optical orthogonal codes with unequal auto and cross correlation constraints an optical orthogonal code ooc is a collection of binary sequences with good auto and cross correlation properties they were defined by salehi and others as a means of obtaining code division multiple access on optical networks up to now all work on oocs have assumed that the constraint placed on the autocorrelation and that placed on the cross correlation are the same we consider codes for which the two constraints are not equal specifically we develop bounds on the size of such oocs and demonstrate constriction techniques for building them the results demonstrate that a significant increase in the code size is possible by letting the autocorrelation constraint exceed the cross correlation constraint these results suggest that for a given performance requirement the optimal ooc may be one with unequal constraints this paper also views oocs with unequal auto and cross correlation constraints as constant weight unequal error protection uep codes with two levels of protection the bounds derived are interpreted from this viewpoint

infinite boundary elements for dynamic problems of 3 d half space in this paper a new procedure for solving 3 d dynamic problems of unbounded foundations in the frequency domain by using bem is studied for simulations of wave propagations due to far field effects a type of infinite boundary element ibem is presented for modelling a 3 d regular or irregular half space the wave type considered could be compressional shear or a combination of the two through the analysis of the asymptotic behaviour of 3 d fundamental solutions for elasto dynamics a rather feasible technique for obtaining singular integral coefficients for dynamic problems has been developed through the analysis of the dynamic response for a 3 d square foundation under a uniform load distribution excellent accuracy has been achieved in agreement with previous numerical solutions another example analysis of the dynamic compliance of a rigid square plate on a half space has also shown very good results the development of this infinite boundary element provides a powerful tool for dealing with 3 d structure foundation interaction or wave propagation problems for irregular foundations such as arch dam canyons

dynamic response of lined tunnels by an isoparametric boundary element method abstract this work investigates the dynamic stress concentration in the lining of a circular cylindrical tunnel excavated in a linear elastic or viscoelastic medium of infinite extent under conditions of plane strain the dynamic load consists of planar waves of a general transient nature the numerical method employed is the boundary element method formulated in the laplace transformed domain a numerical inverse transformation is used to bring the results obtained by the boundary element method back to the time domain isoparametric boundary elements are utilized in the discretization of the surfaces of the problem the results obtained are in very good agreement with known analytic solutions while they compare favorably with other numerical solutions the method is quite general and can be used for cylindrical tunnels of arbitrary cross section

effects of anisotropic fiber packing on stresses in composites a volume integral equation method viem is used to calculate the plane elastostatic field in an unbounded isotropic elastic medium containing multiple orthotropic cylindrical inclusions subject to remote loading a detailed analysis of stress field at the interface between the matrix and the central orthotropic inclusion is carried out for square hexagonal and random packing of the inclusions the influence of a void on the interfacial stress field is analyzed using a modified form of the integral equation the results for the random fibers are compared with those for the regular arrays the methods are shown to be very accurate and effective for investigating the local stresses in composites containing anisotropic fibers

a 2 5d coupled fe be methodology for the dynamic interaction between longitudinally invariant structures and a layered halfspace abstract this paper presents a general 2 5d coupled finite element boundary element methodology for the computation of the dynamic interaction between a layered soil and structures with a longitudinally invariant geometry such as railway tracks roads tunnels dams and pipelines the classical 2 5d finite element method is combined with a novel 2 5d boundary element method a regularized 2 5d boundary integral equation is derived that avoids the evaluation of singular traction integrals the 2 5d green s functions of a layered halfspace computed with the direct stiffness method are used in a boundary element method formulation this avoids meshing of the free surface and the layer interfaces with boundary elements and effectively reduces the computational efforts and storage requirements the proposed technique is applied to four examples a road on the surface of a halfspace a tunnel embedded in a layered halfspace a dike on a halfspace and a vibration isolating screen in the soil

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

p adaptive boundary elements this paper presents the implementation of an adaptive philosophy to plane potential problems using the direct boundary element method after some considerations about the state of the art and a discussion of the standard approach features the possibility of separately treating the modelling of variables and their interpolation through hierarchical shape functions is analysed then the proposed indicators and estimators are given followed by a description of a small computer program written for an ibm pc finally some examples show the kind of results to be expected

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

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 general regularization of the hypersingular integrals in the symmetric galerkin boundary element method the symmetric galerkin boundary element method is used to solve boundary value problems by keeping the symmetric nature of the matrix obtained after discretization the matrix elements are obtained from a double integral involving the double derivative of green s operator which is highly singular the paper presents a regularization of the hypersingular integrals which depend only on the properties of green s tensor the method is presented in the case of laplace s operator with an example of application the case of elasticity is finally addressed theoretically showing an easy extension to any case of anisotropy

