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

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

improved conditioning of infinite elements for exterior acoustics an optimized version of the so called mapped wave envelope elements also known as astley leis elements is introduced these elements extend to infinity in one dimension and therefore provide an approach to the simulation of exterior acoustical problems in both frequency and time domains their formulation is improved significantly through the proper choice of polynomial bases in the direction of radiation in particular certain jacobi polynomials are identified which behave well with respect to conditioning of the system matrices as a consequence the size of the finite element discretization may reduce considerably without any loss of accuracy in addition the new polynomial bases lead to superior performance of the infinite elements in conjunction with iterative solvers

a comparison of approximate boundary conditions and infinite element methods for exterior helmholtz problems we compare the accuracy of a variety of approximate boundary conditions abcs and two versions of an infinite element method iem for approximating solutions of exterior helmholtz problems the infinite elements are of variable order in the radial direction and differ only in whether the test functions in the weak formulation are conjugated or not we find that the accuracy of the abcs decreases with increasing frequency and that at higher frequencies their accuracy is several orders of magnitude lower than that obtained with the iems we show that the convergence rate of the conjugated element is slower than the rate for the unconjugated element and that the latter element fails to converge in the far field

some theorems on reverse inequalities application de la theorie de la programmation dynamique pour formuler des theoremes sur les inegalites inverses

convergence of the infinite element methods for the helmholtz equation in separable domains to the best knowledge of the authors this work presents the first convergence analysis for the infinite element method iem for the helmholtz equation in exterior domains the approximation applies to separable geometries only combining an arbitrary finite element fe discretization on the boundary of the domain with a spectral like approximation in the radial direction with shape functions resulting from the separation of variables the principal idea of the presented analysis is based on the spectral decomposition of the problem

further results on the optimality of the likelihood ratio test for local sensor decision rules in the presence of nonideal channels in this paper we consider the design of local decision rules for distributed detection systems where decisions from peripheral detectors are transmitted over dependent nonideal channels under the conditional independence assumption among multiple sensor observations we show that the optimal detection performance can be achieved by employing likelihood ratio quantizers lrq as local decision rules under both the bayesian criterion and neyman pearson np criterion even for the cases where the channels between the fusion center and local sensors are dependent and noisy this work generalizes the previous work where independence among such channels was assumed a person by person optimization pbpo procedure to obtain the solution is presented along with an illustrative example

diffraction from simple shapes by a hybrid asymptotic finite element method the application of a hybrid asymptotic finite element method to the problem of scattering from two dimensional submerged objects is considered the hybrid method is based on patching a short wavelength asymptotic expansion of the scattered field to a finite element interpolation of the near field in patching the diffracted field shape functions with unknown amplitude are forced to agree smoothly with the solution in the near field along a curve at a prescribed distance from the diffraction points a new hybrid finite element on this artificial boundary represents the effect of the outer domain on the solution within this new boundary this allows the replacement of the original boundary value problem with an asymptotically equivalent boundary value problem the domain of which is small and efficiently discretized the method is applied to diffraction by a blunted wedge which in this context represents a degenerate prism the hybrid scattering solution shall be compared to an analytic field representat

wave envelope examples for progressive waves the wave envelope method due to astley 1 is applied to some simple propagating wave problems governed by the helmholtz equation and similar equations it is shown that the method yields solutions which for some of the problems are exact and for the others are approximate and complex in these cases however when the number of elements is increased the trial function becomes a better approximation

the stability of infinite element schemes for transient wave problems the transformation of conjugated infinite elements from the frequency domain to the time domain is described this procedure yields discrete numerical models for transient acoustics which are local in space and time these can be integrated in time to solve unsteady problems of radiation or scattering in infinite domains provided that the discrete equations themselves are stable with time the conditions under which this is true are investigated in this article a numerical study is presented which shows that the stability of the numerical scheme depends critically upon the form of the inner surface of the infinite element domain solutions for test problems are presented to demonstrate that such criteria also apply when the equations are discretised in time and that stable solutions can be obtained using implicit time integration schemes when simple criteria are correctly applied axisymmetric spherical and spheroidal formulations are considered

