graded c algebras c algebras graded by a semilattice appeared for the first time in the study of the quantum n body problem we show that these algebras are completely described by their homogeneous subalgebras and that they are invariant under several operations of c algebras such as tensor products we give the k theory of graded c algebras and we study some of their properties from the c algebra point of view

on the spectral analysis of quantum field hamiltonians abstract we define c algebras on a fock space such that the hamiltonians of quantum field models with positive mass are affiliated to them we describe the quotient of such algebras with respect to the ideal of compact operators and deduce consequences in the spectral theory of these hamiltonians we compute their essential spectrum and give a systematic procedure for proving the mourre estimate

investigation of nonplanar perfectly matched absorbers for finite element mesh truncation we present a detailed theoretical and numerical investigation of the perfectly matched layer pml concept as applied to the problem of mesh truncation in the finite element method fem we show that it is possible to extend the cartesian pml concepts involving half spaces to cylindrical and spherical geometries appropriate for closed boundaries in two and three dimensions by defining lossy anisotropic layers in the relevant coordinate systems by using the method of separation of variables it is possible to solve the boundary value problems in these geometries the analytical solutions demonstrate that under certain conditions outgoing waves are absorbed with negligible reflection and the transmitted wave is attenuated within the pml to reduce the white space in radiation or scattering problems conformal pmls are constructed via parametric mappings it is also verified that the pml concept which was originally introduced for problems governed by maxwell s equations can be extended to cases governed by the scalar helmholtz equation finally numerical results are presented to demonstrate the use of the pml in fem mesh truncation

graded hilbert c modules the notion of hilbert c modules graded by a semilattice was first introduced in the study of many body systems we show the relationship between these hilbert c modules and their homogeneous subspaces we study the stability of graded hilbert c modules under tensor products and crossed products

non uniform grid accelerated local global boundary condition ng lgbc for acoustic scattering a global absorbing boundary condition utilizing accelerated integration scheme based on the non uniform grid ng approach is hybridized with a local boundary condition producing an accurate and efficient mesh truncation scheme for finite method analysis of open region acoustic scattering problems the method affords arbitrarily shaped in particular non convex boundaries that conform to essentially concave obstacles of dimensions large compared with the wavelength

a method of moments model for vhf propagation predictions of a numerical model for site specific very high frequency vhf propagation over irregular terrain are compared to experimental data and to other propagation models the numerical model is based on an iterative version of the method of moments mom known as the banded matrix flat surface iterative approach bmfsia for either perfectly conducting or penetrable surfaces rough in one direction only due to the large size of the numerical problem 65000 to 130000 unknowns a parallel implementation of the method is presented and applied in the simulations comparisons with measurement data show good agreement overall and also illustrate the sensitivity of the model to input terrain profiles comparisons with other propagation models show good agreement also in cases where these models are expected to be valid and further clarify the limitations of the approximations made in these methods

on the approximation solvability of a class of strongly nonlinear elliptic problems on unbounded domains a class of strongly nonlinear boundary value problems posed on unbounded regions is considered a nonlocal coupling of the linearized far field exterior to an auxiliary boundary allows for approximations to be defined on domains of finite extent constructive existence results for bounded domains are then extended by employing an exhausting sequence of approximating domains in particular well posedness is seen to be equivalent to unique approximation solvability with the rate of convergence dependent upon the radius of the auxiliary boundary application to a model of proteins immersed in an electrolyte solution is made

estimation of the dispersion error in the numerical wave number of standard and stabilized finite element approximations of the helmholtz equation an estimator for the error in the wave number is presented in the context of finite element approximations of the helmholtz equation the proposed estimate is an extension of the ideas introduced in steffens and d iez comput methods appl mech engng 2009 198 1389 1400 in the previous work the error assessment technique was developed for standard galerkin approximations here the methodology is extended to deal also with stabilized approximations of the helmholtz equation thus the accuracy of the stabilized solutions is analyzed including also their sensitivity to the stabilization parameters depending on the mesh topology the procedure builds up an inexpensive approximation of the exact solution using post processing techniques standard in error estimation analysis from which the estimate of the error in the wave number is computed using a simple closed expression the recovery technique used in steffens and diez comput methods appl mech engng 2009 198 1389 1400 is based in a polynomial least squares fitting here a new recovery strategy is introduced using exponential in a complex setup trigonometric local approximations respecting the nature of the solution of the wave problem copyright 2011 john wiley sons ltd

