An efficient method to evaluate hypersingular and supersingular integrals in boundary integral equations analysis
An efficient algorithm is employed to evaluate 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. The substractions involve to multiple derivatives of analytical kernels and the additions require some manipulation to separate the remaining regular terms from singular ones. The regular terms are computed numerically. Three examples on numerical evaluation of singular boundary integrals are presented to show the efficiency and accuracy of the algorithm. In this respect, strongly singular and hypersingular integrals of the potential flow problem are considered.
hypersingular and supersingular integrals
scientific article; zbMATH DE number 1389926