipative then we apply the main results to the following equation x t q t x t x t f t 0

the rational approximation to the acoustic wave equation with bottom interaction the rational linear approximation to the wave equation is a full wave approach to modeling range dependent ocean acoustic propagation with bottom interaction it is a one way wave equation which gives an accurate treatment of high angle propagation to angles of about 40 with respect to the horizontal reflection from sound speed and density discontinuities is treated using the natural wave equation matching conditions bathymetry is allowed to vary in range a tridiagonal implicit finite difference solution of this equation has been implemented it has several advantages over the tridiagonal crank nicholson solution of the parabolic equation it more accurately models high angles of propagation treats attenuation as a function of path length rather than range and models range dependent bathymetry in a way that suits the form of the one way wave equation the numerical methods are fourth order accurate in depth the resulting implicit range step is still in the simple tridiagonal form

pseudo almost periodic solutions of some differential equations ii we first present some results about pseudo almost periodic functions then we use these results to show some theorems about existence and uniqueness of the pseudo almost periodic solutions of the linear and the quasi linear nonautonomous equations finally we set up some theorems of the existence of pseudo almost periodic solutions implying the existence of almost periodic solutions of general ordinary differential equation systems

high order surface radiation conditions for time harmonic waves in exterior domains abstract we formulate a new family of high order on surface radiation conditions to approximate the outgoing solution to the helmholtz equation in exterior domains motivated by the pseudo differential expansion of the dirichlet to neumann operator developed by antoine et al 1999 we design a systematic procedure to apply pseudo differential symbols of arbitrarily high order numerical results are presented to illustrate the performance of the proposed method for solving both the dirichlet and the neumann boundary value problems possible improvements and extensions are also discussed

complex pade approximants for wide angle acoustic propagators procedures for constructing wide angle propagators that attenuate evanescent modes in parabolic equation pe models of underwater sound propagation are examined in this context two new split step pade approximations to exponentiated square root operators are proposed the first method involves a propagator derived from a pade approximant of a square root operator that has been rotated in the complex plane while the propagator of the second method is obtained from a complex coefficient rational approximation of the square root operator numerical evidence confirms that these proposed methods yield improved behavior compared to previously suggested techniques in selected areas of the spectral domain

numerical accuracy of a pade type non reflecting boundary condition for the finite element solution of acoustic scattering problems at high frequency the present text deals with the numerical solution of two dimensional high frequency acoustic scattering problems using a new high order and asymptotic pade type artificial boundary condition the pade type condition is easy to implement in a galerkin least squares iterative finite element solver for arbitrarily convex shaped boundaries the method accuracy is investigated for different model problems and for the scattering problem by a submarine shaped scatterer as a result relatively small computational domains optimized according to the shape of the scatterer can be considered while yielding accurate computations for high frequencies copyright 2005 john wiley sons ltd

bayliss turkel like radiation conditions on surfaces of arbitrary shape this paper addresses the extension of the bayliss turkel second order radiation condition to an arbitrarily shaped surface the derivation is based mainly on the pseudo differential calculus as well as on the introduction of a criterion providing a precise handling of the approximation process involved in the derivation of the radiation condition the radiation condition then ranges among the most accurate of those of order two as a by product of the derivation almost all known radiation conditions of order less than or equal to two are recovered and their respective accuracies are compared

a wide angle split step algorithm for the parabolic equation in this paper we describe a new wide angle parabolic equation based on an operator splitting that permits the use of a marching type fourier transform solution method the equation was first presented by feit and fleck appl opt 17 3990 3998 1978 for studying propagation within optical fibers existing computer codes which numerically solve the standard parabolic equation of ocean acoustics by the split step algorithm of tappert and hardin are easily modified to accommodate the wide angle capability of the new equation in addition since the new wide angle equation is less sensitive to the value of the reference wavenumber the effects of phase errors are greatly reduced the results of a simple error analysis indicate that improved accuracy can be achieved by the new wide angle equation for propagation conditions typical of deep ocean environments this is supported by our numerical experience a summary of which is presented in the paper for test cases where the variation of the acoustic index

