Optimization loops for shape and error control

Alain Dervieux Francois Courty Tristan Roy Mariano Vazquez Bruno Koobus

Book chapter, also INRIA report (44 pages)

Abstract: The power and versatility of the so-called adjoint methods used in optimization problems is addressed by presenting a combined methodology: shape and error control. In a first part we describe novel technologies for solving shape design problems: constrained optimum formulation with adjoint, one-shot optimization algorithms and multi-level optimization preconditioning. The application to a shape design problem related to sonic boom minimization is reported. In a second part, after some remarks on mesh adaptation, we examine the problem of formulating mesh adaptation in terms of an optimization problem, presenting some applications to interpolation and to Partial Differential Equations. The implications of the proposed method become clear: by combining together both ideas cost effective methods can be developed where the optimization loops involve both shape optimization, to improve an aerodynamic design, and mesh adaptivity, to cope with the difficulties of the CFD problem involved.

Keywords: Partial Differential Equations, Finite element method, Mesh adaptivity, Multilevel optimization, CFD, Optimal shape design

Full text (pdf)


@incollection{DCRVK06,
   author = {Dervieux, A. and Courty, F. and Roy, T. and V{\'a}zquez, M. and Koobus, B.},
   title ={Optimization loops for shape and error control},
   booktitle = {Verification and validation methods for challenging multiphysics problems},
   editor = {{B. Bugeda et al.}},
   publisher = {CIMNE, Barcelona},
   note={Extended version in INRIA Research Report 5413},
   year = 2006
}