Search

We present a boundary element based method for fast simulation of brittle fracture. By introducing simplifying assumptions that allow us to quickly estimate stress intensities and opening displacements during crack propagation, we build a fracture algorithm where the cost of each time step scales linearly with the length of the crack-front. The transition from a full boundary element method to our faster variant is possible at the beginning of any time step. This allows us to build a hybrid method, which uses the expensive but more accurate BEM while the number of degrees of freedom is low, and uses the fast method once that number exceeds a given threshold as the crack geometry becomes more complicated. Furthermore, we integrate this fracture simulation with a standard rigid-body solver. Our rigid-body coupling solves a Neumann boundary value problem by carefully separating translational, rotational and deformational components of the collision forces and then applying a Tikhonov regularizer to the resulting linear system. We show that our method produces physically reasonable results in standard test cases and is capable of dealing with complex scenes faster than previous finite- or boundary element approaches. [ABSTRACT FROM AUTHOR]

This work addresses the elastodynamic problem for a finite-sized, elastic solid matrix containing multiple nano-heterogeneities of arbitrary shape, number and geometric configuration. The problem is formulated under plane strain conditions, and time-harmonic motions are assumed to hold. The aim is to evaluate the non-uniform stress and strain fields that develop in the solid matrix and to identify zones of dynamic stress concentration for the case of dynamic loads applied along the matrix boundary. The mechanical model used here is based on a combination of classical elastodynamic theory for the bulk solid under non-classical boundary conditions, supplemented with a localized constitutive equation for the solid-inclusion interface in the framework of the Gurtin–Murdoch theory of surface elasticity. As computational tools we use (a) the 2D boundary element method (BEM) with frequency-dependent fundamental solutions for the bulk solid and (b) the finite element method (FEM) software package ANSYS augmented by a macro-finite element for representing surface effects on the contour of the nano-inclusions. At first, accuracy of the numerical solutions obtained for the dynamic stress concentration factor (DSCF) and for the diffracted displacement wave field is satisfactorily established. Next, comparison studies are conducted to gauge the BEM and FEM separately. These are followed by extensive numerical simulations that show that both BEM and FEM are able to capture the dependence of the diffracted wave field and of the DSCF on the type of the inclusions, their overall configuration and the nature of applied dynamic loads. It is concluded that the interaction effect between the nano-heterogeneities and the external perimeter of the bounded solid matrix is of paramount importance. [ABSTRACT FROM AUTHOR]

We propose and analyze a numerical method to solve an elliptic transmission problem in full space. The method consists of a variational formulation involving standard boundary integral operators on the coupling interface and an ultra-weak formulation in the interior. To guarantee the discrete inf–sup condition, the system is discretized by the DPG method with optimal test functions. We prove that the principal unknowns are approximated quasi-optimally. Numerical experiments for problems with smooth and singular solutions confirm optimal convergence orders. [ABSTRACT FROM AUTHOR]

We present a closed-form frequency-wave number ( ω - k) Green's function for a layered, elastic half-space under SH wave propagation. It is shown that for every ( ω - k) pair, the fundamental solution exhibits two distinctive features: (1) the original layered system can be reduced to a system composed by the uppermost superficial layer over an equivalent half-space; (2) the fundamental solution can be partitioned into three different fundamental solutions, each one carrying out a different physical interpretation, i.e., an equivalent half-space, source image impact, and dispersive wave effect, respectively. Such an interpretation allows the proper use of analytical and numerical integration schemes, and ensures the correct assessment of Cauchy principal value integrals. Our method is based upon a stiffness-matrix scheme, and as a first approach we assume that observation points and the impulsive SH line-source are spatially located within the uppermost superficial layer. We use a discrete wave number boundary element strategy to test the benefits of our fundamental solution. We benchmark our results against reported solutions for an infinitely long circular canyon subjected to oblique incident SH waves within a homogeneous half-space. Our results show an almost exact agreement with previous studies. We further shed light on the impact of horizontal strata by examining the dynamic response of the circular canyon to oblique incident SH waves under different layered half-space configurations and incident angles. Our results show that modifications in the layering structure manifest by larger peak ground responses, and stronger spatial variability due to interactions of the canyon geometry with trapped Love waves in combination with impedance contrast effects. [ABSTRACT FROM AUTHOR]