coupling bem with fem by a direct computation of the boundary stiffness matrix the boundary stiffness matrix characterizing in a discretized form the response of the boundary to given dirichlet boundary conditions allows the coupling between bem and fem the paper presents an approach based on the direct computation of the stiffness matrix from the potential function related to a given dirichlet boundary condition the method produces a symmetric stiffness matrix as for the singular galerkin boundary element method but does not need to compute hypersingular integrals in addition the method uses only the nodal values of the boundary potential but does not need discretized values of the normal gradient at the boundary as for usual boundary element methods which reduces the number of matrices to be constructed the regularization of the integrals is achieved by means used for simply singular integrals introduced for the collocation boundary element method an example of application is produced in the case of the solution of laplace equation within a plane domain

polycyclic by finite groups admit a bounded degree polynomial structure for a polycyclic by finite group gamma of hirsch length h an affine resp polynomial structure is a representation of gamma into rm aff bbb r h resp rm p bbb r h the group of polynomial diffeomorphisms letting gamma act properly discontinuously on bbb r h recently it was shown by counter examples that there exist groups gamma even nilpotent ones which do not admit an affine structure thus giving a negative answer to a long standing question of john milnor we prove that every polycyclic by finite group gamma admits a polynomial structure which moreover appears to be of a special simple type called canonical and as a consequence of this consists entirely of polynomials of a bounded degree the construction of this polynomial structure is a special case of an iterated seifert fiber space construction which can be achieved here because of a very strong and surprising cohomology vanishing theorem

polynomial structures for nilpotent groups if a polycyclic by finite rank k group admits a faithful affine representation making it acting on rk properly discontinuously and with compact quotient we say that admits an affine structure in 1977 john milnor questioned the existence of affine structures for such groups very recently examples have been obtained showing that even for torsion free finitely generated nilpotent groups n affine structures do not always exist it looks natural to consider affine structures as examples of polynomial structures of degree one we introduce the concept of a canonical type polynomial structure for polycyclic by finite groups using the algebraic framework of the seifert fiber space construction and a nice cohomology vanishing theorem we prove the existence and uniqueness up to conjugation of canonical type polynomial structures for virtually finitely generated nilpotent groups applying this uniqueness to a result going back to mal cev it follows that for torsion free finitely generated nilpotent groups each canonical polynomial structure is expressed in polynomials of limited degree the minimal degree needed for obtaining a polynomial structure will determine the affine defect number we prove that the known counterexamples to milnor s question have the smallest possible affine defect i e affine defect number equal to one

elastic scatterer interaction via generalized born series and far field approximations methods for solving elastic wave scattering problems in three dimensions 3d with multiple inhomogeneities are discussed a problem of homogeneous isotropic elastic defects in an otherwise homogeneous isotropic elastic full space is formulated as a boundary integral equation this equation is solved by discretizing the surface of each scatterer in a fashion known as the boundary element method the resulting matrix equation may be solved in a fully implicit manner but an implicit iterative method is more efficient with this hybrid method a portion of the nonsingular integral operator is expanded in a neumann series terms in this series correspond physically to nth order born approximations of the scatterers interaction the relative advantage of this hybrid scheme depends on the number of iterations required except for closely situated strong scatterers terms beyond the first few orders are not significant and thus the method can be quite advantageous when the separation is large another appro

the method of steepest descent for estimating quadrature errors this work presents an application of the method of steepest descent to estimate quadrature errors the method is used to provide a unified approach to estimating the truncation errors which occur when gauss legendre quadrature is used to evaluate the nearly singular integrals that arise as part of the two dimensional boundary element method the integrals considered here are of the form 1 1 h x d x x a 2 b 2 where h x is a well behaved function 0 and 1 a 1 since 0 b 1 the integral is nearly singular with a sharply peaked integrand the method of steepest descent is used to estimate the generally large truncation errors that occur when gauss legendre quadrature is used to evaluate these integrals as well as to estimate the much lower errors that occur when gauss legendre quadrature is performed on such integrals after a sinh transformation has been applied the new error estimates are highly accurate in the case of the transformed integral and are shown to be comparable to those found in previous work by elliott and johnston 2007 one advantage of the new estimates is that they are given by just one formula each for the un transformed and the transformed integrals rather than the much larger set of formulae in the previous work another advantage is that the new method applies over a much larger range of values than the previous method

on an inverse problem from magnetic resonance elastic imaging the imaging problem of elastography is an inverse problem the nature of an inverse problem is that it is ill conditioned we consider properties of the mathematical map which describes how the elastic properties of the tissue being reconstructed vary with the field measured by magnetic resonance imaging mri this map is a nonlinear mapping and our interest is in proving certain conditioning and regularity results for this operator which occurs implicitly in this problem of imaging in elastography in this treatment we consider the tissue to be linearly elastic isotropic and spatially heterogeneous we determine the conditioning of this problem of function reconstruction in particular for the stiffness function we further examine the conditioning when determining both stiffness and density we examine the frechet derivative of the nonlinear mapping which enables us to describe the properties of how the field affects the individual maps to the stiffness and density functions we illustrate how use of the implicit function theorem can considerably simplify the analysis of frechet differentiability and regularity properties of this underlying operator we present new results which show that the stiffness map is mildly ill posed whereas the density map suffers from medium ill conditioning computational work has been done previously to study the sensitivity of these maps but our work here is analytical the validity of the newton kantorovich and optimization methods for the computational solution of this inverse problem is directly linked to the frechet differentiability of the appropriate nonlinear operator which we justify

