non element method of solving 2d boundary problems defined on polygonal domains modeled by navier equation the paper presents a non element method of solving boundary problems defined on polygonal domains modeled by corner points to solve these problems a parametric integral equation system pies is used the system is characterized by a separation of the approximation of boundary geometry from the approximation of boundary functions this feature makes it possible to effectively investigate the convergence of the obtained solutions with no need of performing the approximation of boundary geometry the testing examples included confirm high accuracy of the solutions

abstract functional differential equations and reaction diffusion systems functional differential equations and reaction diffusion systems r h martin jr and h l smith abstract several fundamental results on the existence and behavior of solutions to semilinear functional differential equations are developed in a banach space setting the ideas are applied to reaction diffusion systems that have time delays in the nonlinear reaction terms the techniques presented here include differential inequalities invariant sets and lyapunov functions and therefore they provide for a wide range of applicability the results on inequalities and especially strict inequalities are new even in the context of semilinear equations whose nonlinear terms do not contain delays several fundamental results on the existence and behavior of solutions to semilinear functional differential equations are developed in a banach space setting the ideas are applied to reaction diffusion systems that have time delays in the nonlinear reaction terms the techniques presented here include differential inequalities invariant sets and lyapunov functions and therefore they provide for a wide range of applicability the results on inequalities and especially strict inequalities are new even in the context of semilinear equations whose nonlinear terms do not contain delays suppose q is a bounded domain in rn with aq smooth and a is the laplacian operator on q also let m be a positive integer z a positive number and f fi m a continuous bounded function from 0 xc x q x c z 0 m into rm where c t 0 is the space of continuous functions from z 0 into r the purpose of this paper is to apply abstract results for semilinear functional differential equations in banach spaces to reactiondiffusion systems with time delays having the form a tu x t diau x t i t x ut x t a xeq i 1 m rdd ai x ui x t au i x t 81 x t t a x eaq u x a 0 x x 0 5 t 0 di 0 and ca q 0 o is c and i q x 0 oo r is c2 here an is the outward normal derivative on aq and if di 0 it is assumed that no boundary conditions are specified for this i also tu x t denotes the partial with respect to t whereas ut x denotes the member of c z 0 defined by 0 u x t 0 u x t 0 m our techniques provide basic existence criteria but the main point is that they can also be effectively applied to obtain estimates for solutions especially received by the editors october 7 1987 and in revised form october 7 1988 1980 mathematics subject classification 1985 revision primary 35r10 34k30

the 3 d elastodynamic boundary element method semi analytical integration for linear isoparametric triangular elements a semi analytical integration scheme is described in this paper which is designed to reduce the errors incurred when integrals with singular integrands are evaluated numerically this new scheme can be applied to linear triangular elements for use in steady state elastodynamic bem problems and is particularly useful for predicting displacement to high accuracy close to surfaces for a spectrum of frequencies the scheme involves the application of taylor expansions to formulate the integrals into two parts one part is regular and is evaluated numerically and the other part is singular but sufficiently simple to enable its transforma tion into a line integral the line integral is solved numerically using gauss legendre quadrature this approach caters for all the integral types that appear in steady state elastodynamic boundary elements but in particular no special treatment is required for the evaluation of the cauchy principal value singular integrals numerical tests are performed on a simple test problem for which a known analytical solution exists the results obtained using the semi analytical approach are shown to be considerably more accurate than those obtained using standard quadrature methods copyright 1999 john wiley sons ltd

a bi cubic transformation for the numerical evaluation of the cauchy principal value integrals in boundary methods the numerical strategies employed in the evaluation of singular integrals existing in the cauchy principal value cpv sense are undoubtedly one of the key aspects which remarkably affect the performance and accuracy of the boundary element method bem thus a new procedure based upon a bi cubic co ordinate transformation and oriented towards the numerical evaluation of both the cpv integrals and some others which contain different types of singularity is developed both the ideas and some details involved in the proposed formulae are presented obtaining rather simple and attractive expressions for the numerical quadrature which are also easily embodied into existing bem codes some illustrative examples which assess the stability and accuracy of the new formulae are included

a hermite interpolation algorithm for hypersingular boundary integrals this paper presents a conforming c1 boundary integral algorithm based on hermite interpolation this work is motivated by the requirement that the surface function multiplying a hypersingular kernel be differentiable at the collocation nodes the unknown surface derivatives utilized by the hermite approximation are determined consistent with other boundary values by writing a tangential hypersingular equation hypersingular equations are primarily invoked for solving crack problems and the focus herein is on developing a suitable approximation for this geometry test calculations for the laplace equation in two dimensions indicate that the algorithm is a promising technique for three dimensional problems

a new method for evaluating singular integrals in stress analysis of solids by the direct boundary element method the purpose of this paper is to report on a new and efficient method for the evaluation of singular integrals in stress analysis of elastic and elasto plastic solids respectively by the direct boundary element method bem triangle polar co ordinates are used to reduce the order of singularity of the boundary integrals by one degree and to carry out the integration over mappings of the boundary elements onto plane squares the method was subsequently extended to the cubature of singular integrals over three dimensional internal cells as occur in applications of the bem to three dimensional elasto plasticity for this purpose so called tetrahedron polar co ordinates were introduced singular boundary integrals stretching over either linear triangular or quadratic quadilateral isoparametric boundry elements and singular volume integrals extending over either linear tetrahedral or quadratic hexahedral isoparametric internal cells are treated in case of higher order isoparametric boundary elements and internal cells division into a number of subelements and subcells respectively is necessary the analytical investigation is followed by a numerical study restricted to the use of quadratic quadrilateral isoparametric boundary elements this is justified by the fact that such elements as opposed to linear elements yield singular boundary integrals which cannot be integrated analytically the results of the numerical investigation demonstrate the potential of the developed concept