plane wave interpolation in direct collocation boundary element method for radiation and wave scattering numerical aspects and applications the classical boundary element formulation for the helmholtz equation is rehearsed and its limitations with respect to the number of variables needed to model a wavelength are explained a new type of interpolation for the potential is then described in which the usual boundary element shape functions are modified by the inclusion of a set of plane waves propagating in a range of directions this is termed the plane wave basis boundary element method the modifications needed to the classical procedures in terms of integration of the element matrices and location of collocation points are described the well known singular value decomposition solution technique which is adopted here for the solution of the system matrix equation in its complex form is briefly outlined the conditioning of the system matrix is analysed for a simple radiation problem the corresponding diffraction problem is also analysed and results are compared with analytical and classical boundary element solutions the chief method is adopted to enhance the quality of the solution particularly in the vicinity of irregular frequencies the plane wave basis boundary element method is then applied to two problems scattering of plane waves by an elliptical cylinder and the multiple circular cylinder plane wave scattering problem in both cases results are compared with analytical solutions the results clearly demonstrate that the new method is considerably more efficient than the classical approach for a given number of degrees of freedom the frequency for which accurate results can be obtained using the new technique can be up to three or four times higher than that of the classical method this makes the method a powerful new addition to our tools for tackling high frequency radiation and scattering problems

dynamic programming and inequalities one applies the theory of inequalities to solve mathematical programming problems in association with the method of lagrange parameters and the dynamic programming approach one calls it an integrated method in contrast to the traditional calculus method this is the motivation of this paper

a mesh free method for static and free vibration analyses of thin plates of complicated shape a mesh free method is presented to analyze the static deflection and the natural frequencies of thin plates of complicated shape the present method uses moving least squares mls interpolation to construct shape functions based on a set of nodes arbitrarily distributed in the analysis domain discrete system equations are derived from the variational form of system equation for static analysis a penalty method is presented to enforce the essential boundary conditions for frequency analysis of free vibration the essential boundary conditions are represented through a weak form and imposed using orthogonal transformation techniques the present efg method together with techniques for imposing boundary conditions is coded in fortran numerical examples are presented for rectangular elliptical polygonal and complicated plates to demonstrate the convergence and efficiency of the present method

on the optimality of the likelihood ratio test for local sensor decision rules in the presence of nonideal channels distributed detection has been intensively studied in the past in this correspondence we consider the design of local decision rules in the presence of nonideal transmission channels between the sensors and the fusion center under the conditional independence assumption among multiple sensor observations we show that the optimal local decisions that minimize the error probability at the fusion center amount to a likelihood ratio test lrt given a particular constraint on the fusion rule this constraint turns out to be quite general and is easily satisfied for most sensible fusion rules a design example using a parallel sensor fusion structure with binary symmetric channels bscs between local sensors and the fusion center is given to illustrate the usefulness of the result in obtaining optimal thresholds for local sensor observations the study that incorporates the transmission channel in the sensor system design may have potential applications in the emerging field of wireless sensor networks

a conjugated infinite element method for half space acoustic problems many acoustic problems especially in environmental acoustics involve half space domains bounded by a plane subjected to normal admittance boundary conditions in the low frequency domain the numerical treatment of such problems usually relies on boundary element methods based on a particular green s function suited for the half admittance plane in the present paper an alternative hybrid finite infinite element scheme is proposed the method relies on a direct treatment of nonhomogeneous boundary conditions along infinite element edges or faces the procedure is validated through comparisons with an available reference solution

coupled fixed points for mixed monotone condensing operators and an existence theorem of the solutions for a class of functional equations arising in dynamic programming abstract in this paper the existence and iterative approximation of coupled fixed points for mixed monotone condensing set valued operators are discussed the results presented here extend and improve the corresponding results of d guo and v lakshmikantham coupled fixed points of nonlinear operators 1 2 as an application we utilize the results obtained in section 2 to study the existence problem of solutions for a class of functional equations arising in dynamic programming

a new framework for distributed detection with conditionally dependent observations distributed detection with conditionally dependent observations is known to be a challenging problem in decentralized inference this paper attempts to make progress on this problem by proposing a new framework for distributed detection that builds on a hierarchical conditional independence model through the introduction of a hidden variable that induces conditional independence among the sensor observations the proposed model unifies distributed detection with dependent or independent observations this new framework allows us to identify several classes of distributed detection problems with dependent observations whose optimal decision rules resemble the ones for the independent case the new framework induces a decoupling effect on the forms of the optimal local decision rules for these problems much in the same way as the conditionally independent case this is in sharp contrast to the general dependent case where the coupling of the forms of local sensor decision rules often renders the problem intractable such decoupling enables the use of for example the person by person optimization approach to find optimal local decision rules two classical examples in distributed detection with dependent observations are reexamined under this new framework detection of a deterministic signal in dependent noises and detection of a random signal in independent noises

