two dimensional transient wave propagation in viscoelastic layered media propagation of two dimensional transient waves in multilayered viscoelastic media is investigated the multilayered medium consists of n different isotropic homogeneous and linearly viscoelastic layers with more than one discrete relaxation time the top surface of the layered medium is subjected to dynamic in plane surface tractions whereas the lower surface is free or fixed a numerical technique which combines the fourier transform with the method of characteristics is employed to obtain the solutions the numerical results are displayed in curves denoting the variations of the stress and displacement components with time at different locations these curves reveal clearly the scattering effects caused by the reflections and refractions of waves at the boundaries and at the interfaces of the layers the curves also display the effects of viscous damping in the wave profiles by suitably adjusting the material constants curves for the cases of elastic layers and viscoelastic layers with one relaxation time standard linear solid are also obtained the curves further show that the numerical technique applied in this study is capable of predicting the sharp variations in the field variables in the neighborhood of the wave fronts solutions for some special cases including lamb s problem for the elastic half space are obtained and compared with the existing solutions in the literature very good agreement is found

bipartitioning of random graphs of fixed extensive valence the procedure of fu and anderson ibid vol 19 p 1605 1986 for the application of statistical mechanics to the problem of bipartitioning random graphs is extended to graphs of fixed extensive valence the cost function is shown to be independent of whether the valence is locally or globally constrained

elastodynamic direct boundary element methods with enhanced numerical stability properties evidence of numerical instabilities in two dimensional time domain direct boundary element methods is presented the e ects of numerical versus analytical integration of spatial integrals on stability are shown and two new time stepping algorithms are introduced and compared to existing formulations the so called new direct half step scheme and the epsilon scheme are shown to improve the numerical stability of direct boundary element methods copyright 1999 john wiley sons ltd

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

application of statistical mechanics to np complete problems in combinatorial optimisation recently developed techniques of the statistical mechanics of random systems are applied to the graph partitioning problem the averaged cost function is calculated and agrees well with numerical results the problem bears close resemblance to that of spin glasses the authors find a spin glass transition in the system and the low temperature phase space has an ultrametric structure this sheds light on the nature of hard computation problems

development of a boundary element method for time dependent planar thermoelasticity abstract a new boundary element method is developed for two dimensional quasistatic thermoelasticity this time domain formulation involves only surface quantities consequently volume discretization is completely eliminated and the method becomes a viable alternative to the usual finite element approaches after presenting a brief overview of the governing equations boundary integral equations for coupled quasistatic thermoelasticity are derived by starting with existing fundamental solutions along with an appropriate reciprocal theorem details of a general purpose numerical implementation are then discussed next boundary element methods for the two more practical theories uncoupled quasistatic and steady state thermoelasticity are developed directly from limiting forms of the coupled formulation several numerical examples are provided to illustrate the validity and attractiveness of the boundary element approach for this entire class of problems

the distribution function of the effective field of the ising spin glass on the bethe lattice for the coordination number z 4 5 6 abstract the integral equation for the effective fields of the spin glass is solved analytically for the j ising model on the bether lattice with coordination number z 4 5 and 6 and symmetric distribution functions are obtained the paramagnetic distribution spin glass distribution with three delta functions and spin glass distributions with a continuous distribution are obtained the effect of the truncation of the algebraic equation for solving the integral equation is discussed

relaxation in graph coloring and satisfiability problems using t 0 monte carlo simulation we study the relaxation of graph coloring k col and satisfiability k sat two hard problems that have recently been shown to possess a phase transition in solvability as a parameter is varied a change from exponentially fast to power law relaxation and a transition to freezing behavior are found these changes take place for smaller values of the parameter than the solvability transition results for the coloring problem for colorable and clustered graphs and for the fraction of persistent spins for satisfiability are also presented

