perturbation bounds for least squares problems with equality constraints we present some new results on the perturbation analysis for least squares problems with equality constraints based on an equivalent formation of the problem and the optimal perturbation result for general least squares problems

3 d sound source reconstruction and field reprediction using the helmholtz integral equation abstract a method for reconstruction of the boundary conditions of an arbitrarily shaped three dimensional 3 d sound source from a finite number of field pressures is presented and the associated field is repredicted by using the helmholtz integral equation to minimize the reconstruction error due to noise in the field pressures a filtering method is proposed and it is verified that numerically singular values which correspond to the higher order modes of the evanescent like components of the source velocities are eliminated for arbitrarily shaped sources with complex boundary conditions the reconstruction is performed accurately when the size of each element is less than a quarter wavelength and the field measurement positions are equally or randomly distributed on the surface of a sphere in the vicinity of the source our technique can be used in computer aided loudspeaker design that reconstructs loudspeaker diaphragm velocities from the finite number of field pressures and repredicts the variation of the sound field procuced by a redesigned loudspeaker cabinet on which the reconstructed diaphragm is mounted

on the perturbation bounds of g inverses and oblique projections abstract let a 1 and a 1 be two sets of g inverses of matrices a and a a e respectively for any a a 1 we deduce general formulas of g inverse a a 1 such that the distances between the two g inverses or oblique projections are the smallest under appropriated norms and obtain the corresponding distances with these results we derive perturbation bounds of the nearest perturbed g inverses oblique projections and consistent linear equations under rank preserving condition rank a rank a numerical examples are also provided to verify our analysis

applications of the generalized singular value decomposition method on the eigenproblem using the incomplete boundary element formulation in this paper four incomplete boundary element formulations including the real part singular boundary element the real part hypersingular boundary element the imaginary part boundary element and the plane wave element methods are used to solve the free vibration problem among these incomplete boundary element formulations the real part singular and the hypersingular boundary elements are of the singular type and the other two are of the regular type when the incomplete formulation is used the spurious eigensolution may be encountered an auxiliary system whose boundary conditions are linearly independent of those of the original system is required in the proposed method in order to eliminate the spurious eigensolution a mathematical proof is given to show that the spurious eigensolution will appear in both the original and auxiliary systems as a result one can eliminate spurious eigensolution by means of the generalized singular value decomposition method in addition to the spurious eigensolution problem the regular boundary element formulation further suffers ill conditioned behaviors in the problem solver it is explained analytically using a circular domain why ill conditioned behaviors exist two main ill conditioned problems are the numerical instability of solution and the nonexistence of solution to solve the numerical instability of solution problem existing in these proposed regular formulations the tikhonov s regularization technique is used to improve the condition number of the leading coefficient matrix further the generalized singular value decomposition method is used to eliminate spurious eigensolutions numerical examples are given to verify the performance of these proposed methods and the results match the analytical values well

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

towards a generalized singular value decomposition we suggest a form for and give a constructive derivation of the generalized singular value decomposition of any two matrices having the same number of columns we outline its desirable characteristics and compare it to an earlier suggestion by van loan siam j numer anal 13 1976 pp 76 83 the present form largely follows from the work of van loan but is slightly more general and computationally more amenable than that in the paper cited we also prove a useful extension of a theorem of stewart siam rev 19 1977 pp 634 662 on unitary decompositions of submatrices of a unitary matrix

boundary element analysis for the helmholtz eigenvalue problems with a multiply connected domain for a helmholtz eigenvalue problem with a multiply connected domain the boundary integral equation approach as well as the boundary element method is shown to yield spurious eigenvalues even if the complex valued kernel is used in such a case it is found that spurious eigenvalues depend on the geometry of the inner boundary demonstrated as an analytical case the spurious eigenvalue for a multiply connected problem with its inner boundary as a circle is studied analytically by using the degenerate kernels and circulants an annular case can be studied analytically in a discrete system and can be treated as a special case the proof for the general boundary instead of the circular boundary is also derived the burton miller method is employed to eliminate spurious eigenvalues in the multiply connected case moreover a modified method considering only the real part formulation is provided five examples are shown to demonstrate that the spurious eigenvalues depend on the shape of the inner boundary good agreement between analytical prediction and numerical results are found

analytical study and numerical experiments for radiation and scattering problems using the chief method in this paper the well known failure in numerical computations of the exterior helmholtz integral equation at certain characteristic frequencies is investigated analytically and numerically the combined helmholtz integral equation formulation chief method is a very popular technique that can overcome the non unique problem but this method breaks down if the interior points are not properly chosen the chief method in conjunction with the singular value decomposition svd technique is an easy and efficient method to ensure a unique solution for the exterior problem based on the circulant properties and degenerate kernels an analytical scheme in discrete system of a cylinder is achieved the optimum numbers and proper positions for the collocation points in the interior domain are analytically studied and suggested in the numerical scheme numerical experiments are designed to verify the analytical results one analytical example for a circular cylinder and one numerical example for a square rod are demonstrated to show the validity of the chief method

perturbation analysis for the projection of a point to an affine set abstract we present a perturbation analysis for the projection of a point to an affine set in r n the matrix involved is not assumed to be full rank and the perturbation is arbitrary error bounds for the solution under the rank preserving and rank nondecreasing perturbations are obtained the results given here appear to be the most general up to now

development of an energy boundary element formulation for computing high frequency sound radiation from incoherent intensity boundary conditions an energy boundary element analysis ebea formulation is presented for calculating sound radiation at high frequency from a radiator with arbitrary shape the ebea development presented in this paper compliments previous energy finite element analysis efea developments for computing high frequency vibration of structures immersed in an acoustic medium from the efea solution the structural vibrational energy throughout the structure and the acoustic power radiated from each surface element in contact with the surrounding fluid are computed the ebea utilizes the information for the acoustic power radiated from each element of the outer surface of the structure as a boundary condition in order to compute the acoustic field in an unbound medium with no damping that surrounds the radiating structure since the structural vibration between different elements is considered as incoherent in the efea the acoustic intensity associated with each surface element that radiates in the surrounding medium is also considered as incoherent between different elements in the ebea formulation the governing integral equation of ebea is established and a numerical solution is presented the present method is validated by comparing ebea results to analytical solutions and to numerical results from an axi symmetric hp finite element code with infinite acoustic elements suitable for structural acoustic computations good correlation is demonstrated for all the analyses

spectral and condition number estimates of the acoustic single layer operator for low frequency multiple scattering in dilute media the aim of this paper is to develop an analysis of the distribution of the eigenvalues of the acoustic single layer potential for various low frequency two dimensional multiple scattering problems the obstacles are supposed to be distant dilute media in cite thierrythesis it is shown that an approach based on the gershgorin disks provides limited spectral information we therefore introduce an alternative approach by applying the power iteration method to the limit matrix associated with the zero order spatial modes which results in satisfactory estimates all these approximations are built for circular cylinders and formally extended to ellipses and rectangles for linear boundary element methods with non uniform meshes this study is completed in cite antoinethierrypart2 by spectral estimates for the case of close obstacles

