Galerkin boundary integral method for evaluating surface derivatives

Abstract

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 electromigrationdriven void dynamics in thin ®lm aluminum interconnects. In this application, the tangential component of the electric ®eld on the boundary is required to compute thē ux of atoms at the void surface.

Current-Induced Stabilization of Surface Morphology in Stressed Solids

“…(1)-(3). In the simulations, the electrostatic potential and elastic displacement u fields are computed through a Galerkin boundary-integral method [16] coupled self consistently with the evolving surface morphology expressed in a local coordinate system (ŝ,n) and using an adaptive mesh; the surface propagation is monitored by time stepping @u n =@t ÿ @J s =@s, i.e., Eq. (3) expressed in the local surface coordinates, according to the interface tracking method of Refs.…”

Kinetically Driven Growth Instability in Stressed Solids

“…Given a set of tractions and displacements as boundary conditions, and the elastic constants of the solid, the remaining unknown surface displacements and tractions are obtained through solving boundary integral equations. The full stress tensor on the boundary is then computed using the formulation presented in [8].…”

Evaluation of supersingular integrals: second‐order boundary derivatives

“…However, to extend this interpolation to the boundary flux, second-order derivatives are obviously necessary. Moreover, it is hoped that applications that require a non-linear iteration, such as contact problems [26] or shape optimization [27], can effectively exploit the availability of this higher order derivative information.…”