non singular somigliana stress identities in elasticity the paper presents two fully equivalent and regular forms of the hypersingular somigliana stress identity in elasticity that are appropriate for problems in which the displacement field and resulting stresses is c1 continuous each form is found as the result of a single decomposition process on the kernels of the somigliana stress identity in three dimensions the results show that the use of a simple stress state for regularization arises in a direct manner from the somigliana stress identity just as the use of a constant displacement state regularization arose naturally for the somigliana displacement identity the results also show that the same construction leads naturally to a finite part form of the same identity while various indirect constructions of the equivalents to these findings are published none of the earlier forms address the fundamental issue of the usual discontinuities of boundary data in the hypersingular somigliana stress identity that arise at corners and edges these new findings specifically focus on the corner problem and establish that the previous requirements for continuity on the densities in the hypersingular somigliana stress identity are replaced by a sole requirement on displacement field continuity the resulting regularized and finite part forms of the somigliana stress identity leads to a regularized form of the stress boundary integral equation stress bie the regularized stress bie is shown to properly allow piecewise discontinuity of the boundary data subject only to c1 continuity of the underlying displacement field the importance of the findings is in their application to boundary element modeling of the hypersingular problem the piecewise discontinuity derivation for corners is found to provide a rigorous and non singular basis for collocation of the discontinuous boundary data for both the regularized and finite part forms of the stress bie the boundary stress solution for both forms is found to be an average of the computed stresses at collocation points at the vertices of boundary element meshes collocation at these points is shown to be without any unbounded terms in the formulation thereby eliminating the use of non conforming elements for the hypersingular equations the analytical findings in this paper confirm the correct use of both regularized and finite part forms of the stress bie that have been the basis of boundary element analysis previously published by the first author of the current paper

symmetric galerkin boundary integral formulation for interface and multi zone problems domains containing an internal boundary such as a bi material interface arise in many applications e g composite materials and geophysical simulations this paper presents a symmetric galerkin boundary integral method for this important class of problems in this situation the physical quantities are known to satisfy continuity conditions across the interface but no boundary conditions are specied the algorithm described herein achieves a symmetric matrix of reduced size moreover the symmetry can also be invoked to lessen the numerical work involved in constructing the system of equations and thus the method is computationally very ecient a prototype numerical example with several variations in the boundary conditions and material properties is employed to validate the formulation and corresponding numerical procedure the boundary element results are compared with analytical solutions and with numerical results obtained with the nite element method 1997 by john wiley sons ltd

improved numerical method for the traction boundary integral equation by application of stokes theorem this paper concerns the direct numerical evaluation of singular integrals arising in boundary integral equations for displacement bie and displacement gradients bide and the formulation of a traction boundary integral equation tbie for solving general elastostatic crack problems subject to certain continuity conditions concerning displacements and tractions at the source point singular integrals in the bie and the bide corresponding to coefficients of displacement and displacement gradients at the source point are shown to be of a form that allows application of stokes theorem all the singular integrals in 3 d bie and bide are reduced to non singular line integrals and those in 2 d bie and bide are evaluated in closed form remaining terms involve regular integrals and no references to cauchy or hadamard principal values are required continuous isoparametric interpolations used on continuous elements local to the source point are modified to include unique displacement gradients at the source point which are compatible with all local tractions the resulting numerical bide is valid for source points located arbitrarily on the boundary including corners and a procedure is given for constructing a tbie from the bide some example solutions obtained using the present numerical method for the tbie in 2 d and 3 d are presented british crown copyright 1997 dera int j numer meth engng 40 3141 3161 1997 no of figures 5 no of tables 5 no of references 13

a direct boundary integral method for the three dimensional lifting flow abstract a regularized integral formulation in velocity vector terms for three dimensional incompressible non lifting and lifting flow is developed in the case of lifting flow the circulatory flow around the body is generated by a discrete distribution of inner vortices and a vectorial equality in velocity terms is used as an equivalent of the equal pressure kutta condition the numerical comparison with the panel method in the case of non lifting flow shows the superiority of the present method also a two dimensional lifting flow is simulated using a high spanwise wing and comparison with the analytic solution shows a very good concordance even at high incidence

a boundary integral approach for acoustic radiation of axisymmetric bodies with arbitrary boundary conditions valid for all wave numbers a boundary integral method for solving the exterior acoustic radiation problem of axisymmetric bodies with arbitrary boundary conditions is developed the new formulation derives from the method proposed by burton and miller proc r soc london ser a 323 201 210 1971 which uses a linear combination of the helmholtz integral equation and its normal derivative to ensure the uniqueness of the numerical solution at all frequencies it is shown that the use of tangential operators enables one to easily compute the hypersingular integral without much extra effort by taking advantage of the properties of axisymmetric geometry and using the expansion of the boundary conditions and the surface distribution functions in fourier series with respect to the angle of revolution the surface integral is reduced to a line integral along the generator of the body and fourier integrals of the green s function and its derivatives over the circumferential angle the fourier integrals with singular kernels are eval

toric fiber products abstract we introduce and study the toric fiber product of two ideals in polynomial rings that are homogeneous with respect to the same multigrading under the assumption that the set of degrees of the variables form a linearly independent set we can explicitly describe generating sets and grobner bases for these ideals this allows us to unify and generalize some results in algebraic statistics

