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With the advent of high-performance parallel computers, boundary integral methods have received an increasing interest for the solution of electromagnetic scattering problems of electrically large objects. The Galerkin discretization of integral equations leads to dense and complex linear systems whose size increases linearly with the dimension of the scatterer and quadratically with the frequency of the illuminating radiation. For solving realistic high-frequency problems, iterative Krylov methods can be a viable alternative to out-of-core direct methods provided they are used in combination with fast algorithms for the matrix–vector products and robust parallel preconditioners. In this paper, we present experiments with iterative Krylov solvers combined with an approximate inverse preconditioner and the fast multipole method for the matrix–vector products. Numerical results on a set of problems arising from realistics radar cross-section calculations in industry illustrate the potential of the proposed strategy for solving large-scale problems in electromagnetism. The research described in this paper has been developed in the framework of a joint collaboration between CERFACS (Toulouse), EADS-CCR (Toulouse), INRIA-CERMICS (Sophia Antipolis). Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper a new technique is presented for transferring the domain integrals in the boundary integral equation method into equivalent boundary integrals. The technique has certain similarities to the dual reciprocity method (DRM) in the way radial basis functions are used to approximate the body force term. However, the resulting integrals are evaluated in a much simpler way. Several examples are presented to demonstrate the validity and accuracy of the proposed paper. Copyright © 1998 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper treats a united-form solution for a point force applied at the interior of an infinite transversely isotropic solid. Several heuristic functions are adopted to obtain the expressions of the solution based on the general solution. To exclude some indeterminate attributes, the expressions are rewritten. In the final expressions, unlike previous publications where the solutions are expressed in different forms, or when some individual constants have different definitions depending on the conditions satisfied by the elastic constants, we provide united solutions which are suitable for all stable transversely isotropic materials and isotropic materials. Thus accurate numerical evaluation of the boundary element method can be performed directly without the need to resolve the singularity algebraically. Some numerical examples with BEM are also presented in this paper. © 1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The subject of this paper is the calculation of charge distribution on the surfaces of thin conducting microelectromechanical systems beams, of nearly square cross-section, in electrostatic problems, by the boundary element method (BEM). A line model of a beam is proposed here. This model overcomes the problem of dealing with nearly singular matrices that occur when the standard BEM is applied to very thin features (objects or gaps). This new approach is also very efficient. Numerical results are presented for selected examples. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a fast multipole boundary element method (BEM) for the analysis of two-dimensional elastoplastic problems. An incremental iterative technique based on the initial strain approach is employed to solve the nonlinear equations, and the fast multipole method (FMM) is introduced to achieve higher run-time and memory storage efficiency. Both of the boundary integrals and domain integrals are calculated by recursive operations on a quad-tree structure without explicitly forming the coefficient matrix. Combining multipole expansions with local expansions, computational complexity and memory requirement of the matrix–vector multiplication are both reduced to O(N), where N is the number of degrees of freedom (DOFs). The accuracy and efficiency of the proposed scheme are demonstrated by several numerical examples. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

