Differentiability of strongly singular BIE formulations with respect to boundary perturbations

Abstract

In e.g. shape design analysis, inverse problems or fracture mechanics, one is often faced with the need of computing sensitivities of functional or physical variables with respect to perturbations of the shape of the geometrical domain Ω, under study. This goal is often achieved using analytical material differentiation followed by discretization, in the form of either the adjoint variable approach or the direct differentiation. In a BEM context, the latter is based on material differentiation of the relevant governing BIE formulation, so that a governing BIE for the field sensitivities is available.