There is currently significant interest in freeform, curve-based authoring of graphic images. In particular, "diffusion curves" facilitate graphic image creation by allowing an image designer to specify naturalistic images by drawing curves and setting colour values along either side of those curves. Recently, extensions to diffusion curves based on the biharmonic equation have been proposed which provide smooth interpolation through specified colour values and allow image designers to specify colour gradient constraints at curves. We present a Boundary Element Method (BEM) for rendering diffusion curve images with smooth interpolation and gradient constraints, which generates a solved boundary element image representation. The diffusion curve image can be evaluated from the solved representation using a novel and efficient line-by-line approach. We also describe "curve-aware" upsampling, in which a full resolution diffusion curve image can be upsampled from a lower resolution image using formula evaluated orrections near curves. The BEM solved image representation is compact. It therefore offers advantages in scenarios where solved image representations are transmitted to devices for rendering and where PDE solving at the device is undesirable due to time or processing constraints. [ABSTRACT FROM AUTHOR]

In this paper we present a sufficient and necessary condition to ensure the ellipticity of the bilinear form which is related to the one-equation coupling of finite and boundary element methods to solve a scalar free space transmission problem for a second order uniform elliptic partial differential equation in the case of general Lipschitz interfaces. This condition relates the minimal eigenvalue of the coefficient matrix in the bounded interior domain to the contraction constant of the shifted double layer integral operator which reflects the shape of the interface. This paper extends and improves earlier results [12] on sufficient conditions, but now includes also necessary conditions. Numerical examples confirm the theoretical results on the sharpeness of the presented estimates. [ABSTRACT FROM AUTHOR]

Abstract: The cost of rehabilitation works increases exponentially with time. Therefore, the development of on-site non-destructive tests (NDTs) for early detection of damage in concrete structures is an extremely important goal. However, in spite of the recent new technological developments, current assessment techniques are still based on visual inspections and are therefore only suitable for mapping major damages. An ultrasound-based procedure aiming to detect cracking at an early stage using propagation of ultrasonic waves is herein analysed. Two advanced numerical models were applied to simulate, first, the process of crack propagation and, next, the propagation of ultrasonic waves in a progressively damaged structure. Results are promising and enforce the feasibility of developing ultrasonic equipment for on-site application. Thus, future developments include an experimental validation of the present study. [Copyright &y& Elsevier]

Abstract: The present developments result from the combination of the variationally-based, hybrid boundary element method and a consistent formulation of the conventional, collocation boundary element method. The procedure is simple to implement and turns out to be computationally faster than the mentioned, preceding numerical methods – and almost as accurate – for the analysis of large-scale, two-dimensional and three-dimensional problems of potential and elasticity of general shape and topology, also applicable to time-dependent problems. Both the double-layer and the single-layer potential matrices of the collocation boundary element method, H and G, respectively, whose standard evaluation requires dealing with singular and improper integrals, are obtained in an expedite way that circumvents almost any numerical integration – except for a few regular integrals. Since the resultant matrices do not differ in nature from the ones of the conventional, collocation boundary element method, the developments are suited for a matrix solution in terms of a GMRES algorithm, for example, and in the framework of the fast multi-pole method, so that very large problems can be ultimately dealt with efficiently. A few numerical examples are shown to assess the applicability of the method, its computational effort and some convergence issues. [Copyright &y& Elsevier]

Abstract: Nanofluids are a novel strategy to improve heat transfer characteristics of fluids by the addition of solid particles with diameters below 100nm. Experimental measurements have shown that this approach can greatly increase heat conductivity, even above that predicted by Maxwell’s theory. However, it is still not clear what mechanism accounts for this increase, mainly in thermal conductivity, thus great effort is being put into investigating the different phenomena occurring inside the fluid. This paper shows a direct numerical simulation of the flow and thermal behaviour of a nanofluid loaded with alumina nanoparticles which considers the effects of particle–particle and particle–fluid interactions. The boundary element method is used given its capabilities to deal with moving boundary problems. This formulation was employed to simulate the behaviour and time evolution of a 30nm alumina/water nanofluid at six different particle concentrations, looking to observe flow fields, temperature distributions and total heat flow through the domain. Results showed strong convective currents caused by the presence of the nanoparticles, which in time increased total heat flow in the cavity. As expected, particle concentration increased the total heat flow affecting not only the conductive part of heat transfer, but the convective part as well. [Copyright &y& Elsevier]

Consider uniform flow past an oscillating body generating a time-periodic motion in an exterior domain, modelled by a numerical fluid dynamics solver in the near field around the body. A far-field formulation, based on the Oseen equations, is presented for coupling onto this domain thereby enabling the whole space to be modelled. In particular, examples for formulations by boundary elements and infinite elements are described. [ABSTRACT FROM AUTHOR]