error estimation of quadrature rules for evaluating singular integrals in boundary element problems the efficient numerical evaluation of integrals arising in the boundary element method is of considerable practical importance the superiority of the use of sigmoidal and semi sigmoidal transformations together with gauss legendre quadrature in this context has already been well demonstrated numerically by one of the authors in this paper the authors obtain asymptotic estimates of the truncation errors for these algorithms these estimates allow an informed choice of both the transformation and the quadrature error in the evaluation of boundary element integrals with algebraic or algebraic logarithmic singularities at an end point of the interval of integration copyright 2000 john wiley sons ltd

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

aspherical manifolds with virtually 3 step nilpotent fundamental group a closed aspherical manifold of dimension 3 4 with virtually 3 step nilpotent fundamental group supports a complete affinely flat structure topological and seifert bundle classifications are given for a special case called seifert relatives of flat riemannian manifolds we use the seifert fiber space construction as a main tool 0 introduction it is well known that given a torsion free virtually poly z group ir there exists a closed smooth k r 1 manifold eg a double coset space of a lie group a question we are interested in is whether such a manifold is homeomorphic to a quotient of r by an action of a discrete group of affine motions the best known result seems to be j scheuneman s 18 stating that the answer is yes if ir is 3 step nilpotent in this paper we generalize this to virtually 3 step nilpotent groups in dimension 3 4 the main idea is to refine the seifert fiber space construction of p conner and f raymond 4 this gives rise to an embedding of such ir into the group of affine motions so that rm ir is compact then we apply t farrell and w c hsiang s theorem 6 stating that any two closed aspherical manifolds with isomorphic fundamental groups which are virtually nilpotent are homeomorphic in dimension 3 4 this paper is organized as follows in section 1 we refine the seifert fiber space construction by restricting the coefficient module to some submodules of m w rk the main result is that if the first coboundary homomorphism 6 of certain cohomology exact sequence is surjective then one can convert the algebraic object group into a geometric one group action manuscript received november 23 1981 manuscript revised may 14 1981 this is a part of the author s ph d thesis at the university of michigan 1981 the second part geometric realization will appear as a separate article elsewhere the author wishes to express his sincere appreciation to professor frank raymond for his guidance in this work

transformations for evaluating singular boundary element integrals accurate numerical integration of line integrals is of fundamental importance for the reliable implementation of the boundary element method usually the regular integrals arising from a boundary element method implementation are evaluated using standard gaussian quadrature however the singular integrals which arise are often evaluated in another way sometimes using a different integration method with different nodes and weights this paper presents a straightforward transformation to improve the accuracy of evaluating singular integrals the transformation is in a sense a generalisation of the popular method of telles with the underlying idea being to utilise the same gaussian quadrature points as used for evaluating nonsingular integrals in a typical boundary element method implementation the new transformation is also shown to be equivalent to other existing transformations in certain situations comparison of the new method with existing coordinate transformation techniques shows that a more accurate evaluation of weakly singular integrals can be obtained the technique can also be extended to evaluate certain hadamard finite part integrals based on the observation of several integrals considered guidelines are suggested for the best transformation order to use i e the degree to which nodes should be clustered near the singular point

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

direct evaluation of singular integrals in elastoplastic analysis by the boundary element method this paper presents a new method for the direct and accurate evaluation of strongly singular integrals in the sense of cauchy principal values and weakly singular integrals over quadratic boundary elements in three dimensional stress analysis and quadratic internal cells in two dimensional elastoplastic analysis by the boundary element method a quadratic triangle polar co ordinate transformation technique is applied to reduce the order of singularity of the singular integrals next a form of stokes theorem is introduced in order to remove the singularity in the cauchy principal value integrals therefore the evaluation of these integrals can be carried out by standard gaussian quadrature numerical examples of 2 d elastoplastic problems and a 3 d elastic problem show the effectiveness and efficiency of the method

the real cohomology of virtually nilpotent groups abstract in this paper we present a method to compute the real cohomology of any finitely generated virtually nilpotent group the main ingredient in our setup consists of a polynomial crystallographic action of this group as any finitely generated virtually nilpotent group admits such an action which can be constructed quite easily the approach we present applies to all these groups our main result is an algorithmic way of computing these cohomology spaces as a first application we prove a kind of poincare duality also in the nontorsion free case and we derive explicit formulas in the virtually abelian case

scattering of elastic waves from thin shapes in three dimensions using the composite boundary integral equation formulation in this paper the composite boundary integral equation bie formulation is applied to scattering of elastic waves from thin shapes with small but finite thickness open cracks or thin voids thin inclusions thin layer interfaces etc which are modeled with two surfaces this composite bie formulation which is an extension of the burton and miller s formulation for acoustic waves uses a linear combination of the conventional bie and the hypersingular bie for thin shapes the conventional bie as well as the hypersingular bie will degenerate or nearly degenerate if they are applied individually on the two surfaces the composite bie formulation however will not degenerate for such problems as demonstrated in this paper nearly singular and hypersingular integrals which arise in problems involving thin shapes modeled with two surfaces are transformed into sums of weakly singular integrals and nonsingular line integrals thus no finer mesh is needed to compute these nearly singular integrals

