Regularization of the Integral Equations for Unsteady Heat Conduction Problems

It has been found that the boundary integral equations for steady problems such as those of potential, elasticity, fluid mechanics and so on can be regularized by introducing relative quantities of field functions. We describe that fundamental integral equations for unsteady heat conduction problems can also be regularized by applying the same techniques. The regularized integral equations with relative quantity are obtained by superposing a particular solution under the condition of time-independent uniform potential upon the conventional ones. This approach has made it possible to derive the integral equation of potential gradient on a surface point, which has not been given up to now in the conventional formulation due to hyper-singularity. Through two- and three-dimensional numerical investigations, it is verified that the present integral equations give accurate numerical results everywhere over the domain and that they are valid and effective.