An efficient method to evaluate hypersingular and supersingular integrals in boundary integral equations analysis

摘要

An efficient algorithm is employed to evaluated hyper and super singular integral equations encountered in boundary integral equations analysis of engineering problems. The algorithm is based on multiple subtractions and additions to separate singular and regular integral terms in the polar transformation domain, primarily established in Refs. (Guiggiani M. Krishasamy G, Rudolph TJ, Rizzo FJ. A general algorithm for the numerical solution of hyeprsinular boundary integral equations. Trans ASME 1992;59:604-614; Guiggiant M, Classing P. Direct computation of Cauchy principal value integral in advanced boundary elements. Int J Numer Meth Engng 1987;24:1711-1720. Guiggiani M, Gigante A. Ageneral algorithm for multidimensional Cauchy principal value integrals in the boundary element method.