acoustic scattering by a modified werner method a modified integral werner method is used to calculate pressure scattered by an axisymmetric body immersed in a perfect and compressible fluid subject to a harmonic acoustic field this integral representation is built as the sum of a potential of a simple layer and a potential of volume it is equivalent to the exterior helmholtz problem with neumann boundary condition for all real wave numbers of the incident acoustic field for elastic structure scattering problems the modified werner method is coupled with an elastodynamic integral formulation in order to account for the elastic contribution of the displacement field at the fluid structure interface the resulting system of integral equations is solved by the collocation method with a quadratic interpolation the introduction of a weighting factor in the modified werner method decreases the number of volume elements necessary for a good convergence of results this approach becomes very competitive when it is compared with other integral methods that are valid for all wave numbers a numerical comparison with an experiment on a tungsten carbide end capped cylinder allows a glimpse of the interesting possibilities for using the coupling of the modified werner method and the integral elastodynamic equation used in this research

some efficient boundary integral strategies for time harmonic wave problems in an elastic halfspace abstract when boundary integral equation boundary element methods bie bems are used for halfspace problems such as occur frequently in elastodynamics the fullspace stokes fundamental solution or halfspace lamb fundamental solution can be used to formulate the bie both stokes and lamb approaches have advantages and disadvantages this paper presents systematic strategies based on the bem for 3d halfspace elastodynamic problems wherein the best features of formulations based on the stokes and the lamb solutions are exploited strategies are illustrated and numerical results are given for point sources and radiation from a spherical void in a halfspace

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

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 composite transformation for numerical integration of singular integrals in the bem in this paper we present a composite non linear transformation of a polynomial transformation pt and a sigmoidal transformation st by the name of ct ps composite transformation with polynomial and sigmoidal transformations this new transformation can be used for both cauchy principal value cpv integrals and weakly singular integrals with interior singularities moreover it is implied that the numerical evaluation using ct ps would be more efficient than either pt or st used alone by numerical examples we show that the presented ct ps method with the gauss legendre quadrature rule improves the approximation errors of the existing methods effectively in particular it is demonstrated that the results of the present method are excellent for cpv integrals with near end point singularities copyright 2003 john wiley sons ltd

two dimensional optical orthogonal codes and semicyclic group divisible designs a nxm k two dimensional optical orthogonal code 2 d ooc c is a family of nxm 0 1 arrays of constant weight k such that i 1n j 0m 1a i j b i j m for any arrays a b in c and any integer except when a b and 0 mod m where m denotes addition modulo m such codes are of current practical interest as they enable optical communication at lower chip rate to simplify practical implementation the am oppw at most one pulse per wavelength restriction is often appended to a 2 d ooc an am oppw 2 d ooc is optimal if its size is the largest possible in this paper the notion of a perfect am oppw 2 d ooc is proposed which is an optimal nxm k am oppw 2 d ooc with cardinality m n n 1 n k k 1 k a link between optimal nxm k am oppw 2 d oocs and block designs is developed some new constructions for such optimal codes are described by means of semicyclic group divisible designs several new infinite families of perfect nxm k 1 am oppw 2 d oocs with k 2 3 4 are thus produced

optical orthogonal codes design analysis and applications an optical orthogonal code ooc is a family of 0 1 sequences with good auto and cross correlation properties i e the autocorrelation of each sequence exhibits the thumbtack shape and the cross correlation between any two sequences remains low throughout the use of optical orthogonal codes enables a large number of asynchronous users to transmit information efficiently and reliably the thumbtack shaped autocorrelation facilitates the detection of the desired signal and low profile cross correlation reduces interference from unwanted signals theoretical upper and lower bounds on the maximum possible size of oocs are derived methods for the design and analysis of oocs using tools from projective geometry the greedy algorithm iterative constructions algebraic coding theory block design and various other combinational disciplines are discussed

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

stress analysis of an unbounded elastic solid with orthotropic inclusions and voids using a new integral equation technique a recently developed numerical method based on a volume integral formulation is applied to calculate the elastostatic field in an unbounded isotropic elastic medium containing orthotropic inclusions subject to remote loading a modified form of the method in which the integral equations involve volumes of the inclusions and boundaries of voids or cracks is used to deal with the presence of both types of inhomogeneity a detailed analysis of displacement and stress fields is carried out for orthotropic cylindrical and elliptic cylindrical inclusions as well as voids the accuracy and effectiveness of the new methods are examined through comparison with results obtained from analytical and boundary integral equation methods