Abstract: The present developments result from the combination of the variationally-based, hybrid boundary element method and a consistent formulation of the conventional, collocation boundary element method. The procedure is simple to implement and turns out to be computationally faster than the mentioned, preceding numerical methods – and almost as accurate – for the analysis of large-scale, two-dimensional and three-dimensional problems of potential and elasticity of general shape and topology, also applicable to time-dependent problems. Both the double-layer and the single-layer potential matrices of the collocation boundary element method, H and G, respectively, whose standard evaluation requires dealing with singular and improper integrals, are obtained in an expedite way that circumvents almost any numerical integration – except for a few regular integrals. Since the resultant matrices do not differ in nature from the ones of the conventional, collocation boundary element method, the developments are suited for a matrix solution in terms of a GMRES algorithm, for example, and in the framework of the fast multi-pole method, so that very large problems can be ultimately dealt with efficiently. A few numerical examples are shown to assess the applicability of the method, its computational effort and some convergence issues. [Copyright &y& Elsevier]

Abstract: We investigate the use of the Multipole-accelerated Boundary Element Method (BEM) and of the Singularity Method for studying the interaction of many bubbles rising in a volcanic conduit. Observation shows that the expression of volcanic eruption is extremely variable, from slow release of magma to catastrophic explosive manifestation. We investigate the application of the Fast Multipole Method to the solution of (i) the Boundary Element Formulation of the Stokes flow and of (ii) the particle formulation using the Stokeslets, the Green Function of the Stokes flow law, as a particle kernel. We show how these implementations allow for the first time to numerically model in a dynamic setting a very large number of bubbles, i.e few thousands with the BEM models, allowing investigating the feedback between the single bubble deformation and their collective evolution, and few hundred of thousands of bubbles with the particle approach. We illustrate how this method can be used to investigate the intense interaction of a large number of bubbles and suggest a framework for studying the feedback between many bubbles and a complex thermal nonlinear magmatic [Copyright &y& Elsevier]

New hierarchical vector basis functions for quadrilateral cells are introduced, and the matrix condition numbers associated with their use are compared to those of existing vector basis families to assess the relative linear independence of the functions. Scale factors are employed to improve the condition numbers. In addition, the proper use of subsets of these families to transition from one order to another (as needed for adaptive p-refinement) without exciting spurious modes is considered. [ABSTRACT FROM PUBLISHER]

Abstract: This study describes a sub-domain boundary element procedure for predicting the fatigue life of elastic media under cyclic transient thermal loads. The procedure assumes an initial crack in a two-dimensional medium, and evaluates the crack extension along a path defined by the maximum circumferential stress criterion. Partial closure may occur on the growing crack faces due to thermal loading. Appropriate thermal and mechanical boundary conditions are imposed on the numerical model to account for the contact state. The analysis requires solutions to the equations of quasi-static thermo-elasticity, and uses an iterative procedure to detect the contact region. We investigate cases of pure opening or mixed mode fracture, demonstrating the effects of crack closure on the predicted fatigue life. We compare the obtained results with those of other publications. [Copyright &y& Elsevier]

Abstract: A way of coupling digital image correlation (to measure displacement fields) and boundary element method (to compute displacements and tractions along a crack surface) is presented herein. It allows for the identification of Young’s modulus and fracture parameters associated with a cohesive model. This procedure is illustrated to analyze the latter for an ordinary concrete in a three-point bend test on a notched beam. In view of measurement uncertainties, the results are deemed trustworthy thanks to the fact that numerous measurement points are accessible and used as entries to the identification procedure. [Copyright &y& Elsevier]

The stress concentrations produced by tensile loading of elastic solids with periodic notches are addressed. The criterion suggested by Neuber, which likens the periodic notch to a single notch of similar shape but smaller depth, is evaluated. According to Neuber, the depth reduction factor only depends on the ratio between the depth and pitch of the periodic notch, regardless of its particular shape. This work benchmarks the criterion against many axially loaded flat plates and round bars with periodic V-notches, which are analysed by means of the boundary element method. The investigation highlights a strong disparity between Neuber's predictions and numerical findings. However, upon slight adjustment of the depth reduction factor with respect to Neuber's proposal, a satisfactory agreement is achieved. The good correlation holds true both for shallow notches (notched semi-infinite plate) and for deep notches (notched plates or bars of finite width), which were not covered in Neuber's work. Excellent correspondence is also found for the stress concentration around an infinite row of equispaced circular holes loaded longitudinally, a solution taken from the literature as a test case. These results lead to the conclusion that Neuber's criterion, supplemented with the newly disclosed depth reduction factor, can be applied to periodic notches of whatever geometry under normal stresses. [ABSTRACT FROM AUTHOR]