calculation of electromagnetic scattering by a perfect conductor abstract a new method is presented for calculating the scattering of an arbitrary electromagnetic wave by a bounded perfectly conducting body of general shape the strategy is to replace the corresponding exterior boundary value problem by an approximate problem on the boundary of the scattering body this involves the introduction of a certain bilinear form and non local boundary operator together with the use of a special class of known solutions of the reduced maxwell s equations satisfying the sommerfeld radiation boundary conditions at infinity two computer programs implementing this method are described and numerical results showing the successful application of this method to some model problems are presented

the finite element method with nonuniform mesh sizes for unbounded domains the finite element method with nonuniform mesh sizes is employed to approximately solve elliptic boundary value problems in unbounded domains consider the following model problem du f in w sup c u g on partialw partialu partialr 1 r u o 1 r as r vertical barxvertical bar infinity where w sup c is the complement in r sup 3 three dimensional eucidean space of a bounded set w with smooth boundary partialw f and g are smooth functions and f has bounded support this problem is approximately solved by introducing an artifical bound g sub r near infinity e g a sphere of sufficiently large radius r the intersection of this sphere with w sup c is denoted by w sub r sup c and the given problem is replaced by du sub r f in w sup c sub r u sub r g on partialw partialu sub r partialr 1 r u sub r 0 on g sub r this problem is then solved approximately by the finite element method resulting in an approximate solution u sub r sup h for each h 0 in order to obtain a reasonably small error for u u sub r sup h u u sub r u sub r u sub r sup h it is necessary to make r large this necessitates the solution of amore large number of linear equations so that this method is often not very good when a uniform mesh size h is employed it is shown that a nonuniform mesh may be introduced in such a way that optimal error estimates hold and the number of equations is bounded by ch sup 3 with c independent of h and r less

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

error analysis and preconditioning for an enhanced dtn fe algorithm for exterior scattering problems in this paper we present an error analysis for a high order accurate combined dirichlet to neumann dtn map finite element fe algorithm for solving two dimensional exterior scattering problems we advocate the use of an exact dtn or steklov poincare map at an artificial boundary exterior to the scatterer to truncate the unbounded computational region the advantage of using an exact dtn map is that it provides a transparent condition which does not reflect scattered waves unphysically our algorithm allows for the specification of quite general artificial boundaries which are perturbations of a circle to compute the dtn map on such a geometry we utilize a boundary perturbation method based upon recent theoretical work concerning the analyticity of the dtn map we also present some preliminary work concerning the preconditioning of the resulting system of linear equations including numerical experiments

a comparison of nrbcs for pufem in 2d helmholtz problems at high wave numbers in this work exact and approximate non reflecting boundary conditions nrbcs are implemented with the partition of unity finite element method pufem to solve short wave scattering problems governed by the helmholtz equation in two dimensions by short wave problems we mean situations in which the wavelength is a small fraction of the characteristic dimension of the scatterer various nrbcs are implemented and a comparison of their performance is carried out based on the accuracy of the results ease of implementation and computational cost the aim is to accurately model such problems in a reduced computational domain around the scatterer with fewer elements and without refining the mesh at each wave number

