Shape optimization using a matrix - free

In tackling the problem of minimizing the deformation of a loaded structure, by varying the shape of the original structure, past second order optimization efforts have focused on general Newton techniques like the Davidon-Fletcher-Powell (DFP) update formula and the BroydenFletcher-Goldfarb-Shanno (BFGS) formula which iteratively build estimates of the structure's Hessian. This thesis bypasses the above mentioned need for explicit estimation of the Hessian by exploiting the inherent symmetry of the problem and, thus, is able to use a matrix-free Krylov subspace method like GMRES as the Newton solver. In addition to this computationally efficient solver, the thesis algorithm also uses stochastic perturbations to escape from its Newton stalls. Results will be presented to illustrate the algorithm's convergence. Thesis supervisor: Jacob K. White Title: Assoc. Prof., Dept. of E.E.C.S.