Abstract: A substantial computational advantage can often be obtained by replacing the solver for the governing linear system of equations, inside a linear elastic Finite Element program, with a Boundary Element code implemented so as to calculate displacements (and, if required, stresses) in the same internal points (nodes and Gauss points) where the original Finite Element code would provide an output. The analysis of several test problems shows that, even in the unfavorable case of 2D geometries, this modification of the Finite Element method becomes rapidly convenient as the density of the starting Finite Element mesh increases. [Copyright &y& Elsevier]

In this work, a boundary element formulation to analyse plates reinforced by rectangular beams, with columns defined in the domain is proposed. The model is based on Kirchhoff hypothesis and the beams are not required to be displayed over the plate surface, therefore eccentricity effects are taken into account. The presented boundary element method formulation is derived by applying the reciprocity theorem to zoned plates, where beams are treated as thin sub-regions with larger rigidities. The integral representations derived for this complex structural element consider the bending and stretching effects of both structural elements working together. The standard equilibrium and compatibility conditions along interface are naturally imposed, being the bending tractions eliminated along interfaces. The in-plane tractions and the bending and in-plane displacements are approximated along the beam width, reducing the number of degrees of freedom. The columns are introduced into the formulation by considering domain points where tractions can be prescribed. Some examples are then shown to illustrate the accuracy of the formulation, comparing the obtained results with other numerical solutions. [ABSTRACT FROM AUTHOR]

The present paper presents a self-equilibrated boundary element formulation for elastostatic analysis of Reissner’s plate bending problems. In this formulation, rigid body movements are introduced to the generalized displacement fundamental solution, resulting in modified boundary element matrices with inherent equilibrium satisfaction. The procedure is quite general and easy to implement into existing boundary element codes. In the end of the paper, numerical examples are presented, illustrating the benefits of the proposed formulation. [ABSTRACT FROM AUTHOR]

Graphite at the nanoscale is modeled as a material system consisting of a stack of parallel plates buffered by an elastic material. While the plates represent individual graphene sheets, the buffer material models the Van der Waals interaction between the graphene sheets. As such, the loading on graphite at the nanoscale is characterized by the membrane force, the bending moment, and the shear force in the graphene sheets. Cylindrical nanoindentation of graphite is analyzed by applying a special boundary element method that employs Green's function for multilayers with platelike interfaces. Because Green's function satisfies the traction-free surface, the interfacial displacement continuity and the interfacial traction discontinuity conditions, only the indentation surface area where the boundary condition is altered, are numerically discretized. Numerical results of cylindrical nanoindentation are presented. It is shown that the bending moment and the shear force in the graphene sheets are concentrated around the edge of contact, consistent with the singularities existing in the second and the third derivatives of the surface displacement in the reduced case of a semi-infinite homogeneous solid under cylindrical contact. Kinks of single, double, and triple joints are related to the bending moment, the shear force, and the concentrated force, respectively. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a domain boundary element formulation for inelastic saturated porous media with rate-independent behavior for the solid skeleton. The formulation is then applied to elastic–plastic behavior for the solid. Biot’s consolidation theory, extended to include irreversible phenomena is considered and the direct boundary element technique is used for the numerical solution after time discretization by the implicit Euler backward algorithm. The associated nonlinear algebraic problem is solved by the Newton–Raphson procedure whereby the loading/unloading conditions are fully taken into account and the consistent tangent operator defined. Only domain nodes (nodes defined inside the domain) are used to represent all domain values and the corresponding integrals are computed by using an accurate sub-elementation scheme. The developments are illustrated through the Drucker-Prager elastic–plastic model for the solid skeleton and various examples are analyzed with the proposed algorithms. [Copyright &y& Elsevier]