When the direct current (DC) metallized thin film capacitor is fully charged the electromagnetic fields can be considered to have reached a steady state in which the governing equation is Laplace's equation. It is the computational analysis of the electrostatic state that is considered in this paper. The capacitor is modelled as a stack made up of infinitesimally thin layers of metal on polymer. An integral equation method from the BEMLAP package (www.boundary-element-method.com (Introduction to the Boundary Element Method for Scientists and Engineers: The BEMLAP Fortran Library for Laplace Problems)) for modelling the electric field, based on the methods described in Kirkup (Fortran codes for computing the discrete Helmholtz integral operators; Adv. Comput. Math. 1998; 9:391–409). The method is applied to a typical capacitor structure and encouraging results are obtained. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, the radial integration method is applied to transform domain integrals into boundary integrals in a boundary element formulation for anisotropic plate bending problems. The inertial term is approximated with the use of radial basis functions, as in the dual reciprocity boundary element method. The transformation of domain integrals into boundary integrals is based on pure mathematical treatments. Numerical results are presented to verify the validity of this method for static and dynamic problems and a comparison with the dual reciprocity boundary element method is carried out. Although the proposed method is more time-consuming, it presents some advantages over the dual reciprocity boundary element method as accuracy and the absence of particular solutions in the formulation. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper deals with the boundary integral formulation for solution of 3-D axial symmetric problems of stationary thermo-elasticity with including the domain heat sources. The domain integral of heat sources is converted into boundary integrals of a new field variable and another summation term involving the function values of another field variable at isolated interior points. Making use of the triple-reciprocity method, the unknown boundary densities as well as the interior point unknowns are computed by solving the integral equations without the need to use domain cells in discretization. The integral kernels involved in the developed boundary integral formulation for axial symmetric problems are received by angular integration of 3-D kernels with using cylindrical co-ordinates. The explicit expressions of the kernels are collected in appendix and two numerical examples are considered for illustration of the accuracy and efficiency of the proposed approach. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A higher-order boundary element method (BEM) recently developed by the current authors (Comput Methods Appl Mech Eng 2003; 192: 4281–4298; 4299–4312; 4313–4335) for time-dependent convective heat diffusion in two-dimensions appears to be a very attractive tool for efficient simulations of transient linear flows. However, the previous BEM formulation is restricted to relatively small time step sizes (i.e. &Deltat⩽4κ/V2) owing to the convergence issues of the time series for the kernel representation within a time interval. This paper extends the boundary element formulation in a way to allow time step sizes several orders of magnitude larger than in the previous approach. We consider an example problem of thermal propagation, and investigate the accuracy and efficiency of BEM formulations for Peclet numbers in the range from 103 to 105. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, the eigenanalysis for the multiply-connected domain problem is studied by using the dual boundary element method. The occurrence and treatment of the spurious eigenvalues for multiply-connected domain problem are reviewed when the complex-valued BEM in used. Three approaches, Burton and Miller method, CHIEF concept and SVD updating techniques, are adopted to suppress the occurrence of spurious eigensolutions. Instead of using the singular and hypersingular formulations, the singularity-free methods, the null-field equation approach and the fictitious BEM, are also utilized to deal with the eigenproblem. Both the eigenvalues and eigenmodes are compared with the analytical solutions and those of FEM for the illustrative examples. Good agreement is made. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper is the continuity of our previous work (Commun Numer Meth Engng 2003; 19:25-36) which applies the 2D time domain boundary element method (BEM) to solve the transient scattering of SH waves by an inclusion with a unilateral frictional contact interface. The case of the plane wave (P and/or SV wave) incidence is studied. Localized slip and separation at the interface caused by strong incident waves are considered. Therefore the interface involves three different kinds of unknown intervals: slip, separation and stick regions. In order to determine the unknown intervals, an iterative technique is developed. As an example, we compute the scattering of P waves by a cylinder of circular cross-section embedded in an infinite solid. Numerical results for the near field solutions are presented. The distortion of the response waves and the variation of the interface states are discussed. [ABSTRACT FROM AUTHOR]

