explicit residual based a posteriori error estimation for finite element discretizations of the helmholtz equation computation of the constant and new measures of error estimator quality abstract this paper continues the study of an explicit residual based a posteriori error estimator developed for finite element discretizations of the helmholtz equation in the context of time harmonic exterior acoustics problems in previous papers 1 3 the error estimator was derived and subsequently applied to h adaptive computations of model problems in two dimensions in the present paper a methodology is established for computing error estimates these error estimates are then analyzed in detail the error estimates are made possible by computing the scaling constant which exists in error estimators of this type in our case this constant is difficult to obtain an algorithm for computing the constant is described it is noted that the error indicators used for adaptive computations do not require knowledge of this constant several measures are used to analyze the quality of the error estimates providing a complete description of the error estimator in the context of these problems we compute global effectivity indices and utilize the local element wise effectivity index in computing three additional measures the first of these is the robustness index the others are the modified robustness index and the distribution index which are introduced for the first time it is found that the global effectivity index varies with problem parameters in particular the wave number robustness indices also vary due to the local error definition and wave number values of the distribution index are much better however indicating the suitability of the error estimator in guiding efficient adaptive mesh refinement the analysis of the error estimator is carried out on relatively coarse meshes typical of those used in practical engineering computations

reducing spurious dispersion anisotropy and reflection in finite element analysis of time harmonic acoustics abstract galerkin and stabilized galerkin least squares and galerkin gradient least squares finite element methods for solving problems of time harmonic acoustics are presented and analyzed the error of discretization is related to spurious representation of physical phenomena namely dispersion anisotropy and reflection all of which decrease with mesh refinement the performance of the stabilized methods in terms of dispersion and anisotropy is identical both are superior to the galerkin method relaxing wave resolution requirements further insight into the design of these methods is provided by the analyses the stabilized methods differ in the degree of spurious reflection that is engendered by transitions in mesh size the performance of galerkin gradient least squares deteriorates on non uniform meshes however galerkin least squares maintains its enhanced performance exhibiting low sensitivity to transitions in mesh size thereby reducing spurious dispersion anisotropy and reflection in finite element analysis of time harmonic acoustics guidelines for discretization pertaining to mesh orientation and wave resolution are presented

higher order boundary infinite elements abstract higher order approximations are implemented in a novel approach to infinite element formulations for exterior problems of time harmonic acoustics this approach is based on a functional which provides a general framework for domain based computation of exterior problems two prominent features of this formulation simplify the task of discretization the lack of integration over the unbounded domain and weak enforcement of continuity between finite elements and infinite elements consequently the infinite elements mesh the interface only and need not match the finite elements on the interface various infinite element approximations for two dimensional configurations with circular interfaces are presented numerical results demonstrate the good performance of this scheme

a multi level fast multipole bem for 3 d elastodynamics in the frequency domain to reduce computational complexity and memory requirement for 3 d elastodynamics using the boundary element method bem a multi level fast multipole bem fm bem is proposed the diagonal form for the expansion of the elastodynamic fundamental solution is used with a truncation parameter adjusted to the subdivision level a feature necessary for achieving optimal computational efficiency both the single level and mul ti level forms of the elastodynamic fm bem are considered with emphasis on the latter crucial implementation issues including the truncation of the multipole expansion the optimal number of levels the direct and inverse extrapolation steps are examined in detail with the backing of numerical experiments a complexity analysis for both the single level and multi level versions is conducted the correctness and computational performances of the proposed elastodynamic fmm are demonstrated on numerical examples featuring up to o 10 6 dofs run on a single processor pc and including the diffraction of an incident p plane wave by a semi spherical or semi ellipsoidal canyon representative of topographic site effects

multiscale phenomena green s functions the dirichlet to neumann formulation subgrid scale models bubbles and the origins of stabilized methods abstract an approach is developed for deriving variational methods capable of representing multiscale phenomena the ideas are first illustrated on the exterior problem for the helmholtz equation this leads to the well known dirichlet to neumann formulation next a class of subgrid scale models is developed and the relationships to bubble function methods and stabilized methods are established it is shown that both the latter methods are approximate subgrid scale models the identification for stabilized methods leads to an analytical formula for the intrinsic time scale whose origins have been a mystery heretofore

a comparative study of three boundary element approaches to calculate the transient response of viscoelastic solids with unbounded domains abstract as an alternative to domain discretization methods the boundary element method bem provides a powerful tool for the calculation of dynamic structural response in frequency and time domain field equations of motion and boundary conditions are cast into boundary integral equations bie which are discretized only on the boundary fundamental solutions are used as weighting functions in the bie which fulfil the sommerfeld radiation condition i e the energy radiation into a surrounding medium is modelled correctly therefore infinite and semi infinite domains can be effectively treated by the method the soil represents such a semi infinite domain in soil structure interaction problems the response to vibratory loads superimposed to static pre loads can often be calculated by linear viscoelastic constitutive equations conventional viscoelastic constitutive equations can be generalized by taking fractional order time derivatives into account in the present paper two time domain bem approaches including generalized viscoelastic behaviour are compared with the laplace domain bem approach and subsequent numerical inverse transformation one of the presented time domain approaches uses an analytical integration of the elastodynamic bie in a time step viscoelastic constitutive properties are introduced after laplace transformation by means of an elastic viscoelastic correspondence principle the transient response is obtained by inverse transformation in each time step the other time domain approach is based on the so called convolution quadrature method in this formulation the convolution integral in the bie is numerically approximated by a quadrature formula whose weights are determined by the same laplace transformed fundamental solutions used in the first method and a linear multistep method a numerical study of wave propagation problems in 3 d viscoelastic continuum is performed for comparing the three bem formulations

improved finite element methods for elastic waves abstract in this work we develop finite element methods for exterior problems of time harmonic elastic waves we employ dtn exterior boundary conditions on an artificial boundary to obtain a well posed equivalent problem in a bounded region that is suitable for domain based computation galerkin galerkin least squares and galerkin gradient least squares finite element methods are presented in acoustic wave problems the galerkin least squares method counters the numerical difficulties that result from employing the galerkin method but proves to be insufficient for elastic waves a specialization of the galerkin gradient least squares method to problems of elastic waves yields good results numerical tests validate these conclusions

error bounds for the methods of glimm godunov and leveque the expected error in l 1 r at time t for glimm s scheme when applied to a scalar conservation law is bounded by left h frac 2 sqrt 3 left frac h delta t right 1 2 right left u 0 right bv bf r where h is the mesh size and delta t is the time step we show that the error in godunov s scheme is bounded by the same expression and use this result to analyze a variant of a large time step numerical method of leveque that may be viewed as a combination of godunov s scheme and a method of dafermos