a variable order infinite acoustic wave envelope element abstract a new infinite wave envelope element for analyzing acoustic radiation and scattering problems in an unbounded domain is presented the element is based on a finite to infinite geometry mapping and a wave representation within the shape function it allows for the specification of an arbitrary number of acoustic degrees of freedom in the radial infinite direction yielding a 1 r expansion for the proper modelling of the amplitude decay both two dimensional and axisymmetric problems are presented to show the use and accuracy of this n th order infinite wave envelope element numerical results are compared with analytical and boundary element solutions

element free galerkin method for wave propagation and dynamic fracture abstract element free galerkin method efg is extended to dynamic problems efg method which is based on moving least square interpolants mls requires only nodal data no element connectivity is needed this makes the method particularly attractive for moving dynamic crack problems since remeshing can be avoided in contrast to the earlier formulation for static problems by authors the weak form of kinematic boundary conditions for dynamic problems is introduced in the implementation to enforce the kinematic boundary conditions with this formulation the stiffness matrix is symmetric and positive semi definite and hence the consistency conergence and stability analyses of time integration remain the same as those in finite element method numerical examples are presented to illustrate the performance of this method the relationship between the element free galerkin method and the smooth particle hydrodynamics sph method is also discussed in this paper results are presented for some one dimensional problems and two dimensional problems with static and moving cracks

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

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

the principle and models of dynamic programming v in this article we introduce two new concepts namely dynamic geometry and dynamic pattern the former can be further developed in conjunction with computer graphics while the latter can be further developed in conjunction with the concept of dp in the sense of zelkowitz et al

optimized meshfree methods for acoustics abstract when the helmholtz equation is solved by numerical methods as e g the finite element method fem the solution suffers from the so called pollution effect the pollution is mainly caused by the dispersion meaning that the numerical wave number disagrees with the wave number of the exact solution this leads to inaccurate results especially for high wave numbers in order to obtain acceptable results also for higher wave numbers either a high element resolution or elements of a higher order can be used for either option the consequence is an increased computation time and memory capacity meshfree methods as the element free galerkin method efgm and the radial point interpolation method rpim are not dispersion free either but it has been shown that meshfree methods are able to reduce the dispersion significantly both methods offer several parameters which can be modified in order to obtain optimal results with respect to the dispersion effect this work presents an exhaustive parameter study on both the efgm and the rpim it is shown that the methods can be significantly improved if certain parameters as e g weighting functions shape parameters size of the influence domain are chosen appropriately

a survey of finite element methods for time harmonic acoustics many of the current issues and methodologies related to finite element methods for time harmonic acoustics are reviewed the effective treatment of unbounded domains is a major challenge most prominent among the approaches that have been developed for this purpose are absorbing boundary conditions infinite elements and absorbing layers standard computational methods are unable to cope with wave phenomena at short wave lengths due to resolutions required to control dispersion and pollution errors leading to prohibitive computational demands since computation naturally separates the scales of a problem according to the mesh size multiscale considerations provide a useful framework for viewing these difficulties and developing methods to counter them other issues addressed are related to the efficient solution of systems of specialized algebraic equations and inverse problems of acoustics the tremendous progress that has been made in all of the above areas in recent years will surely continue leading to many more exciting developments

surfaces generated by moving least squares methods an analysis of moving least squares m l s methods for smoothing and interpolating scattered data is presented in particular theorems are proved concerning the smoothness of interpolants and the description of m l s processes as projection methods some properties of compositions of the m l s projector with projectors associated with finiteelement schemes are also considered the analysis is accompanied by examples of univariate and bivariate problems

quickest search over multiple sequences the problem of sequentially finding an independent and identically distributed sequence that is drawn from a probability distribution q1 by searching over multiple sequences some of which are drawn from q1 and the others of which are drawn from a different distribution q0 is considered in the problem considered the number of sequences with distribution q1 is assumed to be a random variable whose value is unknown within a bayesian formulation a sequential decision rule is derived that optimizes a trade off between the probability of false alarm and the number of samples needed for the decision in the case in which one can observe one sequence at a time it is shown that the cumulative sum cusum test which is well known to be optimal for a non bayesian statistical change point detection formulation is optimal for the problem under study specifically the cusum test is run on the first sequence if a reset event occurs in the cusum test then the sequence under examination is abandoned and the rule switches to the next sequence if the cusum test stops then the rule declares that the sequence under examination when the test stops is generated by q1 the result is derived by assuming that there are infinitely many sequences so that a sequence that has been examined once is not retested if there are finitely many sequences the result is also valid under a memorylessness condition expressions for the performance of the optimal sequential decision rule are also developed the general case in which multiple sequences can be examined simultaneously is considered the optimal solution for this general scenario is derived

