In this paper, a set of internal stress integral equations is derived for solving thermoelastic problems.A jump term and a strongly singular domain integral associated with the temperature of the material are produced in these equations. The strongly singular domain integral is then regularizedusing a semi-analytical technique. To avoid the requirement of discretizing the domain into internal cells,domain integrals included in both displacement and internal stress integral equations are transformedinto equivalent boundary integrals using the radial integration method (RIM). Two numerical examples for 2D and 3D, respectively, are presented to verify the derived formulations.

A novel set of auxiliary equations, which supplement the fundamental boundary integral equations, for the treatment of corners and edges arising in discontinuous traction problems and at zonal intersections is derived. Based on these equations, an efficient linear 3D multi-region BEM algorithm is presented which can deal with arbitrarily many regions. Numerical examples demonstrate the effectiveness of this algorithm.

In this paper, a set of boundary integrals are derived based on a radial integration technique to accurately evaluate two dimensional (2D) and three dimensional (3D), regular and singular domain integrals. A self-contained Fortran code is listed and described for numerical implementation of these boundary integrals. The main feature of the theory is that only the boundary of the integration domain needs to be discretized into elements. This feature can not only save considerable efforts in discretizing the integration domain into internal cells (as in the conventional method), but also make computational results for singular domain integrals more accurate since the integrals have been regularized. Some examples are provided to verify the correctness of the presented formulations and the included code.

In this paper, explicit boundary-domain integral equations for evaluating velocity gradients are derived from the basic velocity integral equations. A free term is produced in the new strongly singular integral equation, which is not included in recent formulations using the complex variable differentiation method (CVDM) to compute velocity gradients (Int. J. Numer Meth. Fluids 2004; 45:463-484; Int. J. Numer Meth. Fluids 2005; 47:19-43). The strongly singular domain integrals involved in the new integral equations are accurately evaluated using the radial integration method (RIM). Considerable computational time for evaluating integrals of velocity gradients can be saved by using present formulation than using CVDM. The formulation derived in this paper together with those presented in reference (Int. J. Numer. Meth. Fluids 2004; 45:463-484) for 2D and in (Int. J. Numer Meth. Fluids 2005; 47:19-43) for 3D problems constitutes a complete boundary-domain integral equation system for solving full Navier-Stokes equations using primitive variables. Three numerical examples for steady incompressible viscous flow are given to validate the derived formulations. Copyright 2007 John Wiley & Sons, Ltd.