indirect finite element evaluation of two dimensional finite part integral using fourier transformation a broad class of engineering problems in fracture mechanics thermal fluid transport and electromagnetic theory involve the evaluation of two dimensional finite part integrals of the form a method for evaluation of such integrals is developed by deriving an equivalent integral using fourier transformation this equivalent integral does not involve a kernel with singular behaviour consequently standard numerical integration methodologies with conventional analytical evaluation techniques can be used in the finite element computations the accuracy and convergence of the developed numerical procedure are successfully demonstrated by numerical examples for planar fracture geometries

solution of elasticity problems by a self adaptive mesh refinement technique for boundary element computation a self adaptive mesh refinement technique is developed for boundary element solutions of the two dimensional navier s equation the method is based on error reduction and applied on the element and global level to estimate the residual error associated with each mesh results for several problems employing constant two dimensional isotropic elastostatic boundary elements are presented

a method for direct evaluation of singular integral in direct boundary element method a new method is presented for evaluating the cauchy principal value integral and the free term in the three dimensional elastic boundary element method this method expresses the singular integral as the sum of a weakly singular integral and an integrable cauchy principal value integral the former can be computed by means of the usual standard gaussian quadrature after a transformation suggested by lachat and watson 10 who correctly limited its use only to weakly singular integral the latter can be calculated by direct integration in the cauchy principal value sense this paper also points out some limitations in the use of triangle polar co ordinate suggested by li et al 11 and later extended by zhang and xu 16 the general expression of the free term for a boundary point with arbitrary characteristic surface is also presented simple numerical examples which verify the efficiency and accuracy of the present method are given

computation of thermal stresses in quasistatic non stationary thermoelasticity using boundary elements in this paper we present the boundary integral formulation for the solution of quasi static problems of two dimensional uncoupled thermoelasticity a detailed scheme for the numerical solution of the boundary integral equations and computation of internal stresses by regularized integral representation is developed in time formulation the method is tested in a numerical example

semi analytic solution for multiple interacting three dimensional inhomogeneous inclusions of arbitrary shape in an infinite space this paper develops a semi analytic solution for multiple arbitrarily shaped three dimensional inhomogeneous inclusions embedded in an infinite isotropic matrix under external load all interactions between the inhomogeneous inclusions are taken into account in this solution the inhomogeneous inclusions are discretized into small cuboidal elements each of which is treated as a cuboidal inclusion with initial eigenstrain plus unknown equivalent eigenstrain according to the equivalent inclusion method all the unknown equivalent eigenstrains are determined by solving a set of simultaneous constitutive equations established for each equivalent cuboidal inclusion the final solution is obtained by summing up the closed form solutions for each individual equivalent cuboidal inclusion in an infinite space the solution evaluation is performed by application of the fast fourier transform algorithm which greatly increases the computational efficiency finally the solution is validated by taking eshelby s analytic solution of an ellipsoidal inhomogeneous inclusion as a benchmark and by the finite element analysis a few sample results are also given to demonstrate the generality of the solution the solution may have potentially significant applications in solving a wide range of inhomogeneity related problems copyright 2011 john wiley sons ltd

three dimensional crack analysis using singular boundary elements a multi domain method of solving three dimensional elastic crack problems in an infinite elastic body using the boundary element method is proposed the displacement and traction behaviours near a crack front are incorporated in special crack elements the elimination of singularities arising from the term combined with kelvin s kernel for displacement in the integrals is discussed in detail stress intensity factors of modes i ii and iii are obtained directly from crack front nodal values without any extrapolation as in some other methods no differentiation of conventional boundary integral equations with kelvin s tensor kernels is necessary in the current approach this method is applicable to cracks of arbitrary shape infinite bodies are modelled precisely as such not approximated as large finite bodies numerical solutions of stress intensity factors are given for several problems involving a penny shaped crack

an isogeometric boundary element method for three dimensional potential problems abstract isogeometric analysis iga coupled with boundary element method i e igabem received a lot of attention in recent years in this paper we extend the igabem to solve 3d potential problems this method offers a number of key improvements compared with conventional piecewise polynomial formulations firstly the models for analysis in the igabem are exact geometrical representation no matter how coarse the discretization of the studied bodies is thus the igabem ensures that no geometrical errors are produced in the analysis process secondly a meshing process is no longer required which means redundant computations are eliminated to allow analysis to be carried out with greatly reduced pre processing to accurately evaluate the singular integrals appearing in our method the power series expansion method is employed the integration surface is on the real surface of the model rather than the interpolation surface i e no geometrical errors thus the value of integral is more accurate than the traditional boundary element method which can improve the computation accuracy of the igabem some numerical examples for 3d potential problems are used to validate the solutions of the present method with analytical and numerical solutions available

a boundary element formulation for a class of non local damage models this paper proposes and discusses a boundary element formulation for a particular class of non local damage models the formulation as well as the boundary element computational code developed during this research have proven to be very simple and efficient providing reliable information on the strains and stresses in damage softening models the numerical approach uses a finite grid to estimate the damage values some illustrative numerical examples which show the simplicity and versatility of the proposed approach are included and discussed in detail

large families of asymptotically optimal two dimensional optical orthogonal codes nine new two dimensional optical orthogonal codes 2 d oocs are presented here all sharing the common feature of a code size that is much larger in relation to the number of time slots than those of constructions appearing previously in the literature each of these constructions is either optimal or asymptotically optimal with respect to either the original johnson bound or else a nonbinary version of the johnson bound introduced in this paper the first five codes are constructed using polynomials over finite fields the first construction is optimal while the remaining four are asymptotically optimal the next two codes are constructed using rational functions in place of polynomials and these are asymptotically optimal the last two codes also asymptotically optimal are constructed by composing two of the above codes with a constant weight binary code also presented is a three dimensional optical orthogonal code 3 d ooc that exploits the polarization dimension finally phase encoded optical cdma is considered and construction of two efficient codes are provided

