from one cell to the whole froth a dynamical map we investigate two and three dimensional shell structured inflatable froths which can be constructed by a recursion procedure adding successive layers of cells around a germ cell we prove that any froth can be reduced into a system of concentric shells there is only a restricted set of local configurations for which the recursive inflation transformation is not applicable these configurations are inclusions between successive layers and can be treated as vertices and edges decorations of a shell structured inflatable skeleton the recursion procedure is described by a logistic map which provides a natural classification into euclidean hyperbolic and elliptic froths froths tiling manifolds with different curvatures can be classified simply by distinguishing between those with a bounded or unbounded number of elements per shell without any a priori knowledge on their curvature a result associated with maximal orientational entropy is obtained on topological properties of natural cellular systems the topological characteristics of all experimentally known tetrahedrally close packed structures are retrieved

formulation and analysis of a parameter free stabilized finite element method we present and study a parameter free stabilized finite element method for the scalar advection diffusion equation edge element lifting of diffusive edge fluxes defines the stabilization the amount of edge diffusion varies with the edge peclet number and adapts to solution features without mesh dependent parameters we prove that the method is first order accurate in the advective limit numerical studies confirm the theoretical estimates

long range geometrical correlations in two dimensional foams the statistical properties of two dimensional space filling random cellular structures foams or their dual random triangulations in statistical equilibrium are obtained by maximum entropy inference and topological simulations we show by maximum entropy inference that for a broad class of foams shell structured including three sided cell inclusions all two cell topological correlators aj k n average number of pairs of k cell and n cell at a topological distance j are linear in n and k the numbers of neighbours of the cells this generalizes a correlation known for neighbouring cells j d 1 which implies the linearity of aboav s relation between the total number of neighbours of the cells adjacent to a n neighboured cell andn our results verified by simulations also build up gauss s theorem for cellular structures any additional restriction in exploring local cell configurations besides the constraints of filling space at random will manifest itself through a deviation from linearity of the correlators aj k n and the aboav relation notably foams made of feynman diagrams have additional context dependent restrictions and their aboav relation is slightly curved it is essential that the local random variablen denotes the number of neighbours of the cell and not that of its sides whenever the two are different

the effect of structural elasticity on the efficiency of noise barriers the efficiency of noise barriers is usually estimated neglecting their elastic behaviour in this paper the total vibro acoustical response of simple barriers is considered a variational approach with a boundary element technique is used it is a generalization of an existing formalism developed for the study of two dimensional acoustical problems the case of straight and thin barriers is studied it is found that at low frequencies their vibrations can modify their insertion losses by several decibels

solution of fluid structure interaction problems using a coupled finite element and variational boundary element technique this work is concerned with the numerical modeling of elasto acoustic problems applied to thin shells and specifically curved plates a finite element formulation of the elastic problem is coupled to a variational boundary element solution of the acoustic problem this solution to the acoustic problem proposed by mariem and hamdi j b mariem and m a hamdi int j num methods eng 24 1251 1267 1987 is implemented using high order isoparametric elements and attention is given to techniques of accelerating the numerical implementation for solutions at multiple frequencies these techniques include a reduction in the problem size through the use of symmetry and more importantly the interpolation of the fluid impedance matrix within the frequency regime the advantages in using this variational formulation are first the manner in which a highly singular integral operator is made amenable to numerical approximation second its application to nonclosed thin shells and third its numerical im

a symmetric formulation of coupled bem fem in solving responses of submerged elastic structures for large degrees of freedom this work presents a symmetric formulation for the coupling of boundary element method bem with finite element method fem to compute responses of submerged elastic structures in a heavy acoustic medium the acoustic loading derived from bem is formulated in a symmetric complex matrix the symmetry of the acoustic loading matrix is proven by an acoustic reciprocal principle which relate two sets of arbitrary surface normal velocities and surface pressures in terms of surface integrals the structural equation is represented by fem the fact that the acoustic loading and the structural equation are symmetric allows us to take the storage and computational advantages of the banded matrix which has been widely used in conventional finite element methods consequently the computational efficiency of the proposed coupled fem bem is significantly increased the proposed method involving 20 000 degrees of freedom can be implemented on a personal computer numerical results are verified by analytical solutions of a constant thickness spherical shell subject to a point alternating force as well as the previously published variational solution of a constant thickness spheroidal shell excited by a concentrated force

