A General New Algorithm for Regulaization of Singular Integrals in Three-Dimensional Boundary Elemnts

In this paper an algorithm is presented for the regularization of singular integrals with any degrees of singularity, which may be employed in all three-dimensional problems analyzed by Boundary Elements. The integrals in Boundary Integrals Equations are inherently singular. For example, one can mention the integrals confronted in potential problems to evaluate the flow or the gradient of the flow or the integrals employed to determine the stress or the deformation in elastic problems. Having only the numerator functions and their derivatives derived either explicitly or implicitly, this algorithm may be employed to evaluate the strongly, hyper or supersingular integrals with a satisfactory of accuracy. To regularize the integrals, some functions are either added or subtracted successively so as to differentiate the singular and nonsingular terms. Three examples with their numerical solutions are included which show the efficiency and the accuracy of the proposed algorithm.