boundary integral equation methods for the elastic and thermoelastic waves in three dimensions in this paper we consider the boundary integral equation bie methods for solving the exterior neumann boundary value problems of elastic and thermoelastic waves in three dimensions based on the fredholm integral equations of the first kind the innovative contribution of this work lies in the proposal of the new regularized formulations for the hyper singular boundary integral operators bio associated with the time harmonic elastic and thermoelastic wave equations with the help of the new regularized formulations we only need to compute the integrals with weak singularities at most in the corresponding variational forms of the boundary integral equations the accuracy of the regularized formulations is demonstrated through numerical examples using the galerkin boundary element method bem

the use of chief to obtain unique solutions for acoustic radiation using boundary integral equations this report is concerned with the problem of obtaining a unique solution for radiation problems at characteristic wavenumbers when a boundary integral equation formulation is used it is shown that the combined helmholtz integral equation formulation chief method works even when numerous interior points lie exactly on nodal surfaces of a mode corresponding to an eigenfrequency of the related interior problem when at least one interior point does not lie on a nodal surface the use of chief is illustrated with numerical radiation experiments for the sphere and the finite cylinder chief is compared to the helmholtz gradient formulation hgf for circumventing nonuniqueness and is found to yield a more accurate solution in at least one published example a procedure is used to indicate the solution error when using integral equation methods with or without a technique to circumvent nonuniqueness this procedure uses the velocity potential of an interior point as an indicator of solution error in all cases considered the interior potential correctly indicated a good or bad solution whereas the matrix condition number falsely indicated a bad solution in several instances work supported in part by onr

p sv wave propagation in heterogeneous media velocity stress finite difference method i present a finite difference method for modeling p sv wave propagation in heterogeneous media this is an extension of the method i previously proposed for modeling sh wave propagation by using velocity and stress in a discrete grid the two components of the velocity cannot be defined at the same node for a complete staggered grid the stability condition and the p wave phase velocity dispersion curve do not depend on the poisson s ratio while the s wave phase velocity dispersion curve behavior is rather insensitive to the poisson s ratio therefore the same code used for elastic media can be used for liquid media where s wave velocity goes to zero and no special treatment is needed for a liquid solid interface typical physical phenomena arising with p sv modeling such as surface waves are in agreement with analytical results the weathered layer and corner edge models show in seismograms the same converted phases obtained by previous authors this method gives stable results for step discontinuities as shown for a liquid layer above an elastic half space the head wave preserves the correct amplitude finally the corner edge model illustrates a more complex geometry for the liquid solid interface as the poisson s ratio v increases from 0 25 to 0 5 the shear converted phases are removed from seismograms and from the time section of the wave field

a fast fourier galerkin method solving a boundary integral equation for the biharmonic equation we develop a fast fourier galerkin method for solving a boundary integral equation which is a reformulation of the dirichlet problem of the biharmonic equation the proposed method is based on a splitting of the resulting boundary integral operator that is we write the operator as a sum of two integral operators one having the fourier basis functions as eigenfunctions and the other whose representation matrix in the fourier basis can be compressed to a sparse matrix having only mathcal o n log n number of nonzero entries where n is the order of the fourier basis functions used in the method we then project the solution of the boundary integral equation onto the space spanned by the fourier basis functions this leads to a system of linear equations a fast solver for the system is based on a compression of its coefficient matrix we show that the method has the optimal convergence order mathcal o n q where q denotes the degree of regularity of the exact solution of the boundary int

epipolar plane image analysis an approach to determining structure from motion we present a technique for building a three dimensional description of a static scene from a dense sequence of images these images are taken in such rapid succession that they form a solid block of data in which the temporal continuity from image to image is approximately equal to the spatial continuity in an individual image the technique utilizes knowledge of the camera motion to form and analyze slices of this solid these slices directly encode not only the three dimensional positions of objects but also such spatiotemporal events as the occlusion of one object by another for straight line camera motions these slices have a simple linear structure that makes them easier to analyze the analysis computes the three dimensional positions of object features marks occlusion boundaries on the objects and builds a three dimensional map of free space in our article we first describe the application of this technique to a simple camera motion and then show how projective duality is used to extend the analysis to a wider class of camera motions and object types that include curved and moving objects

an iterative solution to acoustic scattering by rigid objects the scattering problem is formulated as a boundary integral equation over the scattering surface that through the use of a modified green s function is uniquely solvable for all wavenumbers of interest this integral equation is further transformed by operating with the adjoint into a self adjoint equation into which a parameter has been introduced by adding and subtracting multiples of the identity this equation is discretized and is solved in a neumann series that has been shown to converge with a suitable choice of the parameter with no restriction on the wavenumber numerical results from several examples spheres spheroids and finite cylinders are presented and shown to be in complete agreement with those obtained using t matrix methods results of a numerical experiment are presented that show how the parameter choice affects the rate of convergence

existence of solution to supply chain models based on partial differential equation with discontinuous flux function abstract we consider a recently proposed model by armbruster et al 2011 2 for supply chains with finite buffers the continuous model is based on a scalar conservation law and discontinuous flux function a suitable reformulation of the model is introduced and studied analytically the latter include waves with infinite negative wave speed using wave front tracking existence of solutions is obtained for supply chains and sequences of supply chains numerical results are presented

complex wave number dispersion analysis of galerkin and galerkin least squares methods for fluid loaded plates abstract the technique of complex wave number dispersion analysis is used to examine the accuracy of discretized systems in the representation of wave propagation phenomena this technique was applied to study finite element approximations to in vacuo and fluid loaded plates considering discretizations of kirchhoff and reissner mindlin plate theories coupled to an acoustic medium the allowed evanescent waves in the finite element approximation of the in vacuo plate are obtained and compared with theory the finite element dispersion relation for the coupled plate fluid system is derived results for the galerkin structural approximation coupled to galerkin and galerkin least squares gls fluid formulations are presented quantitative errors are reported and the significance of these errors in view of an analytical solution to the problem is given

efficiency of higher order finite elements for the analysis of seismic wave propagation the analysis of wave propagation problems in linear damped media must take into account both propagation features and attenuation process to perform accurate numerical investigations by the finite differences or finite element method one must consider a specific problem known as the numerical dispersion of waves numerical dispersion may increase the numerical error during the propagation process as the wave velocity phase and group depends on the features of the numerical model in this paper the numerical modelling of wave propagation by the finite element method is thus analyzed and dis cussed for linear constitutive laws numerical dispersion is analyzed herein through 1d computations investigating the accuracy of higher order 15 node finite elements towards numerical dispersion concerning the numerical analy sis of wave attenuation a rheological interpretation of the classical rayleigh assumption has for instance been previously proposed in this journal