inelastic transient dynamic analysis of three dimensional problems by bem a direct boundary element formulation and its numerical implementation for inelastic transient dynamic analysis of three dimensional solids is presented the formulation is based on an initial stress approach and is the first ever of its kind in the field of the boundary element method this formulation employs the navier cauchy equation of motion graffi s dynamic reciprocal theorem stokes fundamental solution and the divergence theorem together with kinematical and constitutive equations to obtain the pertinent integral equations of the problem in the time domain within the context of small displacement theory of elastoplasticity the boundary integral equations are cast in an incremental form in which elastoplastic relations of the incremental type are used for the material description these equations are then solved using a time stepping algorithm in conjunction with an iterative solution scheme to satisfy the constitutive relations higher order shape functions are used to approximate the field quantities in space as well as in time finally the applicability of this methodology is demonstrated by presenting a few example problems

two dimensional elastodynamic displacement discontinuity method a time domain elastodynamic displacement discontinuity method is presented for analysing two dimensional problems in solid mechanics linear continuous in time and piecewise linear in space interpolation functions are assumed for the displacement discontinuities causal and analytical integrations are used throughout the resulting numerical algorithms are time marching and implicit the displacement discontinuity method can be used to model a class of traction boundary value problems where the unknowns are the transient shear and normal discontinuities in displacement across the surface of a mathematical crack in an infinite isotropic and homogeneous linear elastic medium

a mean field spin glass with short range interactions we formulate and study a spin glass model on the bethe lattice appropriate boundary fields replace the traditional self consistent methods they give our model well defined thermodynamic properties we establish that there is a spin glass transition temperature above which the single site magnetizations vanish and below which the edwards anderson order parameter is strictly positive in a neighborhood below the transition temperature we use bifurcation theory to establish the existence of a nontrivial distribution of single site magnetizations two properties of this distribution are studied the leading perturbative correction to the gaussian scaling form at the transition and the nonperturbative behavior of the tails

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

optimization of output load in a junction model an optimization problem of minimizing the output load of a junction model with multiple input and output channels is solved by the replica method simulation results show that for the case of extensive connectivity the replica solution obtained by assuming a vanishing solution space is satisfactory however for the case of intensive connectivity the degeneracy of the solution space causes the simulation results to deviate from the replica solution of vanishing volume

graph partitioning and dilute spin glasses the minimum cost solution the authors calculate the ground state cost function energy for graph bipartitioning and spin glasses on networks with fixed finite valences allowing a continuous distribution for the effective field compared with previous calculations using a field distribution in integral multiples of the coupling strength j the ground state energy is higher by less than one per cent although the distribution itself is altered drastically

taylor expansions for singular kernels in the boundary element method the problem treated is the integration of singular functions which arise in three dimensional isoparametric formulations of boundary integral equations a taylor expansion in the local parametric co ordinates is developed for the singular integrand so allowing singular terms to be integrated in closed form even for curved surface elements the remainder integral obtained by subtracting out the worst singularities is integrated by repeated gaussian quadrature two groups of tests are presented first the accuracy of the integrations has been checked for plane parallelograms for which exact solutions have been developed and for curved elements on a sphere secondly results from complete boundary element calculations based on point collocation have been compared with known analytical solutions to two problems zonal surface harmonics on a sphere and the capacitance of an ellipsoid the agreement obtained with few degrees of freedom suggests that errors which have previously been attributed to point collocation might have arisen in the numerical integration

stress oscillations in plane stress modelling of flexure a field consistency interpretation exactly integrated isoparametric plane stress elements13 behave poorly in flexure the 4 noded element locks with13 errors that progress indefinigely as element aspect ratio13 inceases reduced integration of the shear strain energy13 eliminates this locking entirely the 8 noded element does not lock but improves in performance with reduced integration of shear strain energy both elements with their original shape functions show severe shear stress oscillations in flexure in this paper we attribute these oscillations to the lack of consistency of shear strain fields derived directly from independent field variable interpolations we derive error models for specific tractable examples which can confirm the accuracy of this conceptual scheme through digital computation using the finite element models a field consistent re distribution strategy for the shear strain field is offered as an elegant procedure to free the elements of spurious13 oscillations and give a lock free performance

a new family of continuous discontinuous three dimensional boundary elements with application to acoustic wave propagation this paper presents a new family of continuous discontinuous three dimensional boundary elements which has been implemented in a computer system for acoustic wave propagation in the frequency domain the system includes elements of different geometrical shapes order of interpolation and degree of continuity results of several tests are included to show the efficiency of the family of elements

