calculation of the impedance matrix inner integral to prescribed precision we present a new method for evaluating the inner integral of the impedance matrix element in the traditional rao wilton glisson formulation of the method of moments for perfect conductors in this method we replace the original integrand modified by a constant phase factor by its taylor series and keep enough terms to guarantee a number of significant digits in the integration outcome we develop criteria that relate the number of taylor terms to the number of required significant digits we integrate the leading taylor terms analytically and the rest through iteration formulas we show that the iteration formulas converge for all observation points within a sphere with a radius of half a wavelength and center the triangle s centroid we compare results of our method with existing ones and find them in excellent agreement we also outline a procedure for using cubatures outside the region of convergence

calculation of cfie impedance matrix elements with rwg and n spl times rwg functions the method of moments mom solution of combined field integral equation cfie for electromagnetic scattering problems requires calculation of singular double surface integrals when galerkin s method with triangular vector basis functions rao wilton glisson functions and the cfie are applied to solve electromagnetic scattering by a dielectric object both rwg and n spl times rwg functions n is normal unit vector should be considered as testing functions robust and accurate methods based on the singularity extraction technique are presented to evaluate the impedance matrix elements of the cfie with these basis and test functions in computing the impedance matrix elements including the gradient of the green s function we can avoid the logarithmic singularity on the outer testing integral by modifying the integrand in the developed method all singularities are extracted and calculated in closed form and numerical integration is applied only for regular functions in addition we present compact iterative formulas for computing the extracted terms in closed form by these formulas we can extract any number of terms from the singular kernels of cfie formulations with rwg and n spl times rwg functions

on numerical cubatures of singular surface integrals in boundary element methods we present and analyze methods for the accurate and efficient evaluation of weakly cauchy and hypersingular integrals over piecewise analytic curved surfaces in 3 the class of admissible integrands includes all kernels arising in the numerical solution of elliptic boundary value problems in three dimensional domains by the boundary integral equation method the possibly not absolutely integrable kernels of boundary integral operators in local coordinates are pseudohomogeneous with analytic characteristics depending on the local geometry of the surface at the source point this rules out weighted quadrature approaches with a fixed singular weight for weakly singular integrals it is shown that duffy s triangular coordinates leadalways to a removal of the kernel singularity also asymptotic estimates of the integration error are provided as the size of the boundary element patch tends to zero these are based on the rabinowitz richter estimates in connection with an asymptotic estimate of domains of analyticity in 2 it is further shown that the modified extrapolation approach due to lyness is in the weakly singular case always applicable corresponding error and asymptotic work estimates are presented for the weakly singular as well as for cauchy and hypersingular integrals which e g arise in the study of crack problems we analyze a family of product integration rules in local polar coordinates these rules are hierarchically constructed from finite part integration formulas in radial and gaussian formulas in angular direction again we show how the rabinowitz richter estimates can be applied providing asymptotic error estimates in terms of orders of the boundary element size

fast and accurate computation of hypersingular integrals in galerkin surface integral equation formulations via the direct evaluation method hypersingular 4 d integrals arising in the galerkin discretization of surface integral equation formulations are computed by means of the direct evaluation method the proposed scheme extends the basic idea of the singularity cancellation methods usually employed for the regularization of the singular integral kernel by utilizing a series of coordinate transformations combined with a reordering of the integrations the overall algebraic manipulation results in smooth 2 d integrals that can be easily evaluated via standard quadrature rules finally the reduction of the dimensionality of the original integrals together with the smooth behavior of the associated integrands lead up to unmatched accuracy and efficiency

computational analysis of modeling error for the coupling of particle and continuum models by the arlequin method we propose in this paper a 1d model problem to study the convergence of surrogate approximations using an atomistic to continuum coupling method towards the solution of a full particle model the 1d problem consists of a collection of springs that exhibits a local defect materialized by a sudden change in the spring properties the surrogate model is obtained by the arlequin approach which introduces an overlap region in which the continuum and particle models are coupled together using lagrange multipliers the objective of the present work is to show via numerical experiments that the modeling error does indeed converge to zero as the distance of the overlap region from the defect and or its size are increased

