Differentiability of strongly singular and hypersingular boundary integral formulations with respect to boundary perturbations

摘要

In this paper, we establish that the Lagrangian- type material differentiation formulas, that allow to ex- press the first-order derivative of a (regular0 surface in- tegral with respect to a geometrical domain perturbation, still hold true for the strongly singular and hypersingular surface integral usually encountered in boundary integral formulations. As a consequence, this work supports pre- vious investigations where shape sensitivities are com- puted using the so-called direct differentiation approach in connection with singular boundary integral equation for- mulations.