direct evaluation of hypersingular galerkin surface integrals a direct algorithm for evaluating hypersingular integrals arising in a three dimensional galerkin boundary integral analysis is presented the singular integrals are defined as limits to the boundary and by integrating two of the four dimensions analytically the coincident integral is shown to be divergent however the divergent terms can be explicitly calculated and shown to cancel with corresponding singularities in the adjacent edge integrals a single analytic integration is employed for the edge and vertex singular integrals this is sufficient to display the divergent term in the edge adjacent integral and to show that the vertex integral is finite by explicitly identifying the divergent quantities we can compute the hypersingular integral without recourse to stokes s theorem or the hadamard finite part the algorithms are developed in the context of a linear element approximation for the laplace equation but are expected to be generally applicable as an example the algorithms are applied to solve a thermal problem in an exponentially graded material

hypersingular integrals how smooth must the density be hypersingular integrals are guaranteed to exist at a point x only if the density function f in the integrand satises certain conditions in a neighbourhood of x it is well known that a su cient condition is that f has a holder continuous rst derivative this is a stringent condition especially when it is incorporated into boundary element methods for solving hypersingular in tegral equations this paper is concerned with nding weaker conditions for the existence of one dimensional hadamard nite part integrals it is shown that it is sucien t for the even part of f with respect to x to have a holder continuous rst derivative the odd part is al lowed to be discontinuous a similar condition is obtained for cauchy principal value integrals these simple results have non trivial consequences they are applied to the calculation of the tangential derivative of a single layer potential and to the normal derivative of a double layer potential particular attention is paid to discontinuous densities and to discontinuous boundary conditions also despite the weaker sucien t conditions it is rearmed that for hypersingular integral equations collocation at a point x at the junction between two standard conforming boundary elements is not permissible theoretically various modications to the denition of nite part integral are explored

traveling waves for a nonlocal dispersal sir model with delay and external supplies this paper is concerned with the existence nonexistence and minimal wave speed of traveling waves of a nonlocal dispersal delayed sir model with constant external supplies and holling ii incidence rate we find that the existence and nonexistence of traveling waves of the system are not only determined by the minimal wave speed c but also by the so called basic reproduction number r 0 of the corresponding reaction system that is we establish the existence of traveling waves for r 0 1 and each wave speed c c and the nonexistence for r 0 1 and any 0 c c or r 0 1 we also discuss how the latency of infection and the spatial movement of the infective individuals affect the minimal wave speed biologically speaking the longer the latency of infection in a vector is the slower the disease spreads

facets of the linear ordering polytope letd n be the complete digraph onn nodes and letp lo denote the convex hull of all incidence vectors of arc sets of linear orderings of the nodes ofd n i e these are exactly the acyclic tournaments ofd n we show that various classes of inequalities define facets ofp lo e g the 3 dicycle inequalities the simplek fence inequalities and various mobius ladder inequalities and we discuss the use of these inequalities in cutting plane approaches to the triangulation problem of input output matrices i e the solution of permutation resp linear ordering problems

a unified boundary element method for the analysis of sound and shell like structure interactions i formulation and verification a unified boundary element method bem is developed in this paper to model both the exterior acoustic field and the elastic shell like structure in a coupled analysis the conventional boundary integral equation bie for three dimensional 3d elastodynamics is applied to thin shell like structures which can have arbitrary shapes and small thicknesses the nearly singular integrals existing in the bie when applied to thin bodies are transformed to nonsingular line integrals and are evaluated accurately and efficiently for the exterior 3d acoustic domain the burton and miller composite bie formulation is employed to overcome the fictitious eigenfrequency difficulty fed and the thin shape breakdown tsb conforming c0 quadratic elements are employed in the discretization of the two sets of bies the developed bie formulations are valid for both radiation and scattering problems and for all wave numbers numerical examples using spherical and cylindrical shells including nonuniform thickness and nond

powerful short cuts for multiple testing procedures with special reference to gatekeeping strategies in this paper we present a general testing principle for a class of multiple testing problems based on weighted hypotheses under moderate conditions this principle leads to powerful consonant multiple testing procedures furthermore short cut versions can be derived which simplify substantially the implementation and interpretation of the related test procedures it is shown that many well known multiple test procedures turn out to be special cases of this general principle important examples include gatekeeping procedures which are often applied in clinical trials when primary and secondary objectives are investigated and multiple test procedures based on hypotheses which are completely ordered by importance we illustrate the methodology with two real clinical studies

weakly singular stress bem for 2d elastostatics a weakly singular stress bem is presented in which the linear state regularizing field is extended over the entire surface the algorithm employs standard conforming c0 elements with lagrangian interpolations and exclusively uses gaussian integration without any transformation of the integrands other than the usual mapping into the intrinsic space the linear state stress bie on which the algorithm is based has no free term so that the bem treatment of external corners requires no special consideration other than to admit traction discontinuities the self regularizing nature of the somigliana stress identity is demonstrated to produce a very simple and effective method for computing stresses which gives excellent numerical results for all points in the body including boundary points and interior points which may be arbitrarily close to a boundary a key observation is the relation between bie density functions and successful interpolation orders numerical results for two dimensions show that the use of quartic interpolations is required for algorithms employing regularization over an entire surface to show comparable accuracy to algorithms using local regularization and quadratic interpolations additionally the numerical results show that there is no general correlation between discontinuities in elemental displacement gradients and solution accuracy either in terms of unknown boundary data or interior solutions near element junctions copyright 1999 john wiley sons ltd