a general phase transition model for vehicular traffic an extension of the colombo phase transition model is proposed the congestion phase is described by a two dimensional zone defined around an equilibrium flux known as the classical fundamental diagram general criteria to build such a set valued fundamental diagram are enumerated and instantiated on several equilibrium fluxes with different concavity properties the solution of the riemann problem in the presence of phase transitions is obtained through the construction of a riemann solver which enables the definition of the solution of the cauchy problem using wavefront tracking the free flow phase is described using a newell daganzo fundamental diagram which allows for a more tractable definition of phase transition compared to the original colombo phase transition model the accuracy of the numerical solution obtained by a modified godunov scheme is assessed on benchmark scenarios for the different flux functions constructed

studies of domain based formulations for computing exterior problems of acoustics a strategy must be devised to compute solutions over domains which are unbounded exact impedance conditions at an artificial external boundary are specified by the dtn method yielding an equivalent problem that is suitable for domain based computation the dtn boundary condition is non reflective giving rise to exact and thereby unique solutions the truncated dtn operator which is employed in practice fails to inhibit the reflection of higher modes so that non unique solutions may occur at their harmonics simple expressions determine a sufficient number of terms in the truncated operator for unique solutions at any given wave number there are three characteristic length scales in the computational problem the radius of the artificial boundary the geometry of the body represented by the internal boundary and the mesh size

the ultra weak variational formulation for elastic wave problems the ultra weak variational formulation has been used effectively to solve time harmonic acoustic and electromagnetic wave propagation in inhomogeneous media we develop the ultra weak variational formulation for elastic wave propagation in two space dimensions in order to improve the accuracy and stability of the method we find it necessary to approximate the s and p wave components of the solution in a balanced way some preliminary analysis is provided and numerical evidence is presented for the efficiency of the scheme in comparison to piecewise linear finite elements

an accurate boundary element method for the exterior elastic scattering problem in two dimensions this paper is concerned with a galerkin boundary element method solving the two dimensional exterior elastic wave scattering problem the original problem is first reduced to the so called burtonmiller 1 boundary integral formulation and essential mathematical features of its variational form are discussed in numerical implementations a newly derived and analytically accurate regularization formula 2 is employed for the numerical evaluation of hyper singular boundary integral operator a new computational approach is employed based on the series expansions of hankel functions for the computation of weakly singular boundary integral operators during the reduction of corresponding galerkin equations into a discrete linear system the effectiveness of proposed numerical methods is demonstrated using several numerical examples a new and accurate regularization formula which replaces the weak form of hypersingular boundary integral operator by a coupling of several weakly singular boundary integrals is given based on the series expansions of hankel functions several special integrals all weakly singular boundary integrals are evaluated exactly

a new computational method for transient dynamics including the low and the medium frequency ranges this paper deals with a new computational method for transient dynamic analysis which enables one to cover both the low and medium frequency ranges this is a frequency approach in which the low frequency part is obtained through a classical technique while the medium frequency part is handled through the variational theory of complex rays vtcr initially introduced for vibrations preliminary examples are shown

duality and unified analysis of discrete approximations in structural dynamics and wave propagation comparison of p method finite elements with k method nurbs we study the discretization behavior of classical finite element and nurbs approximations on problems of structural vibrations and wave propagation we find that on the basis of equal numbers of degrees of freedom and bandwidth nurbs have superior approximation properties in fact we observe that the high mode behavior of classical finite elements is divergent with the order of approximation a surprisingly negative result on the other hand nurbs offer almost spectral approximation properties and all modes converge with increasing order of approximation

transient spheroidal elements for unbounded wave problems a wave envelope element numerical scheme is applied to the solution of unbounded wave problems the scheme is based on a fourier transformation of a discrete model formulated in the frequency domain this yields a discrete system of ordinary differential equations in time which are local in space oblate and prolate spheroidal element geometries are used the accuracy of the scheme is demonstrated by a comparison of computed and analytic solutions for axisymmetric test cases time harmonic and transient solution are presented an indirect solution procedure is also presented which permits the sparsity of the transient equations to be utilised more effectively

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

stabilized finite element methods for steady advection diffusion with production abstract finite element methods for solving equations of steady advection diffusion with production are constructed employing a linear source to model production the galerkin method requires relatively fine meshes to retain an acceptable degree of accuracy for wide ranges of values of the physical coefficients numerous criteria for improved accuracy via galerkin least squares are proposed and examined in the entire parameter space of these several provide the lowest error in nodal amplification factors each in a certain range of ratios of physical coefficients guidelines for required mesh resolutions are presented for galerkin and galerkin least squares showing that in large parts of the parameter space substantial savings may be obtained by employing galerkin least squares galerkin least squares gradient least squares a new variation of the galerkin method is designed to provide exact nodal amplification factors offering accurate solutions at any resolution numerical tests validate these conclusions

high accuracy quadrature methods for solving boundary integral equations of axisymmetric elasticity problems we investigate the mechanical quadrature methods mqms for solving boundary integral equations bies of the three dimensional axisymmetric elasticity equations with dirichlet s problems the convergence of the mqms is proved based on anselone s collective compact theory moreover an asymptotic error expansion of the mqms shows that the approximation order is of o h 3 numerical examples are tested and the results verify the theoretical analysis

a fast and high order method for the three dimensional elastic wave scattering problem in this paper we present a fast and high order boundary integral equation method for the elastic scattering by three dimensional large penetrable obstacles the algorithm extends the method introduced in 5 for the acoustic surface scattering to the fully elastic case in our algorithm high order accuracy is achieved through the use of the partition of unity and a semi classical treatment of relevant singular integrals the computational efficiency associated with the nonsingular integrals is attained by the method of equivalent source representations on a cartesian grid and fast fourier transform fft the resulting algorithm computes one matrix vector product associated with the discretization of the integral equation with o n 4 3 log n operations and it shows algebraic convergence several numerical experiments are provided to demonstrate the efficiency of the method

a splitting algorithm for lwr traffic models with flux discontinuous in the unknown abstract we propose a finite difference algorithm for a scalar conservation law associated with the lighthill witham richards model of traffic flow for the case where the flux is discontinuous with respect to the unknown specifically the flux has a single decreasing jump which models a transition from free to congested traffic flow we write the flux as a lipschitz continuous flux plus a heaviside flux and then construct a splitting based on this decomposition the portion of the scheme associated with the heaviside flux is implicit but does not require the iterative solution of a system of nonlinear equations the portion associated with the continuous flux is a standard godunov scheme the scheme does not employ a flux regularization nor a riemann solver for the discontinuous flux problem standard hyperbolic time steps are allowed i e the time steps are dictated by the cfl condition associated with the continuous portion of the flux we prove that the approximate solutions converge up to extraction of a subsequence to a weak solution of the conservation law we propose a shock admissibility criterion and present some numerical examples