solution of 3d laplace and helmholtz equations in exterior domains using hp infinite elements abstract this work is devoted to a convergence study for infinite element discretizations for laplace and helmholtz equations in exterior domains the proposed approximation applies to separable geometries only combining an hp fe discretization on the boundary of the domain with a spectral like representation resulting from the separation of variables in the radial direction the presentation includes a convergence proof for the laplace equation and a stability analysis for the variational formulation of the helmholtz equation in weighted sobolev spaces the theoretical investigations are verified and illustrated with numerical examples for the exterior spherical domain

continuous dynamic programming approach to inequalities ii where p and q represent the state and decision vectors respectively t represents the transformation of the process and f p represents the optimal return function with initial state p here opt denotes max or min basically using suitable functional equations of the form l lwamoto 9 io established a class of classical discrete inequalities by he dp approach while wang 16 181 established them by the functional equation approach e g see related references in 133 for a more detailed account very recently lwamoto and wang 133 established the holder

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

element free galerkin methods for static and dynamic fracture abstract element free galerkin efg methods are presented and applied to static and dynamic fracture problems efg methods which are based on moving least square mls interpolants require only nodal data no element connectivity is needed the description of the geometry and numerical model of the problem consists only of a set of nodes and a description of exterior boundaries and interior boundaries from any cracks this makes the method particularly attractive for growing crack problems since only minimal remeshing is needed to follow crack growth in moving least square interpolants the dependent variable at any point is obtained by minimizing a function in terms of the nodal values of the dependent variable in the domain of influence of the point numerical examples involving fatigue crack growth and dynamic crack propagation are presented to illustrate the performance and potential of this method

non reflecting boundary conditions for acoustic propagation in ducts with acoustic treatment and mean flow we consider a time harmonic acoustic scattering problem in a 2d infinite waveguide with walls covered with an absorbing material in the presence of a mean flow assumed uniform far from the source to make this problem suitable for a finite element analysis the infinite domain is truncated this paper concerns the derivation of a non reflecting boundary condition on the artificial boundary by means of a dirichlet to neumann dtn map based on a modal decomposition compared with the hard walled guide case several difficulties are raised by the presence of both the liner and the mean flow in particular acoustic modes are no longer orthogonal and behave asymptotically like the modes of a soft walled guide however an accurate approximation of the dtn map can be derived using some bi orthogonality relations valid asymptotically for high order modes numerical validations show the efficiency of the method the influence of the liner with or without mean flow is illustrated

existence theorems of solutions for certain classes of functional equations arising in dynamic programming in this paper we study the existence uniqueness and iterative approximation of solutions for certain classes of functional equations arising in dynamic programming of multistage decision processes the results presented here generalize improve and unify the corresponding results of other authors

modelling of short wave diffraction problems using approximating systems of plane waves this paper describes a finite element model for the solution of helmholtz problems at higher frequencies that offers the possibility of computing many wavelengths in a single finite element the approach is based on partition of unity isoparametric elements at each finite element node the potential is expanded in a discrete series of planar waves each propagating at a specified angle these angles can be uniformly distributed or may be carefully chosen they can also be the same for all nodes of the studied mesh or may vary from one node to another the implemented approach is used to solve a few practical problems such as the diffraction of plane waves by cylinders and spheres the wave number is increased and the mesh remains unchanged until a single finite element contains many wavelengths in each spatial direction and therefore the dimension of the whole problem is greatly reduced issues related to the integration and the conditioning are also discussed

acoustic infinite elements for non separable geometries we present new infinite element formulations for solving acoustic scattering and radiation problems in the exterior of long slender bodies the new infinite elements are geometrically constructed from a prolate spheroid inscribed by the scatterer these elements need not begin on a level surface of the prolate spheroidal coordinate system instead they may be attached to any convex surface including that of the scatterer itself this scheme reduces or even completely eliminates finite element modeling of the exterior medium the formulations may easily be extended to the cases of an interior oblate spheroid or ellipsoid we present both conjugated and unconjugated formulations without any weighting factors although it would be simple to include them we describe a fast numerical scheme for computing the element integrals based on chebychev approximation we include numerical results for scattering from spheres and capped cylinders these results demonstrate the accuracy and the dramatic reduction in computational expense of our new formulations compared to other coupled finite element infinite element methods

