Accurate numerical evaluation of domain integrals in 3D boundary element method for transient heat conduction problem

This paper presents an improved approach for the numerical evaluation of domain integrals that appear in the solution of transient heat conduction problems when using a time-dependent boundary integral equation method. An implementation of this method requires the accurate evaluation of the domain integrals. As the time step value is very small, the integrand in the domain integral is close to singular, thus rendering accurate evaluation of the integral difficult. First a closest point is introduced when the source point is close to, but not on the cell in the present method. Then a coordinate transformation coupled with a cell subdivision technique is proposed considering the position of the source point or the closest point and the relations between the size of the cell and the time step value. With the new method, accurate evaluation of domain integrals can be obtained. Numerical examples have demonstrated the accuracy and efficiency of the proposed method.