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

new perturbation results for equality constrained least squares problems abstract we present some perturbation results for least squares problems with equality constraints relative errors are obtained on perturbed solutions and lagrange multipliers of the problem based on the equivalence of the problem to a consistent system of linear equations

a modified integral equation method of the nonlinear elliptic equation with globally and locally lipschitz source the paper is devoted to investigating a cauchy problem for nonlinear elliptic pdes in the abstract hilbert space the problem is hardly solved by computation since it is severely ill posed in the sense of hadamard we shall use a modified integral equation method to regularize the nonlinear problem with globally and locally lipschitz source terms convergence estimates are established under priori assumptions on exact solution a numerical test is provided to illustrate that the proposed method is feasible and effective these results extend some earlier works on a cauchy problem for elliptic equations

the method of fundamental solutions for stationary heat conduction problems in rotationally symmetric domains we propose an efficient boundary collocation method for the solution of certain two and three dimensional problems of steady state heat conduction in isotropic bimaterials in particular in two dimensions we consider the case where a circular region composed of one material is coated with an annular region of another material in three dimensions we examine the corresponding case for axisymmetric domains the proposed method involves the use of a domain decomposition technique in conjunction with a matrix decomposition algorithm the circulant structure of the matrices appearing in this method is exploited by using fast fourier transforms the method is tested numerically on several problems

singular boundary method for acoustic eigenanalysis this paper applies the singular boundary method sbm to two 2d and three dimensional 3d acoustics eigenproblems in simply and multiply connected domains the sbm is a strong form boundary discretization numerical method and is meshless integration free and easy to implement by introducing the concept of the source intensity factors the singularity of fundamental solutions can be isolated to avoid the singular numerical integrals in the boundary element method bem similar to the bem the spurious eigenvalues may arise in the sbm computation in order to extract out spurious eigenvalues from sbm results the singular value decomposition updating techniques and the burton miller method are implemented several 2d and 3d benchmark examples subjected to dirichlet and neumann boundaries are tested to examine the accuracy and stability of the present sbm strategy

dual formulation of multiple reciprocity method for the acoustic mode of a cavity with a thin partition abstract the dual formulation of the multiple reciprocity method mrm is employed to solve the acoustic mode of a cavity with a thin partition in order to avoid the spurious eigenvalues and non uniqueness of the solution in the case of zero thickness for the partition the hypersingular equation for mrm is considered to determine the invariant quantity of influence coefficients more efficiently an objectivity concept i e a frame of indifference is used by means of co ordinate transformation a generalized eigenvalue problem is derived and transformed into a standard eigenvalue problem through the state space formulation the spurious roots in mrm are examined and filtered out by using the hypersingular formulation three examples including finite thickness of the partition zero thickness and no partition are shown to check the validity of the proposed method also the analytical solution if available the fem results obtained by petyt and by abaqus and experimental measurements are compared with those of the proposed method and it is found that the agreement between them is very good

a third order boundary element method for exterior acoustics with applications to scattering by rigid and elastic shells abstract in this work a novel third order direct boundary element method for the helmholtz equation is presented the methodology is best understood within the context of the so called puod fictitious eigenvalues difficulty pucd introduced by the typical direct boundary integral approach this problem consists of the existence of fictitious resonance frequencies i e frequencies of the adjoint interior problem and is overcome by the condor technique by burton and miller i e a suitable linear combination of the kirchhoff puen helmholtz integral equation with that obtained by taking its normal derivative this in turn yields the presence of a hypersingular kernel arising in the integral expression for the normal derivative of the kirchhoff puen helmholtz integral equation which is regularized by introducing a novel integral relationship closely related to the equivalence between doublet layers and vortex layers in incompressible potential flows this requires the evaluation of the tangential laplacian of the unknown and hence the use of a high order discretization a piecewise bicubic discretization of the boundary integral equation is used in this paper the resulting equation contains only the nodal values of the unknown numerical applications to particularly taxing problems such as high frequency radiation and scattering problems of rigid and elastic shells are included and validated through comparison with analytical solutions numerical results show that the convergence rate is of order h 3 h being the typical element size even for high frequency analysis indicating that this is a true third order method

spectral and condition number estimates of the acoustic single layer operator for low frequency multiple scattering in dense media the aim of this paper is to derive spectral and condition number estimates of the single layer operator for low frequency multiple scattering problems this work extends to dense media the analysis initiated in antoine and thierry in press 19 estimates are obtained first in the case of circular cylinders by fourier analysis and are next formally adapted to disks ellipses and rectangles in the framework of boundary element methods numerical simulations validating the approach are also given

perturbation theory for the rank deficient equality constrained least squares problem this paper presents perturbation theory for the equality constrained least squares problem min f in s kf g 2 with s f lf h 2 min y in c n ly h 2 lse in which l and begin array 20 c l k end array may not be of full rank the analysis generalizes the results of elden 4 perturbation theorems for the lse problem are proved numerical experiments are also given to verify the error bounds