flux and traction boundary elements without hypersingular or strongly singular integrals the present paper deals with a boundary element formulation based on the traction elasticity boundary integral equation potential derivative for laplace s problem the hypersingular and strongly singular integrals appearing in the formulation are analytically transformed to yield line and surface integrals which are at most weakly singular regularization and analytical transformation of the boundary integrals is done prior to any boundary discretization the integration process does not require any change of co ordinates and the resulting integrals can be numerically evaluated in a simple and efficient way the formulation presented is completely general and valid for arbitrary shaped open or closed boundaries analytical expressions for all the required hypersingular or strongly singular integrals are given in the paper to fulfil the continuity requirement over the primary density a simple be discretization strategy is adopted continuous elements are used whereas the collocation points are shifted towards the interior of the elements this paper pretends to contribute to the transformation of hypersingular boundary element formulations as something clear general and easy to handle similar to in the classical formulation copyright 2000 john wiley sons ltd

on the non singular traction bie in elasticity the work reported herein develops a generalized traction bie formulation which involves only weakly singular integrals in the three dimensional problem or totally regular integrals in the two dimensional problem the first step deals with the terms in the somigliana displacement identity and then the derivatives of these terms the only conditions required for the existence of the traction bie and the related somigliana stress identity are weak continuity of the in plane derivatives of the surface displacements and of the surface tractions it is shown that the cauchy principal value cpv interpretations so commonly used in bie developments are unnecessary the formulation is established not only at a smooth boundary point but also at a corner point the extension of the non singular formulation to discontinuous boundary tractions and tangential derivatives of the boundary displacements applicable to a generalized problem statement as well as the usual bem implementations is also shown in the demonstrated formulation the source points are located directly at the boundary nodes and non conformal elements are not needed

algebraic algorithms for sampling from conditional distributions we construct markov chain algorithms for sampling from discrete exponential families conditional on a sufficient statistic examples include contingency tables logistic regression and spectral analysis of permutation data the algorithms involve computations in polynomial rings using grobner bases

three dimensional curved crack in an elastic body abstract the boundary integral equations which give the relation between the crack opening displacement and traction on the surface of a crack embedded in an infinite isotropic elastic body are formulated the integral equations are transformed into spherical and cylindrical coordinates in the cases of cracks curved in the shape of spherical and cylindrical surfaces respectively so that these boundary integral equations may be converted into a system of algebraic equations by the boundary element method the dependence of stress intensity factors on the curvature of crack has been numerically calculated for the spherical crack with circular contour under a constant load

on the toric algebra of graphical models we formulate necessary and sufficient conditions for an arbitrary discrete probability distribution to factor according to an undirected graphical model or a log linear model or other more general exponential models for decomposable graphical models these conditions are equivalent to a set of conditional independence statements similar to the hammersley clifford theorem however we show that for nondecomposable graphical models they are not we also show that nondecomposable models can have nonrational maximum likelihood estimates these results are used to give several novel characterizations of decomposable graphical models

a nonlocal diffusion model of a single species with age structure abstract using theory of fourier transformation dirac function and von foerster rule with nonlocal diffusion operator we derive a single species population model with two age stages juvenile and mature which includes nonlocal dispersal both in diffusion and reaction we found that the nonlocal reaction kernel function for mature population depends on the kernel function of diffusion for two age stages this model takes the local diffusion model with only laplacian operator or laplacian operator combining with convection operator as particular examples the existence uniqueness positivity and boundedness of initial value problem are also investigated in the present article as a new model its dynamics is worthy to be explored in the future work

on the treatment of corners in the boundary element method abstract a new technique for treating surface discontinuities within boundary element calculations is proposed multiple nodes are used to represent the geometry and the necessary additional equations are obtained by differentiating the usual boundary element integral equation in deriving expressions for the resulting singular integrals it is found that constraints must be placed on the functional approximation at the discontinuity an algorithm for incorporating these constraints is developed and numerical tests for an exactly solvable three dimensional laplace equation problem are presented

symmetric weak form integral equation method for three dimensional fracture analysis a symmetric galerkin boundary element method is developed for the analysis of linearly elastic isotropic three dimensional solids containing fractures the formulation is based upon a weak form displacement integral equation and a weak form traction integral equation recently developed by li and mear 1997 these integral equations are only weakly singular and their validity requires only that the boundary displacement data be continuous hence allowing standard co elements to be employed as part of the numerical implementation a special crack tip element is developed which has a novel feature in that there exist degrees of freedom associated with the nodes at the crack front as a result a higher degree of approximation is achieved for the relevant displacement data on the crack and further the stress intensity factors are obtained directly in terms of the crack front nodal data various examples are treated for cracks in unbounded domains and for cracks in finite domains including both embedded and surface breaking cracks and it is demonstrated that highly accurate results can be achieved using relatively coarse meshes

corner treatment by assigning dual tractions to every node for elastodynamics in td bem in this study a corner treatment on the boundary for time domain boundary element method td bem by assigning dual tractions to every node is proposed the proposed corner treatment on boundary mimics the real mechanical situation on the physical boundary for elastodynamic problem and the computation accuracy is good taking the rectangular boundary as an example the numerical implementation of the proposed corner treatment on boundary by assigning dual tractions to every node is demonstrated two verification examples one dimensional rod in finite medium and two dimensional circular cavity in infinite medium under dynamic loads are conducted in which the results from the td bem based on the proposed corner treatment on boundary are compared with the results from the analytical solutions good agreement between the analytical results and the td bem results based on the proposed corner treatment on boundary for td bem is achieved for the two verification examples