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

polynomial structures on polycyclic groups we know by recent work of benoist and of burde grunewald that there exist polycyclic by finite groups g of rank h the examples given were in fact nilpotent admitting no properly discontinuous affine action on rh on the other hand for such g it is always possible to construct a properly discontinuous smooth action of g on rh our main result is that any polycyclic by finite group g of rank h contains a subgroup of finite index acting properly discontinuously and by polynomial diffeomorphisms of bounded degree on rh moreover these polynomial representations always appear to contain pure translations and are extendable to a smooth action of the whole group g

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

transient analysis of three dimensional wave propagation using the boundary element method in the past the time domain solution of the wave equation has been limited to simplified problems this was due to the limitations of analytical methods and the capacity of computers to manipulate and store large blocks of spatial information with the advent of super computers the ability to solve such problems has significantly increased this paper outlines a method for transient analysis of wave propagation in arbitrary domains using a boundary element method the technique presented will allow the definition of a domain the input of impedance conditions on the domain s surface the specification of inputs on the surface and the specification of initial conditions within the domain it will produce a complete solution of the wave equation inside the domain the techniques are demonstrated using a program with a boundary element formulation of kirchhoff s equation the elements used are triangular and compatible

a general boundary integral formulation for zoned three dimensional media a new boundary integral formulation is proposed to analyse the heat transfer in zoned three dimensional geometries the proposed formulation couples the boundary formula the gradient of the boundary formula and the exterior formula an advantage of this method over the traditional methods is that any linear condition at the interface between subdomains may be incorporated into the formulation at the outset in addition the new method provides a sparse and well conditioned matrix of coefficients with a minimum number of equations

seismic soil structure interaction analysis by direct boundary element methods abstract upon establishing the mathematical framework necessary for a proper understanding of the analytical theory a regularized form of the conventional direct boundary integral equation formulation for three dimensional elastodynamics is presented for a general anisotropic medium founded on the basis of a full decomposition of the greens functions into regular and singular parts the alternative boundary integral equation format is compact and without demand ingmathematical and numerical complexities such as cauchy principal values extended to deal with general seismic soil structure interaction problems in semi infinite media the formulation is implemented computationally together with a rigorous treatment of singular dynamic multi layered viscoelastic half space greens functions and interfacial boundary tractions arising in typical soil structure foundation configurations a set of new benchmark numerical results are included

a comparative study on three boundary element method approaches to problems in elastodynamics in this study three boundary element method approaches are compared by solving a typical problem in linear elastodynamics the first approach formulates and solves the problem in the real time domain in conjunction with a time stepping algorithm the other two approaches formulate and solve the problem in the laplace and the fourier transformed domains which necessitates a numerical inversion of the results to the time domain the results obtained compare favourably with available analytic solutions a detailed tabulation of the computer time and memory requirements of each approach is presented

a volume integral equation technique for multiple scattering problems in elastodynamics abstract a volume integral equation method is introduced as a new numerical scheme for the solution of certain elastodynamic problems in unbounded solids containing multiple inclusions the effectiveness of the method is compared with the boundary integral equation method for different problem geometries for the single inclusion problem both methods are found to work equally well for multiple inclusions the volume integral equation method is shown to be much more convenient for numerical formulation and to give very accurate results

on time harmonic elastic wave analysis by the boundary element method for moderate to high frequencies abstract certain inherent difficulties in obtaining accurate boundary element solutions to problems of elastodynamics at moderate to high frequencies are examined some procedures for overcoming or compensating for these difficulties are described in addition results demonstrating the effectiveness of these procedures are presented finally the use of these procedures in solving transient problems via fourier transform inversion is illustrated

efficient boundary element analysis of sharp notched plates the present paper further develops the boundary element singularity subtraction technique to provide an efficient and accurate method of analysing the general mixed mode deformation of two dimensional linear elastic structures containing sharp notches the elastic field around sharp notches is singular because of the convergence difficulties that arise in numerical modelling of elastostatic problems with singular fields these singularities are subtracted out of the original elastic field using the first term of the williams series expansion this regularization procedure introduces the stress intensity factors as additional unknowns in the problem hence extra conditions are required to obtain a solution extra conditions are defined such that the local solution in the neighbourhood of the notch tip is identical to the williams solution the procedure can take into account any number of terms of the series expansion the standard boundary element method is modified to handle additional unknowns and extra boundary conditions analysis of plates with symmetry boundary conditions is shown to be straightforward with the modified boundary element method in the case of non symmetrical plates the singular tip tractions are not primary boundary element unknowns the boundary element method must be further modified to introduce the boundary integral stress equations of an internal point approaching the notch tip as primary unknowns in the formulation the accuracy and efficiency of the method is demonstrated with some benchmark tests of mixed mode problems new results are presented for the mixed mode analysis of a non symmetrical configuration of a single edge notched plate