In this paper, we apply the coupling of local discontinuous Galerkin and boundary element methods to solve a class of non-linear exterior transmission problems in the plane. As a model, we consider a non-linear elliptic equation in an annular polygonal domain coupled with the Poisson equation in the surrounding unbounded exterior region. In addition, we assume discontinuous transmission conditions on the interface boundary. Our approach constitutes an extension to non-linear problems of the a priori error analysis developed recently for linear exterior transmission problems. Most of the techniques employed here are similar to the linear case but some differences appear. In particular, because of the non-homogeneous transmission conditions, the so-called numerical fluxes need to be suitably defined. We prove stability of the resulting discrete scheme with respect to a mesh-dependent norm and derive a Strang-type estimate for the associated error. Then, we apply local and global approximation properties of the discrete spaces to obtain the a priori error estimates in the energy norm. [ABSTRACT FROM PUBLISHER]

Abstract: Singularity-reduced integral relations are developed for displacement discontinuities in three-dimensional, anisotropic linearly elastic media. An isolated displacement discontinuity is considered first, and a systematic procedure is followed to develop relations for the displacement and stress fields induced by the discontinuity. The singularity-reduced relation for the stress is particularly important since it is in a form which allows a weakly-singular, weak-form traction integral equation to be readily established. The integral relations obtained for a general displacement discontinuity are then specialized to an isolated crack and to dislocations; the relations for dislocations are introduced to emphasize their direct connection to corresponding results for cracks and to allow earlier independent findings for these two types of discontinuities to be put into proper context. Next, the singularity-reduced integral equations obtained for an isolated crack are extended to allow treatment of cracks in a finite domain, and a pair of weakly-singular, weak-form displacement and traction integral equations is established. These integral equations can be combined to obtain a final formulation which is in a symmetric form, and in this way they serve as the basis for a weakly-singular, symmetric Galerkin boundary element method suitable for analysis of cracks in anisotropic media. [Copyright &y& Elsevier]

The Boundary Element Tearing and Interconnecting (BETI) methods were recently introduced as boundary element counterparts of the well established Finite Element Tearing and Interconnecting (FETI) methods. Here we combine the BETI method preconditioned by the projector to the “natural coarse grid” with recently proposed optimal algorithms for the solution of bound and equality constrained quadratic programming problems in order to develop a theoretically supported scalable solver for elliptic multidomain boundary variational inequalities such as those describing the equilibrium of a system of bodies in mutual contact. The key observation is that the “natural coarse grid” defines a subspace that contains the solution, so that the preconditioning affects also the non-linear steps. The results are validated by numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper we consider the numerical solution of discrete boundary integral equations on polyhedral surfaces in three dimensions. When the solution contains typical edge singularities, highly stretched meshes are preferred to uniform meshes, since they reduce the number of degrees of freedom needed to obtain a fixed accuracy. The classical panel-clustering method can still be applied in the presence of such highly stretched meshes. However, we will show that the savings in computation time and storage become suboptimal because the nearfield matrix arising in the panel-clustering algorithm is no longer as sparse as it is in the case of uniform meshes. Hence, a natural question arises as to whether a new enhanced panel-clustering algorithm can be designed which performs efficiently even in the presence of highly stretched meshes. The main result of this paper is to formulate such an enhanced version of the panel-clustering algorithm. The key features of the algorithm are (i) the employment of partial analytic integration in the direction of stretching, yielding a new kernel function on a one-dimensional manifold where the influence of high aspect ratios in the stretched elements is removed, and (ii) the introduction of a generalized admissibility condition with respect to the partially integrated kernel, which ensures that certain stretched clusters which are inadmissible in the classical sense now become admissible. In the context of a model problem, we prove that our algorithm yields an accurate (up to the discretization error) matrix-vector multiplication which requires ...(NlogκN) operations, where N is the number of degrees of freedom and k is small and independent of the aspect ratio. The generalized admissibility condition can be viewed as an addition to the classical method which may be useful in general when stretched meshes are present. We also have performed a numerical experiment which shows that the sparsity of the nearfield matrix for the enhanced panel-clustering method is not negatively affected by stretched elements, and the method will perform optimally. [ABSTRACT FROM AUTHOR]

A boundary element method (BEM) formulation to predict the behavior of solids exhibiting displacement (strong) discontinuity is presented. In this formulation, the effects of the displacement jump of a discontinuity interface embedded in an internal cell are reproduced by an equivalent strain field over the cell. To compute the stresses, this equivalent strain field is assumed as the inelastic part of the total strain. As a consequence, the non-linear BEM integral equations that result from the proposed approach are similar to those of the implicit BEM based on initial strains. Since discontinuity interfaces can be introduced inside the cell independently on the cell boundaries, the proposed BEM formulation, combined with a tracking scheme to trace the discontinuity path during the analysis, allows for arbitrary discontinuity propagation using a fixed mesh. A simple technique to track the crack path is outlined. This technique is based on the construction of a polygonal line formed by segments inside the cells, in which the assumed failure criterion is reached. Two experimental concrete fracture tests were analyzed to assess the performance of the proposed formulation. [ABSTRACT FROM AUTHOR]