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

two methods for the numerical solution of bueckner s singular integral equation for plane elasticity crack problems abstract the classical collocation and galerkin methods are used for the numerical solution of singular integral equations of the first kind involving a finite part integral with a double pole singularity such equations appear in plane elasticity crack problems where they were suggested by bueckner and the unknown function in them is proportional to the crack opening displacement function an application of the proposed methods to the problem of a straight crack under an exponential normal loading distribution is also made and shows the rapid convergence of the obtained numerical results for the stress intensity factors at the crack tips to their theoretical values

some improvements of accuracy and efficiency in three dimensional direct boundary element method numerical analysis with the boundary element method bem has been used more and more in various engineering fields in recent years in numerical techniques however there are some problems which have not been fully solved even now the most essential one is the drop in the accuracy of results for internal points near the boundary of the structure where the singularity of integrands in the boundary integral equation is too strong to be evaluated with the normal numerical method for the boundary integral equation of stress this problem became more serious and the accuracy can be improved only partly even though very refined boundary elements are used in this paper the boundary integral equation is newly formulated using a relative quantity of displacement in this way the singularity of boundary integrals is reduced by the order of 1 r and the accuracy of solution is improved significantly furthermore in order to integrate it more accurately two kinds of numerical integral methods are newly developed by using these methods both displacement and stress can be obtained with excellent accuracy at almost any point in the structure without any numerical difficulty although the discretization may be comparatively coarse the generality and practicability of the present formulation and integral methods are confirmed through some examples of three dimensional elastic problems

a self adaptive co ordinate transformation for efficient numerical evaluation of general boundary element integrals almost all general purpose boundary element computer packages include a curved geometry modelling capability thus numerical quadrature schemes play an important role in the efficiency of programming the technique the present work discusses this problem in detail and introduces efficient means of computing singular or nearly singular integrals currently found in two dimensional axisymmetric and three dimensional applications emphasis is given to a new third degree polynomial transformation which was found greatly to improve the accuracy of gaussian quadrature scheme s within the near singularity range the procedure can easily be implemented into existing be codes and presents the important feature of being self adaptive i e it produces a variable lumping of the gauss stations toward the singularity depending on the minimum distance from the source point to the element the self adaptiveness of the scheme also makes it inactive when not useful large source distances which makes it very safe for general usage

direct computation of cauchy principal value integrals in advanced boundary elements this paper presents a new method for the direct computation of strongly singular integrals existing in the cauchy principal value sense it can be usefully applied in the solution by the direct boundary element method of many different problems initially some considerations are provided in order to summarize the state of the art on this issue then the features of the proposed method are reported the procedure allows the direct calculation of cauchy principal value integrals with first order singularity and it is applicable even in advanced boundary element methods employing high order elements it requires only the use of standard gaussian quadrature formulae plus the computation of a logarithmic term some examples show the effectiveness and efficiency of the procedure

error analysis and adaptivity in three dimensional linear elasticity by the usual and hypersingular boundary contour method abstract two related topics are addressed in this article the first part of the article proves that for a certain admissible class of problems in linear elasticity the hypersingular boundary contour method hbcm can be collocated at all boundary points on the surface of a three dimensional 3 d body including those on boundary contours edges and corners because the hbcm shape functions satisfy a priori all the smoothness requirements for collocation at these points in contrast the hypersingular boundary element method needs in general relaxation of some of these smoothness requirements for its shape functions even for collocation at regular points that lie on the boundaries of boundary elements a hypersingular residual obtained from the standard and hypersingular boundary integral equations hbies has been recently proposed as a local error estimator for a boundary element for the boundary integral equation the second part in the present article is concerned with a definition of an analogous local error estimator for the boundary contour method for 3 d linear elasticity this error estimator is then used to drive an h adaptive meshing procedure numerical results are presented to demonstrate adaptive meshing for selected example problems

parametrizations of toric varieties over any field abstract the columns of an integral matrix d give rise to the toric variety v k i d and also provide a parametrization of a subset of v k i d the so called toric set k d we completely determine the toric set k d over any field we provide conditions under which v k i d is fully parametrized by the columns of d that means k d v k i d in particular we prove that normal toric varieties over any field are always fully parametrized by the columns of an appropriate matrix

a general and effective way for evaluating the integrals with various orders of singularity in the direct boundary element method a general and efficient technique is developed for the evaluation of the integrals with various orders of singularity such as occur in the three dimensional boundary element method bem generalized extended triangle tetrahedron polar co ordinate mappings together with two conditions are used to remove the singularity of the integrals and to evaluate the corresponding non singular ones in a new numerical space triangle and tetrahedron polar co ordinates in reference 1 are proved to be a special case of the generalized ones in this paper with the developed idea boundary element results converge rapidly towards the analytical solutions for the strongly singular integrals evaluated directly and the analytical solutions can be gained in principle even when employing higher order triangular boundary elements and tetrahedral cells the generality and practicability of the method are demonstrated in the case of higher order elements discontinuous elements and large engineering problems

non singular boundary integral equation implementation the basis of the boundary integral equation bie development is the singular field solution for the kelvin point load problem the presence of the mathematical singularity in an otherwise non singular problem has created over the years a variety of numerical coping strategies the current paper extends some of the earlier works in a simple manner that eliminates the mathematical singularity through analytical integration of the critical terms the resulting formulation is fully non singular and is shown to be amenable to simple low order gaussian integration the critical class of problems involving thin sections and or highly graded bie meshes now can be solved without previous problems and concerns the accuracy of the numerical integrations used in creating the linear bie equations extension of the formulation approach to remove hypersingular formulation problems in fracture mechanics is seen to be a future beneficiary of the semi analytical bie implementation reported herein