a galerkin least squares finite element method for the two dimensional helmholtz equation in this paper a galerkin least squares gls finite element method in which residuals in least squares form are added to the standard galerkin variational equation is developed to solve the helmholtz equation in two dimensions an important feature of gls methods is the introduction of a local mesh parameter that may be designed to provide accurate solutions with relatively coarse meshes previous work has accomplished this for the one dimensional helmholtz equation using dispersion analysis in this paper the selection of the gls mesh parameter for two dimensions is considered and leads to elements that exhibit improved phase accuracy for any given direction of wave propagation an optimal gls mesh parameter is determined using two dimensional fourier analysis in general problems the direction of wave propagation will not be known a priori in this case an optimal gls parameter is found which reduces phase error for all possible wave vector orientations over elements the optimal gls parameters are derived for both consistent and lumped mass approximations several numerical examples are given and the results compared with those obtained from the galerkin method the extension of gls to higher order quadratic interpolations is also presented

exterior problems of acoustics by fractal finite element mesh abstract the propagation and attenuation of acoustic waves in an exterior domain is an essential ingredient in the study of acoustic structure interaction in this paper the problems of acoustic radiation from an arbitrarily shaped vibrating body in an infinite exterior region are investigated by using a fractal two level finite element mesh fem with self similar layers in the media enclosing the conventional fem for the vibrating body the fractal two level fem has been successfully used in stress intensity factor prediction with self similar ratio smaller than one so that the mesh converges to the crack tip in this paper the similarity ratio is bigger than one so that the mesh extends to infinity by means of the hankel functions satisfying automatically sommerfeld s radiation conditions at infinity the different unknown nodal pressures in different layers are transformed to some common unknowns of the hankel coefficients the final matrix size of the exterior region is equal to the number of terms in the hankel expansion the set of infinite number of unknowns of nodal pressure is reduced to a set of small finite number of hankel s coefficients all layers have the same unknowns after the transformation due to self similarity the transformed stiffness matrix of the first layer is proportional to that of the second and so on therefore the stiffness matrices of the infinite layers can be summed by using just one layer numerical examples show that this method is efficient and accurate in solving unbounded acoustic problems

galerkin gradient least squares formulations for transient conduction heat transfer this paper presents the benefits provided by the use of the galerkin gradient least squares ggls method for transient conduction heat transfer the consistency of the gls method for this type of problem is also discussed the ggls method is compared with standard galerkin formulation on problems having an analytical solution a semi infinite solid solved on one and three dimensional meshes and a three dimensional thin plate for three dimensional applications the principle of including gradient least squares terms is extended to stabilize robin convection boundary conditions numerical simulations show that additional boundary gradient least squares terms improve the behavior of the solution on boundaries subject to convection boundary conditions new procedures used to obtain the gls and ggls stabilized finite element formulations are also presented the methodology consists in modifying the equation to be solved and then to obtain the variational equation by a standard galerkin method

design of galerkin generalized least squares methods for timoshenko beams abstract a class of finite element methods the galerkin generalized least squares methods are developed and applied to model the steady state response of timoshenko beams an optimal method is designed using a linear interpolation of the response such that there is zero finite element dispersion error the classical method of selective reduced integration and a modified version of selective reduced integration with mass lumping are shown to fall under the galerkin generalized least squares framework numerical experiments in wave propagation demonstrate the dramatic superiority of the new optimal method over the standard approaches the goal of the new methods is to decrease the computational burden required to achieve a desired accurcy level at a particular frequency thereby enabling larger scale higher frequency computations for a given platform

dispersion analysis and error estimation of galerkin finite element methods for the helmholtz equation when applying numerical methods for the computation of stationary waves from the helmholtz equation one obtains numerical waves that are dispersive also in non dispersive media the numerical wave displays a phase velocity that depends on the parameter k of the helmholtz equation in dispersion analysis the phase difference between the exact and the numerical solutions is investigated in this paper the authors recent result on the phase difference for one dimensional problems is numerically evaluated and discussed in the context of other work directed to this topic it is then shown that previous error estimates in h1 norm are of nondispersive character but hold for medium or high wavenumber on extremely refined mesh only on the other hand recently proven error estimates for constant resolution contain a pollution term with certain assumptions on the exact solution this term is of the order of the phase difference thus a link is established between the results of dispersion analysis and the results of numerical analysis throughout the paper the presentation and discussion of theoretical results is accompanied by numerical evaluation of several model problems special attention is given to the performance of the galerkin method with a higher order of polynomial approximation p h p version

a boundary element method for acoustic radiation valid for all wavenumbers a boundary element method for solving the exterior acoustic radiation problem that is valid for all wavenumbers has been developed the new formulation derives from the earlier work of burton and miller proc r soc london ser a 323 201 210 1971 which uses a linear combination of the helmholtz integral equation and its gradient to overcome the uniqueness problem a main feature of this formulation is the absence of integral singularities by restricting the field points of the kernels of the integrals to interior regions well away from radiating boundaries the usual complication of dealing with singular kernels is circumvented the new formulation has been named chi for coupled helmholtz integrals a corresponding computer program chi 4 35 can be used to compute the surface acoustic pressure on an arbitrary body for a given specified surface normal velocity results generated with chi 4 35 are presented for the spherical monopole and dipole along with results for parametric studies on the acc

a new stabilized finite element method for reaction diffusion problems the source stabilized petrov galerkin method this paper proposes a new stabilized finite element method to solve singular diffusion problems described by the modified helmholtz operator the galerkin method is known to produce spurious oscillations for low diffusion and various alternatives were proposed to improve the accuracy of the solution the mostly used methods are the well known galerkin least squares and galerkin gradient least squares ggls the ggls method yields the exact nodal solution in the one dimensional case and for a uniform mesh however the behavior of the method deteriorates slightly in the multi dimensional case and for non uniform meshes in this work we propose a new stabilized finite element method that leads to improved accuracy for multi dimensional problems for the one dimensional case the new method leads to the same results as the ggls method and hence provides exact nodal solutions to the problem on uniform meshes the proposed method is a galerkin discretization used to solve a modified equation that includes a term depending on the gradient of the original partial differential equation copyright 2008 john wiley sons ltd