the conjugated vs the unconjugated infinite element method for the helmholtz equation in exterior domains abstract this work is devoted to a convergence study of infinite element ie discretizations for the helmholtz equation in exterior domains the different behavior of the conjugated and the unconjugated ie formulation is analyzed in context of 1 1 a formulation following a mathematical existence theory by leis 2 2 a formulation not based on an available existence theory following burnett four variational formulations are presented and the differences in implementing them are discussed the effect of using or not using the complex conjugate in the weak formulation is carefully studied the numerical and theoretical results clearly indicate which of the four presented formulations is the most efficient that can still give reliable results

an infinite element for maxwell s equations a new infinite element ie approximation for steady state maxwell s equations is proposed the ie is compatible with a new class of hp finite element fe discretizations presented in 13 32 following 12 a convergence analysis for the proposed coupled fe ie approximations is presented

a few new facts about infinite elements we discuss the conjugated bubnov galerkin and petrov galerkin infinite element ie discretizations to helmholtz equation including the use of elements of locally variable order optimal choice of ie shape functions calculation of echo area ea and automatic hp adaptivity the discussion is illustrated with 2d numerical experiments

three dimensional wave envelope elements of variable order for acoustic radiation and scattering part i formulation in the frequency domain a variable order infinite wave envelope element scheme is formulated for transient unbounded acoustical problems the transient formulation which is local in space and time is obtained by applying an inverse fourier transformation to a time harmonic wave envelope model whose formulation is described in a companion article this procedure yields a coupled system of second order differential equations which can be integrated in time to yield transient pressure histories at discrete nodal points far field transient pressures can also be obtained at adjusted times the method can be applied quite generally to two dimensional and three dimensional problems and is compatible with a conventional finite element model in the near field the utility of the method is confirmed by the presentation of transient solutions for axisymmetric and fully three dimensional test problems an implicit time integration scheme is used and computed results are compared to analytic solutions and to solutions obtained from alternative numerical schemes close correspondence is demonstrated and the scheme is shown to be stable for the problems which are presented cpu times for a large three dimensional problem are shown to compare favorably with those required for an equivalent transient boundary element computation

an hp adaptive finite element method for electromagnetics part 3 a three dimensional infinite element for maxwell s equations this paper is a continuation of reference 26 cecot demkowicz and rachowicz computer methods in applied mechanics and engineering 2000 188 625 643 and describes an implementation of the infinite element for three dimensional time harmonic maxwell s equations proposed in reference 15 demkowicz and pal computer methods in applied mechanics and engineering 1998 164 77 94 the element is compatible with the hp finite element discretizations for maxwell s equations in bounded domains reported in references 16 18 computer methods in applied mechanics and engineering 1998 152 103 124 1999 169 331 344 2000 187 307 337 copyright 2003 john wiley sons ltd

the performance of spheroidal infinite elements a number of spheroidal and ellipsoidal infinite elements have been proposed for the solution of unbounded wave problems in the frequency domain i e solutions of the helmholtz equation these elements are widely believed to be more effective than conventional spherical infinite elements in cases where the radiating or scattering object is slender or flat and can therefore be closely enclosed by a spheroidal or an ellipsoidal surface the validity of this statement is investigated in the current article the radial order which is required for an accurate solution is shown to depend strongly not only upon the type of element that is used but also on the aspect ratio of the bounding spheroid and the non dimensional wave number the nature of this dependence can partially be explained by comparing the non oscillatory component of simple source solutions to the terms available in the trial solution of spheroidal elements numerical studies are also presented to demonstrate the rates at which convergence can be achieved in practice by unconjugated burnett and conjugated astley leis type elements it will be shown that neither formulation is entirely satisfactory at high frequencies and high aspect ratios