a reaction diffusion model for a single species with age structure i travelling wavefronts on unbounded domains in this paper we derive the equation for a single species population with two age classes and a fixed maturation period living in a spatially unbounded environment we show that if the mature deat

on the extraction technique in boundary integral equations in this paper we develop and analyze a bootstrapping algorithm for the extraction of potentials and arbitrary derivatives of the cauchy data of regular three dimensional second order elliptic boundary value problems in connection with corresponding boundary integral equations the method rests on the derivatives of the generalized green s representation formula which are expressed in terms of singular boundary integrals as hadamard s finite parts their regularization together with asymptotic pseudohomogeneous kernel expansions yields a constructive method for obtaining generalized jump relations these expansions are obtained via composition of taylor expansions of the local surface representation the density functions differential operators and the fundamental solution of the original problem together with the use of local polar coordinates in the parameter domain for boundary integral equations obtained by the direct method this method allows the recursive numerical extraction of potentials and their derivatives near and up to the boundary surface

sysygies of unimodular lawrence ideals infinite hyperplane arrangements whose vertices form a lattice are studied from the point of view of commutative algebra the quotient of such an arrangement modulo the lattice action represents the minimal free resolution of the associated binomial ideal which defines a toric subvariety in a product of projective lines connections to graphic arrangements and to beilinson s spectral sequence are explored

spreading speed for a nonlocal diffusive delayed model without quasi monotonicity abstract in this article we study the spatial spreading dynamics for a nonlocal diffusive equation with general nonmonotone monostable nonlinearity on the basis of a sandwich technique and a comparison theorem for solutions of the cauchy problems of three systems the spreading speed c is established for the model as an application of the results we consider some models as special cases it is shown that the results in this article generalize and improve some results in the existing literature

accurate numerical integration of singular boundary element kernels over boundaries with curvature use of the green function for the solution of boundary value problems frequently results in singular integral equations algorithms are presented for the accurate and efficient treatment of singular kernels frequently encountered in the boundary element method bem they are based upon the use of appropriately weighted gaussian quadrature formulae together with numerical geometrical transformations of the region of integration the use of high order subdomain expansion functions for interpolation over nonplanar elements allows boundary curvature to be accommodated in particular the handling of green functions with logarithmic and r 1 behaviour are detailed volume integrals with r 2 singularity are outlined operations are performed on a simplex thus resulting in generality and ease of automation this scheme has been incorporated into boundary element method software and successfully applied to a variety of problems

analysis of three dimensional anisotropic heat conduction problems on thin domains using an advanced boundary element method abstract in this paper an advanced boundary element method bem is developed for solving three dimensional 3d anisotropic heat conduction problems in thin walled structures the troublesome nearly singular integrals which are crucial in the applications of the bem to thin structures are calculated efficiently by using a nonlinear coordinate transformation method for the test problems studied promising bem results with only a small number of boundary elements have been obtained when the thickness of the structure is in the orders of micro scales 10 6 which is sufficient for modeling most thin walled structures as used in for example smart materials and thin layered coating systems the advantages disadvantages as well as potential applications of the proposed method as compared with the finite element method fem are also discussed

numerical implementation of the lumped parameter model for the acoustic power output of a vibrating structure in a previous paper a lumped parameter model for the acoustic radiation from a vibrating structure was defined by dividing the surface of the structure into elements expanding the acoustic field from each of the elements in a multipole expansion and truncating all but the lowest order terms in the expansion here the lumped parameter model is implemented numerically by requiring the boundary condition for the normal surface velocity to be satisfied in a lumped parameter sense this alleviates the difficulties typically encountered in enforcing the boundary condition leading to a relatively simple numerical solution with well defined convergence properties the basis functions for the numerical analysis are taken as the acoustic fields of discrete simple dipole and tripole sources located at the geometrical centers of the surface elements the different source types are used to represent the radiation from different kinds of surface elements simple sources for elements in the plane of an infinite baffle dipole sources for very thin structures which deform only in bending and tripole sources for elements associated with parts of a structure enclosing a finite volume the convergence of the numerical solution for the power output as a function of both frequency and element size is demonstrated through several example problems

the simple boundary element method for multiple cracks in functionally graded media governed by potential theory a three dimensional galerkin approach the simple boundary element method consists of recycling existing codes for homogeneous media to solve problems in non homogeneous media while maintaining a purely boundary only formulation within this scope this paper presents a simple galerkin boundary element method for multiple cracks in problems governed by potential theory in functionally graded media steady state heat conduction is investigated for thermal conductivity varying either parabolically exponentially or trigonometrically in one or more co ordinates a three dimensional implementation which merges the dual boundary integral equation technique with the galerkin approach is presented special emphasis is given to the treatment of crack surfaces and boundary conditions the test examples simulated with the present method are verified with finite element results using graded finite elements the numerical examples demonstrate the accuracy and efficiency of the present method especially when multiple interacting cracks are involved copyright 2005 john wiley sons ltd

new green s function for stress field and a note of its application in quantum wire structures abstract the elastic field caused by the lattice mismatch between the quantum wires and the host matrix can be modeled by a corresponding two dimensional hydrostatic inclusion subjected to plane strain conditions the stresses in such a hydrostatic inclusion can be effectively calculated by employing the green s functions developed by downes and faux which tend to be more efficient than the conventional method based on the green s function for the displacement field in this study downes and faux s paper is extended to plane inclusions subjected to arbitrarily distributed eigenstrains an explicit green s function solution which evaluates the stress field due to the excitation of a point eigenstrain source in an infinite plane directly is obtained in a closed form here it is demonstrated that both the interior and exterior stress fields to an inclusion of any shape and with arbitrarily distributed eigenstrains are represented in a unified area integral form by employing the derived green s functions in the case of uniform eigenstrain the formulae may be simplified to contour integrals by green s theorem however special care is required when green s theorem is applied for the interior field the proposed green s function is particularly advantageous in dealing numerically or analytically with the exterior stress field and the non uniform eigenstrain two examples concerning circular inclusions are investigated a linearly distributed eigenstrain is attempted in the first example resulting in a linear interior stress field the second example solves a circular thermal inclusion where both the interior and exterior stress fields are obtained simultaneously

