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
}