analytical study and numerical experiments for true and spurious eigensolutions of a circular cavity using the real part dual bem it has been found recently that the multiple reciprocity method mrm chen and wong engng anal boundary elements 1997 20 1 25 33 chen processings of the fourth world congress on computational mechanics onate e idelsohn sr eds argentina 1998 106 chen and wong j sound vibration 1998 217 1 75 95 or real part bem liou chen and chen j chinese inst civil hydraulics 1999 11 2 299 310 in chinese results in spurious eigenvalues for eigenproblems if only the singular ut or hypersingular lm integral equation is used in this paper a circular cavity is considered as a demonstrative example for an analytical study based on the framework of the real part dual bem the true and spurious eigenvalues can be separated by using singular value decomposition svd to understand why spurious eigenvalues occur analytical derivation by discretizing the circular boundary into a finite degree of freedom system is employed resulting in circulants for influence matrices based on the properties of the circulants we find that the singular integral equation of the real part bem for a circular domain results in spurious eigenvalues which are the zeros of the bessel functions of the second kind y k while the hypersingular integral equation of the real part bem results in spurious eigenvalues which are the zeros of the derivative of the bessel functions of the second kind yn k it is found that spurious eigenvalues exist in the real part bem and that they depend on the integral representation one uses singular or hypersingular single layer or double layer no matter what the given types of boundary conditions for the interior problem are furthermore spurious modes are proved to be trivial in the circular cavity through analytical derivations numerically they appear to have the same nodal lines of the true modes after normalization with respect to a very small nonzero value two examples with a circular domain including the neumann and dirichlet problems are presented the numerical results for true and spurious eigensolutions match very well with the theoretical prediction copyright 2000 john wiley sons ltd

a hybrid bie ffp scheme for predicting barrier efficiency outdoors to assess the acoustical performance of noise screens in the presence of an arbitrary sound speed profile a numerical scheme based on a combination of the boundary integral and fast field program methods is developed the green s function required in the boundary integral is evaluated by a fast field formulation the procedure is validated by comparing its predictions with other numerical results for simple cases and with measurements for indoor model experiments simulating downward refracting conditions it is predicted that the performance of a noise screen placed 50 m from the source is reduced considerably by moderate downwind conditions

iterative solution of high order boundary element method for acoustic impedance boundary value problems abstract a high order boundary element method for time harmonic acoustic impedance boundary value problems is presented the method is based on the galerkin type formulation of the burton miller integral equation bmie with high order polynomial basis and testing functions this formulation has several important advantages it is free of the interior resonance problem the hypersingular integral operator of the traditional bmie formulation can be avoided it leads to faster convergence in terms of the number of unknowns than the low order methods and it shows a good performance with iterative solvers to avoid the numerical difficulties associated to the implementation of the singular surface integral equations the singularity extraction technique is applied to evaluate the integrals in the singular and near singular cases the resulting matrix equation is solved iteratively with the generalized minimal residual method gmres and a simple preconditioner based on the incomplete lu factorization is applied to expedite the convergence numerical results indicate that the bmie formulation with galerkin method and high order basis functions has good convergence properties for various geometries and boundary conditions on a wide frequency range when the gmres method is applied to solve the matrix equation iteratively this in turn indicates that the formulation is well suited for an efficient application of fast solution procedures such as the fast multipole method

numerical treatment of acoustic problems with boundary singularities by the singular boundary method abstract the singular boundary method sbm is a novel boundary type meshless method based on the fundamental solution of the given governing equation the sbm employs the origin intensity factors to circumvent the singularities resulting from the fundamental solutions in this paper we investigate the acoustic problems with boundary singularities using the sbm this is achieved by combining the sbm with the singularity subtraction techniques where the solution is decomposed into the singular solution and the regular solution the singular solution is derived analytically which satisfies the governing equation and the corresponding boundary conditions containing the singularities then the regular solution is obtained by the sbm numerical examples show the excellent performance of the proposed technique

a comparison of techniques for overcoming non uniqueness of boundary integral equations for the collocation partition of unity method in two dimensional acoustic scattering the partition of unity method has become an attractive approach for extending the allowable frequency range for wave simulations beyond that available using piecewise polynomial elements the non uniqueness of solution obtained from the conventional boundary integral equation cbie is well known the cbie derived through green s identities suffers from a problem of non uniqueness at certain characteristic frequencies two of the standard methods of overcoming this problem are the so called combined helmholtz integral equation formulation chief method and that of burton and miller the latter method introduces a hypersingular integral which may be treated in various ways in this paper we present the collocation partition of unity boundary element method pubem for the helmholtz problem and compare the performance of chief against a burton miller formulation regularised using the approach of li and huang

a new technique of quaternion equality constrained least squares problem by means of complex representation of a quaternion matrix we study the relationship between the solutions of the quaternion equality constrained least squares problem and that of complex equality constrained least squares problem and obtain a new technique of finding a solution of the quaternion equality constrained least squares problem

spurious and true eigensolutions of helmholtz bies and bems for a multiply connected problem the spurious eigenvalues of an annular domain have been verified for the singular and hypersingular boundary element methods bems and circumvented by using the burton miller approach do they also occur in other formulations continuous formulations such as the singular and hypersingular boundary integral equations bies the null field bies and the fictitious bies or such discrete formulations as the null field bems and the fictitious bems for the ten formulations of the multiply connected problem the study of otherwise the same issues is continued in the present paper by using the degenerate kernels and the fourier series it is demonstrated analytically for the six continuous formulations of bies that spurious eigensolutions depend on the geometry of the inner boundary but not on that of the outer boundary this conclusion can be extended to the six discrete formulations of bems to filter out the spurious eigenvalues the chief combined helmholtz integral equation formulation method is used here instead of the burton miller approach the optimum number and appropriate positions of the chief points are also addressed it is then shown that in the null field and fictitious bems the spurious and true eigenvalues can be detected and distinguished by using the singular value decomposition updating techniques in conjunction with the fredholm alternative theorem illustrative examples show the validity of the proposed methodologies