some notes on singular integral techniques in boundary element analysis the paper presented here reviews the numerical techniques used currently to calculate the singular integrals and nearly singular integrals in the boundary element analysis some incorrect algorithms published before are discussed and a new numerical technique to calculate the nearly singular integral is developed the numerical results show a significant improvement in both accuracy and efficiency compared to the traditional adaptive gaussian quadrature and subdivision techniques

a hybrid micro macro bem with micro scale inclusion crack interactions local analysis schemes capable of detailed representations of micro features of a problem are integrated with a macro scale bem technique capable of handling finite geometries and realistic boundary conditions this paper focuses on micro scale interactions among cracks and inclusions as well as their ramifications on macro scale damage evaluations the micro scale effects are introduced into the macro scale bem computations through an augmented fundamental solution obtained from an integral equation representation of the micro scale features the proposed hybrid micro macro bem formulation allows complete decomposition of the real problem into two sub problems one residing entirely at the micro level while the other resides at the macro level this allows for investigations of the micro structural attributes while retaining the macro scale geometric features and actual boundary conditions for the structural component under consideration as a first attempt dilute inclusion densities with strong inclusion crack and crack crack interactions are considered the numerical results obtained from the hybrid bem analysis establish the accuracy and effectiveness of the proposed micro macro computational scheme for this class of problems the proposed micro macro bem formulation can be easily extended to investigate the effects of other micro features e g interfaces short or continuous fibers in the context of linear elasticity on macro scale failure modes observed in structural components

on the singularities of green s formula and its normal derivative with an application to surface wave body interaction problems the paper presents the non singular forms of green s formula and its normal derivative of exterior problems for three dimensional laplace s equation the main advantage of these modified formulations is that they are amenable to solution by directly using quadrature formulas thus the conventional boundary element approximation which locally regularizes the singularities in each element is not required the weak singularities are treated by both the gauss flux theorem and the property of the associated equipotential body the hypersingularities are treated by further using the boundary formula for the associated interior problems the efficacy of the modified formulations is examined by a sphere in an infinite domain subject to neumann and dirichlet conditions respectively the modified integral formulations are further applied to a practical problem i e surface wave body interactions using the conventional boundary integral equation formulation is known to break down at certain discrete frequencies for such a problem removing the irregular frequencies is performed by linearly combining the standard integral equation with its normal derivative computations are presented of the added mass and damping coefficients and wave exciting forces on a floating hemisphere comparing the numerical results with that by other approaches demonstrates the effectiveness of the method copyright 2000 john wiley sons ltd

hypersingular integrals in boundary element fracture analysis a new general purpose boundary element method for domains with cracks has been recently developed this technique avoids the use of a multi domain decomposition by including an additional integral equation expressing the boundary condition on the crack the principal requirement of this technique is the analytic determination of certain hypersingular integrals of the green s function which arise from this equation in order to establish the applicability of this method for fracture these integrals are evaluated herein for the kelvin solution of the three dimensional navier equations of linear elasticity numerical results for fracture problems using the single domain boundary element analysis are also presented

on boundary integral equations for crack problems a ubiquitous linear boundary value problem in mathematical physics involves solving a partial differential equation exterior to a thin obstacle one typical example is the scattering of scalar waves by a curved crack or rigid strip neumann boundary condition in two dimensions this problem can be reduced to an integrodifferential equation which is often regularized we adopt a more direct approach and prove that the problem can be reduced to a hypersingular boundary integral equation similar reductions will obtain in more complicated situations computational schemes for solving this equation are described with special emphasis on smoothness requirements extensions to three dimensional problems involving an arbitrary smooth bounded crack in an elastic solid are discussed

mm algorithms for generalized bradley terry models the bradley terry model for paired comparisons is a simple and muchstudied means to describe the probabilities of the possible outcomes when individuals are judged against one another in pairs among the many studies of the model in the past 75 years numerous authors have generalized it in several directions sometimes providing iterative algorithms for obtaining maximum likelihood estimates for the generalizations building on a theory of algorithms known by the initials mm for minorization maximization this paper presents a powerful technique for producing iterative maximum likelihood estimation algorithms for a wide class of generalizations of the bradley terry model while algorithms for problems of this type have tended to be custom built in the literature the techniques in this paper enable their mass production simple conditions are stated that guarantee that each algorithm described will produce a sequence that converges to the unique maximum likelihood estimator several of the algorithms and convergence results herein are new

the traction boundary contour method for linear elasticity this paper presents a further development of the boundary contour method the boundary contour method is extended to cover the traction boundary integral equation a traction boundary contour method is proposed for linear elastostatics the formulation of traction boundary contour method is regular for points except the ends of the boundary element and corners the present approach only requires line integrals for three dimensional problems and function evaluations at the ends of boundary elements for two dimensional cases the implementation of the traction boundary contour method with quadratic boundary elements is presented for two dimensional problems numerical results are given for some two dimensional examples and these are compared with analytical solutions this method is shown to give excellent results for illustrative examples copyright 1999 john wiley sons ltd

