A fast approach evaluating origin intensity factors on Neumann boundary in the singular boundary method

This study introduces a rapid methodology based on recursive skeletonization factorization (RSF), for the determination of origin intensity factors (OIFs) at Neumann boundaries within the framework of the singular boundary method (SBM). The conventional formula for OIFs, which is derived using the subtracting and adding-back technique (SABT), is reformulated into a matrix-vector product representation. The components of the matrix consist of the fundamental solutions of the double-layer potential that adhere to the governing equations. Consequently, the RSF facilitates the implicit construction of a hierarchically generalized LU decomposition of the matrix, producing decomposition factors that allow for efficient multiplication with any vector. This innovative approach significantly reduces the computational cost associated with the calculation of OIFs, thereby meeting the demands of simulating large-scale problems. Numerical results demonstrate that this method is both accurate and stable, and it is applicable to a variety of problems characterized by irregular geometries.