The numerical solution of the free boundary Bernoulli problem is addressed. An iterative method based on a level-set formulation and boundary element method is proposed. Issues related to the implementation, the accuracy, and the generality of the method are discussed. The efficiency of the approach is illustrated by numerical results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we propose and analyse a novel numerical method for a Helmholtz transmission problem in a bounded domain, with non-homogeneous mixed conditions on the exterior boundary. The method relies on the superposition of a classical Lagrange finite element method on a triangulation of the domain without the interior obstacles and a general stable boundary element method for an exterior Helmholtz transmission problem. The analysis of the scheme is carried out by transforming the exact and the approximated equations into an abstract operator equation of the second kind with a non-standard approximation of it. A numerical example for a two dimensional case shows the good behaviour of the method and its advantages for some particular geometries. [Copyright &y& Elsevier]

An overview of the main theoretical aspects of finite-element and boundary-element modelling of the response to moving loads is given. The moving loads represent sources of noise and vibration generated by moving vehicles, and the analysis describes the propagation of the disturbances generated in soil. A finite-element time-domain analysis in convected coordinates with a simple upwind scheme is presented, including a special set of boundary conditions permitting the passage of outgoing waves in the convected coordinate system. The modification of frequency-dependent damping to convected coordinates is described, and the convected formulation of boundary elements is presented and used for illustrating the effect of ‘high-speed’ motion. Finally, a procedure for the coupling of a local finite-element model with a boundary-element model of an exterior, or open, domain is described. The paper uses recent results from the Danish research programme ‘Damping Mechanisms in Dynamics of Structures and Materials’ as a basis for a general discussion and review of the recent literature on the subject. [Copyright &y& Elsevier]

Abstract: In this work, a particular sub-region technique that does not require traction approximations along interfaces is used to model rigid and soft inclusions. The stability and the accuracy of the formulation have been studied for several applications, including the degenerated cases where one dimension is strongly reduced to represent an embedded bar. The rigid inclusions have been modelled by increasing their elastic modulus. On the other hand thin inclusions with elastic modulus reduced to nearly zero can accurately model crack problems. In all analysed cases, the obtained results have shown that this simple strategy is reliable and can be applied to complex stress analysis problems. [Copyright &y& Elsevier]

Abstract: Variational methods for boundary integral equations deal with the weak formulations of boundary integral equations. Their numerical discretizations are known as the boundary element methods. This paper gives an overview of the method from both theoretical and numerical point of view. It summarizes the main results obtained by the author and his collaborators over the last 30 years. Fundamental theory and various applications will be illustrated through simple examples. Some numerical experiments in elasticity as well as in fluid mechanics will be included to demonstrate the efficiency of the methods. [Copyright &y& Elsevier]

Abstract: We considered a nonlinear parabolic equation in a bounded domain of coupled with the Laplace equation in the corresponding exterior region. This kind of problems appears in the modelling of quasi-stationary electromagnetic fields. We chose a regular artificial boundary containing the nonlinear region in its interior. Then, we applied a symmetric FEM-BEM coupling procedure including a parameterization of the artificial boundary. We used the backward Euler method for the time discretization and an exact triangulation of the finite element domain. Assuming that the nonlinear operator is strongly monotone and Lipschitz-continuous, we proved convergence and obtained optimal error estimates for the solution of the discrete problem. Finally, we proposed a fully discrete scheme with quadrature formulas of low order and, under some additional conditions on the nonlinearity, proved that the order of convergence remains optimal. [Copyright &y& Elsevier]

Operator preconditioning offers a general recipe for constructing preconditioners for discrete linear operators that have arisen from a Galerkin approach. The key idea is to employ matching Galerkin discretizations of operators of complementary mapping properties. If these can be found, the resulting preconditioners will be robust with respect to the choice of the bases for trial and test spaces. I survey the application of operator preconditioning to finite elements and boundary elements. [Copyright &y& Elsevier]