nystrom method for elastic wave scattering by three dimensional obstacles nystrom method is developed to solve for boundary integral equations bie s for elastic wave scattering by three dimensional obstacles to generate the matrix equation from a bie nystrom method applies a quadrature rule to the integrations of smooth integrands over a discretized element directly and chooses the values of the unknown function at quadrature points as the system s unknowns to be solved this leads to a simple procedure to form the off diagonal entries of matrix by simply evaluating the integrands without numerical integrations for the diagonal or near diagonal entries corresponding to the integrals over a singular or near singular element where the kernels are singular or near singular we develop a systematic singularity treatment technique known as the local correction scheme based on the linear approximation of elements the scheme differs from the singularity regularization or subtraction technique used in the boundary element method bem it applies the series expansion of scalar green s function to the kernels and derives analytical solutions for the strongly singular integrals under the cauchy principal value like cpv like sense since the approach avoids the need for reformulating the bie for singularity removal in bem and solves for the somigliana s equation directly it is easy to implement and efficient in calculation numerical examples are used to demonstrate its robustness

discontinuous conservation laws for production networks with finite buffers in this study we use discontinuous conservation laws to model production networks with finite buffers a network formulation is characterized by the interaction between several production units described by discontinuous conservation laws under the assumption that no parts are lost therefore we discuss appropriate riemann problems and coupling conditions which are derived from a regularized model to solve the discontinuous problem in an accurate and fast way we introduce a novel algorithm based on different settings the new method is compared numerically with standard approaches

sound source localization in a randomly inhomogeneous medium using matched statistical moment method this paper investigates the problem of sound source localization from acoustical measurements obtained by an array of microphones the sound propagation medium is assumed to be randomly inhomogeneous being modelled by a random function of space in this case classical source localization methods e g beamforming near field acoustical holography and time reversal cannot be used anymore therefore an approach based on the statistical moments of acoustical measurement is proposed to solve the aforementioned problem in this work a karhunen loeve expansion is used so that the random medium can be represented by a small number of uncorrelated and identically distributed random variables the statistical characteristics of the measurements in terms of probability density function and statistical moments are also studied then the sound source is localized by minimizing the error of statistical moments between the real measurements obtained from the microphone array and the measurements simulated from an assumed source finally a numerical example is introduced to justify the proposed method this experiment shows that the random field can be replicated by a very small number of random variables the statistical moments of measurements guarantee the convergence and the source location can be accurately estimated using the proposed source localization method

non reflective planar boundary condition based on gauss filter a non reflecting boundary condition based on the gauss filter is employed for the determination of scattered potential governed by the equation a filtering layer is used for closing infinite domain calculations an expression for the reflection coefficient is derived and an optimal filtering layer is designed numerical results validate the performance of this method for unbounded wave guide problems copyright 2000 john wiley sons ltd

hyperbolic conservation laws with space dependent flux i characteristics theory and riemann problem in the paper a kind of one dimensional scalar hyperbolic conservation laws with flux functions dependent on space variable is discussed and analyzed a better understanding about the behavior of wave propagation of the kind problems is presented especially some sufficient and necessary conditions that ensure the unique physically relevant solution to the riemann problem are proposed because the numerical flux obtained from the riemann s solver is theoretically correct and exact to the problem it must also be of high resolution in its nature for comparison some convincing numerical examples from traffic flow problems are given at the end of the paper

boundary element methods in three dimensional thermoelasticity abstract a boundary element method is developed for the solution of time dependent problems in three dimensional thermoelasticity the time domain boundary only formulation represents the first of its kind for quasistatic analysis which by definition considers transient heat conduction but ignores the effects of inertia by eliminating the need for volume discretization the method becomes an attractive alternative to finite element analysis for this class of problems additionally because an exact green s function is used in the interior steep thermal gradients can be captured much more readily than with standard domain based methods the presentation includes details of the fundamental solution a derivation of the boundary integral equations and an overview of a general purpose numerical implementation this implementation permits the solution of large multiregion problems with arbitrary geometry and boundary conditions several examples are included to validate the proposed method as well as to highlight its usefulness

a general framework for regularized similarity based image restoration any image can be represented as a function defined on a weighted graph in which the underlying structure of the image is encoded in kernel similarity and associated laplacian matrices in this paper we develop an iterative graph based framework for image restoration based on a new definition of the normalized graph laplacian we propose a cost function which consists of a new data fidelity term and regularization term derived from the specific definition of the normalized graph laplacian the normalizing coefficients used in the definition of the laplacian and associated regularization term are obtained using fast symmetry preserving matrix balancing this results in some desired spectral properties for the normalized laplacian such as being symmetric positive semidefinite and returning zero vector when applied to a constant image our algorithm comprises of outer and inner iterations where in each outer iteration the similarity weights are recomputed using the previous estimate and the updated objective function is minimized using inner conjugate gradient iterations this procedure improves the performance of the algorithm for image deblurring where we do not have access to a good initial estimate of the underlying image in addition the specific form of the cost function allows us to render the spectral analysis for the solutions of the corresponding linear equations in addition the proposed approach is general in the sense that we have shown its effectiveness for different restoration problems including deblurring denoising and sharpening experimental results verify the effectiveness of the proposed algorithm on both synthetic and real examples

application of the perfectly matched absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media we present and analyze a perfectly matched absorbing layer model for the velocity stress formulation of elastodynamics the principal idea of this method consists of introducing an absorbing layer in which we decompose each component of the unknown into two auxiliary components a component orthogonal to the boundary and a component parallel to it a system of equations governing these new unknowns then is constructed a damping term finally is introduced for the component orthogonal to the boundary this layer model has the property of generating no reflection at the interface between the free medium and the artificial absorbing medium in practice both the boundary condition introduced at the outer boundary of the layer and the dispersion resulting from the numerical scheme produce a small reflection which can be controlled even with very thin layers as we will show with several experiments this model gives very satisfactory results namely the reflection coefficient even in the case of heterogeneous anisotropic media is about 1 for a layer thickness of five space discretization steps

perfectly matched layers for time harmonic elastodynamics of unbounded domains theory and finite element implementation abstract one approach to the numerical solution of a wave equation on an unbounded domain uses a bounded domain surrounded by an absorbing boundary or layer that absorbs waves propagating outwards from the bounded domain a perfectly matched layer pml is an unphysical absorbing layer model for linear wave equations that absorbs almost perfectly outgoing waves of all non tangential angles of incidence and of all non zero frequencies this paper develops the pml concept for time harmonic elastodynamics in cartesian coordinates utilising insights obtained with electromagnetics pmls and presents a novel displacement based symmetric finite element implementation of the pml for time harmonic plane strain or three dimensional motion the pml concept is illustrated through the example of a one dimensional rod on elastic foundation and through the anti plane motion of a two dimensional continuum the concept is explored in detail through analytical and numerical results from a pml model of the semi infinite rod on elastic foundation and through numerical results for the anti plane motion of a semi infinite layer on a rigid base numerical results are presented for the classical soil structure interaction problems of a rigid strip footing on a i half plane ii layer on a half plane and iii layer on a rigid base the analytical and numerical results obtained for these canonical problems demonstrate the high accuracy achievable by pml models even with small bounded domains

