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This paper presents a boundary element formulation for the transient Stokes equations in which the well known closed form fundamental solution to the steady Stokes equations is employed and the time derivative is taken to the boundary with dual reciprocity method. This approach has the advantage of simplicity of formulation and implementation in relation to the alternative boundary element schemes previously presented. In addition in this paper the dual reciprocity method is presented in a more formal mathematical way using well established interpolation theories which guarantee the convergence of the method. Results are presented for a series of three‐dimensional internal problems in which the accuracy of the method is shown.

This work compares the performance of the three boundary element techniques for solving Helmholtz problems: dual reciprocity, multiple reciprocity and direct interpolation. All techniques transform domain integrals into boundary integrals, despite using different principles to reach this purpose.

Comparisons here performed include the solution of eigenvalue and response by frequency scanning, analyzing many features that are not comprehensively discussed in the literature, as follows: the type of boundary conditions, suitable number of degrees of freedom, modal content, number of primitives in the multiple reciprocity method (MRM) and the requirement of internal interpolation points in techniques that use radial basis functions as dual reciprocity and direct interpolation.

Among the other aspects, this work can conclude that the solution of the eigenvalue and response problems confirmed the reasonable accuracy of the dual reciprocity boundary element method (DRBEM) only for the calculation of the first natural frequencies. Concerning the direct interpolation boundary element method (DIBEM), its interpolation characteristic allows more accessibility for solving more elaborate problems. Despite requiring a greater number of interpolating internal points, the DIBEM has presented higher-quality results for the eigenvalue and response problems. The MRM results were satisfactory in terms of accuracy just for the low range of frequencies; however, the neglected higher-order primitives impact the accuracy of the dynamic response as a whole.

There are safe alternatives for solving engineering stationary dynamic problems using the boundary element method (BEM), but there are no suitable comparisons between these different techniques. This paper presents the particularities and detailed comparisons approaching the accuracy of the three important BEM techniques, aiming at response and frequency evaluation, which are not found in the specialized literature.

The axisymmetric steady‐state convective‐diffusive thermal field problem associated with direct‐chill, semi‐continuously cast billets has been solved using the dual reciprocity boundary element method. The solution is based on a formulation which incorporates the one‐phase physical model, Laplace equation fundamental solution weighting, and scaled augmented thin plate splines for transforming the domain integrals into a finite series of boundary integrals. Realistic non‐linear boundary conditions and temperature variation of all material properties are included. The solution is verified by comparison with the results of the classical finite volume method. Results for a 0.500[m] diameter Al 4.5 per cent Cu alloy billet at typical casting conditions are given.

The purpose of this paper is to describe an extension of the boundary element method (BEM) and the dual reciprocity boundary element method (DRBEM) formulations developed for one- and two-dimensional steady-state problems, to analyse transient convection–diffusion problems associated with first-order chemical reaction.

The mathematical modelling has used a dual reciprocity approximation to transform the domain integrals arising in the transient equation into equivalent boundary integrals. The integral representation formula for the corresponding problem is obtained from the Green’s second identity, using the fundamental solution of the corresponding steady-state equation with constant coefficients. The finite difference method is used to simulate the time evolution procedure for solving the resulting system of equations. Three different radial basis functions have been successfully implemented to increase the accuracy of the solution and improving the rate of convergence.

The numerical results obtained demonstrate the excellent agreement with the analytical solutions to establish the validity of the proposed approach and to confirm its efficiency.

Finally, the proposed BEM and DRBEM numerical solutions have not displayed any artificial diffusion, oscillatory behaviour or damping of the wave front, as appears in other different numerical methods.

This paper presents an application of the dual reciprocity boundary element method (DRBEM) to transient advection‐diffusion problems. Radial basis functions and augmented thin plate splines (TPS) have been used as coordinate functions in DRBEM approximation in addition to the ones previously used in the literature. Linear multistep methods have been used for time integration of differential algebraic boundary element system. Numerical results are presented for the standard test problem of advection‐diffusion of a sharp front. Use of TPS yields the most accurate results. Further, considerable damping is seen in the results with one step backward difference method, whereas higher order methods produce perceptible numerical dispersion for advection‐dominated problems.

This paper presents a boundary element formulation for transient convection‐diffusion problems employing the fundamental solution of the corresponding steady‐state equation with constant coefficients and a dual reciprocity approximation. The formulation allows the mathematical problem to be described in terms of boundary values only. Numerical results show that the BEM does not present oscillations or damping of the wave front as appear in other numerical techniques.