This paper presents a fast approach for rapidly solving problems with multiple load cases using the boundary element method (BEM). The basic idea of this approach is to assemble the BEM matrices separately and to compress them using fast wavelet transforms. Using a technique called ‘virtual assembly’, the matrices are then combined inside an iterative solver according to the boundary conditions of the problem, with no need for recompression each time a new load case is solved. This technique does not change the condition number of the matrices—up to a small variation introduced by compression—so that previous theoretical convergence estimates are still valid. Substantial savings in computer time are obtained with the present technique. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper develops a 2D time domain boundary element method (BEM) to solve the transient SH-wave scattering from an inclusion with a unilateral frictional interface. The incident SH-wave is assumed strong enough to break friction so that localized slip takes place along the interface. The present problem is indeed a non-linear boundary value problem since the mixed boundary conditions involve unknown intervals (the slip and stick zones). In order to determine the intervals, an iterative technique is developed. As an example, we consider the scattering of a circular cylinder embedded in an infinite solid. The numerical results of the interface traction and relative slip velocity are presented. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The standard boundary node method (BNM) uses a (meshless) diffuse interpolation (in terms of neighbouring scattered boundary points) for the primary variables. The method is not ‘truly meshless’, however, since cells on the boundary of a body are used for integration. This paper presents a ‘pure’ version of the BNM in which integration cells are dispensed with. Instead (overlapping), regions of influence (ROIs) of boundary nodes are used for integration. Initial results for 2-D potential theory, presented here, are encouraging. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents an application of the boundary element method to the analysis of plate structures subjected to arbitrary loadings. Using a multi-region technique to assemble plate structures, boundary element formulation for a shear deformable plate bending are coupled with the formulation for plane stress elasticity. Additional equations required to solve the problem are obtained by imposing the compatibility and equilibrium conditions along interface edges. Several examples with different configurations and loadings are presented to demonstrate the effectiveness of the proposed method. Copyright © 2001 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In the solution of Poisson's equation using either the dual reciprocity boundary element method or the method of fundamental solution, radial basis functions (RBFs) are used to approximate the right-hand side of the governing partial differential equation to eliminate the domain integration. This paper shows that if the RBF interpolation is collocated on the Gaussian quadrature nodes, we seem to observe superconvergence behaviour. This behaviour is demonstrated using a series of numerical examples. Copyright © 2001 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper the boundary element method is applied to linear elastic axisymmetric solids under general non-symmetrical surface loads. The formulation is based on transforming the well-known three-dimensional boundary integral equations into cylindrical co-ordinates system. Then, the behaviour of the loads and displacements in the circumferential direction is expressed in Fourier series. As a result, the original problem is solved as a sequence of one-dimensional problems each with a specified harmonic mode of the applied load. The integration through the circumferential direction is performed numerically, with the use of an appropriate transformation to improve the accuracy of the numerical integration. Consequently, the mathematical complexities are further simplified, and the work with nth-order harmonics of the applied load is greatly facilitated. The validity, accuracy and generality of the present approach are demonstrated via solving some numerical examples with different harmonic modes. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper revisits the real variable fundamental solution approach to the Boundary Integral Equation (BIE) method in two-dimensional orthotropic elasticity. The numerical implementation was carried out using quadratic isoparametric elements. The strong and weakly singular integrals were directly evaluated using Euler's transformation technique. The limiting process was done in intrinsic coordinates and no separate numerical treatment for strong and weak singular integrals was necessary. For strongly singular integrals a priori interpretation of the Cauchy principal value is not necessary. Two problems from plane stress and strain are presented to demonstrate the numerical efficiency of the approach. Excellent agreement between BEM results and exact solutions was obtained even with relatively coarse mesh discretizations. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The conventional boundary integral equation in two dimensions is non-equivalent to its corresponding boundary value problem when the scale in the fundamental solution reaches its degenerate scale values. An equivalent boundary integral equation was recently derived. This equation has the same solution as the boundary value problem of differential equations. This paper presents the boundary contour method based on the equivalent boundary integral equation for two-dimensional linear elasticity. The method requires only numerical evaluation of potential functions and gives correct equivalent results to the boundary value problem of differential equations in two dimensions. Numerical results are presented for some examples. The present approach is shown to give excellent results in illustrative examples. Meanwhile, the traction results from the BCM based on the conventional displacement boundary integral equation are incorrect. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper is concerned with the application of the Overhauser C(1) continuous boundary element method to the calculation of electromagnetic scattering. The method preserves C(1) continuity of the smooth parts of the surface of a scatterer and of the unknown functions which are defined on it. Results for a perfectly conducting sphere have been compared with those obtained from Mie theory and the C(0) formulation. They show that the C(1) version requires fewer surface nodes and significantly less computer time for higher frequencies to provide results of equivalent accuracy. Some results from an Ogive have also been calculated and compared using the C(0) and C(1) formulations. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The integrals required in the computation of influence coefficient matrices of the boundary element method (BEM) depend on the distance r(x,x′) from the collocation point or field point x to the source or load point x′. As a consequence, a distinction must be made between the case where the collocation point does not belong to the integration domain (proper integrals) and the case where the collocation point does belong to the integration domain (improper integrals). Moreover, situations arise where x comes close to x′ and the integrals, albeit of a regular character, behave almost as improper, this case being referred to as nearly singular integration. Analytical integration captures best the singular or nearly singular kernel behavior, but this technique can only be carried out in very simple situations as, for instance, boundary integrals over straight elements. In the present paper a set of useful analytical integration formulas for the 2D BEM with curved elements is deduced, employing a symbolic computational algebra system. © 1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a novel dual reciprocity formulation for elasticity problems with body forces in which the approximating functions are given in terms of augmented thin plate splines (ATPS). It is shown that the ATPS approximation is capable of correctly representing gravitational and centrifugal body forces, and provides superior accuracy for general load cases. [ABSTRACT FROM AUTHOR]