an adaptive strategy for the control of modeling error in two dimensional atomic to continuum coupling simulations an adaptive approach to control modeling error in multiscale simulations that involve molecular and continuum scales is presented the modeling error is defined as the difference between the solution of a reference particle model which is considered intractable in practice and the solution of a manageable multiscale surrogate problem based on the arlequin framework the method relies on computable error estimates of the modeling error in specific outputs of interest that require the solution of an adjoint problem these are the so called goal oriented error estimates which are used to adapt the surrogate model i e to find the optimal configuration of the overlap region between the molecular and continuum models in order to deliver approximations of quantities of interest within some preset accuracy performance of the adaptive strategy is demonstrated on two dimensional numerical examples

hybrid integration scheme for the evaluation of strongly singular and near singular integrals in surface integral equations the accurate and efficient evaluation of surface source integrals is a key step in obtaining reliable solutions to electromagnetic problems using integral equation formulations in this paper we propose to combine two of the most extensively used schemes to efficiently evaluate strongly singular and near singular source integrals such as those arising in the mathcal k operator in the proposed approach singularity subtraction is first applied to remove the most dominant singular part singularity cancellation using the radial angular variable transformation is then employed to treat the remaining integrand the method is compared to other common numerical schemes to demonstrate its effectiveness

broadband muller mlfma for electromagnetic scattering by dielectric objects the multilevel fast multipole algorithm mlfma is very efficient for solving large scale electromagnetic scattering problems however at low frequencies or when the discretization is small compared with the wavelength both the mlfma and the underlying integral equation formulation typically suffer from a subwavelength breakdown for the electromagnetic scattering from a homogeneous dielectric object we obtain a stable and well conditioned surface integral formulation using a variant of the classical muumlller formulation and linear basis functions to overcome the subwavelength breakdown of the mlfma we use both propagating and evanescent plane waves to represent the fields the implementation is based on a combination of the spectral representation of the green s function and rokhlin s translation formula we also present a new interpolation scheme for the evanescent part which significantly improves the error controllability of the mlfma implementation several numerical results verify both the error controllability and scalability of the proposed algorithm

computation of galerkin double surface integrals in the 3 d boundary element method the galerkin boundary element method bem also known as the method of moments is a powerful method for solving the laplace equation in three dimensions there are advantages to galerkin formulations for integral equations as they treat problems associated with kernel singularity and lead to symmetric and better conditioned matrices however the galerkin method requires the computation of double surface integral over pairs of triangles there are many semianalytical methods to treat these integrals which all have some issues and are discussed in this paper novel methods inspired by the treatment of these kernels in the fast multipole method are presented for computing all the integrals that arise in the galerkin formulation to any accuracy integrals involving completely geometrically separated triangles are nonsingular and are computed using a technique based on spherical harmonics and multipole expansions and translations which require the integration of polynomial functions over the triangles integrals involving cases where the triangles have common vertices edges or are coincident are treated via scaling and symmetry arguments combined with automatic recursive geometric decomposition of the integrals the methods are validated and example results are presented

control of modeling errors in the coupling of linear transport and diffusion models we consider in this paper the initial boundary value problem for the 1d neutron transport equation with isotropic scattering set in some bounded interval with inflow boundary conditions the usual parabolic scaling yields the diffusive limit a surrogate model coupling transport and diffusion equations is then introduced in order to accurately assess the value of specific quantities of interest the control of the quality of the computation with respect to such a quantity of interest is performed by means of an approach for modeling error estimation combined with an adaptive strategy to control the surrogate model if necessary

on the generalization of directfn for singular integrals over quadrilateral patches a set of fully numerical algorithms for evaluating the 4 d singular integrals arising from galerkin surface integral equation methods over conforming quadrilateral meshes is presented this paper is an extension of directfn which was recently developed for the case of triangular patches utilizing in the same fashion a series of coordinate transformations together with appropriate integration reorderings and is applicable to coincident edge adjacent or vertex adjacent elements the resulting formulas consist of sufficiently smooth kernels and exhibit several favorable characteristics when compared with the vast majority of the methods currently available more specifically they can be applied without modifications to the following challenging cases 1 weakly and strongly singular kernels 2 basis and testing functions of arbitrary order 3 planar and curvilinear patches 4 problem specific green functions e g expressed in spectral integral form and 5 spectral convergence to machine precision finally we show that the overall performance of the fully numerical schemes can be further improved by a judicious choice of the integration order for each dimension

