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In this paper, the implementation of a 3-D parallel CFD code using the meshless method. Reproducing Kernel Particle Method (RKPM) is described. A novel procedure for implementing the essential boundary condition using the hierarchical enrichment method is presented. The Total Arbitrary Lagrangian Eulerian (ALE) formulations using Finite Element Method are developed and implemented in the parallel code. The flow past a cylinder problem served as examples throughout the paper. Both methods have shown promising results compared with analytical solution. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, it is shown that the symmetric Galerkin boundary element formulation cannot be used in its standard form for multiple connected bodies. This is because the traction integral equation used for boundaries with Neuman boundary condition give non-unique solutions. While this fact is well known from the classical theory of integral equations, the problem has not been fully addressed in the literature related to symmetric Galerkin formulations. In this paper, the problem is reviewed and a general way to deal with it is proposed. The details of the numerical implementation are discussed and an example is solved to demonstrate the effectiveness of the proposed solution. Copyright © 2001 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A linear θ method is used in this paper to improve the stability of the standard time-domain BEM formulation. The time-stepping procedure is similar to that of the Wilson θ method; however, unlike in the FEM, where linear time variation of acceleration (for elastodynamic problems) is assumed, here linear time variation for both potential and flux (for scalar waves) is assumed in the time interval θΔt. A comparison between numerical results obtained from the standard formulation and from the linear θ method studied here shows the latter to be more stable than the former. The effect of varying θ for different values of time steps is also studied in this 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]

A variant of the boundary element method, called the boundary contour method (BCM), offers a further reduction in dimensionality. Consequently, boundary contour analysis of two-dimensional (2-D) problems does not require any numerical integration at all. The method is thus very computationally effective and accurate as shown in previous related studies. This paper presents a further development of the BCM for multi-region problems in 2-D elasticity, and an application of this development, coupled with the displacement correlation technique, to evaluating the stress intensity factors K1 and K2 for bimaterial interface cracks. Some preliminary tests conducted within this work suggest that the proposed technique is robust and able to provide highly accurate results of both K1 and K2 for this challenging class of fracture problems. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper considers the exact integration of discontinuous quadratic element for boundary element analysis of two-dimensional potential problems. It is proved by the mathematical induction that singular integral in Cauchy principal value (CPV) and hypersingular integral in Hadamard finite part (HFP) need no special treatment with the derived exact integration for discontinuous quadratic element. The evaluation of CPV and HFP without special treatment leads to an easy way to compute the potential and flux on the boundary. The differences of the recovered flux and those by solving algebraic equation at collocation points are interpolated as error indicator for adaptive boundary element analysis. Two numerical examples are given to verify the correctness of the exact integration and the feasibility of the proposed error indicator. Copyright © 2007 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 simple time domain fundamental solutions for the three-dimensional (3D) well known u–p formulation of saturated porous media, neglecting the compressibility of fluid and solid particles. At first, the corresponding boundary integral equations as well as the explicit Laplace transform domain fundamental solutions are obtained in terms of solid displacements and fluid pressure. Subsequently, the closed form time domain fundamental solutions are derived by analytical inversion of the Laplace transform domain solutions. Finally, a set of numerical results are presented which demonstrate the accuracies and some salient features of the derived analytical transient fundamental solutions. 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]

This paper presents the preliminary results of an extensive numerical parametric study on seismic behaviour of two-dimensional semi-sine-shaped valleys subjected to vertically propagating incident in-plane compression and shear waves. The medium is assumed to have a linear elastic constitutive behaviour. All calculations are executed in time-domain using the direct boundary element method. Clear perspectives of the amplification patterns of the valley are presented by investigation of the frequency-domain responses. It is shown that wavelength, site geometry and in a less order of importance, wave type and material parameters, are the independent key parameters governing the valley's amplification pattern. Some simple rules are obtained which could be used in seismic microzonation and seismic design of structures founded inside the valley. 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]

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]

The FEM analysis of hyper elastic, elastomeric materials has been formulated and implemented for various material models (strain energy functions) over the years. More recently, the analysis of elastomeric materials has been attempted in the boundary element method. This has been achieved by the addition of non-linear domain terms to the basic linear boundary element equation. These non-linear domain terms require the evaluation of the displacement derivative components directly from displacement derivative boundary integral equations. In the solution to the boundary problem it is required to regularize the different types of singularities occurring in the system of non-linear boundary integral equations. This paper discusses the necessary theory for the boundary element method as applied to elastomers and presents a comparison between semi-analytical and numerical solutions for various test cases. Copyright © 2004 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]