extended multilevel prime codes for optical cdma in this paper a new family of multilevel wavelength time codes with expanded code cardinality flexible code length zero autocorrelation sidelobes and the maximum cross correlation function of any arbitrary positive integer n is constructed and analyzed besides having asymptotically optimal cardinality the new codes can be partitioned into n levels such that the cross correlation function between any two code matrices in level l is at most l where 1 l n the hardlimiting performance of these multilevel codes is analyzed algebraically our results show that the unique partitioning property of these multilevel codes supports a trade off between code cardinality and performance for meeting different system requirements such as user capacity and throughput

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

extended reed solomon codes for optical cdma in this paper the extended reed solomon codes are modified to construct a new family of 2 d codes for asynchronous optical code division multiple access o cdma in addition of having expanded and asymptotically optimal cardinality these 2 d asynchronous optical codes can be partitioned into multiple tree structures of code subsets in which code cardinality is a function of the periodic cross correlation value assigned to the subset the performance of these 2 d optical codes is analyzed and compared with that of the multilevel prime codes our results show that the unique partition property of the new optical codes supports a trade off between code cardinality and performance for meeting different system requirements such as user capacity and throughput in addition the multiple tree structures of the new codes potentially support applications that require rapid switching of many codewords such as in o cdma network gateway or in strategic environments where code obscurity is essential

coupled finite element hierarchical boundary element methods for dynamic soil structure interaction in the frequency domain summary this paper discusses the coupling of finite element and fast boundary element methods for the solution of dynamic soil structure interaction problems in the frequency domain the application of hierarchical matrices in the boundary element formulation allows considering much larger problems compared to classical methods three coupling methodologies are presented and their computational performance is assessed through numerical examples it is demonstrated that the use of hierarchical matrices renders a direct coupling approach the least efficient as it requires the assembly of a dynamic soil stiffness matrix iterative solution procedures are presented as well and it is shown that the application of such schemes to dynamic soil structure interaction problems in the frequency domain is not trivial as convergence can hardly be achieved if no relaxation procedure is incorporated aitken s 2 method is therefore employed in sequential iterative schemes for the calculation of an optimized interface relaxation parameter while a novel relaxation technique is proposed for parallel iterative algorithms it is demonstrated that the efficiency of these algorithms strongly depends on the boundary conditions applied to each subdomain the fastest convergence is observed if neumann boundary conditions are imposed on the stiffest subdomain the use of a dedicated solver for each subdomain hence results in a reduced computational effort a monolithic coupling strategy often used for the solution of fluid structure interaction problems is also introduced the governing equations are simultaneously solved in this approach while the assembly of a dynamic soil stiffness matrix is avoided copyright 2013 john wiley sons ltd

a boundary integral equation method for radiation and scattering of elastic waves in three dimensions etude du rayonnement et de la diffusion d ondes elastiques par des obstacles de forme arbitraire

multiple wavelength optical orthogonal codes under prime sequence permutations for optical cdma a new family of two dimensional 2 d wavelength hopping time spreading codes which employs wavelength hopping algebraically under prime sequence permutations on top of time spreading optical orthogonal codes is studied and analyzed different from other 2 d codes our new codes allow the number of wavelengths and code length to be chosen independently and at the same time the code cardinality is a quadratic function of the number of wavelengths without sacrificing the maximum cross correlation value i e still at most one they are particularly suitable for high bit rate optical code division multiple access systems with broadband mode locked lasers in which the number of time slots is very limited and system capacity can only be grown by increasing the number of wavelengths rather than code length finally a novel wavelength aware detector for wavelength hopping time spreading codes is discussed and shown to provide improved code performance

construction of optimal 2d optical codes using n w 2 2 optical orthogonal codes two dimensional 2d wavelength time coding schemes have recently been studied for optical code division multiple access in this paper we propose a new family of 2d codes which use synchronized quadratic congruence sequences for wavelength hopping and n w 2 2 optical orthogonal codes for time spreading the new 2d codes provide larger asymptotically optimal code cardinality than other 2d codes by relaxing the maximum cross correlation function from one to two our study shows that the heavier code weight supported by our 2d codes results in better code performance than some of previously proposed 2d codes of the maximum cross correlation functions of one and two the new codes potentially support more subscribers and heavier bursty asynchronous traffic with gradual performance degradation as traffic load increases