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

finite element methods applied to nearly one way wave propagation abstract a numerical method is developed for approximately solving stationary wave propagation problems for which most of the energy propagates in an angle band of less than 90 about a fixed direction this property often occurs in realistic physical models the numerical method is based on factoring out the principal propagation direction in the solution and then applying the finite element method the method is applied to wave propagation in a duct or waveguide and to the exterior scattering problem it is shown both theoretically and by means of numerical examples that this method requires considerably less grid points and computational cost than standard discretization methods

on the spectral theory of dispersive n body hamiltonians in this work we describe a general class of dispersive n body hamiltonians for which we prove the hunziker van winter and zislin hwz theorem and a mourre estimate outside a closed and countable set of energies called thresholds as a consequence of the mourre estimate we prove a strong form of the limiting absorption principle which implies the absence of a singular continuous spectrum and gives criteria of local smoothness

numerical solution of the three dimensional ginzburg landau models using artificial boundary for three dimensional simulations of the vortex phenomena in superconductors based on the ginzburg landau gl theory the physical variables must be solved in the whole space in general exact boundary conditions on an artificial boundary are discussed to reformulate the problem in a finite domain approximations of these boundary conditions with high accuracy are given and their convergence properties are examined error estimates are derived for the finite element approximations with the approximate boundary conditions

new convexity and fixed point properties in hardy and lebesgue bochner spaces we show that for the hardy class of functions h1 with domain the ball or polydisc in cn a certain type of uniform convexity property the uniform kadec klee huff property holds with respect to the topology of pointwise convergence on the interior which coincides with both the topology of uniform convergence on compacta and the weak topology on bounded subsets of h1 also we show that if a banach space x has a uniform kadec klee huff property then the lebesgue bochner space lp x 1 p must have a related uniform kadec klee huff property consequently by known results the above spaces have normal structure properties and fixed point properties for non expansive mappings

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

graded c algebras in the n body problem an algebraic formalism is presented which simplifies and makes natural various arguments in the theories where some notion of connected operator appears as a first example in this paper the case of n body systems is considered

on the spectral analysis of many body systems we describe the essential spectrum and prove the mourre estimate for quantum particle systems interacting through k body forces and creation annihilation processes which do not preserve the number of particles for this we compute the hamiltonian algebra of the system i e the c algebra c generated by the hamiltonians we want to study and show that as in the n body case it is graded by a semilattice hilbert c modules graded by semilattices are involved in the construction of c for example if we start with an n body system whose hamiltonian algebra is cn and then we add field type couplings between subsystems then the many body hamiltonian algebra c is the imprimitivity algebra of a graded hilbert cn module

construction of local boundary conditions for an eigenvalue problem using micro local analysis application to optical waveguide problems we present a general procedure based on the pseudo differential calculus for deriving artificial boundary conditions for an eigenvalue problem that characterizes the propagation of guided modes in optical waveguides this new approach allows the construction of local conditions that a are independent of the frequency regime b preserve the sparsity pattern of the finite element discretization and c are applicable to arbitrarily shaped convex artificial boundaries the last feature has the potential for reducing the size of the computational domain numerical results are presented to highlight the potential of conditions of order 1 2 and 1 for improving significantly the computational efficiency of finite element methods for the solution of optical waveguide problems

computing acoustic waves in an inhomogeneous medium of the plane by a coupling of spectral and finite elements in this paper we analyze a galerkin procedure based on a combination of finite and spectral elements for approximating a time harmonic acoustic wave scattered by a bounded inhomogeneity the finite element method used to approximate the near field in the region of inhomogeneity is coupled with a nonlocal boundary condition which consists in a linear integral equation this integral equation is discretized by a spectral galerkin approximation method we provide error estimates for the galerkin method propose fully discrete schemes based on elementary quadrature formulas and show that the perturbation due to this numerical integration gives rise to a quasi optimal rate of convergence we also suggest a method for implementing the algorithm using the preconditioned gmres method and provide some numerical results

a fredholm integral equation method for propagation predictions over small terrain irregularities two dimensional propagation of vertical line source fields over lossy irregular terrain is considered using the magnetic field integral equation the terrain is characterized by its elevation profile and the local surface impedance both of which may vary with distance for treatment via the fredholm integral equation the domain under consideration is made finite by enclosing the terrain irregularity and the source within an arbitrary outer boundary absorbing boundary conditions are imposed on the outer boundary to reduce unwanted reflections from it the integral equation is solved by the boundary element method with quadratic elements substantial comparison is made with specific canonical problems with previously published results of other workers and with measurements to validate the method