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 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

time dependent axisymmetric thermoelastic boundary element analysis a boundary element method is developed for problems of quasistatic axisymmetric thermoelasticity unlike previous approaches this new time domain formulation is written exclusively in terms of surface quantities thereby eliminating the need for volume discretization furthermore since the exact three dimensional infinite space fundamental solutions are employed very accurate solutions are obtainable including the determination of surface stresses in the integral formulation the fundamental solutions are separated into steady state and transient components the steady state portion which contains all of the singularities is integrated analytically in the circumferential direction yielding the familiar axisymmetric kernels the remaining non singular transient integrands are treated by a combination of analytical and numerical quadrature the method is implemented in a general purpose boundary element code which includes multiregion capability along with higher order conforming surface elements several numerical examples are provided to illustrate the validity of the formulation and the attractiveness of this approach for practical engineenring analysis

extremal optimization of graph partitioning at the percolation threshold the benefits of a recently proposed method to approximate hard optimization problems are demonstrated on the graph partitioning problem the performance of this new method called extremal optimization eo is compared with simulated annealing sa in extensive numerical simulations while generally a complex np hard problem the optimization of the graph partitions is particularly difficult for sparse graphs with average connectivities near the percolation threshold at this threshold the relative error of sa for large graphs is found to diverge relative to eo at equalized runtime on the other hand eo based on the extremal dynamics of self organized critical systems reproduces known results about optimal partitions at this critical point quite well

a semi analytical algorithm for the evaluation of the nearly singular integrals in three dimensional boundary element methods the nearly singular integrals occur in the boundary integral equations when the source point is close to an integration element as compared to its size but not on the element in this paper the concept of a relative distance from a source point to the boundary element is introduced to describe possible influence of the singularity of the integrals then a semi analytical algorithm is proposed for evaluating the nearly strongly singular and hypersingular integrals in the three dimensional bem by using integration by parts the nearly singular surface integrals on the elements are transformed to a series of line integrals along the contour of the element the singular behavior which appears as factor is separated from remaining regular integrals consequently standard numerical quadrature can provide very accurate evaluation of the resulting line integrals the semi analytical algorithm is applied to analyzing the three dimensional elasticity problems such as very thin walled structures meanwhile the displacements and stresses at the interior points very close to its bounding surface are also determined efficiently the results of the numerical investigation demonstrate the accuracy and effectiveness of the algorithm

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

boundary element methods in three dimensional thermoelasticity abstract a boundary element method is developed for the solution of time dependent problems in three dimensional thermoelasticity the time domain boundary only formulation represents the first of its kind for quasistatic analysis which by definition considers transient heat conduction but ignores the effects of inertia by eliminating the need for volume discretization the method becomes an attractive alternative to finite element analysis for this class of problems additionally because an exact green s function is used in the interior steep thermal gradients can be captured much more readily than with standard domain based methods the presentation includes details of the fundamental solution a derivation of the boundary integral equations and an overview of a general purpose numerical implementation this implementation permits the solution of large multiregion problems with arbitrary geometry and boundary conditions several examples are included to validate the proposed method as well as to highlight its usefulness

a time dependent incompressible viscous bem for moderate reynolds numbers the boundary element method is applied to transient viscous incompressible flow the time domain formulation allows a boundary only solution for linear stokes flow for higher speed flows in which the non linear convective effects cannot be ignored a volume integral must be retained however the introduction of reference velocities often limits the non linear region to the vicinity of obstacles or bounding surfaces additionally the volume terms are rewritten to eliminate the need for the calculation of velocity gradients a general purpose numerical implementation of this new formulation then produces a very attractive tool for engineering analysis this implementation includes a newton raphson algorithm permitting accurate solutions up to the moderate reynolds number range several numerical examples are provided to validate the present approach

the free energy at t 0 of the spin glass in the case of the continuous distribution of the effective field on the bethe lattice for z 4 5 6 abstract we evaluated the free energy at t 0 of the j random ising model on the bethe lattice of the coordination number z 4 5 6 in the case where the distribution function of the effective field has a continuous distribution by using the method of the integral equation of the effective field