polynomial alternatives for the group of affine motions it is known that every polycyclic by finite group even if it admits no affine structure allows a polynomial structure of bounded degree a major obstacle to a further development of the theory of these polynomial structures is that the group of the polynomial diffeomorphisms of mathbb r n in contrast to the group of affine motions is no longer a finite dimensional lie group in this paper we construct a family of finite dimensional lie groups even linear algebraic groups of polynomial diffeomorphisms which we call weighted groups of polynomial diffeomorphisms it turns out that every polycyclic by finite group admits a polynomial structure via these weighted groups in the nilpotent and other case s we can sharpen by specifying a nice set of weights the existence results obtained in earlier work we introduce unipotent polynomial structures of nilpotent groups and show how the existence of such polynomial structures is closely related to the existence of simply transitive actions of the corresponding mal cev completion this and other properties provide a strong analogy with the situation of affine structures and simply transitive affine actions considered e g in the work of fried goldman and hirsch

an elastodynami c hybrid boundary element study for elastic guided wave interactions with a surface breaking defect elastic guided wave interactions with various defects are explored for investigating defect characterization possibilities by using a hybrid boundary element method bem in combination with an elastodynamic boundary integral equation and the lamb wave normal mode expansion technique the bem code accuracy is verified based on energy conservation and available bench marking data for guided wave scattering problems through two dimensional 2 d parametric studies for an arbitrarily shaped defect from a surface breaking crack model to a round surface defect a waveguide cross section including a defect is locally selected as a model for a given incident mode frequency and a specific set of material properties mode reflection and transmission factors are numerically calculated to evaluate mode sensitivities and to obtain the potentially good classification features it turns out that the guided wave scattering profiles show quite different behaviors as functions of incident mode frequency defect shape and size in providing us with enough rich feature extraction information for defect classification and sizing analysis the theoretical analysis can be used to establish efficient guidelines for both data acquisition and feature selection in a pattern recognition analysis program of study sample results are presented

a boundary integral formulation for complex three dimensional geometries a new boundary integral formulation is proposed to analyse the heat transfer in complex three dimensional geometries one example of such geometry is the die sets in the injection moulding process networks of cooling conduits within the mould and the closely spaced die surfaces require special attention both in formulation and numerical treatment of the integral equations the proposed formulation couples the boundary formula the gradient of the boundary formula and the exterior formula the derivation of the integral equations is presented here along with an efficient method for integration of some of the kernels in these equations and a semi analytical procedure for the integration of the highly singular integrands which result from differentiating the boundary formula although the techniques introduced here are applied to a particular problem in heat transfer their potential application is much broader

a first order k space model for elastic wave propagation in heterogeneous media a pseudospectral model of linear elastic wave propagation is described based on the first order stress velocity equations of elastodynamics k space adjustments to the spectral gradient calculations are derived from the dyadic green s function solution to the second order elastic wave equation and used to a ensure the solution is exact for homogeneous wave propagation for timesteps of arbitrarily large size and b also allows larger time steps without loss of accuracy in heterogeneous media the formulation in k space allows the wavefield to be split easily into compressional and shear parts a perfectly matched layer pml absorbing boundary condition was developed to effectively impose a radiation condition on the wavefield the staggered grid which is essential for accurate simulations is described along with other practical details of the implementation the model is verified through comparison with exact solutions for canonical examples and further examples are given to show the efficiency of the method for practical problems the efficiency of the model is by virtue of the reduced point per wavelength requirement the use of the fast fourier transform fft to calculate the gradients in k space and larger time steps made possible by the k space adjustments

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

hybrid modelling of semi infinite media abstract an accurate and efficient hybrid formulation based on lagrange s equations of motion is presented to solve geometrically axisymmetric problems associated with layered semi infinite media under arbitrary loading a near field region containing all inhomogeneities is modelled using conventional finite elements the contribution of the exterior semi infinite domain to the equations of motion is represented by a surface integral defined over the finite element boundary the integrand of this integral involves a matrix relationship between harmonics of nodal displacements and tractions at the finite element boundary a boundary traction displacement relationship for the exterior domain is established in terms of traction and displacement green s functions for a uniform undisturbed half space the present formulation guarantees a symmetric stiffness matrix for the entire system therefore both direct and indirect versions of the boundary integral equation method can be used the accuracy of the hybrid modelling algorithm is confirmed by solving a few elastostatic and elastodynamic boundary value problems for which analytical solutions can be derived

hard limiting performance analysis of 2 d optical codes under the chip asynchronous assumption the traditional chip synchronous assumption used in the analyses of optical codes in optical code division multiple access gives a pessimistic performance upper bound while a more realistic chip asynchronous assumption gives a more accurate performance it is also known that a hard limiter can be placed at the front end of an optical decoder to reduce the effects of multiple access interference and the near far problem in this paper the hard limiting performance of two dimensional 2 d optical codes is analyzed under the chip asynchronous assumption we apply a markov chain method for a more accurate analysis which can be generalized to 2 d optical codes with arbitrary maximum cross correlation values the performance of 2 d optical codes with the hard limiting and chip asynchronous assumptions is also compared with the soft limiting and chip synchronous assumptions