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

analytical investigation for true and spurious eigensolutions of multiply connected membranes containing elliptical boundaries using the dual biem it is well known that the boundary element method may induce spurious eigenvalues while solving eigenvalue problems the finding that spurious eigenvalues depend on the geometry of inner boundary and the approach utilized has been revealed analytically and numerically in the literature however all the related efforts were focused on eigenproblems involving circular boundaries on the other hand the extension to elliptical boundaries seems not straightforward and lacks of attention accordingly this paper performs an analytical investigation of spurious eigenvalues for a confocal elliptical membrane using boundary integral equation methods biem in conjunction with separable kernels and eigenfunction expansion to analytically study this eigenproblem the elliptic coordinates and mathieu functions are adopted the fundamental solution is expanded into the separable kernel by using the elliptic coordinates and the boundary densities are expanded by using the eigenfunction expansion the jacobian terms may exist in the separable kernel boundary density and boundary contour integration and they can cancel each other out therefore the orthogonal relations are reserved in the boundary contour integration in this way a similar finding about the mechanism of spurious eigenvalues is found and agrees with those corresponding to the annular case to verify this finding the boundary element method and the commercial finite element code abaqus are also utilized to provide eigensolutions respectively for comparisons good agreement is observed from comparisons based on the adaptive observer system the present approach can deal with eigenproblems containing circular and elliptical boundaries at the same time in a semi analytical manner by using the biem it is found that spurious eigenvalues are the zeros of the modified mathieu functions which depend on the inner elliptical boundary and the integral formulation finally several methods including the chief method the svd updating technique and the burton miller method are employed to filter out the spurious eigenvalues respectively in addition the efficiency of the chief method is better than those of the svd updating technique and the burton miller approach since not only hypersingularity is avoided but also computation effort is saved

a new form of the hypersingular boundary integral equation for 3 d acoustics and its implementation with c0 boundary elements abstract an improved weakly singular form of the hypersingular boundary integral equation hbie for 3 d acoustic wave problems is presented in this paper compared with the weakly singular form of the hbie published earlier y j liu and f j rizzo a weakly singular form of the hypersingular boundary integral equation applied to 3 d acoustic wave problems comput methods appl mech engrg 96 1992 271 287 this new form involves only tangential derivatives of the density function and thus its discretization using the boundary element method bem is easier to perform instead of using nonconforming and c1 continuous boundary elements advocated earlier c0 continuous conforming quadratic elements are employed in the discretization of this weakly singular form of the hbie some justifications on using c0 elements for hbies are provided to reflect the current views on this crucial issue for hbies it is postulated that the original c1 continuity requirement for the density function in the analytical hbie formulation can be relaxed to piecewise c1 continuity in the numerical implementation of the weakly singular forms of the hbie numerical examples of both scattering and radiation problems clearly demonstrate the accuracy and versatility of the new weakly singular form of the hbie for 3 d acoustics

diffraction of acoustic waves by rigid plane baffles the integral equation method is applied to study the diffraction of acoustic waves by rigid plane baffles such as a circular disk and a ring a set of six real fredholm integral equations of the second kind is solved simultaneously to determine the velocity potentials on a circular disk these equations are transformed into discrete forms by applying the gauss legendre quadrature formula in the radial direction and the best possible numerical integration formula in the angular direction the discrete equations are solved by the method of successive approximations which is also called the direct integral equation method a new method is also developed to take care of integrations involving the cauchy principal values which occur when the moving point coincides with the fixed point the accuracy of the present numerical approach has been tested by computing the excess pressure ratio p p0 on the surfaces of a circular disk exposed to a plane wave and by comparing it with both analytical and experimental

analytical and numerical studies of free vibrations of plate by imaginary part bem formulations abstract in this paper the spurious solution of characteristic equation for the eigenproblems of a circular plate is studied in the continuous and discrete systems since any two boundary integral equations in the plate formulation four equations can be chosen 6 c 2 4 options are considered instead of only two approaches single layer and double layer methods or singular and hypersingular equations the occurring mechanism of the spurious solution for the circular plate in the imaginary part formulations is studied analytically for the continuous system degenerate kernels for the fundamental solution and the fourier series expansion for the boundary density are employed to derive the true and spurious solutions of characteristic equation analytically for the discrete system the degenerate kernels for the fundamental solution and circulants resulting from the circular boundary are employed to determine the spurious solution of characteristic equation it is found that true solution for characteristic equation depends on the specified boundary condition while spurious one is embedded in each formulation also we provide two methods singular value decomposition updating technique and the burton and miller method to suppress the occurrence of the spurious eigenvalues a general purpose program of imaginary part boundary element method was developed for general cases several examples including circular and noncircular cases were demonstrated to check the validity of the formulation

global consensus of time varying multiagent systems without persistent excitation assumptions we establish a new condition for global consensus of continuous time multiagent systems with undirected switching interaction graphs the condition is strictly weaker than the persistency of excitation one recently shown in 1 to be necessary and sufficient for global exponential consensus the price paid for the relaxation of the excitation requirement is twofold on one hand we establish only global asymptotic consensus without the exponential qualifier on the other hand we prove that our condition is not necessary we also prove in this paper that an additional assumption is needed in 1 to extend the consensus result to the case of negatively weighted edges

regularization of the cauchy problem for the helmholtz equation by using meyer wavelet in this paper we investigate a cauchy problem associated with helmholtz type equation in an infinite strip this is a classical severely ill posed problem i e the solution if it exists does not depend continuously on the data or cauchy data a small perturbation in the data can cause a dramatically large error in the solution for 0

on the error estimate for the projection of a point onto a linear manifold abstract suppose that the linear system a h x b is consistent the problem of finding the solution x to min a h x b 1 2 x p 2 2 is studied where a c n m b c m x p c n and a b p are given when a b and p are perturbed an error bound for the solution x is obtained roundoff error bounds for the singular value decomposition method the column pivoting method and the rank revealing method are obtained the results in this paper extend those of arioli laratta and menchi to the case when a is not of full rank and either m n or m n

a simple method avoiding non uniqueness in the boundary element method for acoustic scattering problem the boundary element method bem is widely used for sound field analysis problems however it has a non uniqueness problem in the exterior domain various methods to avoid this problem have been developed however these are not easily applied to the bem in this paper a simple method called the ica ring inner cavity ringing method is proposed for avoiding the non uniqueness problem and this method is applied to the bem in both single and plural domains the concept of the ica ring method is that a scatterer in free space is hollowed as a shell and the volume is smaller the eigenfrequencies are shifted to a higher range next the mechanism of the non uniqueness problem in plural domains and a reason of the application of the ica ring method to the case of plural domains are explained finally some results calculated by the bem using the ica ring method are shown the calculational condition is that a cylinder with radius 0 125m floats in two dimensional free space in this case no calculationa