a bridging domain method for coupling continua with molecular dynamics abstract a bridging domain method for coupling continuum models with molecular models is described in this method the continuum and molecular domains are overlapped in a bridging subdomain where the hamiltonian is taken to be a linear combination of the continuum and molecular hamiltonians we enforce the compatibility in the bridging domain by lagrange multipliers or by the augmented lagrangian method an explicit algorithm for dynamic solutions is developed results show that this multiscale method can avoid spurious wave reflections at the molecular continuum interface without any additional filtering procedures even for problems with significant nonlinearities the method is also shown to naturally handle the coupling of the continuum energy equation with the molecular subdomain a multiple time step algorithm is also developed within this framework

singularity treatment and high order rwg basis functions for integral equations of electromagnetic scattering we present numerical implementation of high order rwg basis functions for electromagnetic scattering for curved conductor surfaces with a procedure for treating the singularities of dyadic green s functions in the mixed potential formulation of electromagnetic scattering copyright 2001 john wiley sons ltd

hierarchal vector boundary elements and p adaption for 3 d electromagnetic scattering this paper describes the development of new vector boundary elements for solving electromagnetic em scattering problems the new elements are suitable for the magnetic field integral equation mfie electrical field integral equation efie or the combination field integral equation cfie the basis functions are assigned to the edges of an element rather than to its nodes the new element guarantees the continuity of the normal component of the surface current across element edges furthermore the basis functions are hierarchical from linear to higher order which enables one to use the new elements in a p adaption scheme

analysis and adaptive modeling of highly heterogeneous elastic structures in this paper we develop a theory and methodology for obtaining approximate solutions to boundary value problems describing the deformation of highly heterogeneous linearly elastic structures the method which represents a significant departure from traditional homogenization methods provides a systematic and rigorous approach towards resolving the effects of microstructure of different scales on the macroscopic response of complex heterogeneous structures an early variant of this method was first introduced in io the method referred to as hdpm homogenized dirichlet projection method proceeds by first solving an auxiliary homogenized boundary value problem describing the deformation of a structure with the same exterior geometry but with a selected set of uniform material properties the adequacy of this homogenized solution is then determined using an a posteriori error estimate that provides a measure of the error of the homogenized solution in subdomains of the structure compared to the solution of the fine scale heterogeneous problem without specific knowledge of this fine scale solution in those subdomains where the homogenized solution is deemed acceptable it is retained however in subdomains where the homogenized solution is inadequate as is determined when the estimated error exceeds a preset tolerance a local boundary value problem is constructed by projecting the homogenized displacements onto a partition designed to isolate these subdomains these local boundary value problems are then solved in those subdomains where the homogenized solution is inaccurate using the exact microstructure with the approximate local boundary conditions a posteriori error estimates are made to ascertain the quality of the resulting solution if the quality of the solution remains inadequate above a preset error tolerance a two stage adaptive procedure is implemented stage i material adaptivity corresponds to modifying the homogenized structure s material properties if after stage i the solution quality is still inadequate the subdomains of local solution are enlarged thereby modeling in greater detail the actual microstructure and the local solution process is repeated stage ii subdomain unrefinement the main feature of this method is that only in subdomains where the error in the usual homogenized solution is above a preset tolerance is the microstructure taken into account the cost of this method is shown to be orders of magnitude cheaper than direct huge scale computational simulations of micromechanical events the results of several numerical experiments are provided to demonstrate the method and verify theoretical estimates in this work we present a method for the solution of boundary value problems modeling the deformation of structures composed of highly heterogeneous linearly elastic materials we concentrate on materials formed by a homogeneous matrix embedded with particulate matter of different properties fig 1 however the results presented are not limited to materials of this type and can in theory be used for materials with virtually any microstructure a straightforward calculation reveals that an accurate numerical approximation of fine scale solutions of

a novel grid robust higher order vector basis function for the method of moments a set of novel grid robust higher order vector basis functions is proposed for the method of moments mom solution of integral equations for three dimensional 3 d electromagnetic em problems these basis functions are defined over curvilinear triangular patches and represent the unknown electric current density within each patch using the lagrange interpolation polynomials the highlight of these basis functions is that the lagrange interpolation points are chosen to be the same as the nodes of the well developed gaussian quadratures as a result the evaluation of the integrals in the mom is greatly simplified additionally the surface of an object to be analyzed can be easily meshed because the new basis functions do not require the side of a triangular patch to be entirely shared by another triangular patch which is a very stringent requirement for traditional vector basis functions the proposed basis functions are implemented with point matching for the mom solution of the electric field integral equation the magnetic field integral equation and the combined field integral equation numerical examples are presented to demonstrate the higher order convergence and the grid robustness for defective meshes using the new basis functions

