Accurate empirical formulas for the evaluation of origin intensity factor in singular boundary method using time-dependent diffusion fundamental solution

This paper presents the simple empirical formulas for the accurate evaluation of the origin intensity factor in singular boundary method (SBM) when the time-dependent diffusion fundamental solution is employed. These new formulas makes the SBM more fast, straightforward, and efficient for transient diffusion problems while being truly meshless, integration-free and easy-to-implement. Three benchmark examples are tested to demonstrate the accuracy and efficiency of the proposed scheme. It is shown that the SBM using these empirical formulas works well especially for one and two-dimensional transient diffusion problems. In the three-dimensional case, we have obtained the SBM empirical formula of the origin intensity factors at initial time, and numerical experiments on benchmark problems have verified its efficiency and accuracy. It is worth noting that we need to two different formulas for a specific dimensionality. However, the empirical formula with time variation in three-dimensional case is not available and still under investigation.