collocation approach to the helmholtz eigenvalue problem on multiply connected domains we present a collocation approach to the numerical solution of the helmholtz eigenvalue problem on multiply connected domains of arbitrary shape in two dimensions a suitable representation of the helmholtz equation on an uniform grid is obtained and the problem is converted to the calculation of the first few eigenvalues and eigenvectors of a large sparse matrix the accuracy of this approach is tested by performing a comparison with results available in the literature the flexibility and simplicity of the method make easy the application to arbitrary geometries

a boundary integral equation method for two dimensional acoustic scattering problems this work formulates the singularity free integral equations to study 2 d acoustic scattering problems to avert the nonuniqueness difficulties burton s and burton and miller s methods are employed to solve the dirichlet and neumann problems respectively the surface helmholtz integral equations and their normal derivative equations in bounded form are derived the weakly singular integrals are desingularized by subtracting a term from the integrand and adding it back with an exact value depending on the relevant problem the additional integral can finally be either expressed in an explicit form or transformed to form a surface source distribution of the related equipotential body the hypersingular kernel is desingularized further using some properties of an interior laplace problem the new formulations are advantageous in that they can be computed by directly using standard quadrature formulas also discussed is the contour a unique feature of 2 d problems instead of dividing the boundary surface into several small elements a parametric representation of a 2 d boundary curve is further proposed to facilitate a global numerical implementation calculations consist of acoustic scattering by a hard and a soft circular cylinder respectively comparing the numerical results with the exact solutions demonstrates the proposed method s effectiveness

2 d time harmonic bem for solids of general anisotropy with application to eigenvalue problems abstract we present the direct formulation of the two dimensional boundary element method bem for time harmonic dynamic problems in solids of general anisotropy we split the fundamental solution obtained by radon transform into static singular and dynamics regular parts we evaluate the boundary integrals for the static singular part analytically and those for the dynamic regular part numerically over the unit circle we apply the developed bem to eigenvalue analysis we determine eigenvalues of full non symmetric complex valued matrices depending non linearly on the frequency by first reducing them to the generalized linear eigenvalue problem and then applying the qz algorithm we test the performance of the qz algorithm thoroughly in comparison with the fem solution the proposed bem is not only a strong candidate to replace the fem for industrial eigenvalue problems but it is also applicable to a wider class of two dimensional time harmonic problems

the method of fundamental solutions for eigenproblems in domains with and without interior holes the main purpose of the present paper is to provide a general method of fundamental solution mfs formulation for two and three dimensional eigenproblems without spurious eigenvalues the spurious eigenvalues are avoided by utilizing the mixed potential method illustrated problems in the annular and concentric domains are studied analytically and numerically to demonstrate the issue of spurious eigenvalues by the discrete and continuous versions of the mfs with and without the mixed potential method the proposed numerical method is then verified with the exact solutions of the benchmark problems in circular and spherical domains with and without holes further studies are performed in a three dimensional peanut shaped domain in the spirit of the mfs this scheme is free from meshes singularities and numerical integrations

some new properties of the equality constrained and weighted least squares problem abstract in this paper some new properties of the equality constrained and weighted least squares problem wlse min w 1 2 kx g 2 subject to lx h are obtained we derive a perturbation bound based on an unconstrained least squares problem and deduce some equivalent formulae for the projectors of this unconstrained ls problem we also present a new way to compute the minimum norm solution x wlse of the wlse problem by using the qr decomposition of the corresponding matrices and propose an algorithm to compute x wlse using the qr factorizations some numerical examples are provided to compare different methods for solving the wlse problem

comments on the boundary point method for the calculation of exterior acoustic radiation problem s y zhang x z chen journal of sound and vibration 228 4 1999 761 772 abstract zhang and chen the boundary point method for the calculation of exterior acoustic radiation problem journal of sound and vibration 228 1999 761 772 proposed a boundary point method bpm for exterior acoustic problems the idea is similar to the chunky chief by wu a weighted residual formulation for the chief method in acoustic journal of acoustical society of america 90 1991 1608 1614 but chunky chief provides constraints using null field equations while the bpm used the chunky block singularity outside the domain the mathematical structure is similar to trefftz method and method of fundamental solutions j t chen et al on the equivalence of the trefftz method and method of fundamental solutions for laplace and biharmonic equations computers mathematics with applications 53 2007 851 879 since the interpolation function satisfies the governing equation later wu commented twice sean f wu comments on the boundary point method for the calculation of exterior acoustic radiation by s y zhang x z chen journal of sound and vibration 228 4 1999 761 772 journal of sound and vibration 298 2006 1173 sean f wu comments on reply to the comments on the boundary point method for the calculation of exterior acoustic radiation by s y zhang x z chen journal of sound and vibration 228 4 1999 761 772 journal of sound and vibration 298 2006 1176 1177 that the formulation of bpm is wrong and the authors replied also twice x z chen c x bi reply to the comments on the boundary point method for the calculation of exterior acoustic radiation by s y zhang x z chen journal of sound and vibration 228 4 1999 761 772 journal of sound and vibration 298 2006 1174 1175 x z chen c x bi reply to the comments on reply to the comments on the boundary point method for the calculation of exterior acoustic radiation by s y zhang x z chen journal of sound and vibration 228 4 1999 761 772 journal of sound and vibration 298 2006 1178 1179 to defend themselves here we would like to say a few words for the discussions in two aspects one is the formulation and the other is the occurrence of fictitious frequencies

a semi analytical approach for radiation and scattering problems with circular boundaries in this paper the radiation and scattering problems with circular boundaries are studied by using the null field integral equations in conjunction with degenerate kernels and fourier series to avoid calculating the cauchy and hadamard principal values in implementation the null field point can be located on the real boundary owing to the introduction of degenerate kernels for fundamental solution an adaptive observer system of polar coordinate is considered to fully employ the property of degenerate kernels for the hypersingular equation vector decomposition for the radial and tangential gradient is carefully considered this method can be seen as a semi analytical approach since errors attribute from the truncation of fourier series neither hypersingularity in burton and miller approach nor the chief concepts were required to deal with the problem of irregular frequencies four gains well posed model singularity free boundary layer effect free and exponential convergence are achieved by using the present approach a fast convergence rate in exponential order than algebraic one in bem stems from the series expansions three examples were demonstrated to see the validity of the present formulation and show the better accuracy than bem