A symmetric Galerkin boundary-element method is used for the solution of boundary-value problems with mixed boundary conditions of Dirichlet and Neumann type. As a model problem we consider the Laplace equation. When an iterative scheme is employed for solving the resulting linear system, the discrete boundary integral operators are realized by the fast multipole method. While the single-layer potential can be implemented straightforwardly as in the original algorithm for particle simulation, the double-layer potential and its adjoint operator are approximated by the application of normal derivatives to the multipole series for the kernel of the single-layer potential. The Galerkin discretization of the hypersingular integral operator is reduced to the single-layer potential via integration by parts. We finally present a corresponding stability and error analysis for these approximations by the fast multipole method of the boundary integral operators. It is shown that the use of the fast multipole method does not harm the optimal asymptotic convergence. The resulting linear system is solved by a GMRES scheme which is preconditioned by the use of hierarchical strategies as already employed in the fast multipole method. Our numerical examples are in agreement with the theoretical results. [ABSTRACT FROM PUBLISHER]

Abstract: It has recently been demonstrated that, for pressure die casting, high rates of heat extraction are possible with the use copper–alloyed dies suitably protected with a thermally sprayed steel layer. The structural integrity of dies of this type is paramount as the thermally sprayed layer has the potential to de-bond necessitating repair or retirement of the dies. In this paper, an efficient three-dimensional elastostatic stress model for the pressure die casting process is described. The collocation based boundary element method is used for the prediction of transient stress fields over a thermally stabilised casting cycle. A peculiar feature of the pressure die casting process is that transient thermal penetration into the die is limited to regions close to the surface of the die cavity and nozzle. The presence of a transient thermal field necessitates the evaluation of domain integrals in the boundary element stress formulation. Two methods for evaluating these integrals are presented in the paper: (i) a simplex method on a mesh local to the cavity surface; (ii) a modified reciprocity method utilising Gaussian radial-basis functions, interpolating on a perturbed thermal field. The simplex method is shown to be superior, providing high accuracy, stability and computational efficiency. The dies present a multi-domain environment for stress predictions making it necessary to utilise a suitably constructed coarse preconditioner to enhance numerical stability and provide for efficient computation. A multiplicative Schwarz method is presented that enables parameter matrix accelerated GMRES to be applied on each domain. Numerical experiments are performed to demonstrate the computational effectiveness of the approach. Predicted strain fields are compared with strain gauge measurements obtained on a purpose built rig designed to be representative of the casting process. [Copyright &y& Elsevier]

The adaptive cross approximation method can be used to efficiently approximate stiffness matrices arising from boundary element applications by hierarchical matrices. In this article an approximativeLUdecomposition in the same format is presented which can be used for preconditioning the resulting coefficient matrices efficiently. If theLUdecomposition is computed with high precision, it may even be used as a direct yet efficient solver. [ABSTRACT FROM AUTHOR]

The efficient treatment of dense matrices arising, e.g., from the finite element discretisation of integral operators requires special compression techniques. In this article, we use a hierarchical low-rank approximation, the so-called-matrix, that approximates the dense stiffness matrix in admissible blocks (corresponding to subdomains where the underlying kernel function is smooth) by low rank matrices. The low rank matrices are assembled by the ACA+ algorithm, an improved variant of the well-known ACA method. We present an algorithm that can determine a coarser block structure that minimises the storage requirements (enhanced compression) and speeds up the arithmetic (e.g., inversion) in the-matrix format. This coarse approximation is done adaptively and on-the-fly to a given accuracy such that the matrix is assembled with minimal storage requirements while keeping the desired approximation quality. The benefits of this new recompression technique are demonstrated by numerical examples. [ABSTRACT FROM AUTHOR]

We aim to provide a framework for the analysis of convergence for the Galerkin approximation for a class of noncoercive problems. We provide a sufficient condition on the finite element space for the convergence and optimality of the Galerkin scheme. This theory is then applied to the study of the well-posedness and approximability of two problems in electromagnetism. [ABSTRACT FROM AUTHOR]

In this work, a boundary element formulation to analyse slabs reinforced by beams, combined or not to define a grid sub-system, is proposed. Kirchhoff ‘s hypothesis is assumed for the plate elements. The beams elements are not required to be displayed over the plate surface, therefore eccentricity effects are taken into account. The formulation is derived by assuming a zoned body where beam elements are introduced by degenerating plate sub-regions. After finding properly a single reciprocity for the whole body, the required integral representations are derived. The integral representations derived for this complex structural element take into account the bending and stretching effects of booth structural elements working together. The standard equilibrium and compatibility conditions along interface are naturally imposed. Moreover, the amount of degrees of freedom required along the interfaces is substantially reduced, leading therefore to small and more accurate algebraic system of linear equations. Several examples are then shown to illustrate the accuracy of the formulation, comparing the obtained results with analytical and other numerical solutions. [ABSTRACT FROM AUTHOR]