coupling of polynomial approximations with application to a boundary meshless method new bridging techniques are introduced to match high degree polynomials this permits piecewise resolutions of elliptic partial differential equations pdes in the framework of a boundary meshless method introduced recently this new meshless method relies on the computation of taylor series approximations deduced from the pde the shape functions being high degree polynomials in this way the pde is solved quasi exactly inside the subdomains so that only discretization of the boundary and the interfaces are needed which leads to small size matricial problems the bridging techniques are based on the introduction of lagrange multipliers and a set of collocation points on the boundary and the interfaces several numerical applications establish that the method is robust and permits an exponential convergence with the degree

on the use of xfem within the arlequin framework for the simulation of crack propagation abstract the arlequin method is a generic numerical method that allows by local superposition and coupling of models to address multimodel and multiscale mechanical problems in particular this method has already been used to super impose cracked patches on sound structures reducing this way the global simulation resources a classical finite element approach would have required in this paper one of the key features of the extended finite element method namely the heaviside enrichment function is used within the arlequin framework to further reduce the costs of crack propagation simulations the main goal of the paper is to describe the proposed methodology and to assess its performance through numerical experiments

efficient surface integral equation using hierarchical vector bases for complex em scattering problems a set of hierarchical divergence conforming vector basis functions based on curved triangular patches is presented for method of moment mom solutions of surface integral equations in this paper the higher order method of combined field integral equation cfie solves perfect electric conductor electromagnetic scattering problems the higher order electric magnetic current combined field integral equation jmcfie formulations solves dielectric objects and their combination is able to efficiently analyzes the scattering of hybrid pec dielectric objects the expressions of the divergence conforming hierarchical basis functions up to order 3 5 are reported in this paper the multilevel fast multipole algorithm mlfma is then employed to reduce the memory requirements and computational complexity numerical experiments indicate that the proposed hierarchical vector basis functions can provide well conditioned linear system for iterative solution

radial angular singularity cancellation transformations derived by variable separation the variable separation method is utilized to construct new radial angular r n coordinate transformation schemes for the singularity cancellation technique derived from the concept of achieving an ideal jacobian of the transformations and with different parameter settings in the variable separation method a new augmented radial angular r 1 transformation new radial angular r 2 and radial angular r 2 cosh transformations as well as a new radial angular r 3 an augmented radial angular r 3 and an arcsinh r 3 transformation are introduced the proposed r 2 and r 3 transformations are efficient and applicable to all types of near singular kernels occurring in the method of moments mom solution of electromagnetic surface integral equations whereas the r 1 transformation is only suitable for the first order singular integrals the newly proposed transformation schemes are verified and they are also applied to deformed triangles where good performances are still achieved

higher order interpolatory vector bases for computational electromagnetics low order vector basis functions compatible with the nedelec 1980 representations are widely used for electromagnetic field problems higher order functions are receiving wider application but their development is hampered by the complex procedures used to generate them and lack of a consistent notation for both elements and bases in this paper fully interpolatory higher order vector basis functions of the nedelec type are defined in a unified and consistent manner for the most common element shapes it is shown that these functions can be obtained as the product of zeroth order nedelec representations and interpolatory polynomials with specially arranged arrays of interpolation points the completeness properties of the vector functions are discussed and expressions for the vector functions of arbitrary polynomial order are presented sample numerical results confirm the faster convergence of the higher order functions

numerical evaluation via singularity cancellation schemes of near singular integrals involving the gradient of helmholtz type potentials in this paper we present a purely numerical procedure to evaluate strongly near singular integrals involving the gradient of helmholtz type potentials for observation points at finite arbitrarily small distances from the source domain in the proposed approach the source domain is subdivided into a disc plus truncated subtriangles and proper variable transformations are applied in each integration domain to exactly cancel the kernel singularity a novel feature of the proposed angular transform is that required discrete values of the inverse transform which is transcendental are determined via a root finding procedure the same idea can also be applied to other transforms that arise in singularity cancellation methods the resulting integral may then evaluated via a low order gauss legendre quadrature scheme