numerical simulation for the problem of infinite elastic foundation in this paper we consider the numerical simulation for the problem of infinite elastic foundation a half circle artificial boundary is introduced and discrete artificial boundary condition on it is designed by using the direct method of lines then the original problem is reduced to a boundary value problem on a bounded computational domain furthermore finite element approximation of this boundary value problem defined in the bounded domain is considered the numerical results show that the artificial boundary condition given in this paper is very effective and more accurate than the neumann boundary condition which is often used in engineering literatures

direct solution of current density induced on a rough surface by forward propagating waves a new volterra integral equation of the second kind with square integrable kernel is derived for paraxial propagation of radiowaves over a gently varying perfectly conducting rough surface the integral equation is solved exactly in terms of a infinite series and the necessary and sufficient conditions for the solution to exist and converge are established super exponential convergence of the neumann series for arbitrary surface slope is established through asymptotic analysis expressions are derived for the determination of the number of terms needed to achieve a given accuracy the latter depending on the parameters of the rough surface the frequency of operation and the maximum range numerical results with truncated series are compared with that obtained by solving the integral equation numerically for a sinusoidal surface gaussian hill and a random rough surface with pierson moskowitz spectrum

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

fast frequency sweep computations using a multi point pade based reconstruction method and an efficient iterative solver problems of the form z u f where z is a given matrix f is a given vector and is a circular frequency or circular frequency related parameter arise in many applications including computational structural and fluid dynamics and computational acoustics and electromagnetics the straightforward solution of such problems for fine increments of is computationally prohibitive particularly when z is a large scale matrix this paper discusses an alternative solution approach based on the efficient computation of u and its successive derivatives with respect to at a few sample values of this parameter and the reconstruction of the solution u in the frequency band of interest using multi point pade approximants this computational methodology is illustrated with applications from structural dynamics and underwater acoustic scattering in each case it is shown to reduce the cpu time required by the straightforward approach to frequency sweep computations by two orders of magnitude copyright 2006 john wiley sons ltd

determination of the complex acoustic scattering matrix of a right angled duct a method for determining the complete higher order scattering matrix of an acoustic discontinuity is developed the method is demonstrated for a right angled waveguide bend and the magnitude and phase of the reflection and transmission coefficients are extracted precisely the procedure is straightforward and based on the solutions to the helmholtz equation by the finite element method fem the consistency of the scattering coefficients found by this method is verified by their properties of symmetry and their accuracy is established by the conservation of energy the reliability of the new technique is further proved by means of an arbitrary sound source and by comparing the direct fem response to the reflection matrix calculation some features of the scattering matrix as a function of frequency are surprising such as the steps and reversion of the phase evolution or the complete loss of transmission of the incoming wave the methodology detailed in this paper can be extended to other multiport junctions such as t junctions or size discontinuities in ducts

high frequency numerical analytic approximations for the separable acoustic wave equation abstract an algorithm which employs a combination of asymptotic and numerical methods to solve a sturm liouville problem arising from a separable acoustic wave equation is presented error criteria for switching between methods are derived implementation requires a decomposition of the index of refraction profile into separable subprofiles computing times and accuracies are compared with conventional methods

the weak chebyshev x greedy algorithm in the unweighted bergman space we study a greedy algorithm called the weak chebyshev x greedy algorithm wcxga and investigate its application to unweighted bergman spaces we first show that the wcxga converges for a wide class of real and complex banach spaces and dictionaries we then prove that certain bergman spaces and their holomorphic monomial dictionaries belong to the class of banach spaces for which the wcxga converges

decomposing the essential spectrum abstract we use c algebra theory to provide a new method of decomposing the essential spectra of self adjoint and non self adjoint schrodinger operators in one or more space dimensions

