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

fuzzy topological vector spaces topological generation and normability abstract increasing awareness of the utility of fuzzy systems in modeling real life situations necessitates a thorough understanding of fuzzy topological vector spaces in this paper the first of several to follow on this topic the generation of a fuzzy vector topology from an ordinary vector topology on a vector space is discussed also obtained is a condition for the fuzzy normability of a fuzzy vector topology induced by a family of fuzzy seminorms finally an example indicating that the earlier mentioned condition is only sufficient is given

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

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 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

fuzzy topological vector spaces over r in this paper the concepts of fuzzy vector fuzzy vector space and fuzzy topological vector space are investigated a topology called sendograph topology which is compatible with the algebraic structure is given

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

packing dimers on 2p 1 x 2q 1 lattices we use computational method to investigate the number of ways to pack dimers on m x n lattices where both m and n are odd in this case there is always a single vacancy in the lattices we show that the dimer configuration numbers on 2k 1 x 2k 1 odd square lattices have some remarkable number theoretical properties in parallel to those of close packed dimers on 2k x 2k even square lattices for which an exact solution exists furthermore we demonstrate that there is an unambiguous logarithmic term in the finite size correction of free energy of odd by odd lattice strips with any width n or 1 this logarithmic term determines the distinct behavior of the free energy of odd square lattices these findings reveal a deep and previously unexplored connection between statistical physics models and number theory and indicate the possibility that the monomer dimer problem might be solvable

recursion transform method for computing resistance of the complex resistor network with three arbitrary boundaries we develop a general recursion transform r t method for a two dimensional resistor network with a zero resistor boundary as applications of the r t method we consider a significant example to illuminate the usefulness for calculating resistance of a rectangular m ifmmode times else texttimes fi n resistor network with a null resistor and three arbitrary boundaries a problem never solved before since green s function techniques and laplacian matrix approaches are invalid in this case looking for the exact calculation of the resistance of a binary resistor network is important but difficult in the case of an arbitrary boundary since the boundary is like a wall or trap which affects the behavior of finite network in this paper we obtain several general formulas of resistance between any two nodes in a nonregular m ifmmode times else texttimes fi n resistor network in both finite and infinite cases in particular 12 special cases are given by reducing one of the general formulas to understand its applications and meanings and an integral identity is found when we compare the equivalent resistance of two different structures of the same problem in a resistor network

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

dimer model on a triangular lattice we analyze the partition function of the dimer model on an mathcal m ifmmode times else texttimes fi mathcal n triangular lattice wrapped on a torus obtained by fendley moessner and sondhi phys rev b 66 214513 2002 from a finite size analysis we have found that the dimer model on such a lattice can be described by a conformal field theory having a central charge c ensuremath 2 the shift exponent for the specific heat is found to depend on the parity of the number of lattice sites mathcal n along a given lattice axis e g for odd mathcal n we obtain the shift exponent ensuremath lambda 1 while for even mathcal n it is infinite ensuremath lambda ensuremath infty in the former case therefore the finite size specific heat pseudocritical point is size dependent while in the latter case it coincides with the critical point of the thermodynamic limit

on local bases of fuzzy topological vector spaces abstract in this paper the relations between neighborhood base introduced by warren and quasi coincidence neighborhood base introduced by pu and liu in fuzzy topological spaces are studied the characterizations of these two kind of local bases for fuzzy topological vector spaces are further discussed moreover we prove a necessary and sufficient condition for a family of fuzzy sets in a vector space to be the q prebase of a ql type fuzzy topological vector space

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

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

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

theory of impedance networks the two point impedance and lc resonances we present a formulation of the determination of the impedance between any two nodes in an impedance network an impedance network is described by its laplacian matrix l which has generally complex matrix elements we show that by solving the equation lu u with orthonormal vectors ua the effective impedance between nodes p and q of the network is zpq u p u q 2 where the summation is over all not identically equal to zero and u p is the pth component of u for networks consisting of inductances l and capacitances c the formulation leads to the occurrence of resonances at frequencies associated with the vanishing of this curious result suggests the possibility of practical applications to resonant circuits our formulation is illustrated by explicit examples

the equivalent resistance of a 3 n cobweb network and its conjecture of an m n cobweb network we investigate the equivalent resistance of a 3 n cobweb network the difference equations of the model are constructed by network analysis and their general solution is obtained by matrix transformations it is found that the equivalent resistance can be expressed by the trigonometric function of k 7 which decreases with the increase of the order n by analyzing and comparing the equivalent resistances of the 1 n 2 n and 3 n cobweb networks a conjecture on the equivalent resistance of the m n cobweb network is proposed