The present paper deals with the shape design optimization of bodies subjected to a non-homogeneous Helmholtz equation. Using the adjoint variable method the material derivative of a general integral functional is obtained analytically. Boundary integral equations defined only on the boundary are derived using auxiliary fundamental solutions to be used in the boundary element method. Some constrained shape design optimization problems are solved by the proposed numerical procedure. [ABSTRACT FROM AUTHOR]

The paper reveals the conditions under which the approximations of the normal vector and global coordinates of interior points of two segments on a smooth contour can fail using the C¹-continuous Overhauser elements. A new continuous modelling of the normal vector is developed using the standard Lagrange elements. The derivation is consistent with the assumptions employed in the boundary element method formulations of potential problems. Test numerical examples are considered in order to analyse the accuracy of the approximations based on the use of standard C0-continuous elements, Overhauser C1-continuous elements and the proposed 'smooth' C0 elements. [ABSTRACT FROM AUTHOR]

In the paper we apply the boundary element multiple reciprocity method to the Brinkman equation, showing that the technique yields an incomplete series representation of the corresponding fundamental solution, incompleteness that is due to a weakness in the way the method is usually applied. For the present case an additional integral relation is found that makes the series complete. Unfortunately, the relation is particular to this problem and cannot be generalized in a simple way. The result found in this work suggests that in multiple reciprocity it is necessary to have an extra relation in integral form to define the missing terms in the series representation. This extra relation has to yield zero contribution for cases when the multiple reciprocity method gives the complete series representation. [ABSTRACT FROM AUTHOR]

The paper investigates the convergence of the h-, p- and hp-versions of a variational symmetric boundary element method (BEM) in plane elasticity by numerical experiments. The study discusses mixed boundary value problems on polygonal domains, i.e. problems for which the exact solution is analytic except in a finite number of points. The convergence of the error in energy norm is displayed for all versions of the BEM. All results are also compared with those obtained by the corresponding finite element methods. The theoretically predicted asymptotic convergence rates for all versions of the method can be observed in the numerical experiments. A comparison of computer times is given as well. [ABSTRACT FROM AUTHOR]

In the paper the application of the dual boundary element method to three-dimensional crack growth problems is presented. A procedure for remeshing of the free surfaces is presented to allow the simulation of surface breaking crack growth. [ABSTRACT FROM AUTHOR]

Owing to a technical problem in the submission process, selected presentations from the 7th International Conference on Boundary Elements, which took place in Paris, France, in September 2006 (http://beteq.engineeringconferences.net/), will not be published in a separate special issue. Links to these papers as they were published in the journal are listed at the end of this editorial. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]