composite boundary valued solution of the 2 5 d green s function for arbitrary acoustic media theoretically the green s function can be used to calculate the wavefield response of a specified source and the frechet derivative with respect to the model parameters for crosshole seismic full waveform inversion in this paper we apply the finite element method to numerically compute the 2 5 d green s function for an arbitrary acoustic medium by solving a composite boundary valued problem in the wavenumber frequency domain the composite boundary condition consists of a 2 5 d absorbing boundary condition for the propagating wave field and a mixed boundary condition for the evanescent field in inhomogeneous media modeling a numerical experiment performed for a uniform earth having a known exact solution shows the accuracy of the computation in the frequency and time domain an inhomogeneous medium test involving an embedded low velocity layer demonstrates that the permissible range of ky at each frequency can be determined rationally from the critical wavenumber value of the medium around the sou

high order numerical simulation of the transmission and scattering of waves using the method of difference potentials the method of difference potentials generalizes the method of calderon s operators from pdes to arbitrary difference equations and systems it offers several key advantages such as the capability of handling boundaries interfaces that are not aligned with the discretization grid variable coefficients and nonstandard boundary conditions in doing so the complexity of the algorithm remains comparable to that of an ordinary finite difference scheme on a regular structured grid previously we have applied the method of difference potentials to solving several variable coefficient interior helmholtz problems with fourth and sixth order accuracy we have employed compact finite difference schemes as a core discretization methodology those schemes enable high order accuracy on narrow stencils and hence require only as many boundary conditions as needed for the underlying differential equation itself numerical experiments corroborate the high order accuracy of our method for variable coefficients regular grids and non conforming boundaries in the current paper we extend the previously developed methodology to exterior problems we present a complete theoretical analysis of the algorithm as well as the results of a series of numerical simulations specifically we study the scattering of time harmonic waves about smooth shapes subject to various boundary conditions we also solve the transmission scattering problems in which not only do the waves scatter off a given shape but also propagate through the interface and travel across the heterogeneous medium inside in all the cases our methodology guarantees high order accuracy for regular grids and non conforming boundaries and interfaces

characterization of woodwind instrument toneholes with the finite element method a method is proposed to determine the transfer matrix parameters of a discontinuity in a waveguide with the finite element method fem this is used to characterize open and closed woodwind instrument toneholes and develop expressions for the shunt and series equivalent lengths two types of toneholes are characterized unflanged toneholes made of thin material such as found on saxophones and concert flutes and toneholes drilled through a thick material such as found on most instruments made of wood the results are compared with previous tonehole models from the literature in general the proposed expressions provide a better fit across a wide range of frequencies and tonehole sizes than previous results for tall toneholes the results are in general agreement with previous models for shorter tonehole heights some discrepancies from previous results are found that are most important for larger diameter toneholes finally the impact of a main bore taper conicity on the characterization of toneholes was investigated and found to be negligible for taper angles common in musical instruments

terrain based propagation model for rural area an integral equation approach a terrain based propagation model for vertically polarized radio waves is described based on the field integral equation for a smooth surface the model is simplified from a 3d integral equation model to a one dimensional integral equation by assuming that the surface is magnetically perfectly conducting a soft surface with no transverse variations by assuming no back scattering the integral equation is turned into a simple integral the method is tested numerically with known solutions the integral equation model is also applied to actual terrain profiles at four frequencies 144 435 970 1900 mhz and the results are compared with results from the hata model and measurements the standard deviation std of the error is a growing function of frequency from 3 to 9 db

a fast method for solving acoustic scattering problems in frequency bands abstract we present a methodology for computing efficiently scattered fields in a frequency band the main feature of this methodology is the construction of a series of discrete problems that differ only by their right hand sides rather than by both their left and right hand sides its key steps are a the reformulation of the acoustic scattering problem in a bounded domain using any preferred absorbing boundary condition b the characterization of the repeated derivatives with respect to the frequency of the scattered field as solutions of scattering type problems with different source terms and boundary conditions and c the reconstruction of a scattered field by either the pade approximants or wynn s algorithm we report on several multifrequency acoustic scattering examples that illustrate the accuracy and computational efficiency of the proposed solution methodology