a new partition of unity finite element free from the linear dependence problem and possessing the delta property partition of unity based finite element methods pufems have appealing capabilities for p adaptivity and local refinement with minimal or even no remeshing of the problem domain however pufems suffer from a number of problems that practically limit their application namely the linear dependence ld problem which leads to a singular global stiffness matrix and the difficulty with which essential boundary conditions can be imposed due to the lack of the kronecker delta property in this paper we develop a new pu based triangular element using a dual local approximation scheme by treating boundary and interior nodes separately the present method is free from the ld problem and essential boundary conditions can be applied directly as in the fem the formulation uses triangular elements however the essential idea is readily extendable to other types of meshed or meshless formulation based on a pu approximation the computational cost of the present method is comparable to other pufem elements described in the literature the proposed method can be simply understood as a pufem with composite shape functions possessing the delta property and appropriate compatibility

a new mapped infinite wave element for general wave diffraction problems and its validation on the ellipse diffraction problem the theory for an improved infinite element for wave diffraction is presented the improvement is on the original wave element presented by bettess zienkiewicz and others the modification involves the introduction of one extra term in the original shape function derivatives and a change in the numerical integration sequence the modification enables the element to be used with elliptical and other non circular meshes similar mappings have already been used with wave envelope infinite elements by astley and others as a test of the element accurate results are demonstrated for a range of elliptical cylinder diffraction problems the element has not yet been tested for other non circular problems

beckenbach inequality and its variants on montre que deux theoremes sur l inegalite de beckenbach peuvent s obtenir de facon unifiee par une utilisation directe de l inegalite de holder usuelle

the ill conditioning of infinite element stiffness matrices abstract in this paper a method for improving the conditioning of infinite element stiffness matrices is proposed and examined for one dimensional and two dimensional infinite elements this method is a preconditioning technique which is based on a gram schmidt like transformation induced by general sesquilinear forms although the preconditioning method can be applied to many types of infinite elements it will be applied to improve the conditioning of the popular multipole infinite element the paper is concluded with numerical examples demonstrating improved conditioning and convergence properties of the preconditioned multipole infinite elements

dynamic programming and the lagrange multipliers one considers a problem so that a detailed comparison of the dynamic programming dp technique and the method of lagrange parameters lps can be given one demonstrates that the dp technique is far superior to the method of lps

a two dimensional infinite element for maxwell s equations abstract the paper describes an implementation of the infinite element for two dimensional steady state maxwell s equations proposed by l demkowicz and m pal comput meth appl mech engrg in press the element is compatible with the hp fe element discretizations for maxwell s equations in bounded domains reported in l demkowicz and l vardapetyan comput meth appl mech engrg 152 1 2 1996 103 124 and w rachowicz and l demkowicz comput meth appl mech engrg in press

a trefftz based numerical modelling framework for helmholtz problems with complex multiple scatterer configurations the aim of the work presented in this paper is the numerical solution of low and mid frequency time harmonic acoustic multiple scattering problem a novel so called multi level modelling approach is proposed which is applicable to the study of a configuration of well separated obstacles of arbitrary shape on which any type of acoustic boundary condition can be applied the generic character of the method is obtained by embedding the superposition principle for the multiple scattering influence in a state of the art acoustic modelling technique the so called wave based method the resulting approach successfully alleviates the geometrical limitations of the underlying trefftz based method and preserves the method s computational efficiency resulting in a generic multiple scattering modelling framework with a superior computational efficiency in the low as well as the mid frequency range several numerical validation examples show that the proposed approach is as accurate as the classical single scattering wave based method and illustrate the computational efficiency as compared to boundary element methods

a finite element alternative to infinite elements abstract in this paper a simple idea based on midpoint integration rule is utilized to solve a particular class of mechanics problems namely static problems defined on unbounded domains where the solution is required to be accurate only in an interior and not in the far field by developing a finite element mesh that approximates the stiffness of an unbounded domain directly without approximating the far field displacement profile first the current formulation provides a superior alternative to infinite elements ies that have long been used to incorporate unbounded domains into the finite element method fem in contrast to most ies the present formulation a requires no new shape functions or special integration rules b is proved to be both accurate and efficient and c is versatile enough to handle a large variety of domains including those with anisotropic stratified media and convex polygonal corners in addition to this the proposed model leads to the derivation of a simple error expression that provides an explicit correlation between the mesh parameters and the accuracy achieved this error expression can be used to calculate the accuracy of a given mesh a priori this in turn allows one to generate the most efficient mesh capable of achieving a desired accuracy by solving a mesh optimization problem we formulate such an optimization problem solve it and use the results to develop a practical mesh generation methodology this methodology does not require any additional computation on the part of the user and can hence be used in practical situations to quickly generate an efficient and near optimal finite element mesh that models an unbounded domain to the required accuracy numerical examples involving practical problems are presented at the end to illustrate the effectiveness of this method