efficient analytical integration of symmetric galerkin boundary integrals over curved elements thermal conduction formulation abstract substantial improvements are reported in the computational efficiency of galerkin boundary element analysis bea employing curved continuous boundary elements a direct analytical treatment of the singular double integrations involved in galerkin bea adapting a limit to the boundary concept used successfully in collocation bea is used to obviate significant computation in the determination of the galerkin coefficient matrices symbolic manipulation has been strategically employed to aid in the analytical evaluation of the singular contributions to these double integrals the analytical regularization procedure separates the potentially singular galerkin integrands into an essentially singular but simple part plus a regular remainder that can be integrated numerically the finite contribution from the simplified singular term is then computed analytically it is shown that the key to containing the explosive growth in the length of the formulae associated with such a hybrid analytical numerical integration scheme is the strategic timing of when to take the limit to the boundary this regularization also isolates the contribution from the curvature of the boundary element thus facilitating enhanced computational efficiency in problems with many straight elements example problems are presented to quantify the performance of this approach it is concluded that with these techniques galerkin symmetric bea can be more efficient than its collocation based counterpart

a new control volume finite element method for the stable and accurate solution of the drift diffusion equations on general unstructured grids abstract we present a new control volume finite element method with multi dimensional scharfetter gummel upwinding cvfem sg for the drift diffusion equations the method combines a conservative formulation of the carrier density continuity equations with an edge element lifting of the one dimensional scharfetter gummel edge currents into curl conforming elemental currents these elemental currents combine the upwind effect from all element edges and enable accurate computation of the flux on arbitrary surfaces inside the elements in so doing we obtain a formulation that is stable and accurate on general unstructured finite element grids this approach sets our formulation apart from other methods which require the control volumes to be topologically dual to the primal grid numerical studies of the cvfem sg for a suite of scalar advection diffusion test problems confirm the accuracy and the robustness of the new formulation simulations of a pn diode and an n channel mosfet device demonstrate the performance of the method for the fully coupled drift diffusion system

exponentially fitted shape functions for advection dominated flow problems in two dimensions we sketch out the basic properties of three novel exponentially fitted shape functions that generalize to two dimensional triangular elements the one dimensional functions used in the well known scharfetter gummel method this scheme is widely employed in the finite element approximation of the drift diffusion equations arising in semiconductor device modelling

a high order discontinuous galerkin approach to the elasto acoustic problem abstract we address the spatial discretization of an evolution problem arising from the coupling of elastic and acoustic wave propagation phenomena by employing a discontinuous galerkin scheme on polygonal and polyhedral meshes the coupled nature of the problem is ascribed to suitable transmission conditions imposed at the interface between the solid elastic and fluid acoustic domains we state and prove a well posedness result for the strong formulation of the problem present a stability analysis for the semi discrete formulation and finally prove an a priori h p version error estimate for the resulting formulation in a suitable mesh dependent energy norm we also discuss the time integration scheme employed to obtain the fully discrete system the convergence results are validated by numerical experiments carried out in a two dimensional setting

a coupled fe and boundary integral equation method based on exterior domain decomposition for fluid structure interface problems abstract a coupled finite element and exterior domain decomposition based boundary integral formulations for the solutions of two or three dimensional time harmonic fluid structure interaction problems is described in this paper it is known that the memory limitation of computers has been one of the major obstacles for solving large scale high frequency fluid structure interface systems using various existing nonlocal finite element and boundary integral equation coupling techniques due to the fully populated resultant matrix generated from the boundary integral equation representation the essence of this study is to decompose through domain decomposition of the exterior region the original exterior problem into arbitrary subproblems with data sharing only at the interfaces by decomposing the exterior infinite domain into an appropriate number of infinite subdomains this method not only ensures the validity of the formulation for all frequencies but also leads to a diagonalized blockwise banded system of discretized equations the size of an individual submatrix i e a block that is associated with an exterior subdomain may be decided by the user and may be selected such that the restriction due to the memory limitation of a given computer may be accommodated in addition the method is suited for parallel processing since the data associated with each subdomain impedance matrices load vectors etc may be generated in parallel and the communication needed will be only for the interface values most significantly unlike the existing coupled finite element and boundary integral equation techniques that are valid for all frequencies our method avoids the use of both the hypersingular operator and the double integrals therefore reducing the computational complexity numerical experiments have been performed for elastic cylindrical shells subjected to a plane incident wave the results have demonstrated the accuracy of the method for wavenumbers ranging from 0 to 30 both directly on the shell and in the far field and have confirmed that the procedure is valid for all frequencies