An algorithm based upon the residue calculus for computing three-dimensional anisotropic elastic Green's function and its derivatives has been presented in Sales and Gray (Comput. Structures 1998; 69:247–254). It has been shown that the algorithm runs three to four times faster than the standard Wilson–Cruse interpolation scheme. However, the main concern of the Sales–Gray algorithm is its numerical instability that could lead to significant errors due to the existence of multiple poles of the residue. This paper proposes a remedy for the problem by adding the capability to evaluate the Green's function in case of multiple poles of the residue. Further, an improved numerical implementation based on the use of double-subscript-notation elastic constants in determining the Christoffel tensor is also at issue. Copyright © 2004 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]

In this paper the Tikhonov regularization method is analysed for the ill-conditioned system of linear equations which arises from the discretization of an ill-posed boundary value problem in linear elasticity. The choice of the regularization parameter is achieved according to the L-curve method. Then the regularization method is numerically implemented using the boundary element method (BEM). Copyright © 2002 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]

The question of the accurate numerical evaluation of weakly singular integrals arising in the boundary element method has attracted considerable recent attention. A popular method is to use a non-linear transformation with zero derivative at the singular point to adjust the position of the Gauss–Legendre quadrature points, resulting in a more accurate evaluation of the integral. This paper presents a simple algebraic device to overcome a numerical round-off problem which has limited previous implementations of non-linear transformations. Utilization of this device allows higher orders of transformation to be used, resulting in lower relative errors in the numerical evaluation of the weakly singular integrals. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, to solve the problems of the interaction between the unilateral interface cracks and elastic wave, a new numerical method based on boundary element method (BEM) has been proposed. In this method, an iterating–correcting process of the solution in frequency domain and the correction in time domain has been designed to eliminate the mutual interference between the time and frequency domain. As an illustration to the algorithm, an interface crack between two half-planes under the attack of harmonic plane elastic wave has been analysed in detail. The contact configurations and stress field at the crack surface, and dynamic stress intensity factor (DSIF) at the crack tip have been given. 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]

Domain decomposition methods for Laplace's equation are investigated in the present paper. An optimization approach is adopted to satisfy the Dirichlet and/or Neumann interface conditions. The adjoint variable method is used to find the sensitivity of the objective function of optimization. The boundary element method is utilized for the discretization of the primary and adjoint problems. Two example problems are studied with the proposed solution method. Comparisons are also provided by using two other techniques, namely the Uzawa and Schwarz methods, already available in the literature. It is also suggested that a parallel implementation of the method could be performed leading to computational efficiency. Copyright © 2000 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]

In this paper, a quadratic polynomial expression is used as the displacement shape function to develop the Boundary Contour Method. In this work, the divergence free property of the J integral is proved; the evaluation of the J integral is transformed, through an application of Stokes' theorem, into a linear combination of the displacement and traction at the boundary point that have been calculated by the Quadratic Boundary Contour Method such that numerical integrals are not needed at all. Numerical results are presented for two-dimensional problems, and these are compared against conventional solutions. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A posteriori error estimation for the boundary element method is developed. The nodal error is estimated from the difference of two solutions—one from the original BEM solution, and the other from interpolation of the original solution. Based on nodal errors, a matrix analysis is carried out to calculate the corresponding errors at source points. Two formulae for estimating global percentage errors are proposed in the paper. The first formula uses nodal errors directly to estimate element error, and the second uses an integral form to calculate element error to eliminate extremely high mesh concentration near areas with singular solutions. An h-version adaptive mesh refinement is implemented to study the accuracy of the proposed error estimation. Numerical examples show that the error estimator can correctly guide mesh refinement, and a final mesh can be obtained in a few iterations. © 1998 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

By continuous transformation for a domain, this paper develops a new boundary element technique, mapping semi-analytical BEM. Applied to static/dynamic analysis of 3D embedded arbitrarily shaped crack problems, it only needs one-dimensional discretization, so the computational work can be considerably reduced. Some typical examples demonstrate its effectiveness. © 1997 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]