hyperbolic phase transitions in traffic flow this paper provides a mathematical model of the phenomenon of phase transitions in traffic flow the model consists of a scalar conservation law coupled with a 2 2 system of conservation laws the coupling is achieved via a free boundary where the phase transition takes place for this model the riemann problem is stated and globally solved the cauchy problem is proved to admit a solution defined globally in time without any assumption about the smallness of the initial data or the number of phase boundaries qualitative properties of real traffic flow are shown to agree with properties of the solutions of the model

a high order spectral algorithm for elastic obstacle scattering in three dimensions in this paper we describe a high order spectral algorithm for solving the time harmonic navier equations in the exterior of a bounded obstacle in three space dimensions with dirichlet or neumann boundary conditions our approach is based on combined field boundary integral equation cfie reformulations of the navier equations we extend the spectral method developed by ganesh and hawkins 20 for solving second kind boundary integral equations in electromagnetism to linear elasticity for solving cfies that commonly involve integral operators with a strongly singular or hypersingular kernel the numerical scheme applies to boundaries which are globally parametrised by spherical coordinates the algorithm has the interesting feature that it leads to solve linear systems with substantially fewer unknowns than with other existing fast methods the computational performances of the proposed spectral algorithm are demonstrated using numerical examples for a variety of three dimensional convex and non convex smooth obstacles

the boundary integro differential equations of three dimensional neumann problem in linear elasticity in this paper we mainly consider the three dimensional neumann problem in linear elasticity which is reduced to a system of integro differential equations on the boundary based on a new representation of the derivatives of the double layer potential furthermore a new boundary finite element method for this neumann problem is presented

riemann solver for a kinematic wave traffic model with discontinuous flux we investigate a model for traffic flow based on the lighthill whitham richards model that consists of a hyperbolic conservation law with a discontinuous piecewise linear flux a mollifier is used to smooth out the discontinuity in the flux function over a small distance email protected 1 and then the analytical solution to the corresponding riemann problem is derived in the limit as e 0 for certain initial data the riemann problem can give rise to zero waves that propagate with infinite speed but have zero strength we propose a godunov type numerical scheme that avoids the otherwise severely restrictive cfl constraint that would arise from waves with infinite speed by exchanging information between local riemann problems and thereby incorporating the effects of zero waves directly into the riemann solver numerical simulations are provided to illustrate the behavior of zero waves and their impact on the solution the effectiveness of our approach is demonstrated through a careful convergence study and comparisons to computations using a third order weno scheme

two feti based heterogeneous time step coupling methods for newmark and α schemes derived from the energy method abstract the purpose of this paper is to describe a general methodology to obtain multi time step coupling methods for different time integration schemes newmark hht wbz ch on the basis of energetic considerations the general framework of the feti method is considered for building the heterogeneous time step coupling methods by ensuring the gluing of subdomains with lagrange multipliers the proposed methods for coupling subdomains with different time integration schemes and time steps fine and large time steps are based on the pseudo energy measure as introduced by hughes in the so called energy method employed for proving the stability of implicit explicit algorithms assuming a given variation of the lagrange multipliers over the large time step kinematic conditions are derived by ensuring the zero pseudo energy at the interface two methods will be derived in this paper the first new method for which the interface problem involving the lagrange multipliers is solved at the large time scale can handle the popular dissipative schemes hht wbz ch in the particular case of the newmark schemes the new method matches with the ph method proposed by prakash and hjelmstad the second new method is based at the micro time scale it can be viewed as an extension of the method proposed by gravouil and combescure gc method for the coupling of the schemes nonetheless like the gc method the new micro time based method turns out to be dissipative when non dissipative second order accurate schemes are involved and looses one order of accuracy

incorporation of attenuation into time domain computations of seismic wave fields the only numerically tractable way yet found to incorporate attenuation into numerical time domain computations of seismic wave fields is to approximate the viscoelastic modulus by a low order rational function of frequency the coefficients of this function can be determined by the pade approximation our test computations show however that this approximation generally is of poor quality therefore we suggest a new approach which is based on the rheological model of the generalized maxwell body which has a modulus of the desired rational form we choose the relaxation frequencies logarithmically equidistant in the frequency band of interest and determine the weight factors by simple numerical curve fitting to an arbitrary q law this approach is superior to the method above both in accuracy and in computational efficiency for most practical applications approximations of orders 2 or 3 are sufficient the computing time and memory requirements for a finite difference calculation are then approximately twice those of a purely elastic calculation as a first application of the method we compute sh channel waves in discontinuous coal seams with q 50 within the coal the results show that the high frequency airy phase is strongly attenuated this indicates that care has to be taken in comparing the results of purely elastic model calculations of the propagation of seam waves with experimental data

discontinuous galerkin finite element scheme for a conserved higher order traffic flow model by exploring riemann solvers the discontinuous galerkin dg scheme is used to solve a conserved higher order cho traffic flow model by exploring several riemann solvers the second order accurate dg scheme is found to be adequate in that the accuracy is comparable to the weighted essentially non oscillatory weno scheme with fifth order accuracy and much better than the scheme with first order accuracy in resolving a wide moving jam with a shock profile moreover it considerably reduces the differences between the proposed solvers in generating numerical viscosities or errors thus this scheme can maintain high efficiency when a simple solver is adopted the scheme could be extended to solve more complex problems such as those related to traffic flow in a network

the variational theory of complex rays a predictive tool for medium frequency vibrations abstract today the main numerical modeling techniques for the analysis of medium frequency vibrations are all based on finite element or boundary element approaches in order to represent small wavelength phenomena in complex structures such as car chassis satellites or ships these techniques require a huge number of degrees of freedom at least seven elements per wavelength are required to represent oscillating solutions in addition the solution obtained is highly sensitive to material properties and boundary conditions the use of high frequency approaches such as the statistical energy analysis sea or any of its improvements does not appear to be suitable for medium frequency vibrations the vibrational behavior becomes too smooth and in general the coupling loss factor cannot be calculated in a predictive way in this paper a new and multiscale approach to the calculation of the vibrations of elastic structures in the medium frequency range called the variational theory of complex rays is presented the feasibility and effectiveness of the method are demonstrated for structures made of plate assemblies several 3d examples are analyzed and compared to the results from a classical finite element approach and from a sea code this comparison shows that our method is able to predict the effective quantities at a very low numerical cost