higher order paraxial wave equation approximations in heterogenous media a new family of paraxial wave equation approximations is derived these approximations are of higher order accuracy than the parabolic approximation and they can be applied to the same computationa

rate distortion optimization for h 264 interframe coding a general framework and algorithms rate distortion rd optimization for h 264 interframe coding with complete baseline decoding compatibility is investigated on a frame basis using soft decision quantization sdq rather than the standard hard decision quantization we first establish a general framework in which motion estimation quantization and entropy coding in h 264 for the current frame can be jointly designed to minimize a true rd cost given previously coded reference frames we then propose three rd optimization algorithms a graph based algorithm for near optimal sdq in h 264 baseline encoding given motion estimation and quantization step sizes an algorithm for near optimal residual coding in h 264 baseline encoding given motion estimation and an iterative overall algorithm to optimize h 264 baseline encoding for each individual frame given previously coded reference frames with them embedded in the indicated order the graph based algorithm for near optimal sdq is the core given motion estimation and quantization step sizes it is guaranteed to perform optimal sdq if the weak adjacent block dependency utilized in the context adaptive variable length coding of h 264 is ignored for optimization the proposed algorithms have been implemented based on the reference encoder jm82 of h 264 with complete compatibility to the baseline profile experiments show that for a set of typical video testing sequences the graph based algorithm for near optimal sdq the algorithm for near optimal residual coding and the overall algorithm achieve on average 6 8 and 12 respectively rate reduction at the same psnr ranging from 30 to 38 db when compared with the rd optimization method implemented in the h 264 reference software

a higher order energy conserving parabolic equqation for range dependent ocean depth sound speed and density outgoing solutions of the wave equation including parabolic equation pe and normal mode solutions are usually formulated so that pressure is continuous with range for range dependent problems the accuracy of normal mode solutions has been improved by conserving energy rather than maintaining continuity of pressure porter et al the problem of energy conservation in one way equations j acoust soc am 89 1058 1067 1991 this approach is applied to derive a higher order energy conserving pe that provides improved accuracy for problems involving large ocean bottom slopes and large range and depth variations in sound speed and density a special numerical approach and complex pade coefficients are applied to suppress gibbs oscillations the back propagated half space field an improved pe starter is applied to handle wide propagation angles reference solutions generated with a complex ray model and with the rotated pe are used for comparison

rapid solution of integral equations of scattering theory in two dimensions abstract the present paper describes an algorithm for rapid solution of boundary value problems for the helmholtz equation in two dimensions based on iteratively solving integral equations of scattering theory cpu time requirements of previously published algorithms of this type are of the order n 2 where n is the number of nodes in the discretization of the boundary of the scatterer the cpu time requirements of the algorithm of the present paper are n 4 3 and can be further reduced making it considerably more practical for large scale problems

non overlapping domain decomposition algorithm based on modified transmission conditions for the helmholtz equation abstract a square root based transmission conditions domain decomposition method was recently introduced for the helmholtz equation it produces an effective algorithm where the convergence is independent of the wavenumber and the mesh discretization we modify here these conditions in order to guarantee well posedness of local problems and further improve the efficiency of the whole method numerical results in particular in the three dimensional case show significant reduction of the computational time needed in the iterative procedure while preserving the iteration number when compared with the original algorithm

a high order absorbing boundary condition for 2d time harmonic elastodynamic scattering problems abstract in this paper we are concerned with the construction of a new high order absorbing boundary condition abc for 2d elastic scattering problems it is defined by an approximate local dirichlet to neumann dtn map first we explain the derivation of this approximation next a detailed analytical study in terms of hankel functions in the circular case is addressed the new abc is compared with the standard low order lysmer kuhlemeyer abc finally its accuracy and efficiency are investigated for various numerical examples particularly at high frequencies