Based on the same concept as generalized differential quadrature (GDQ), the method of Fourier expansion-based differential quadrature (FDQ) was developed and then applied to solve the Helmholtz eigenvalue problems with periodic and non-periodic boundary conditions. In FDQ, the solution of a partial differential equation is approximated by a Fourier series expansion. The details of the FDQ method and its implementation to sample problems are shown in this paper. It was found that the FDQ results are very accurate for the Helmholtz eigenvalue problems even though very few grid points are used. ©1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The dual reciprocity boundary element method traditionally uses the linear radial basis function r for interpolation. Recently, however, the use of the r function has been questioned both in relation to accuracy and in relation to the number and position of internal nodes required to obtain satisfactory solutions. Much research has been done in an attempt to fix criteria for choosing which approximation function should be used. One of the alternatives recently suggested is the augmented thin plate spline function, which consists of a thin plate spline function, r2 log(r), augmented with the first three terms of a Pascal triangle expansion. In this paper families of similar functions are obtained by augmenting radial basis functions with appropriate global expansions: these functions will be called hybrid approximate functions. It will be shown that using an appropriate hybrid function accurate results can be obtained for many body forces or pseudo body forces in elasticity without the need for internal nodes.© 1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The fundamental solution of the temperature field in an infinite three-dimensional body under the periodic unit thermal source is given in the present paper. According to the indirect boundary element method (IBEM) with fictitious heat sources, the problem of 3-D periodic heat conduction in a finite body is solved. By use of a quadratic inharmonic element, the problem of the corner region and the indetermination of the normal direction at boundary points can be solved in the numerical process. The validity of the present method is checked with two examples of which analytical solutions exist. It offers a useful method for the actual simulated calculation of the 3-D temperature field in engineering. [ABSTRACT FROM AUTHOR]

The paper investigates the accuracy and numerical stability of a class of wavelet Galerkin formulations on irregular domains. The method of numerical boundary measures is based upon a domain embedding strategy in which the irregular domain of interest is embedded in a larger domain having regular geometry. One advantage of the domain embedding method is that the boundary conditions on the larger, regular domain can be enforced in a straightforward manner, and the solution procedure can exploit the highly structured form of the resulting governing equations. The defining characteristic of this method is that the calculation of integrals along the irregular boundary are carried out using recently derived numerical boundary measures. In addition, the coercive bilinear forms characterizing the boundary value problem of interest must be calculated when restricted to the actual domain. In the case of wavelet Galerkin formulations, this calculation is accomplished with the three term connection coefficients that characterize the numerical boundary measure. The numerical stability and accuracy of the domain embedding procedure is compared to a newly developed wavelet-based finite element formulation. [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 attempts to improve the efficiency of a general method developed previously for computing nearly singular kernel integrals. Three new formulations are presented by following an approach similar to that used in the previous method. Their numerical efficiency is compared with the previous method. The results indicate that these new formulations are substantially more efficient than the previous method. In particular, the new formulation in which the same sampling points for all n values are used is the most efficient. This new formulation remains highly efficient even when the field point is as close to the panel surface as 0-1 per cent of the panel diagonal. [ABSTRACT FROM AUTHOR]

The contributions of distributed sources to the mathematical expectations and variances of the response variables are analysed in the paper using the stochastic boundary element method. The validity and the accuracy of the particular integral approach in representing statistical properties of the domain are investigated. To this end domain integration techniques to calculate the contributions of the distributed sources and their derivatives with respect to random variables that may represent both random configuration of the domain and random material parameter are developed. Several models for the random interior are presented and their influence on the response statistics is investigated. The accuracy of the particular integral approach is demonstrated through numerical comparisons with the direct integration formulation. [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 the authors investigate the conditions of optimal mesh, and prove that the element errors in the optimal mesh should be identical for all existing elements. Also, it is shown that the correct mesh refinement formulations should be derived at an element level rather than the global level. Thus the element permissible errors need to be determined. The method to determine these permissible element errors is described. [ABSTRACT FROM AUTHOR]

When solving non-linear algebraic equations resulting from a typical finite element discretization it is quite common that the popular Newton-Raphson iteration fails to converge or requires an excessive number of iterations. To solve this problem, line searches have been proposed in conjunction with load control and quadratic arc-length control, which has proved to be highly successful. In the paper we first review a number of the most popular arc-length controls. Then we highlight the severe drawbacks associated with the coupling of the cylindrical arc-length control and line searches. Next, various other forms of arc-length controls are scrutinized in the light of this coupling. It is shown that for some of the arc-length controls such a combination is extremely simple and straightforward, yet at the same time efficient and effective. For the rest the same complications incurred for the cylindrical arc-length method remain. [ABSTRACT FROM AUTHOR]