mathematical analysis and numerical study to free vibrations of annular plates using biem and bem in this paper the spurious eigenequations for annular plate eigenproblems by using biem and bem are studied in the continuous and discrete systems since any two boundary integral equations in the plate formulation 4 equations can be chosen 6 c options can be considered instead of only two approaches single layer and double layer methods or singular and hypersingular equations which are adopted for the eigenproblems of the membrane and acoustic problems the occurring mechanism of the spurious eigenequation for annular plates in the complex valued formulations is studied analytically for the continuous system degenerate kernels for the fundamental solution and the fourier series expansion for the circular boundary density are employed to derive the true and spurious eigenequations analytically for the discrete system the degenerate kernels for the fundamental solution and circulants resulting from the circular boundary are employed to determine the true and spurious eigenequations true eigenequation depends on the specified boundary condition while spurious eigenequation is embedded in each formulation it is found that the spurious eigenvalue for the annular plate is the true eigenvalue of the associated interior problem with an inner radius of the annular domain also we provide three methods svd updating technique burton and miller method and chief method to suppress the occurrence of the spurious eigenvalues several examples were demonstrated to check the validity of the formulations copyright 2005 john wiley sons ltd

perturbation of the least squares problem consider the least squares solutions to ax b ax b where a a a and b b b are perturbed from a b respectively in an earlier paper the author deduced the perturbation bounds for the solution when b r a in this paper we extend the results to cover more general cases when b r a and a is not of full rank

algebraic properties of the rank deficient equality constrained and weighted least squares problems abstract we study the algebraic properties of the solutions of the equality constrained least squares problem min f s v kf g v 2 with s f v h lf v 2 min z c n v v h lz v 2 lse and corresponding weighted least squares problem wls in which l and l k may not be of full rank general formulas for the solutions are given and the algebraic relations between the lse and the wls solutions are obtained

an integral equation approach to three dimensional acoustic radiation and scattering problems this paper provides numerical implementation and tests for a boundary integral equation method proposed recently by krutitskii ima j appl math 64 259 269 2000 for evaluating three dimensional acoustic radiation and scattering fields in the exterior neumann problem for several obstacles auxiliary boundaries with certain prescribed boundary conditions are introduced inside the obstacles for the purpose of eliminating the fictitious characteristic frequencies applying the simple source formulation on all boundaries leads to a set of uniquely solvable integral equations with weakly singular kernels to facilitate the numerical implementation the modified integral equations are further transformed to ordinary ones that contain nonsingular kernels only test cases consist of the acoustic radiation and scattering by one sphere and a pair of equal spheres comparisons are made with analytical solutions and schenck s chief method numerical results demonstrate the efficiency robustness and accuracy of

iterative tikhonov regularization for the cauchy problem for the helmholtz equation abstract the cauchy problem for the helmholtz equation appears in various applications the problem is severely ill posed and regularization is needed to obtain accurate solutions we start from a formulation of this problem as an operator equation on the boundary of the domain and consider the equation in h 1 2 spaces by introducing an artificial boundary in the interior of the domain we obtain an inner product for this hilbert space in terms of a quadratic form associated with the helmholtz equation perturbed by an integral over the artificial boundary the perturbation guarantees positivity property of the quadratic form this inner product allows an efficient evaluation of the adjoint operator in terms of solution of a well posed boundary value problem for the helmholtz equation with transmission boundary conditions on the artificial boundary in an earlier paper we showed how to take advantage of this framework to implement the conjugate gradient method for solving the cauchy problem in this work we instead use the conjugate gradient method for minimizing a tikhonov functional the added penalty term regularizes the problem and gives us a regularization parameter that can be used to easily control the stability of the numerical solution with respect to measurement errors in the data numerical tests show that the proposed algorithm works well

determination of spurious eigenvalues and multiplicities of true eigenvalues in the dual multiple reciprocity method using the singular value decomposition technique the dual multiple reciprocity method mrm has been employed by the authors group 3 to solve the acoustic modes of a cavity with or without a thin partition in this paper we propose the singular value decomposition technique to filter our spurious eigenvalues and to determine the multiplicity of true eigenvalues by combining the dual equations in mrm also the role of the dual mrm for problems with a degenerate boundary is examined four examples including a square cavity with multiple eigenvalues a rectangular cavity a rectangular cavity with a zero thickness partition and a rectangular cavity with a partition with finite thickness are presented to demonstrate the validity of the proposed method also the analytical solution if available the finite element method results obtained by petyt et al and by abaqus and experimental measurements are compared with those of the proposed method and it is found that the agreement between them is very good

a boundary integral algorithm for the laplace dirichlet neumann mixed eigenvalue problem we present a novel integral equation algorithm for evaluation of zaremba eigenvalues and eigenfunctions that is eigenvalues and eigenfunctions of the laplace operator with mixed dirichlet neumann boundary conditions of course slight modifications of our algorithms are also applicable to the pure dirichlet and neumann eigenproblems expressing the eigenfunctions by means of an ansatz based on the single layer boundary operator the zaremba eigenproblem is transformed into a nonlinear equation for the eigenvalue for smooth domains the singular structure at dirichlet neumann junctions is incorporated as part of our corresponding numerical algorithm which otherwise relies on use of the cosine change of variables trigonometric polynomials and to avoid the gibbs phenomenon that would arise from the solution singularities the fourier continuation method fc the resulting numerical algorithm converges with high order accuracy without recourse to use of meshes finer than those resulting from the cosine transformation for non smooth lipschitz domains in turn an alternative algorithm is presented which achieves high order accuracy on the basis of graded meshes in either case smooth or lipschitz boundary eigenvalues are evaluated by searching for zero minimal singular values of a suitably stabilized discrete version of the single layer operator mentioned above the stabilization technique is used to enable robust non local zero searches the resulting methods which are fast and highly accurate for high and low frequencies alike can solve extremely challenging two dimensional dirichlet neumann and zaremba eigenproblems with high accuracies in short computing times enabling in particular evaluation of thousands of eigenvalues and corresponding eigenfunctions for a given smooth or non smooth geometry with nearly full double precision accuracy