the finite element method with non uniform mesh sizes applied to the exterior helmholtz problem the finite element method with non uniform mesh sizes is employed to approximately solve helmholtz type equations in unbounded domains the given problem on an unbounded domain is replaced by an approximate problem on a bounded domain with the radiation condition replaced by an approximate radiation boundary condition on the artificial boundary this approximate problem is then solved using the finite element method with the mesh graded systematically in such a way that the element mesh sizes are increased as the distance from the origin increases this results in a great reduction in the number of equations to be solved it is proved that optimal error estimates hold inl 2 h 1 andl provided that certain relationships hold between the frequency mesh size and outer radius

application of pade via lanczos approximations for efficient multifrequency solution of helmholtz problems this paper addresses the efficient solution of acoustic problems in which the primary interest is obtaining the solution only on restricted portions of the domain but over a wide range of frequencies the exterior acoustics boundary value problem is approximated using the finite element method in combination with the dirichlet to neumann dtn map the restriction domain problem is formally posed in transfer function form based on the finite element solution in order to obtain the solution over a range of frequencies a matrix valued pade approximation of the transfer function is employed using a two sided block lanczos algorithm this approach provides a stable and efficient representation of the pade approximation in order to apply the algorithm it is necessary to reformulate the transfer function due to the frequency dependency in the nonreflecting boundary condition this is illustrated for the case of the dtn boundary condition but there is no restriction on the approach which can also be applied to other radiation boundary conditions numerical tests confirm that the approach offers significant computational speed up

finite difference analysis of borehole flows involving domain contractions around three dimensional anomalies a finite difference analysis in cylindrical coordinates of borehole flows governed by poisson s equation yields an infinite cylindrical electrical grid as a model the customary technique of truncating the medium in order to obtain a finite grid can be avoided at least to some extent by using the recently developed theory of infinite electrical networks when the medium around the borehole is either uniform or cylindrically layered except for a three dimensional anomalous region near the borehole infinite electrical network theory allows one to represent the medium outside any cylinder s containing the anomaly and centered on the borehole by an infinite continued fraction of circulant laurent operators the continued fraction in turn can be represented by scalar conductances connected to the grid s nodes on s by choosing s just large enough to contain the anomaly one can replace the large system of equations resulting from the usual medium truncations far removed from the anomaly by a much smaller systems of equations for the grid within and on s an operational calculus for the circulant laurent operators and the fast fourier transform expedites the computations and moreover allows a rapidly computed determination of the solution outside s

a fast finite difference method for propagation predictions over irregular inhomogeneous terrain propagation of electromagnetic waves over irregular inhomogeneous terrain is solved by a finite difference scheme the method is fast and requires considerably less memory than the integral equation methods the method requires a storage space of order o n and an execution time of order o n sup 2 fields generated by a te sub 2 line source are represented in an integral form in terms of the field over a flat constant impedance plane the incident field and the field scattered by the terrain irregularities and inhomogeneities accurate expressions are provided for the incident field and the green s function whose evaluation is otherwise accomplished by the rather time consuming sommerfeld s integrals measured equation of invariance is used to terminate the computational domain the sparse matrix generated by the method is inverted by the ricatti transform numerical results are presented for the ground wave as well as for the sky wave comparison is made for known geometries to establish the validity and limitations of the method

spectral analysis of n body schrodinger operators for a large class of two body potentials we solve two of the main problems in the spectral analysis of multiparticle quantum hamiltonians explicitly we prove that the point spectrum lies in a closed countable set and describe that set in terms of the eigenvalues of hamiltonians of subsystems and that there is no singular continuous spectrum we accomplish this by extending mourre s work on three body problems to n body problems