a runge kutta discontinuous galerkin scheme for hyperbolic conservation laws with discontinuous fluxes the paper proposes a scheme by combining the runge kutta discontinuous galerkin method with a mapping algorithm for solving hyperbolic conservation laws with discontinuous fluxes this hybrid scheme is particularly applied to nonlinear elasticity in heterogeneous media and multi class traffic flow with inhomogeneous road conditions numerical examples indicate the scheme s efficiency in resolving complex waves of the two systems moreover the discussion implies that the so called mapping algorithm can also be combined with any other classical methods for solving similar problems in general

boundary infinite elements for the helmholtz equation in exterior domains a novel approach to the development of infinite element formulations for exterior problems of time harmonic acoustics is presented this approach is based on a functional which provides a general framework for domain based computation of exterior problems special cases include non reflecting boundary conditions such as the dtn method a prominent feature of this formulation is the lack of integration over the unbounded domain simplifying the task of discretization the original formulation is generalized to account for derivative discontinuities across infinite element boundaries typical of standard infinite element approximations continuity between finite elements and infinite elements is enforced weakly precluding compatibility requirements various infinite element approximations for two dimensional configurations with circular interfaces are presented implementation requirements are relatively simple numerical results demonstrate the good performance of this scheme 1998 john wiley sons ltd

on the existence and the uniqueness of the solution of a fluid structure interaction scattering problem the existence and uniqueness of the solution of a fluid structure interaction problem is investigated the proposed analysis distinguishes itself from previous studies by employing a weighted sobolev space framework the dtn operator properties and the fredholm theory the proposed approach allows to extend the range of validity of the standard existence and uniqueness results to the case where the elastic scatterer is assumed to be only lipschitz continuous which is of more practical interest

diffraction of short waves modelled using new mapped wave envelope finite and infinite elements we consider a two dimensional wave diffraction problem from a closed body such that the complex progressive wave potential satisfies the sommerfield condition and the helmholtz equation we are interested in the case where the wavelength is much smaller than any other length dimensions of the problem we introduce new mapped wave envelope infinite elements to model the potential in the far field and test them for some simple dirichlet boundary condition problems they are used in conjuction with wave envelope finite elements developed earlier 1 to model the potential in the near field an iterative procedure is used in which an initial estimate of the phase is iteratively improved the iteration scheme by which the wave envelope and phase are recovered is described in detail copyright 1999 john wiley sons ltd

hypersingular boundary integral equations for radiation and scattering of elastic waves in three dimensions abstract a weakly singular form of the hypersingular boundary integral equation bie traction equation for 3 d elastic wave problems is developed in this paper all integrals involved are at most weakly singular and except for a stronger smoothness requirement on boundary elements regular quadrature and collocation procedures used for conventional bies are sufficient for the discretization of the original hypersingular bie this weakly singular form of the hypersingular bie is applied to the composite bie formulation which uses a linear combination of the conventional bie and the hypersingular bie to remove the fictitious eigenfrequencies existing in the conventional bie formulation for elastic wave problems numerical examples employing different types of boundary elements clearly demonstrate the effectiveness and efficiency of the developed formulation

the spectral element method for elastic wave equations application to 2 d and 3 d seismic problems a spectral element method for the approximate solution of linear elastodynamic equations set in a weak form is shown to provide an efficient tool for simulating elastic wave propagation in realistic geological structures in two and three dimensional geometries the computational domain is discretized into quadrangles or hexahedra defined with respect to a reference unit domain by an invertible local mapping inside each reference element the numerical integration is based on the tensor product of a gauss lobatto legendre 1 d quadrature and the solution is expanded onto a discrete polynomial basis using lagrange interpolants as a result the mass matrix is always diagonal which drastically reduces the computational cost and allows an efficient parallel implementation absorbing boundary conditions are introduced in variational form to simulate unbounded physical domains the time discretization is based on an energy momentum conserving scheme that can be put into a classical explicit implicit predictor multicorrector format long term energy conservation and stability properties are illustrated as well as the efficiency of the absorbing conditions the accuracy of the method is shown by comparing the spectral element results to numerical solutions of some classical two dimensional problems obtained by other methods the potentiality of the method is then illustrated by studying a simple three dimensional model very accurate modelling of rayleigh wave propagation and surface diffraction is obtained at a low computational cost the method is shown to provide an efficient tool to study the diffraction of elastic waves and the large amplification of ground motion caused by three dimensional surface topographies copyright 1999 john wiley sons ltd

a simple multi directional absorbing layer method to simulate elastic wave propagation in unbounded domains the numerical analysis of elastic wave propagation in unbounded media may be difficult due to spurious waves reflected at the model artificial boundaries this point is critical for the analysis of wave propagation in heterogeneous or layered solids various techniques such as absorbing boundary conditions infinite elements or absorbing boundary layers e g perfectly matched layers lead to an important reduction of such spurious reflections in this paper a simple absorbing layer method is proposed it is based on a rayleigh caughey damping formulation which is often already available in existing finite element softwares the principle of the caughey absorbing layer method is first presented including a rheological interpretation the efficiency of the method is then shown through 1d finite element simulations considering homogeneous and heterogeneous damping in the absorbing layer 2d models are considered afterwards to assess the efficiency of the absorbing layer method for various wave types and incidences a comparison with the pml method is first performed for pure p waves and the method is shown to be reliable in a more complex 2d case involving various wave types and incidences it may thus be used for various types of problems involving elastic waves e g machine vibrations seismic waves etc copyright 2010 john wiley sons ltd

geometry consistent light field super resolution via graph based regularization light field cameras capture the 3d information in a scene with a single exposure this special feature makes light field cameras very appealing for a variety of applications from post capture refocus to depth estimation and image based rendering however light field cameras suffer by design from strong limitations in their spatial resolution off the shelf super resolution algorithms are not ideal for light field data as they do not consider its structure on the other hand the few super resolution algorithms explicitly tailored for light field data exhibit significant limitations such as the need to carry out a costly disparity estimation procedure with sub pixel precision we propose a new light field super resolution algorithm meant to address these limitations we use the complementary information in the different light field views to augment the spatial resolution of the whole light field at once in particular we show that coupling the multi view approach with a graph based regularizer which enforces the light field geometric structure permits to avoid the need of a precise and costly disparity estimation step extensive experiments show that the new algorithm compares favorably to the state of the art methods for light field super resolution both in terms of visual quality and in terms of reconstruction error