a novel exponentially fitted triangular finite element method for an advection diffusion problem with boundary layers in this paper we develop an exponentially fitted finite element method for a singularly perturbed advection diffusion problem with a singular perturbation parameter this finite element method is based on a set of novel piecewise exponential basis functions constructed on unstructured triangular meshes the basis functions can not be expressed explicitly but the values of each of them and its associated flux at a point are determined by a set of two point boundary value problems which can be solved exactly a method for evaluating elements of the stiffness matrix is also proposed for the case that is small numerical results presented to validate the method show that the method is stable for a large range of it is also shown by the numerical results that the rate of convergence of the method in an energy norm is of orderh1 2when is small

symmetric galerkin boundary formulations employing curved elements accounts of the symmetric galerkin approach to boundary element analysis bea have recently been published this paper attempts to add to the understanding of this method by addressing a series of fundamental issues associated with its potential computational efficiency a new symmetric galerkin theoretical formulation for both the harmonic heat conduction and the biharmonic elasticity problem that employs regularized singular and hypersingular boundary integral equations bies is presented the novel use of regularized bies in the galerkin context is shown to allow straightforward incorporation of curved isoparametric elements a symmetric reusable intrinsic sample point risp numerical integration algorithm is shown to produce a galerkin i e double integration strategy that is competitive with its counterpart i e singular integration procedure in the collocation bea approach when the time saved in the symmetric equation solution phase is also taken into account this new formulation is shown to be capable of employing hypersingular bies while obviating the requirement of c 1 continuity a fact that allows the employment of the popular continuous element technology the behavior of the symmetric galerkin bea method with regard to both direct and iterative equation solution operations is also addressed a series of example problems are presented to quantify the performance of this symmetric approach relative to the more conventional unsymmetric bea in terms of both accuracy and efficiency it is concluded that appropriate implementations of the symmetric galerkin approach to bea indeed have the potential to be competitive with if not superior to collocation based bea for large scale problems

complex networks on hyperbolic surfaces abstract we explore a novel method to generate and characterize complex networks by means of their embedding on hyperbolic surfaces evolution through local elementary moves allows the exploration of the ensemble of networks which share common embeddings and consequently share similar hierarchical properties this method provides a new perspective to classify network complexity both on local and global scale we demonstrate by means of several examples that there is a strong relation between the network properties and the embedding surface

stability assessment of a unified variational boundary integral method applicable to thin scatterers and scatterers with corners abstract the objective of this study is to assess the stability especially at and near critical frequencies of a new unified stable symmetric domain finite element and boundary integral methodology for solving time harmonic interface problems for scatterers of arbitrary shape the validity of this energy based variational procedure for rigid and penetrable smooth scatterers including the existence uniqueness and optimal convergence of the corresponding numerical approximations has been proved rigorously in the context of fluid structure interaction problems the emphasis here is on investigating the applicability of this procedure to the case of scatterers with corners using square and thin rectangular two dimensional rigid obstacles as prototypes we also establish that the apparently distinct direct boundary integral formulation due to burton and miller and the combined single and double layer indirect formulation due to leis brakhage and werner and panich introduced to insure that boundary integral equations for scattering problems are uniquely solvable for all wavenumbers are entirely equivalent within our variational setting by examining the condition number of the matrix of coefficients of the discretized equations as well as the resulting solutions both directly on the surface of the scatterers and in the far field it is demonstrated that the new methodology is robust and completely insensitive to critical frequencies even for thin objects most significantly the precise singular behaviour of the pressure field at corners is also predicted quite accurately by using standard finite elements along the boundary of the scatterer without having to introduce special singularity functions which for general interface problems may not be known in advance

towards multiscale functions enriching finite element spaces with local but not bubble like functions in this paper we propose a novel way via finite elements to treat problems that can be singular perturbed a reaction diffusion equation in our case we enrich the usual piecewise linear or bilinear finite element trial spaces with local solutions of the original problem as in the residual free bubble rfb setting but do not require these functions to vanish on each element edge a departure from the rfb paradigm such multiscale functions have an analytic expression for triangles and rectangles bubbles are the choice for the test functions allowing static condensation thus our method is of petrov galerkin type we perform several numerical validations which confirm the good performance of the method 2004 elsevier b v all rights reserved

