Generalized boundary integral equation for heat conduction in non-homogeneous media: recent developments on the sifting property

Abstract

In this paper, we address concerns which were raised with respect to the sifting property of the forcing function D which is crucial in deriving an integral equation for heat conduction in non-homogeneous media. The error in the sifting property (which we neglected in our previous papers) is expanded in a series which leads to evaluation of the error in terms of boundary integrals. This provides a practical estimate of the approximation encountered in the analysis of particular problems, as this may be small in certain cases and significant in others. The correction can be implemented directly or iteratively. In this paper, both methods are used. The iterative approach provides a quantitative measure of the correction and is shown to rapidly converge and improve results, particularly in the case of boundary fluxes. The boundary-only feature of our original boundary integral formulation for heat conduction in non-homogeneous media is thus retained.