on non reflecting boundary conditions in unbounded elastic solids problems in unbounded domains can be solved using domain based computation by introducing an artificial boundary and then selecting appropriate boundary conditions the dtn method which specifies such boundary conditions is investigated in this work for wave problems in elastic solids the dtn method defines an exact relation between the displacement field and its normal and tangential tractions on an artificial boundary this relation is expressed in terms of an infinite series the dtn boundary conditions are shown to be non reflective thus uniqueness of the solution is guaranteed for practical purposes the full dtn operator is truncated the truncated dtn operator fails to completely inhibit reflections of higher modes resulting in loss of uniqueness at characteristic wave numbers of higher harmonics guidelines for determining a sufficient number of terms in the truncated operator to retain uniqueness of the solution at any given wave number are derived the validity of these guidelines is examined and verified by numerical examples local dtn boundary conditions are also investigated and it is shown that local boundary conditions guarantee uniqueness of the solution for all wave numbers regardless of the number of terms in the operator this property is used here to modify the truncated dtn operator and to enhance its capability to retain uniqueness of solutions a modified dtn operator combining the truncated operator with the local one is introduced the modified dtn operator is shown to retain uniqueness of solutions regardless of the number of terms and regardless of the wave number

time harmonic elasticity with controllability and higher order discretization methods the time harmonic solution of the linear elastic wave equation is needed for a variety of applications the typical procedure for solving the time harmonic elastic wave equation leads to difficulties solving large scale indefinite linear systems to avoid these difficulties we consider the original time dependent equation with a method based on an exact controllability formulation the main idea of this approach is to find initial conditions such that after one time period the solution and its time derivative coincide with the initial conditions the wave equation is discretized in the space domain with spectral elements the degrees of freedom associated with the basis functions are situated at the gauss lobatto quadrature points of the elements and the gauss lobatto quadrature rule is used so that the mass matrix becomes diagonal this method is combined with the second order central finite difference or the fourth order runge kutta time discretization as a consequence of these choices only matrix vector products are needed in time dependent simulation this makes the controllability method computationally efficient

image super resolution via sparse representation this paper presents a new approach to single image superresolution based upon sparse signal representation research on image statistics suggests that image patches can be well represented as a sparse linear combination of elements from an appropriately chosen over complete dictionary inspired by this observation we seek a sparse representation for each patch of the low resolution input and then use the coefficients of this representation to generate the high resolution output theoretical results from compressed sensing suggest that under mild conditions the sparse representation can be correctly recovered from the downsampled signals by jointly training two dictionaries for the low and high resolution image patches we can enforce the similarity of sparse representations between the low resolution and high resolution image patch pair with respect to their own dictionaries therefore the sparse representation of a low resolution image patch can be applied with the high resolution image patch dictionary to generate a high resolution image patch the learned dictionary pair is a more compact representation of the patch pairs compared to previous approaches which simply sample a large amount of image patch pairs reducing the computational cost substantially the effectiveness of such a sparsity prior is demonstrated for both general image super resolution sr and the special case of face hallucination in both cases our algorithm generates high resolution images that are competitive or even superior in quality to images produced by other similar sr methods in addition the local sparse modeling of our approach is naturally robust to noise and therefore the proposed algorithm can handle sr with noisy inputs in a more unified framework

h adaptive finite element computation of time harmonic exterior acoustics problems in two dimensions abstract in this paper we carry out adaptive finite element computations of the helmholtz equation in two dimensions in the context of time harmonic exterior acoustics the purpose is to demonstrate potentially significant cost savings engendered through adaptivity for propagating solutions at moderate wave numbers ka 2 4 the computations are performed on meshes of linear triangles and are adapted to the solution by locally changing element sizes h refinement the adaptive procedure involves applying an explicit residual based a posteriori error estimator and an h adaptive strategy which were derived in a previous paper the adaptive meshes are then obtained through global mesh regeneration using an advancing front mesh generator two different finite element formulations are considered the galerkin and galerkin least squares gls methods the infinite physical domain is truncated by an artificial exterior boundary on which a fully coupled dirichlet to neumann dtn boundary condition is applied two different problems are computed plane wave scattering by a rigid infinite surface circular and square cross sections and nonuniform radiation from an infinite circular cylinder detailed cost studies with respect to an active column direct solver are performed for the nonuniform radiation problem the adaptive mesh is twenty times more cost effective than a uniform mesh for galerkin when coupled with the gls formulation the adaptive mesh is forty times more efficient than galerkin computations on a uniform mesh

boundary integral equation methods for the two dimensional fluid solid interaction problem this paper is concerned with boundary integral equation methods for solving the two dimensional fluid solid interaction problem we reduce the problem to three different systems of boundary integral equations via direct and indirect approaches existence and uniqueness results for variational solutions of boundary integral equations are established since in all these variational formulations the hypersingular boundary integral operator associated with the time harmonic navier equation is a dominating integral operator we also include a new regularization formulation for this hypersingular operator which allows us to treat the hypersingular kernel by a weakly singular kernel numerical examples are presented to verify and validate the theoretical results

calculation of medium frequency vibrations over a wide frequency range abstract an enhancement of the variational theory of complex rays vtcr is being developed in order to calculate the vibrations of slightly damped elastic structures in the medium frequency range here the emphasis is put on the extension of this theory to the analysis over a wide frequency range the solution is sought in the form of an original decomposition the mean value and its complementary part over the frequency range numerical examples show the capability of the vtcr to predict the vibrational response of a structure in a frequency range

multilevel fast multipole algorithm for elastic wave scattering by large three dimensional objects multilevel fast multipole algorithm mlfma is developed for solving elastic wave scattering by large three dimensional 3d objects since the governing set of boundary integral equations bie for the problem includes both compressional and shear waves with different wave numbers in one medium the double tree structure for each medium is used in the mlfma implementation when both the object and surrounding media are elastic four wave numbers in total and thus four fma trees are involved we employ nystrom method to discretize the bie and generate the corresponding matrix equation the mlfma is used to accelerate the solution process by reducing the complexity of matrix vector product from o n 2 to o nlogn in iterative solvers the multiple tree structure differs from the single tree frame in electromagnetics em and acoustics and greatly complicates the mlfma implementation due to the different definitions for well separated groups in different fma trees our nystrom method has made use of the cancellation of leading terms in the series expansion of integral kernels to handle hyper singularities in near terms this feature is kept in the mlfma by seeking the common near patches in different fma trees and treating the involved near terms synergistically due to the high cost of the multiple tree structure our numerical examples show that we can only solve the elastic wave scattering problems with 0 3 0 4 millions of unknowns on our dell precision 690 workstation using one core

studies of fe pml for exterior problems of time harmonic elastic waves the equation of an absorbing layer for time harmonic elastic waves based on the perfectly matched layer pml concept is formulated in a manner that is easily implemented in finite element software in the proposed approach the layer is viewed as an anisotropic material with continuously varying complex material properties the effect of the pml parameters on its discrete representation is investigated through dispersion analysis guidelines for proper selection of the pml parameters are presented the formulation with the parameters selected according to the guidelines proposed performs well in computation