degenerate scale problem when solving laplace s equation by bem and its treatment in this paper laplace problems are solved by using the dual boundary element method bem it is found that a degenerate scale problem occurs if the conventional bem is used in this case the influence matrix is rank deficient and numerical results become unstable both the circular and elliptical bars are studied analytically in the continuous system in the discrete system the fredholm alternative theorem in conjunction with the svd singular value decomposition updating documents is employed to sort out the spurious mode which causes the numerical instability three regularization techniques method of adding a rigid body mode hypersingular formulation and cheef combined helmholtz exterior integral equation formulation concept are employed to deal with the rank deficiency problem the addition of a rigid body term c in the fundamental solution is proved to shift the original degenerate scale to a new degenerate scale by a factor e c the torsion rigidities are obtained and compared with analytical solutions numerical examples including elliptical square and triangular bars were demonstrated to show the failure of conventional bem in case of the degenerate scale after employing the three regularization techniques the accuracy of the proposed approaches is achieved copyright 2004 john wiley sons ltd

an accelerated alternating procedure for the cauchy problem for the helmholtz equation in this paper we study the cauchy problem for the helmholtz equation this problem appears in various applications and is severely ill posed the modified alternating procedure has been proposed by

a new method for true and spurious eigensolutions of arbitrary cavities using the combined helmholtz exterior integral equation formulation method integral equation methods have been widely used to solve interior eigenproblems and exterior acoustic problems radiation and scattering it was recently found that the real part boundary element method bem for the interior problem results in spurious eigensolutions if the singular ut or the hypersingular lm equation is used alone the real part bem results in spurious solutions for interior problems in a similar way that the singular integral equation ut method results in fictitious solutions for the exterior problem to solve this problem a combined helmholtz exterior integral equation formulation method cheef is proposed based on the cheef method the spurious solutions can be filtered out if additional constraints from the exterior points are chosen carefully finally two examples for the eigensolutions of circular and rectangular cavities are considered the optimum numbers and proper positions for selecting the points in the exterior domain are analytically studied also numerical experiments were designed to verify the analytical results it is worth pointing out that the nodal line of radiation mode of a circle can be rotated due to symmetry while the nodal line of the rectangular is on a fixed position

a note on methods for circumventing non uniqueness when using integral equations comparaison de la formulation de l equation integrale d helmholtz combinee et de la formulation du gradient d helmholtz pour resoudre les problemes de rayonnement acoustique et de diffusion acoustique

comparison of regularization methods for solving the cauchy problem associated with the helmholtz equation in this paper several boundary element regularization methods such as iterative conjugate gradient tikhonov regularization and singular value decomposition methods for solving the cauchy problem associated to the helmholtz equation are developed and compared regularizing stopping criteria are developed and the convergence as well as the stability of the numerical methods proposed are analysed the cauchy problem for the helmholtz equation can be regularized by various methods such as the general regularization methods presented in this paper but more accurate results are obtained by classical methods such as the singular value decomposition and the tikhonov regularization methods copyright 2004 john wiley sons ltd

comments on vibration analysis of arbitrary shaped membranes using non dimensional dynamic influence function in reference 1 the authors presented the so called non dimensional dynamic in uence function method for membrane vibration a regular formulation and singularity free method were obtained also a symmetry and meshless formulation can be achieved the auxiliary system is a complementary solution instead of fundamental function it is source free in the in uence function many successful examples of the dirichlet types were demonstrated it seems that this method is very attractive however this method can be treated as one kind of the tre tz method 2 4 based on the dual formulation developed by chen and hong 5 6 the in uence function is nothing but the imaginary part of the fundamental solution s x ih 1 0 kr 7 the method by kang et al 1 can be treated as a special case of the imaginary part dual bem also the real part dual bem was developed and many references can be referred 8 9 mrm formulation can also be viewed as a real part formulation and its occurrence of spurious eigenvalues have been found in references 10 15 it is well known that the real part imaginary part formulations and multiple reciprocity method all result in spurious eigensolutions particularly the imaginary part formulation also results in an ill posed problem since the condition number for the in uence matrix is very large many approaches have been employed to lter out the spurious solutions and extract the true solution for example residue method 11 12 singular value decomposition svd technique 9 13 15 generalized singular value decomposition gsvd technique 16 and domain partition technique 17 it is expected that the kang s method has the problems of spurious solutions and ill conditioned behavior since it is an imaginary part formulation however no such information was addressed some points will be discussed as follows 1 spurious eigensolution it is interesting to nd that all the examples in reference 1 are of the dirichlet type according to the theoretical derivation the neumann problem has the problems of spurious solutions using the imaginary part formulation we will prove that in the following as mentioned earlier spurious eigenvalues occur in the real part of mrm formulation 9 11 12 also the imaginary part bem results in spurious solutions 7 here we will derive the true and spurious solutions in the discrete system analytically for a circular domain by using the non dimensional in uence function method 1 and the imaginary part dual bem 7 in a uni ed way the degenerate kernels and circulants are employed to study the discrete system in an exact form the relation between the non dimensional in uence function method and the imaginary part dual bem is also addressed and is summarized in table 1 the symbols in table 1 follow the dual model of chen and hong 6

the boundary collocation method with meshless concept for acoustic eigenanalysis of two dimensional cavities using radial basis function abstract in this paper a meshless method for the acoustic eigenfrequencies using radial basis function rbf is proposed the coefficients of influence matrices are easily determined by the two point functions in determining the diagonal elements of the influence matrices two techniques limiting approach and invariant method are employed based on the rbf in the imaginary part kernel the method results in spurious eigenvalues which can be separated by using the singular value decomposition svd technique in conjunction with the fredholm alternative theorem to understand why the spurious eigenvalues occur analytical study in the discrete system by discretizing the circular boundary is conducted by using circulants by using the svd updating terms and documents the true and spurious eigensolutions can be extracted out respectively several examples are demonstrated to see the validity of the present method