a summary of infinite element formulations for exterior helmholtz problems this work is devoted to a study and summary of different infinite element ie formulations for helmholtz problems in arbitrary exterior domains the theoretical setting for each of the different formulations is presented and related to the mathematical existence theory the influence of a bilinear or a sesquilinear formulation is discussed as well as possible extensions to other elements the implementation of the infinite element method iem incorporates the use of 2d and 3d hp finite elements and allows for hp adaptive refinements numerical results show the computational efficiency of the coupled finite infinite element methodology

mapped wave envelope elements for acoustical radiation and scattering wave envelope elements provide an alternative to boundary element methods for the solution of exterior wave problems applications to date have been to axisymmetric geometries and have involved the use of large but finite wave envelope meshes compatibly matched to denser near field meshes of conventional elements in the present paper the wave envelope idea is extended by the inclusion of an element mapping taken directly from infinite element methodology and by modifications to the residual formulation taken in conjunction these two measures permit the outer boundary of the wave envelope region to be moved to infinity while preserving the boundedness of the acoustic mass and stiffness integrals the present formulation is developed initially with reference to a simple one dimensional model and is then applied in two and three dimensions comparisons between computed results and those obtained from analytic solutions where applicable and from boundary element codes demonstrate the effectiveness of the method

dynamic programming and penalty functions one manipulates the optimization problems with a constraint or constraints related to three basic inequalities the arithmetic and geometric inequality the holder inequality and the minkowski inequality one reveales notably the versatility adaptability and flexibility of the dynamic programming technique in conjunction with the method of penalty functions

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

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 two dimensional infinite elements utilizing basis functions with compact support in this paper improvements are made in the numerical conditioning of infinite element stiffness matrices by replacing the characteristic eigenfunction basis functions which have global support with basis functions which have local support and appropriate preconditioning the conditioning and convergence properties of these new infinite elements are presented in solving two dimensional exterior problems for the helmholtz equation

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

element free method for static and free vibration analysis of spatial thin shell structures the implementation of the element free galerkin method efg for spatial thin shell structures is presented in this paper both static deformation and free vibration analyses are considered the formulation of the discrete system equations starts from the governing equations of stress resultant geometrically exact theory of shear flexible shells moving least squares approximation is used in both the construction of shape functions based on arbitrarily distributed nodes as well as in the surface approximation of general spatial shell geometry discrete system equations are obtained by incorporating these interpolations into the galerkin weak form the formulation is verified through numerical examples of static stress analysis and frequency analysis of spatial thin shell structures for static load analysis essential boundary conditions are enforced through penalty method and lagrange multipliers while boundary conditions for frequency analysis are imposed through a weak form using orthogonal transformation techniques the efg results compare favorably with closed form solutions and that of finite element analyses

three dimensional infinite elements utilizing basis functions with compact support abstract in this paper improvements are made in the numerical conditioning of three dimensional infinite element stiffness matrices by replacing the characteristic eigenfunction basis functions which have global support with basis functions which have local support and appropriate preconditioning the conditioning and convergence properties of these new infinite elements are presented in solving three dimensional exterior problems for the helmholtz equation

characteristics of nonlinear positive functionals and their applications in 1966 1967 beckenbach 3 4 extended among other things the holder and minkowski inequalities by a method of the differentiability of multivariable real functions in 1979 wang 21 established the a g arithmetic geometric holder minkowski and beckenbach inequalities by means of the convexity of multivariable real functions however their results dealt with only the discrete case of the inequalities in the development of the theory of inequalities the discrete and continuous cases of the inequalities have always been examined hand in hand see beckenbach and bellman s hardy littlewood and polya 111 iwamoto and wang 131 and mitrinovic 16 this examination has concerned not only the forms of the inequalities but also the methods used to establish them e g see iwamoto and wang 131 for this reason we investigate here the continuous counterparts of the works of beckenbach and wang mentioned above indeed the set of classical inequalities for integrals has been established by various other methods e g see s 11 13 161 as well it is evident that the forms of inequalities for integrals can be regarded as nonlinear functionals see 7 14 191 on the other hand in the study of nonlinear operators and or functionals the differentiability of operators has been intensively and successfuly used to provide approximate solutions for nonlinear functional equations e g see 7 14 19 while their convexity has been used in a somewhat restricted manner see collatz 7 334 341 i although the differentiability and convexity of nonlinear functionals have attracted considerable attention of many investigators see 7 9 14 15 17 19 it seems to have escaped notice that they can be employed to establish the

