A simple accurate formula evaluating origin intensity factor in singular boundary method for two-dimensional potential problems with Dirichlet boundary

In this work, a simple accurate formula is presented to evaluate the origin intensity factor of the singular boundary method (SBM) for two-dimensional Dirichlet potential problems. The SBM is considered as an improved version of the method of fundamental solutions and remedies the controversial auxiliary boundary outside the computational domain in the latter. The origin intensity factor is a central concept in the SBM to overcome the source singularity of the fundamental solution while placing source points on the physical boundary. In literature, the origin intensity factor for the Dirichlet boundary condition is numerically obtained which may cause numerical instability in large-scale simulations. This work proposes a simple formula to calculate the origin intensity factor for two-dimensional Dirichlet potential problems. Numerical experiments show that it is feasible and perform robustly for problems under various irregular domains.