The purpose of this paper is to describe further developments on a novel formulation of the boundary element method (BEM) for inelastic problems using the dual reciprocity method (DRM) but using object-oriented programming (OOP). As the BEM formulation generates a domain integral due to the inelastic stresses, the DRM is employed in a modified form using polyharmonic spline approximating functions with polynomial augmentation. These approximating functions produced accurate results in BEM applications for a range of problems tested, and have been shown to converge linearly as the order of the function increases.

A programming class named DRMOOP, written in C++ language and based on OOP, was developed in this research. With such programming, general matrix equations can be easily established and applied to different inelastic problems. A vector that accounts for the influence of the inelastic strains on the displacements and boundary forces is obtained.

The C++ DRMOOP class has been implemented and tested with the BEM formulation applied to classical elastoplastic problem and the results are reported at the end of the paper.

An object-oriented technology and the C++ DRMOOP class applied to elastoplastic problems.

Building on reciprocity and crossover theory, this paper aims to examine how mood crossover from one partner in a relational dyad influences the likelihood of reciprocal mood crossover from the other partner.

Using a survey sample of 180 dual‐career married couples, the paper explores this phenomenon for both positive and negative mood crossover from husbands to wives and wives to husbands.

The data supported the paper's four hypotheses. Mood crossover was found to operate in a similar fashion for both husbands and wives after controlling for negative and positive affectivity, work and home demands, work autonomy, and support from the organization, non‐work friends, and spouse. Specifically, when wives (husbands) reported positive (negative) mood crossover from their husbands (wives), their husbands (wives) also reported positive (negative) mood crossover from them.

The findings suggest positive and negative mood crossover is reciprocated among individuals in a dual‐career marriage context. This implies that the effects of positive and negative crossover may be magnified through relational interactions at home. However, the design of this study is not sufficient to determine the causality of this relationship.

The findings suggest that the positive and negative work experiences of one partner in a relationship affect the well being and moods of their partner at home. Consequently, organizations may consider wellness or positive reinforcement programs to encourage positive crossover between the domains of work and home.

This study examines how individuals in a dual‐partner reciprocate the negative and positive crossover of moods of their partner from work to home.

The purpose of this paper is to present an inverse analysis procedure based on a coupled numerical formulation through which the coefficients describing non‐linear thermal properties of blood perfusion may be identified.

The coupled numerical technique involves a combination of the dual reciprocity boundary element method (DRBEM) and a genetic algorithm (GA) for the solution of the Pennes bioheat equation. Both linear and quadratic temperature‐dependent variations are considered for the blood perfusion.

The proposed DRBEM formulation requires no internal discretisation and, in this case, no internal nodes either, apart from those defining the interface tissue/tumour. It is seen that the skin temperature variation changes as the blood perfusion increases, and in certain cases flat or nearly flat curves are produced. The proposed algorithm has difficulty to identify the perfusion parameters in these cases, although a more advanced genetic algorithm may provide improved results.

The coupled technique allows accurate inverse solutions of the Pennes bioheat equation for quantitative diagnostics on the physiological conditions of biological bodies and for optimisation of hyperthermia for cancer therapy.

The proposed technique can be used to guide hyperthermia cancer treatment, which normally involves heating tissue to 42‐43°C. When heated up to this range of temperatures, the blood flow in normal tissues, e.g. skin and muscle, increases significantly, while blood flow in the tumour zone decreases. Therefore, the consideration of temperature‐dependent blood perfusion in this case is not only essential for the correct modelling of the problem, but also should provide larger skin temperature variations, making the identification problem easier.

The purpose of this paper is to develop a meshless numerical method for three‐dimensional isotropic thermoelastic problems with arbitrary body forces.

This paper combines the method of fundamental solutions (MFS) and the dual reciprocity method (DRM) as a meshless numerical method (MFS‐DRM) to solve three‐dimensional isotropic thermoelastic problems with arbitrary body forces. In the DRM, the arbitrarily distributed temperature and body force are approximated by polyharmonic splines with augmented polynomial basis, whose particular solutions and the corresponding tractions are reviewed and given explicitly. The MFS is then applied to solve the complementary solution. Numerical experiments of Dirchlet, Robin, and peanut‐shaped‐domain problems are carried out to validate the method.

In literature, it is commented that the Gaussian elimination can be used reliably to solve the MFS equations for non‐noisy boundary conditions. For noisy boundary conditions, the truncated singular value decomposition (TSVD) is more accurate than the Gaussian elimination. In this paper, it was found that the particular solutions obtained by the DRM act like noises and the use of TSVD improves the accuracy.

It is the first time that the MFS‐DRM is derived to solve three‐dimensional isotropic thermoelastic problems with arbitrary body forces.