responses of partially immersed elastic structures using a symmetric formulation for coupled boundary element and finite element methods using a coupled bem fem this work describes a numerical method to compute the response and acoustic radiation for structures partially immersed in fluid the structures and their responses are assumed to be symmetric about a symmetric plane a symmetric complex matrix derived from the bem and a reciprocal principle for surface acoustics is also used to represent the acoustic loading against the structures in addition selecting a proper green s function based on image source method satisfies the boundary conditions of pressure release on the fluid surface and null normal velocity on the symmetric plane moreover a boundary integral equation emerges when the field point approaches the structural surface where the normal derivative of the green s function over partial infinitesimal spheres is evaluated these limiting values depend on locations of the field point on the surface owing to the symmetry of the acoustic loading matrix the matrix for the coupled bem fem is a banded symmetric one thereby allowing us to employ a variable banded storage method and invert of the matrix doing so markedly increases computational efficiency furthermore an analytical solution of a spherical thin shell with the lower semi sphere immersed in water is carried out by characteristic function expansions for shell equation and acoustic loading these analytical solutions compare with the results obtained from the proposed numerical method a good correlation for low frequencies is obtained and minor discrepancies are observed with an increasing frequency

roughness and scaling in cellular patterns analysis of a simple model a foam can be decomposed into successive layers of cells at the same topological distance to an origin which is either an arbitrary cell or a basal plane the shape of these layers profile and thickening indicates the degree of randomness of the cellular pattern to support this idea we analyse the layer shapes in 2d rectangular models of foam as confirmed by numerical simulations the fluctuations in the direction normal to the layers are self affine on a significant range of scales with values of the exponents compatible with the kpz universality class 0 5 for the roughness exponent and z 1 5 for the dynamic exponent measuring the increase of the intralayer correlation length these fluctuations are not sufficient however to affect the dominant behaviour of the number of cells per layer found to saturate in cylindrical geometry and to increase linearly in concentric geometry

an acoustic boundary integral formulation for open shells allowing different impedance conditions top and bottom surfaces abstract in the automotive aerospace industries as well as the underwater acoustics defense applications the addition of coatings to modify the response of the vibrating structure is commonplace the formulation developed is an extension of the existing thin body formulation currently found in commercial noise prediction codes such as sysnoise in order to allow problems requiring different boundary condition on both sides of the thin shell to be solved for instance a generalised thin body acoustic formulation would allow for a local impedance boundary condition to be specified on the top surface and a hard neumann boundary condition to be specified on the bottom surface such a formulation would allow for different local impedance coatings to be specified on the top and bottom surfaces due to the lack of analytical solutions for such problems even for the simplest geometries it is difficult to validate such a formulation however three test cases are presented two flat plate examples and a open cylinder with a point monopole source excitation at its centre

topology of slightly polydisperse real foams the topology of slightly polydisperse meta stable real foams was investigated by means of optical tomography associated with a numerical reconstruction procedure the values of the mean numbers of faces per bubble and edges per face were very close to matzke s data 1946 the real foams were essentially disordered and possessed a noncentered symmetry and ideal structures also could not be observed the disorder was quantified by the second moment of the edge per face and face per bubble distributions and also by a statistical correlation coefficient between the numbers of edges of adjacent faces it was found that the edge distributions of the internal bubbles and not of the external ones were significantly anticorrelated even during foam aging which provided a measure of the disorder in the foam no obvious relationship could be deduced between the isoperimetric quotient and the face combination in an individual bubble eventually it was shown that the physical boundaries of the foam sample had no influence on the foam topology beyond a single bubble layer

a new family of mixed finite elements in ir 3 we introduce two families of mixed finite element on conforming inh div and one conforming inh curl these finite elements can be used to approximate the stokes system

