Newton Method in 3-Dimensional Shape Optimization Problems
Abstract
Our goal is to introduce a Newton method to compute the stationary points of a total energy with respect to the shape. We produce a precise description of the second order shape derivative which is given by a symmetrical boundary integral operator, useful for numerical calculations. We apply this method to a particular shape optimization problem, the electromagnetic casting problem. The algorithm to compute the shape gradient and the shape Hessian is adapted to a MIMD computer with distributed memory using M.P.I. message passing interface.