Explicit empirical formula evaluating original intensity factors of singular boundary method for potential and Helmholtz problems

This short communication proposes two new explicit empirical formulas to determine the original intensity factors on Neumann and Dirichlet boundary in the singular boundary method (SBM) solution of 2D and 3D potential and Helmholtz problems. Without numerical integration and subtracting and adding-back technique, the original intensity factors can be obtained directly by implementing the proposed explicit empirical formulas. The numerical investigations show that the SBM with these new explicit empirical formulas can provide the accurate solutions of several benchmark examples in comparison with the analytical, Boundary element method (BEM) and Regularized meshless method (RMM) solutions. In most cases, the present SBM with empirical formulas yields the similar numerical accuracy as the BEM and the SBM in which the original intensity factors are evaluated by the other time-consuming approaches. It is worthy of noting that the empirical formula costs far less CPU and storage requirements at the same number of boundary nodes and performs more stably than the inverse interpolation technique in the SBM.