high degree efficient symmetrical gaussian quadrature rules for the triangle gaussian quadrature is required for the computation of matrices based on the isoparametric formulztion of the finite element method a brief review of existing quadrature rules for the triangle is given and the method for the determination of high degree efficient symmetrical rules for the triangle is discussed new quadrature rules of degree 12 20 are presented and a short fortran program is included

quadrature over a pyramid or cube of integrands with a singularity at a vertex a simple transformation is introduced which facilitates the evaluation of integrals over certain square based pyramids or cubes in cases where the integrand has a singularity at a vertex

goal oriented error estimation and adaptivity for the finite element method abstract in this paper we study a new approach in a posteriori error estimation in which the numerical error of finite element approximations is estimated in terms of quantities of interest rather than the classical energy norm these so called quantities of interest are characterized by linear functionals on the space of functions to where the solution belongs we present here the theory with respect to a class of elliptic boundary value problems and in particular show how to obtain accurate estimates as well as upper and lower bounds on the error we also study the new concept of goal oriented adaptivity which embodies mesh adaptation procedures designed to control error in specific quantities numerical experiments confirm that such procedures greatly accelerate the attainment of local features of the solution to preset accuracies as compared to traditional adaptive schemes based on energy norm error estimates

singularity extraction technique for integral equation methods with higher order basis functions on plane triangles and tetrahedra a numerical solution of integral equations typically requires calculation of integrals with singular kernels the integration of singular terms can be considered either by purely numerical techniques e g duffy s method polar co ordinate transformation or by singularity extraction in the latter method the extracted singular integral is calculated in closed form and the remaining integral is calculated numerically this method has been well established for linear and constant shape functions in this paper we extend the method for polynomial shape functions of arbitrary order we present recursive formulas by which we can extract any number of terms from the singular kernel defined by the fundamental solution of the helmholtz equation or its gradient and integrate the extracted terms times a polynomial shape function in closed form over plane triangles or tetrahedra the presented formulas generalize the singularity extraction technique for surface and volume integral equation methods with high order basis functions numerical experiments show that the developed method leads to a more accurate and robust integration scheme and in many cases also a faster method than for example duffy s transformation copyright 2003 john wiley sons ltd

singularity subtraction technique for high order polynomial vector basis functions on planar triangles in this paper a singularity subtraction technique is developed for computing the impedance matrix elements of various electromagnetic surface integral equation formulations with the galerkin method and high order basis functions analytical closed form formulas for computing surface integrals with r r sup n n spl ges 3 singularities times polynomial nodal shape functions of arbitrary order on a planar triangle are presented

a high order locally corrected nystrom scheme for charge current integral equations a high order nystrom scheme is developed for electromagnetic em scattering problems of smooth objects the implementation is based on different well known charge current formulations this study aims to develop a novel quadrature scheme to compute different singular integrals that appear on integral equation methods in ems the proposed quadrature scheme is used on a locally corrected nystrom method and applied to charge current integral equations to obtain a fast accurate and a low frequency stable method to solve em scattering problems the proposed method allows obtaining accuracy in the range 4 10 digits in the near electric and magnetic scattered field for certain simple geometries and a wide range of frequencies we also do a preliminary research on nonsmooth geometries obtaining a certain degree of accuracy depending on the particular charge current integral equation used

estimation of local modeling error and goal oriented adaptive modeling of heterogeneous materials i error estimates and adaptive algorithms abstract a theory of a posteriori estimation of modeling errors in local quantities of interest in the analysis of heterogeneous elastic solids is presented these quantities may for example represent averaged stresses on the surface of inclusions or mollifications of pointwise stresses or displacements or in general local features of the fine scale solution characterized by continuous linear functionals these estimators are used to construct goal oriented adaptive procedures in which models of the microstructure are adapted to deliver local features to a preset level of accuracy algorithms for implementing these procedures are discussed and preliminary numerical results are given the analysis is restricted to linear static heterogeneous elastic materials