The paper concentrates on the numerical evaluation of nearly singular kernel integrals commonly encountered in boundary element analysis. Limitations of the method developed recently by Huang and Cruse (1993) for the direct evaluation of nearly singular kernel integrals are analyzed and pointed out. A general method is developed that extends the idea for all practical cases. Example results are presented, demonstrating the effectiveness of the method. [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]

The paper describes a procedure to generate boundary characteristic orthogonal polynomials (BCOPs) over a domain in Rn. The method is based upon the Gram-Schmidt process of orthogonalization. The orthogonal polynomial sequence (OPS) is generated from a set of linearly independent functions which satisfy the given boundary conditions. The procedure is illustrated by taking several examples in R², the most important case from the application point of view. Extensive numerical work has been carried out for simple domains like the circle, square and isosceles right-angled triangle. The following cases have been considered: (a) when the BCOPs vanish on the boundary; (b) when they and their normal derivatives vanish on the boundary; (c) when no conditions have been imposed on the boundary. The results for other geometries such as an ellipse, a parallelogram and an arbitrary triangle follow by some simple transformations. The procedure is also applicable to one-dimensional problems and can be easily extended to R³. [ABSTRACT FROM AUTHOR]

The paper presents boundary integral equation to two-dimensional elasticity with the stress component σijtitj as one of the boundary values, where t1 are direction cosines of the tangent on the boundary. This form of BEM has an advantage in that the stress component σijtitj on the boundary can be calculated directly from the numerical solution. The present formulation for planar problems uses two kernels, one of which is logarithmic singular and the other is 1/r singular. The effectiveness of the approach is also discussed through some test examples. [ABSTRACT FROM AUTHOR]

In the paper the BEM and FEM results have been compared in the context of 2D electromagnetic field analysis in a zoned medium with eddy current subregions. The practical problem concerning the turbo- generator end region has been discussed. The magnetic flux density over the surface of the end package and the current density in the non-magnetic pressure plate have been analysed. [ABSTRACT FROM AUTHOR]

It is known that the boundary-element coefficient matrices in steady-state elastodynamics are frequency- dependent. For a multifrequency run, the coefficient matrices have to be reformed at each different frequency. This procedure usually involves heavy numerical integration, and hence is very time consuming. In this paper, two interpolation schemes are initially introduced to accelerate the process of matrix reformation without sacrificing the solution accuracy. In the first scheme, the coefficient matrices are first slightly transformed and then interpolated in the frequency domain. In the second scheme, the Green function is interpolated in the spatial domain. Comparison between these two schemes both in terms of accuracy and efficiency is presented. Finally, a hybrid scheme that takes advantage of the best of both interpolation schemes is proposed. Numerical examples are given to demonstrate the three different interpolation schemes. [ABSTRACT FROM AUTHOR]

The symmetric boundary-element method for mixed boundary-value problems is currently gaining increasing interest as it permits the derivation of symmetric matrices. It is even possible to obtain positive-definite finite-element stiffness matrices for BEM subregions, and therefore the method provides a very straightforward coupling to the finite-element method (FEM). The BEM subregions can be handled like FEM substructures in a domain decomposition context. The symmetric BEM uses the full set of integral representations for the 2n types of boundary data for self-adjoint problems of order 2n and solves them in a weighted residual (Galerkin) sense. The main difficulty of the method is caused by the need to compute hypersingular integrals arising from the integral representations of the Neumann boundary data. It is the object of the paper to show that, for 2-D problems on polygonal domains, these hypersingular integrands pose no problem at all, even for higher-order approximations. The present approach makes use of analytical integrations as far as possible. The integrals of the hypersingular expressions are derived completely within the framework of simple engineering mathematics. The problem is reduced to the computation of weakly singular integrals even for C0 continuous approximations. [ABSTRACT FROM AUTHOR]

There has been considerable effort put into determining the motion of a single bubble in a fluid in a variety of different situations. The boundary integral method has proved to be a convenient tool in such studies as it reduces the unbounded, three-dimensional fluid-filled domain of the governing partial differential equation to the finite, two-dimensional surface of the bubble. In this paper the author's work, which considered the motion of a bubble close to a fixed rigid structure, is extended to the case where the structure may be moving.