normal polytopes arising from finite graphs abstract let g be a finite connected graph on the vertex set 1 d allowing loops and having no multiple edge let k t 1 t d denote the polynomial ring in d indeterminates over a field k and let k g be the subalgebra of k t 1 t d generated by all quadratic monomials t i t j such that i j is an edge of g and by all quadratic monomials t 2 i such that g has a loop at i we describe the normalization of k g explicitly and we give a combinatorial criterion for k g to be normal

toric ideals generated by quadratic binomials abstract a combinatorial criterion for the toric ideal arising from a finite graph to be generated by quadratic binomials is studied such a criterion guarantees that every koszul algebra generated by squarefree quadratic monomials is normal we present an example of a normal non koszul squarefree semigroup ring whose toric ideal is generated by quadratic binomials as well as an example of a non normal koszul squarefree semigroup ring whose toric ideal possesses no quadratic grobner basis in addition all the affine semigroup rings which are generated by squarefree quadratic monomials and which have 2 linear resolutions will be classified moreover it is shown that the toric ideal of a normal affine semigroup ring generated by quadratic monomials is generated by quadratic binomials if its underlying polytope is simple

smoothness relaxation strategies for singular and hypersingular integral equations three stages are involved in the formulation of a typical direct boundary element method derivation of an integral representation taking a limit to the boundary ltb so as to obtain an integral equation and discretization we examine the second and third stages focussing on strategies that are intended to permit the relaxation of standard smoothness assumptions two such strategies are indicated therst is the introduction of various apparent or pseudo ltbs the second is relaxed regularization in which a regularized integral equation derived rigorously under certain smoothness assumptions is used when less smoothness is available both strategies are shown to be based on inconsistent reasoning nevertheless reasons are oered for having some condence in numerical results obtained with certain strategies our work is done in two physical contexts namely two dimensionalpotential theory using functions of a complex variable and three dimensionalelastostatics 1998 john wiley sons ltd

on the computation of the derivatives of potentials on a boundary by using boundary integral equations this work presents a new recursion scheme to compute the cartesian derivatives of potentials on the smooth surface of a connected solid the advocated strategy solely appeals to boundary integral equations and a very few informations regarding the surface geometry the whole algorithm is carefully tested against analytical solutions both for interior and exterior problems by implementing a collocation points method

three dimensional fracture simulation with a single domain direct boundary element formulation an efficient hypersingular boundary integral equation method for three dimensional fracture mechanics was presented in a previous paper the details of the numerical implementation of this method are further discussed herein in particular an algorithm for achieving the required differentiability of the crack surface displacement function is discussed to illustrate the utility of the method computational results for several strongly interacting multiple crack geometries are presented the calculated stress intensity factors are in excellent agreement with those obtained by an approximate analytical method due to kachanov and laures

a single domain boundary element method for 3 d elastostatic crack analysis using continuous elements summary a boundary element method is presented for single domain analysis of cracked three dimensional isotropic elastostatic solids a numerical treatment for the hypersingular boundary integro differential equation bide for displacement derivatives is described in which continuous boundary elements may be used hadamard principal values of the hypersingular integrals arising in the formulation are evaluated using polar co ordinates defined on the tangent planes at the source point and the free term coefficients are calculated directly using a numerical technique the forms of the boundary integral equation bie and the bide are considered for a source point on the coincident surfaces of a crack and a scheme is given for defining the traction boundary integral equation tbie so that it optimally incorporates the traction information deficient in its complementary partner the bie numerical results for some example mixedmode crack problems are presented

monostable waves in a class of non local convolution differential equation abstract the current paper is devoted to the study of wave propagation dynamics for a class of convolution equation with monostable structure it is shown that this equation admits traveling wave solution connecting the zero steady state even when the nonlinear term of this equation is without monotonicity a sufficient condition for the traveling wave solution that converges to the positive steady state is also established

use of simple solutions for boundary integral methods in elasticity and fracture analysis the simple solutions or indirect method of analysing cauchy and hypersingular integrands in the gradient flux or traction boundary integral equation bie is applied to linear elastic fracture analysis because of the geometric singularity of the crack surface application of the simple solutions formulas on the crack face requires integration over a temporary closure surface rather than the remainder of the body closure surface constructions are exhibited for crack surfaces allowing the gradient bie to be applied as a constraint equation on a crack surface where the primary bie is degenerate computational results are given for two benchmark fracture problems

commutative algebra of statistical ranking abstract a model for statistical ranking is a family of probability distributions whose states are orderings of a fixed finite set of items we represent the orderings as maximal chains in a graded poset the most widely used ranking models are parameterized by rational function in the model parameters so they define algebraic varieties we study these varieties from the perspective of combinatorial commutative algebra one of our models the plackett luce model is non toric five others are toric the birkhoff model the ascending model the csiszar model the inversion model and the bradley terry model for these models we examine the toric algebra its lattice polytope and its markov basis

crack tip interpolation revisited it is well known that the near tip displacement eld on a crack surface can be represented in a power series in the variable p r where r is the distance to the tip it is shown herein that the coecients of the linear terms on the two sides of the crack are equal equivalently the linear term in the crack opening displacement vanishes the proof is a completely general argument valid for an arbitrary e g multiple nonplanar crack conguration and applied boundary conditions moreover the argument holds for other equations such as laplace a limit procedure for calculating the surface stress in the form of a hypersingular boundary integral equation is employed to enforce the boundary conditions along the crack faces evaluation of the nite surface stress and examination of potentially singular terms lead to the result inclusion of this constraint in numerical calculations should result in a more accurate approximation of the displacement and stress elds in the tip region and thus a more accurate evaluation of stress intensity factors