An Invariant Imbedding Method for Singular Integral Evaluation on Finite Domains

Abstract

The “invariant imbedding” technique is used to develop versatile and powerful integration formulae for the evaluation of singular integrals on finite domains encountered in continuum problems in engineering and applied science. This method is considerably simpler than the several ad hoc integral evaluation methods presented in the recent literature. Moreover, the method provides new insight into the central role played by the residue in the evaluation of principal value integrals. This relationship is embodied as a “gauge condition.” The main emphasis of the paper is on developing a general approach from which specific cases follow. Several examples chosen from different areas of engineering computation are provided in order to show the advantage of this approach.