Accuracy of desingularized boundary integral equations for plane exterior potential problems

Abstract

In this article, computational results from boundary integral equations and their normal derivatives for the same test cases are compared. Both kinds of formulations are desingularized on their real boundary. The test cases are chosen as a uniform flow past a circular cylinder for both the Dirichlet and Neumann problems. The results indicate that the desingularized method for the standard boundary integral equation has a much larger convergence speed than the desingularized method for the hypersingular boundary integral equation. When uniform nodes are distributed on a circle, for the standard boundary integral formulation the accuracies in the test cases reach the computer limit of 10 −15 in the Neumann problems; and O(N −3) in the Dirichlet problems. However, for the desingularized hypersingular boundary integral formulation, the convergence speeds drop to only O(N −1) in both the Neumann and Dirichlet problems.