an accurate and efficient scheme for acoustic structure interaction problems based on unstructured mesh abstract this paper focuses on the accurate and efficient numerical implementation of acoustic structure coupling formulations using the edge based smoothed finite element method for the flexible shell and the gradient weighted finite element method for the acoustic fluid field namely the es gw fem the shell is discretized using the simplest linear triangular elements and the edge based smoothing domain is then constructed by introducing an edge local coordinate system the edge based smoothing operation is performed on the smoothing domain as for the acoustic fluid domain the tetrahedron elements are adopted a compacted support domain is then constructed and the gradient weighted operation is performed on the support domain to model the exterior acoustic domain an artificial boundary is introduced and the dirichlet to neumann dtn boundary condition is imposed based on the appropriate compatibility and equilibrium conditions on the interface boundaries the coupled es gw fem formulation is finally obtained both the interior acoustic structure coupled problems and exterior acoustic structure coupled problems are available as the dtn boundary is considered numerical examples demonstrate that the coupled es gw fem achieves much higher accuracy and works more reliably compared with the coupled fem fem in solving practical engineering problems

efficient analytical integration of symmetric galerkin boundary integrals over curved elements elasticity formulation abstract substantial improvements are reported in the computational efficiency of galerkin boundary element analysis bea 1employing curved continuous boundary elements for elasticity problems a direct analytical treatment of the singular and hypersingular double integrations employing a limit to the boundary definition is adapted to gain computational economy symbolic manipulation has been employed to derive the analytical expressions for the singular contributions to these double integrals the analytical regularization procedure separates the potentially singular galerkin integrands into an essentially singular but simple part plus a regular remainder that can be integrated numerically the exact finite contributions from the simplified singular terms are then computed analytically it is shown that the key to containing the explosive growth in the length of the formulae associated with such a hybrid analytical numerical integration scheme is the strategic timing of when to take the limit to the boundary this regularization also isolates the contribution from the curvature of the boundary element thus facilitating enhanced computational efficiency in problems with many straight elements although the evaluation of the integrals of the kelvin fundamental solution essentially follows the procedures described earlier for the scalar laplace equation the analytical treatment is now more involved in terms of the complexity and number of terms present in each of these second rank tensor kernel functions the complete analytical formulation is explicitly provided in a series of tables example problems indicate that with these techniques galerkin symmetric bea can be more efficient than collocation for moderate or large scale problems

constrained geometries in soap froth dynamics abstract soap froths as archetypal disordered cellular structures exhibiting spatial and temporal evolution have been predominantly studied in terms of their topological properties recently constrained geometries in froth have attracted attention since these arise both from existing or natural structure or more usually can be artificially configured using a direct simulation method which retains detailed information on bubble cell mechanisms we have investigated dynamics in 2d froths with various initial structures corresponding to controlled disorder in particular we examine the special case of a defect ring surrounding a central inclusion in a uniform froth for different number of defects and ring radius this geometry permits comparison with shell theory as well as insight on dynamics of a virtual phase as defined for persistence and non equilibrium processes in general it appears that defect location and pattern of inclusion in the virtual phase cause considerable variation in the evolutionary behaviour leading to non universal exponents for the phase dynamics this is probably explained by the fact that the froth is still in the transient period over simulation time scales rather than achieving the final stage of persistence however distinctive patterns of response can be identified for the different froth regions despite system size limitations with topological and other properties indicating that a quasi equilibrium results

two dimensional exponential fitting and applications to drift diffusion models a class of methods is introduced that generalizes the so called exponential fitting method to two dimensional problems and more specifically to equations of the type operatorname div underset raise0 3em hbox smash scriptscriptstyle nabla u u underset raise0 3em hbox smash scriptscriptstyle nabla psi f with psi given and underset raise0 3em hbox smash scriptscriptstyle nabla psi big in a part of the domain the basic idea is the following i write the equation as operatorname div e psi underset raise0 3em hbox smash scriptscriptstyle nabla rho f through the change of variables u rho e psi ii discretize the symmetric equation by means of a method that uses some kind of harmonic average for the coefficient e psi mixed hybrid etc iii write the discrete scheme in terms of the nodal values of u e psi rho this produces an m matrix

a coupling of multi zone curved galerkin bem with finite elements for independently modelled sub domains with non matching nodes in elasticity when the different parts of a structure are modelled independently by bem or fem methods it is sometimes necessary to put the parts together without remeshing of the nodes along the part interfaces frequently the nodes do not match along the interface in this work the symmetric galerkin multi zone curved boundary element is a fully symmetric formulation and is the method used for the boundary element part for bem fem coupling it is then necessary to interpolate the tractions in between the non matching nodes for the fem part finally the coupling is achieved by transforming the finite element domains to equivalent boundary element domains in a block symmetric formulation this system is then coupled with a boundary element domain with non matching nodes in between copyright 2004 john wiley sons ltd

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100