element free galerkin solutions for helmholtz problems fomulation and numerical assessment of the pollution effect abstract the element free galerkin method efgm a particular case of the meshless methods is examined in its application to acoustic wave propagation addressed by the helmholtz equation dispersion and pollution effects two problems encountered by the classical numerical methods are reviewed numerical tests on two dimensional problems focus on the parameters governing the formulation of the efgm they also demonstrate that the efgm is affected by dispersion and pollution effects as well as fem but these effects are rather low showing that the efgm is a promising method

on an inequality of ky fan on presente deux nouvelles demonstrations courtes et simples de l inegalite de ky fan i 1 n x i i 1 n 1 x i 1 n i 1 n x i i 1 n 1 x i avec x i 0 1 2 i 1 n avec l egalite si x 1 x n

error probability bounds for balanced binary relay trees we study the detection error probability associated with a balanced binary relay tree where the leaves of the tree correspond to n identical and independent sensors the root of the tree represents a fusion center that makes the overall detection decision each of the other nodes in the tree is a relay node that combines two binary messages to form a single output binary message only the leaves are sensors in this way the information from the sensors is aggregated into the fusion center via the relay nodes in this context we describe the evolution of the type i and type ii error probabilities of the binary data as it propagates from the leaves toward the root tight upper and lower bounds for the total error probability at the fusion center as functions of n are derived these characterize how fast the total error probability converges to 0 with respect to n even if the individual sensors have error probabilities that converge to 1 2

lo keng hua inequality and dynamic programming 2 where k cx n lx h n a 3 inequality 1 is a very interesting and useful as indicated in hua s inequality it appears that this inequality has not been cited as a problem or example elsewhere in an english text however ozeki and aoyagi cited it as an example on page 157 of their inequalities 9 in japanese with a proof indeed there are at least four proofs availabe for inequality 1 moreover inequality 1 can be naturally generalized and its continuous counterpart can also be given this is a major purpose of this paper we now summarize our findings in two theorems as follows

a coupled interpolating meshfree method for computing sound radiation in infinite domain summary in this paper the coupling of the improved interpolating element free galerkin iiefg method and the variable order infinite acoustic wave envelope element wee method is studied a coupled iiefg wee method for computing sound radiation is proposed to make use of their advantages while evading their disadvantages the coupling is achieved by constructing the hybrid shape function of continuity and compatibility on the interface between the iiefg and wee domains in the iiefg domain the improved interpolating moving least squares iimls method is employed to form the shape functions satisfying the kronecker delta condition while nonsingular weight functions can be used the impacts of the size of the influence domain and the shape parameter on the performance of this coupled method are investigated the numerical results show that the coupled iiefg wee method can take full advantage of both the iiefg and wee methods and that it not only can achieve higher accuracy but also has a faster convergence speed than the conventional method of the finite element coupled with the wee the experimental results show that the method is very flexible for acoustic radiation prediction in the infinite domain this article is protected by copyright all rights reserved

a generalization of the holder inequality through dynamic programming approach on etablit une generalisation de l inegalite de holder basee sur la programmation dynamique on etablit les equations de recurrence associees

mapped spheroidal wave envelope elements for unbounded wave problems this paper describes a family of axisymmetric spheroidal wave envelope elements for modelling exterior wave problems they are of variable radial order and can be used to represent steady and transient wave fields the formulation is presented for the axisymmetric case using elements which are based on oblate and prolate spheroidal geometries these offer the prospect of reduced dimensionality in comparison to conventional spherically formulated elements when used to represent wave fields in the vicinity of slender or flat objects conjugated weighting functions are used to give frequency independent acoustic mass stiffness and damping matrices this facilitates a simple extension of the method to transient problems the effectiveness and accuracy of the method is demonstrated by a comparison of computed and analytic solutions for sound fields generated by a rigid sphere in steady harmonic oscillation by a rigid sphere excited from rest and by a circular plate vibrating in a plane baffle

acoustic propagation on irrotational mean flows using transient finite and infinite elements a formulation is presented for the computation of transient wave fields propagating on unbounded irrotational mean flows the numerical scheme is based on an inner mesh of conventional finite elements which is matched to high order multipole infinite elements in the far field the scheme is validated against simple transient test solutions and shown to be effective for large three dimensional problems provided that iterative solvers are used to advance the solution at each time step