an accurate and efficient acoustic eigensolver based on a fast multipole bem and a contour integral method an accurate numerical solver is developed in this paper for eigenproblems governed by the helmholtz equation and formulated through the boundary element method a contour integral method is used to convert the nonlinear eigenproblem into an ordinary eigenproblem so that eigenvalues can be extracted accurately by solving a set of standard boundary element systems of equations in order to accelerate the solution procedure the parameters affecting the accuracy and efficiency of the method are studied and two contour paths are compared moreover a wideband fast multipole method is implemented with a block idr s solver to reduce the overall solution cost of the boundary element systems of equations with multiple right hand sides the burton miller formulation is employed to identify the fictitious eigenfrequencies of the interior acoustic problems with multiply connected domains the actual effect of the burton miller formulation on tackling the fictitious eigenfrequency problem is investigated and the optimal choice of the coupling parameter as i k is confirmed through exterior sphere examples furthermore the numerical eigenvalues obtained by the developed method are compared with the results obtained by the finite element method to show the accuracy and efficiency of the developed method

on the estimation of the consensus rate of convergence in graphs with persistent interconnections abstractthe aim of the current article is to establish myriad convergence rate estimates to consensus for time varying graphs with persistent interaction several novel analysis methodologies for consensus protocols employing the notions of persistence of excitation and lyapunov functions are provided the estimates are compared with each other and existing literature numerical simulations on test examples are illustrated to support the theoretical findings

an alternating iterative algorithm for the cauchy problem associated to the helmholtz equation in this paper the iterative algorithm proposed by kozlov et al comput maths math phys 31 1991 45 for obtaining approximate solutions to the ill posed cauchy problem for the helmholtz equation is analysed the technique is then numerically implemented using the boundary element method bem the numerical results confirm that the iterative bem produces a convergent and stable numerical solution with respect to increasing the number of boundary elements and decreasing the amount of noise added into the input data an efficient stopping regularising criterion is also proposed

treatment of singularities in helmholtz type equations using the boundary element method abstract in many engineering problems boundaries with sharp corners or abrupt changes in the boundary conditions and or the material properties give rise to singularities of various types which tend to slow down the rate of convergence with respect to decreasing the mesh size of any standard numerical method used for obtaining the solution in this paper in order to develop a method which overcomes this difficulty the singular solutions of isotropic and anisotropic helmholtz type equations with homogeneous dirichlet and or neumann boundary conditions in the neighbourhood of a singular point are derived the standard boundary element method bem is then modified to take account of the form of singularity without an appreciable increase in the computational effort and at the same time keeping a uniform discretization three examples are carefully investigated and the numerical results presented show an excellent performance of the approach developed

continuous time consensus under persistent connectivity and slow divergence of reciprocal interaction weights in this paper we present new results on consensus for continuous time multiagent systems we introduce the assumptions of persistent connectivity of the interaction graph and of slow divergence of reciprocal interaction weights persistent connectivity can be considered as the counterpart of the notion of ultimate connectivity used in discrete time consensus protocols slow divergence of reciprocal interaction weights generalizes the assumption of cut balanced interactions we show that under these two assumptions the continuous time consensus protocol succeeds the states of all the agents converge asymptotically to a common value moreover our proof allows us to give an estimate of the rate of convergence towards the consensus we also provide examples that make us think that both of our assumptions are tight

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

fading regularization mfs algorithm for the cauchy problem associated with the two dimensional helmholtz equation abstract in this paper we combine the fading regularization method with the method of fundamental solutions mfs and investigate its application to the cauchy problem for the two dimensional helmholtz equation we present a numerical reconstruction of the missing data on an inaccessible part of the boundary from the knowledge of overprescribed noisy data taken on the remaining accessible boundary part for both smooth and piecewise smooth two dimensional geometries the accuracy convergence stability and efficiency of the proposed numerical algorithm as well as its capability to deblur the noisy data are validated by three numerical examples

evaluation of the helmholtz boundary integral equation and its normal and tangential derivatives in two dimensions abstract this paper presents a means of evaluating singular integrals in the helmholtz boundary integral equation and its normal and tangential derivatives in two dimensions the subtraction addition technique is applied to the singular integral equations to convert the singular integrals to either ordinary integrals with bounded integrands or modified singular integrals including hypersingular integrals with exact integration values this regularization is performed before any discretization the modified integral equations can be calculated by directly applying standard quadrature rules over the entire integration domain numerical computations involve evaluating the acoustic field associated with a radiating inverse elliptic cylinder the velocity potential is obtained by applying the burton miller method which linearly combines the helmholtz boundary integral equation with its normal derivative to treat the fictitious characteristic frequencies further substituting the velocity potential into the regularized tangential derivative yields the surface tangential velocity comparing the numerical results with the analytical solutions verifies the effectiveness of the presented approach

a boundary integral equation method using auxiliary interior surface approach for acoustic radiation and scattering in two dimensions this paper presents an effective solution method for predicting acoustic radiation and scattering fields in two dimensions the difficulty of the fictitious characteristic frequency is overcome by incorporating an auxiliary interior surface that satisfies certain boundary condition into the body surface this process gives rise to a set of uniquely solvable boundary integral equations distributing monopoles with unknown strengths over the body and interior surfaces yields the simple source formulation the modified boundary integral equations are further transformed to ordinary ones that contain nonsingular kernels only this implementation allows direct application of standard quadrature formulas over the entire integration domain that is the collocation points are exactly the positions at which the integration points are located selecting the interior surface is an easy task moreover only a few corresponding interior nodal points are sufficient for the computation numerical calculations consist of the acoustic radiation and scattering by acoustically hard elliptic and rectangular cylinders comparisons with analytical solutions are made numerical results demonstrate the efficiency and accuracy of the current solution method

convergence and state reconstruction of time varying multi agent systems from complete observability theory we study continuous time consensus dynamics for multi agent systems with undirected switching interaction graphs we establish a necessary and sufficient condition for exponential asymptotic consensus based on the classical theory of complete observability the proof is remarkably simple compared to similar results in the literature and the conditions for consensus are mild this observability based method can also be applied to the case where negatively weighted edges are present additionally as a by product of the observability based arguments we show that the nodes initial value can be recovered from the signals on the edges up to a shift of the network average