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

on the structure of the essential spectrum of elliptic operators on metric spaces abstract we give a description of the essential spectrum of a large class of operators on metric measure spaces in terms of their localizations at infinity these operators are analogues of the elliptic operators on euclidean spaces and our main result concerns the ideal structure of the c algebra generated by them

axial green s function method for multi dimensional elliptic boundary value problems axial green s function method is proposed to solve multi dimensional second order elliptic partial differential equations with the geometrical complexity of solution domains instead of directly dealing with 2d or 3d green s functions the proposed method systematically decomposes a multi dimensional elliptic differential operator into id ones consequently the method only requires id green s function associated with each coordinate axis theoretical formulation and simple axial discretization result in the system of equations of which the solutions represent the numerical solution of the original multi dimensional elliptic problem which is otherwise intractable to obtain by the traditional multi dimensional green s function technique the method employs analytical form of id green s function and integral schemes so that it can potentially be more robust than both the finite difference method and the boundary element method in addition the simple discretization procedure which uses only axially orthogonal straight lines and boundary data demonstrates its convenience over the finite element method of comparable accuracy numerical examples verify these advantages by demonstrating the second order convergence in various discretized models of complex geometries

edged based smoothed point interpolation method for acoustic radiation with perfectly matched layer abstract it is known that for exterior acoustics the domain based finite element method always encounters the accuracy loss for high wavenumbers and the difficulty in dealing with the sommerfeld radiation condition in this work by using the polynomial and radial bases with specific node selection schemes the point interpolation method with the generalized gradient smoothing technique is employed to improve the accuracy for acoustic computations the appropriately softened acoustical stiffness of the discrete model is constructed based on the edge based smoothing domains via the gradient smoothing technique in addition the perfectly matched layer technique enables the smoothed point interpolation method to investigate exterior acoustics the complex coordinate transformation is utilized to determine the proper parameters for the perfectly matched layer through theoretical and numerical analyses several typical acoustic problems are analyzed revealing that better accuracy is obtained by the present method compared with the finite element method especially for high wavenumbers

enriched isogeometric collocation for two dimensional time harmonic acoustics abstract in this work the isogeometric collocation iga c is paired with two types of enrichment plane wave pw and generalized harmonic polynomial ghp functions to solve 2d problems for the helmholtz equation a parametric study is conducted and a detailed assessment of the performance of the method in a number of benchmark problems is provided three different collocation methods are tested for the non enriched formulation namely greville abscissae ga approximated cauchy galerkin acg and superconvergent sc points showing that the acg scheme is the best choice in terms of overall error convergence rate and ease of solving the linear system then the influence of the number of shape functions in the original and enriched basis location and number of collocation points and wave number over both the convergence rate as well as the condition number of the stiffness matrix are studied the numerical results show that 1 there is an improvement over the non enriched formulation 2 the improvement depends on the choice of the number and type of enrichment and 3 the pollution error is not completely alleviated with the enriched formulations

three dimensional approximate local dtn boundary conditions for prolate spheroid boundaries we propose a new class of approximate local dtn boundary conditions to be applied on prolate spheroidal shaped exterior boundaries when solving problems of acoustic scattering by elongated obstacles these conditions are a exact for the first modes b easy to implement and to parallelize c compatible with the local structure of the computational finite element scheme and d applicable to exterior ellipsoidal shaped boundaries that are more suitable in terms of cost effectiveness for surrounding elongated scatterers we investigate analytically and numerically the effect of the frequency regime and the slenderness of the boundary on the accuracy of these conditions we also compare their performance to the second order absorbing boundary condition bgt2 designed by bayliss gunzburger and turkel when expressed in prolate spheroid coordinates the analysis reveals that in the low frequency regime the new second order dtn condition dtn2 retains a good level of accuracy regardless of the slenderness of the boundary in addition the dtn2 boundary condition outperforms the bgt2 condition such superiority is clearly noticeable for large eccentricity values

on a conjecture of huber concerning the convergence of projection pursuit regression we generalize the projection pursuit procedure of friedman and stuetzle abstract version and prove strong convergence this answers a question of huber