Abstract: A three-dimensional boundary element method (BEM) implementation of the interaction integral methodology for the numerical analysis of mixed-mode three-dimensional cracks is presented in this paper. The interaction integral is evaluated from a domain representation naturally compatible with the BEM, since stresses, strains and derivatives of displacements at internal points can be evaluated using their appropriate boundary integral equations. Special emphasis is put in the selection of the auxiliary function that represents the virtual crack advance in the domain integral. This is found to be a key feature to obtain reliable results at the intersection of crack fronts with free surfaces. Several examples are analysed to demonstrate the efficiency and accuracy of the implementation. [Copyright &y& Elsevier]

Numerical methods for computing the three-dimensional pressure field in a flat fluid channel bounded either by a rigid boundary, an elastic semi-infinite medium or by a layer of sediment, subjected to incoherent line sources are presented. After verification Greens functions are incorporated in a Boundary Element Method (BEM) code that simulates the pressure variation inside the fluid channel in the vicinity of a rigid or elastic inclusion, avoiding the discretization of the fluid and solid channel interfaces. After the verification of the solution, the models developed are then used to simulate the pressure variation within the fluid channel in the presence of infinitely long rigid and elastic inclusions of differing sizes, when the channel is struck by a spatially-sinusoidal harmonic pressure line load. The results are then compared with those obtained when the channel floor is assumed to be rigid. Time domain results are given by means of inverse Fourier transforms, to help understand how the mechanical properties of the channel floor may affect the variation of the pressure field within the channel. [ABSTRACT FROM AUTHOR]

A numerical method combining the approaches of C.I. Goldstein and L.-A. Ying is used for the simulation in three-dimensional magnetostatics related to an exterior problem in magnetic induction. Recently introduced, this method is based on the use of a graded mesh obtained by gluing homothetic layers in the exterior domain and has been performed in the case of edge element discretizations. In this work, the theoretical and practical aspects of the method are inspected in the case of face element and volume element discretizations, for computing a magnetic induction. Error estimates, implementations, and numerical results are provided. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with the symmetric linear systems of equations arising in the Galerkin boundary element method. In particular, we consider the application of several variants of the conjugate-gradient method to these systems and present some numerical results which shows that a simple preconditioning strategy can lead to significant improvements in solution times. [Copyright &y& Elsevier]

This paper presents the parallel implementation of a boundary element code for the solution of 2D elastostatic problems using linear elements. The original code is described in detail in a reference text in the area [Boundary elements techniques: theory and applications in engineering, 1984]. The Fortran code is reviewed and rewritten to run on shared and distributed memory systems using standard and portable libraries: OpenMP, LAPACK and ScaLAPACK. The implementation process provides guidelines to develop parallel applications of the Boundary Element Method, applicable to many science and engineering problems. Numerical experiments on a SGI Origin 2000 shows the effectiveness of the proposed approach. [Copyright &y& Elsevier]

A new boundary integral formulation for the aerodynamic analysis of an aircraft (in particular, a tiltrotor) in arbitrary motion is presented. The formulation is based on the velocity potential for compressible flows, and as such is an extension of past work of the authors. The distinguishing feature is that the boundary integral representation is written for a surface in arbitrary motion with respect to a frame of reference which in turn moves in arbitrary motion with respect to the undisturbed air. Thus, the integrals are evaluated on the emission surface, which is the locus of the emitting points at the locations (in the moving frame) that they had when the signal influencing a given point at a given time was emitted. The differences with respect to related formulations (e.g., Ffowcs Williams and Hawkings) are outlined. Also, the advantages of the present formulation with respect to the preceding ones by the authors are discussed. Numerical validation results are presented for the limited case of helicopter rotors in hover. [ABSTRACT FROM AUTHOR]

An incremental symmetric boundary integral formulation for the problem of many domains connected by non-linear cohesive interfaces is here presented. The problem of domains with traction-free cracks and/or rigid connections are particular instances of the proposed cohesive formulation. The numerical approximation of the considered problem is achieved by the symmetric Galerkin boundary element method. [ABSTRACT FROM AUTHOR]