Galerkin Boundary Integral Method for Evaluating Surface Derivatives

A Galerkin boundary integral procedure for evaluating the complete derivative, e.g., potential gradient or stress tensor, is presented. The expressions for these boundary derivatives involve hypersingular kernels, and the advantage of the Galerkin approach is that the integrals exist when a continuous surface interpolation is employed. As a consequence, nodal derivative values, at smooth surface points or at corners, can be obtained directly. This method is applied to the problem of electromigration-driven void dynamics in thin lm aluminum interconnects. In this application, the tangential component of the electric eld on the boundary is required to compute the ux of atoms at the void surface.