an indirect elastodynamic boundary element method with analytic bases an indirect time domain boundary element method bem is presented here for the treatment of 2d elastodynamic problems the approximated solution in this method is formulated as a linear combination of a set of particular solutions which are called bases the displacement and stress fields of a basis are analytically derived by means of solving lame s displacement potentials a semi collocation method is proposed to be the time stepping algorithm this method is equivalent to a displacement discontinuity method with piecewise linear discontinuities in both space and time the resulting time stepping scheme is explicit the bem is implemented to solve three numerical examples lamb s problem half plane with a buried crack and selberg s problem though lamb s problem is considered a difficult problem for numerical methods the current numerical results for the surface displacements show accurately the characteristics of the rayleigh wave this method is efficient and accurate copyright 2003 john wiley sons ltd

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

axisymmetric transient elastodynamic analysis by boundary element method abstract the first formulation of an axisymmetric transient elastod namic analysis by time domain boundary element method is presented and is implemented in a general purpose system gpbest for the evaluation of boundary convolution integrals both constant and linear variations in the time domain of displacement and traction fields are given transformation of 3 d dynamic kernels into cylindrical coordinates and the integration of kernels along circumferential direction leads directly to an axisymmetric analysis with only 2 d boundary discretization the numerical integration of these kernels has been done carefully by preserving the causality so that very good accuracy and reliability of the present analysis have been achieved as can be seen in the examples presented

graph bipartitioning and spin glasses on a random network of fixed finite valence the authors study the problem of bipartitioning a random graph of fixed finite valence using a mean field replica symmetric theory of an ising ferromagnet with zero magnetisation constraint the thermodynamics is determined by the probability distribution of an auxiliary field the expression for the ground state energy agrees with that proposed by mezard and parisi 1986 using a cavity field method but their expression for the fraction of crazy spins is reinterpreted

minimizing unsatisfaction in colourful neighbourhoods colouring sparse graphs under various restrictions is a theoretical problem of significant practical relevance here we consider the problem of maximizing the number of different colours available at the nodes and their neighbourhoods given a predetermined number of colours in the analytical framework of a tree approximation carried out at both zero and finite temperatures solutions obtained by population dynamics give rise to estimates of the threshold connectivity for the incomplete to complete transition which are consistent with those of existing algorithms the nature of the transition as well as the validity of the tree approximation are investigated

time domain transient elastodynamic analysis of 3 d solids by bem the numerical implementation of the direct boundary element formulation for time domain transient analysis of three dimensional solids is presented in a most general and complete manner the present formulation employs the space and time dependent fundamental solution stokes solution and graffi s dynamic reciprocal theorem to derive the boundary integral equations in the time domain a time stepping scheme is then used to solve the boundary initial value problem by marching forward in time higher order shape functions are used to approximate the field quantities in space as well as in time and a combination of analytical time integration and numerical spatial integration integration is carried out to form a system of linear equations at the end of each time step these equations are solved to obtain the unknown field quantities at that time finally the accuracy and reliability of this algorithm is demonstrated by solving a number of example problems and comparing the results against the available analytical and numerical solution

analysis of symmetric domains in advanced applications with the boundary element method the strategy in the boundary element method for the analysis of symmetric domains that does not require the modelling of contours corresponding to the axes of symmetry is investigated for a number of advanced applications these applications include treatment of domain loadings two dimensional time domain transient elastodynamics and the analysis of probabilistic problems in elastostatics with a random geometric configuration both symmetric as well as arbitrary loadings acting on the symmetric objects are considered a number of case studies are presented to provide comparisons of computer memory and cpu time requirements for the analyses of the entire object versus the analyses of only the symmetric portion of the object the numerical data presented clearly demonstrates the advantages of developing efficient symmetric formulations for advanced applications

