Evaluation of the Hypersingular and Regularized Boundary Integral Equations for the Boundary Potential Gradients in 2D Field.

Abstract

This paper presents a new scheme for the evaluation of the hypersingular and regularized boundary integral equations for the boundary potential gradients. In the process of taking the limit of the exterior collocation point to an arbitrary point on the boundary, no interpolation function is employed and continuity of the potential gradients at the collocation point is taken into account strictly. The regularized boundary integral equation for the boundary potential gradients is also derived and applicability of the conventional C0 elements to the discretization of the hypersingular and regularized boundary integral equations is discussed. A new interpolation scheme that satisfies the C1 continuity of the potential at any point on the boundary is presented for the potential and the flux, and is effectiveness is demonstrated through a numerical example.