higher order frequency domain computational electromagnetics a review of the higher order computational electromagnetics cem for antenna wireless and microwave engineering applications is presented higher order cem techniques use current field basis functions of higher orders defined on large e g on the order of a wavelength in each dimension curvilinear geometrical elements which greatly reduces the number of unknowns for a given problem the paper reviews all major surface volume integral and differential equation electromagnetic formulations within a higher order computational framework focusing on frequency domain solutions with a systematic and unified review of generalized curved parametric quadrilateral triangular hexahedral and tetrahedral elements and various types of higher order hierarchical and interpolatory vector basis functions in both divergence and curl conforming arrangements a large number of actual higher order techniques representing various combinations of formulations elements bases and solution procedures are identified and discussed the examples demonstrate the accuracy efficiency and versatility of higher order techniques and their advantages over low order discretizations the most important one being a much faster higher order convergence of the solution it is demonstrated that both components of the higher order modeling namely higher order geometrical modeling and higher order current field modeling are essential for accurate and efficient cem analysis of general antenna scattering and microwave structures

evaluation of weakly singular integrals via generalized cartesian product rules based on the double exponential formula various weakly singular integrals over triangular and quadrangular domains arising in the mixed potential integral equation formulations are computed with the help of novel generalized cartesian product rules the proposed integration schemes utilize the so called double exponential quadrature rule originally developed for the integration of functions with singularities at the endpoints of the associated integration interval the final formulas can easily be incorporated in the context of singularity subtraction singularity cancellation and fully numerical methods often used for the evaluation of multidimensional singular integrals the performed numerical experiments clearly reveal the superior overall performance of the proposed method over the existing numerical integration methods

potential integrals for uniform and linear source distributions on polygonal and polyhedral domains formulas for the potentials due to uniform and linearly varying source distributions defined on simply shaped domains are systematically developed and presented domains considered are infinite planar strips infinite cylinders of polygonal cross sections planar surfaces with polygonal boundaries and volumetric regions with polyhedral boundaries the expressions obtained are compact in form and their application in the numerical solution of electromagnetics problems by the method of moments is illustrated

coupling of nonlocal and local continuum models by the arlequin approach summary the objective of this work is to develop and apply the arlequin framework to couple nonlocal and local continuum mechanical models a mechanically based model of nonlocal elasticity which involves both contact and long range forces is used for the fine scale description in which nonlocal interactions are considered to have non negligible effects classical continuum mechanics only involving local contact forces is introduced for the rest of the structure where these nonlocal effects can be neglected both models overlap in a coupling subdomain called the gluing area in which the total energy is separated into nonlocal and local contributions by complementary weight functions a weak compatibility is ensured between kinematics of both models using lagrange multipliers over the gluing area the discrete formulation of this specific arlequin coupling framework is derived and fully described the validity and limits of the technique are demonstrated through two dimensional numerical applications and results are compared against those of the fully nonlocal elasticity method copyright 2011 john wiley sons ltd

numerical strategy for unbiased homogenization of random materials summary this paper presents a numerical strategy that allows to lower the costs associated to the prediction of the value of homogenized tensors in elliptic problems this is performed by solving a coupled problem in which the complex microstructure is confined to a small region and surrounded by a tentative homogenized medium the characteristics of this homogenized medium are updated using a self consistent approach and are shown to converge to the actual solution the main feature of the coupling strategy is that it really couples the random microstructure with the deterministic homogenized model and not one deterministic realization of the random medium with a homogenized model the advantages of doing so are twofold a the influence of the boundary conditions is significantly mitigated and b the ergodicity of the random medium can be used in full through appropriate definition of the coupling operator both of these advantages imply that the resulting coupled problem is less expensive to solve for a given bias than the computation of homogenized tensor using classical approaches examples of 1 d and 2 d problems with continuous properties as well as a 2 d matrix inclusion problem illustrate the effectiveness and potential of the method copyright 2013 john wiley sons ltd

estimation of local modeling error and goal oriented adaptive modeling of heterogeneous materials part ii a computational environment for adaptive modeling of heterogeneous elastic solids this paper addresses a classical and largely unsolved problem given a structural component constructed of a heterogeneous elastic material that is in equilibrium under the action of applied loads determine local micromechanical features of its response e g local stresses and displacements in or around phase boundaries or in inclusions to an arbitrary preset level of accuracy it being understood that the microstructure is a priori unknown may be randomly distributed may exist at multiple spatial scales and may contain millions even billions of microscale components the approach described in this work begins with a mathematical abstraction of this problem in which the material body is modeled as an elastic solid with highly variable possibly randomly distributed elastic properties information on the actual character of the microstructure of given material bodies is determined by computerized tomography ct imaging a procedure is given for determining the effective material properties from imaging data using either deterministic or stochastic methods an algorithm is then described for determining local quantities of interest such as average stresses on inclusion boundaries to arbitrary accuracy relative to the fine scale model a new computational environment for implementing such analyses is presented which employs parallel adaptive hp finite element methods ct interfaces automatic meshing procedures and effectively adaptive modeling schemes within the basic premises on which the approach is based results of any specified accuracy can be obtained independently of the number of microscale components and constituents the results of several numerical experiments are presented