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

asymptotic expansion for the resistance between two maximally separated nodes on an m by n resistor network we analyze the exact formulae for the resistance between two arbitrary notes in a rectangular network of resistors under free periodic and cylindrical boundary conditions obtained by wu j phys a 37 6653 2004 based on such expression we then apply the algorithm of ivashkevich izmailian and hu j phys a 35 5543 2002 to derive the exact asymptotic expansions of the

theory of resistor networks the two point resistance the resistance between two arbitrary nodes in a resistor network is obtained in terms of the eigenvalues and eigenfunctions of the laplacian matrix associated with the network explicit formulae for two point resistances are deduced for regular lattices in one two and three dimensions under various boundary conditions including that of a mobius strip and a klein bottle the emphasis is on lattices of finite sizes we also deduce summation and product identities which can be used to analyse large size expansions in two and higher dimensions

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

a transfer matrix approach to random resistor networks introduces a transfer matrix formulation to compute the conductance of random resistor networks the authors apply this method to strips of width up to 40 and use finite size scaling arguments to obtain an estimate for the conductivity critical exponent in two dimensions t 1 28 or 0 03

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

separation of fuzzy normed linear spaces abstract this paper deals with hausdorff separation axiom for fuzzy topological spaces the necessary and sufficient condition obtained in the fuzzy vector topology induced by a fuzzy norm is separated properties of separated and non separated fuzzy norms along with examples are studied separation of a fuzzy norm in terms of the ordinary norm it induces and its consequences are characterised separation of quotient fuzzy semi norm is studied

fuzzy topological vector spaces ii abstract some of the properties of fuzzy topological vector spaces are investigated also there are given necessary and sufficient conditions for a family of fuzzy sets in a vector space e to be the family of all neighborhoods of zero for a fuzzy linear topology

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

logarithmic corrections in the free energy of monomer dimer model on plane lattices with free boundaries using exact computations we study the classical hard core monomer dimer models on m x n plane lattice strips with free boundaries for an arbitrary number v of monomers or vacancies we found a logarithmic correction term in the finite size correction of the free energy per lattice site the coefficient of the logarithmic correction term depends on the number of monomers present v and the parity of the width n of the lattice strip the coefficient equals to v when n is odd and v 2 when n is even the results are generalizations of the previous results for a single monomer in an otherwise fully packed lattice of dimers we also study the finite size correction in the low dimer density limit where the number of dimers d is fixed in this case the coefficient of the logarithmic correction term equals to d for both odd and even n

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

fuzzy continuity of linear maps on vector spaces abstract this paper studies the fuzzy continuity of linear maps from one vector space into another through a simple characterization of fuzzy convergence of fuzzy points a fuzzy norm is defined on the set of all fuzzy continuous linear maps from a vector space into another convergence of a sequence of fuzzy continuous linear maps to a fuzzy continuous linear map is obtained it is observed that unlike in the ordinary case fuzzy normed topological vector spaces cannot be imbedded in their second duals

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

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

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

finite size effects for the ising model on helical tori we analyze the exact partition function of the ising model on a square lattice under helical boundary conditions obtained by liaw et al phys rev e 73 055101 r 2006 based on such an expression we then extend the algorithm of ivashkevich izmailian and hu j phys a 35 5543 2002 to derive an exact asymptotic expansion of the logarithm of the partition function and its first to fourth derivatives at the critical point from such results we find that the shift exponent for the specific heat is ensuremath lambda 1 for all values of the helicity factor d we also find that finite size corrections for the free energy the internal energy and the specific heat of the model in a crucial way depend on the helicity factor of the lattice

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

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