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

zero temperature hysteresis in the random field ising model on a bethe lattice we consider the single spin flip dynamics of the random field ising model on a bethe lattice at zero temperature in the presence of a uniform external field we determine the average magnetization as the external field is varied from to by setting up the self consistent field equations which we show are exact in this case the qualitative behaviour of magnetization as a function of the external field unexpectedly depends on the coordination number z of the bethe lattice for z 3 with a gaussian distribution of the quenched random fields we find no jump in magnetization for any non zero strength of disorder for for weak disorder the magnetization shows a jump discontinuity as a function of the external uniform field which disappears for a larger variance of the quenched field we determine exactly the critical point separating smooth hysteresis curves from those with a jump we have checked our results by monte carlo simulations of the model on three and four coordinated random graphs which for large system sizes give the same results as on the bethe lattice but avoid surface effects altogether

two dimensional transient wave propagation problems by time domain bem abstract in this paper an advanced formulation of time domain boundary element method bem for linear elastodynamics is used to study a number of problems involving wave propagation through half space as well as multi layered soils the algorithm incorporates isoparametric quadratic elements which facilitate proper modelling of problem geometry and can represent the field variables in dynamic problems very accurately which are very often wavy in nature also higher order temporal variation of functions is introduced improved techniques are employed for the accurate evaluation of both the singular and non singular spatial integrals most importantly this formulation incorporates simpler and better behaved kernels compared to those that have appeared in the recent bem literature by the present and other previous researchers with all these new and efficient features the present formulation is superior to the existing ones and as such represents a very effective tool for solving 2d transient wave propagation problems especially in infinite and semi infinite domains where other numerical methods have considerable difficulty in producing accurate solutions

graph bipartitioning and the bethe spin glass the problem of the equipartitioning of a random graph of fixed finite valence is studied by comparison with a ferromagnetic bethe lattice with random boundary conditions the simplicity of recursion relations for effective fields due to descendents on bethe lattices provides simple approximations for the optimal cost in quite good agreement with simulations

advanced time domain formulation of bem for two dimensional transient elastodynamics the traction kernel is derived by using the causality of the waves and the resulting kernel is explicite an appropriate set of linear time interpolation functions together with quadratic spatial variations are incorporated the algorithm has a capability of handling problems with multiply connected regions this above algorithm is now a part of the general purpose bem code known as gpbest

q partitioning of graphs with finite coordination number the np complete optimisation problem of q partitioning of graphs with finite connectivity is discussed using the effective local field method the authors obtain the local field distributions with and without the continuous part and use them to calculate the ground state energies of the three state potts spin glass on lattices with finite coordination number equal to three this in turn gives analytic results for the optimal cost of the 3 partitioning of graphs they perform simulations of actual 3 partitions of random graphs to compare with their theoretical results and obtain very good agreement ways for further improvement of the estimates are discussed

advanced development of time domain bem for two dimensional scalar wave propagation an improved formulation for solving 2d transient scalar wave propagation problems by the boundary element method bem is presented the kernels presented are simpler and better behaved than those that have appeared in the published literature an appropriate set of temporal shape functions for linear variation is used for spatial variations isoparametric quadratic elements are used all of these represent significant improvements over the present level of sophistication in the analysis of 2d transient scalar problems the algorithm is implemented in a general purpose boundary element code known as gpbest

stability analysis and design of time stepping schemes for general elastodynamic boundary element models summary in the literature there is growing evidence of instabilities in standard time stepping schemes to solve boundary integral elastodynamic models 1 3 however there has been no theory to support scientists and engineers in assessing the stability of their boundary element algorithms or to help them with the design of new more stable algorithms in this paper we present a general framework for the analysis of the stability of any time domain boundary element model we illustrate how the stability theory can be used to assess the stability of existing boundary element models and how the insight gained from this analysis can be used to design more stable time stepping schemes in particular we describe a new time stepping procedure that we have developed which has substantially enhanced stability characteristics and greater accuracy for the same computational eort the new scheme which we have called the half step scheme is shown to have substantially improved performance for the displacement discontinuity boundary element method commonly used to model dynamic fracture interaction and propagation