massively parallel computation for acoustical scattering problems using boundary element methods abstract this paper is concerned with the parallel implementation of the boundary element method and its application to the exterior acoustical scattering problem the numerical implementation is based on a galerkin type formulation of a burton miller equation proposed in references 1 2 this scheme can avoid sensitive properties of hypersingular integration simplify the numerical implementation and improve the quality of the numerical solutions especially in the range of high frequencies ana posteriorierror estimate proposed in reference 1 is implemented in essence a complete parallel implementation of the boundary element method including the parallel formation of the linear system a parallel dense solver and a parallel algorithm for postprocessing error estimation are presented in this paper

on the numerical integration of the linear shape functions times the 3 d green s function or its gradient on a plane triangle formulas for the static and dynamic potentials due to linearly varying source distributions defined on a planar triangle are presented the general linear variation of the source is represented in terms of three linear basis functions each one associated with a different vertex of the triangular domain the singular kernels considered are given by the 3 d green s function and its gradient both for the static and dynamic case in the static case the evaluation of potentials is performed analytically and compact form results are given in the dynamic case the results are given in a form suited for numerical integration

a projection height independent adaptive radial angular r 2 transformation for singular integrals a new radial angular r 2 adaptive singularity cancellation transformation is proposed this new transformation is flexible and applicable to singular integrals over triangular domains when the height tends to zero and the observation point is in the plane of the source domain the transformation remains stable and approaches the corresponding transformation within the source plane usually the green s function and its gradient appear in the integral kernels leading to first order and second order singularities the newly derived transformation formula provides an efficient solution for second order singular coupling integral kernels and the formula is in particular more efficient than alternative schemes for singular vector integral kernels however it is also effective for the lower order singular integral kernels in electromagnetic boundary integral equation formulations the proposed transformation is efficient for all types of singular integrals

higher order hierarchical legendre basis functions for electromagnetic modeling this paper presents a new hierarchical basis of arbitrary order for integral equations solved with the method of moments mom the basis is derived from orthogonal legendre polynomials which are modified to impose continuity of vector quantities between neighboring elements while maintaining most of their desirable features expressions are presented for wire surface and volume elements but emphasis is given to the surface elements in this case the new hierarchical basis leads to a near orthogonal expansion of the unknown surface current and implicitly an orthogonal expansion of the surface charge in addition all higher order terms in the expansion have two vanishing moments in contrast to existing formulations these properties allow the use of very high order basis functions without introducing ill conditioning of the resulting mom matrix numerical results confirm that the condition number of the mom matrix obtained with this new basis is much lower than existing higher order interpolatory and hierarchical basis functions as a consequence of the excellent condition numbers we demonstrate that even very high order mom systems e g tenth order can be solved efficiently with an iterative solver in relatively few iterations

the arlequin method as a flexible engineering design tool by superposing and gluing models the arlequin method offers an extended modelling framework for the design of engineering structures this paper aims at developing the numerical aspects of the approach and at showing how it can be used with great flexibility and in a consistent manner to change locally a global mechanical model the capabilities of the arlequin method and the effectiveness of the implemented numerical tools are exemplified by 1 d 2 d and 3 d numerical applications

ghost forces and spurious effects in atomic to continuum coupling methods by the arlequin approach the main objective of this work is to identify spurious effects and propose a corrective method when coupling a particle model involving long range interaction potentials with a first gradient homogenized model using the arlequin framework the most significant spurious effects are generally created by the so called ghost forces that arise in coupling methods based on the minimization of a global energy functional they depend as well on the coupling formulation itself on the notion of representative volume element and on the discretization of the continuum model the proposed corrective technique is based on post processing of the approximate solution by introducing dead forces that can be systematically evaluated and consistently inserted within the arlequin formulation efficiency of the corrective procedure is demonstrated on 1d and 2d examples copyright 2010 john wiley sons ltd