conforming versus non conforming boundary elements in three dimensional elastostatics in this work we present a critical comparison of two basic ways of implementing the boundary element method in three dimensional elastostatics the first way is by using non conforming elements i e elements which have the collocation nodes removed from their perimeter the number of nodes used for the collocation of the boundary tractions and displacements need not coincide with the number of nodes placed along the perimeter of the element for the purpose of describing the geometry the second way is by placing the collocation nodes along the perimeter of the element usually in coincidence with the geometry nodes thus interelement continuity of the displacements is obtained the basic reasons for the use of non conforming elements in the boundary element method are twofold first simplification in the assembly and solution of the system equations and secondly easy computation of the free and cauchy principal value terms appearing in the integral equations the state of the art in the boundary element method however has advanced in the last decade to the point where both of the aforementioned reasons are no longer problematic as will be shown in what follows conforming elements are able to produce more accurate results than non conforming ones with substantial economy in the final size of the system equations

graph bipartitioning and statistical mechanics the problem of bipartitioning a random graph of fixed finite local valence connectivity so as to minimise the number of cross edges is studied by the application of monte carlo simulation of thermodynamics and annealing this problem is np complete and is relevant as an idealisation of several practical organisation problems evidence is presented for the existence of a multiplicity of metastable states and for non self averaging and ultrametricity in the space of overlaps albeit with a possible critical valence an empirical formula is presented for the optimal cost in excellent accord with values obtained by simulation and those known exactly

solution of radiation problems by collocation of integral formulations in terms of single and double layer potentials abstract the purpose of this paper is the solution of the exterior steady state acoustic radiation problem for an arbitrary surface of which the normal velocity is specified by using integral formulations to obtain integral formulations both a direct method based on the surface helmholtz integral equation and an indirect method based on single and double layer potentials have been used filippi s method with a hybrid potential ensures uniqueness for any wavenumber three different surface elements have been used as a basis for obtaining approximate solutions by collocation of the integral equations a comparison of the rates of convergence for the three surface elements is presented based on a suitably defined overall error there is no overall convergence for the double layer representation when a constant approximate solution is used for each surface element in spite of the good local convergence at the centers of the elements the rate of convergence also appears to be highly dependent on the normal interpolation technique special care has been taken in the calculation of the singular integrals which are the terms of self influence the numerical implementation of the method which has been tested for special cases is applicable to general three dimensional sound radiation problems since no special symmetry conditions are involved

the graph partitioning and the spin glass comments on papers by sherrington and his group the recent theory of graph partitioning proposed by sherrington and his group 1987 1988 used the integral equation to determine the field distribution this integral equation and its solution are pointed out to be the same as those used by katsura and co workers 1979 1980 for spin glasses

elastodynamic boundary element method for piecewise homogeneous media a general higher order formulation for the time domain elastodynamic direct boundary element method is presented for computing the transient displacements and stresses in multiply connected two dimensional solids the displacement and traction interpolation functions are linear in time and quadratic in space all integrations are analytical and are expressed in terms of twelve basic recurring integrals causality is ensured by integrating only over the dynamically active parts of each element and the algorithm presented is time marching and implicit the use of analytical integrations allows both unbounded and bounded domain problems to be solved without having to introduce special enclosing elements all of these improved features allow for a formulation that is very efficient and accurate the stability and accuracy of the elastodynamic boundary element algorithm is demonstrated by solving several example problems and comparing the results with available analytical and numerical solutions 1998 john wiley sons ltd

topological sensitivity for 3d elastodynamic and acoustic inverse scattering in the time domain building on previous work for 3d inverse scattering in the frequency domain this article develops the concept of topological derivative for 3d elastic and acoustic wave imaging of media of arbitrary geometry using data in the time domain the topological derivative which quantifies the sensitivity of the cost functional associated with the inverse scattering problem due to the creation at a specified location of an infinitesimal hole for the elastodynamic case or rigid inclusion for the acoustic case is found to be expressed in terms of the time convolution of the free field and a supplementary adjoint field the derivation of the topological derivative follows the generic pattern proposed in previous studies which is transposable to a variety of other physical problems a numerical example where the featured cost function is defined in terms of synthetic data arising from the scattering of plane acoustic waves by a rigid spherical inclusion illustrates the utility of the topological derivative concept for defect identification using time varying data