Latest revision as of 11:01, 22 July 2019

Abstract

This work presents a new methodology base on the use adaptive mesh refinement (AMR) techniques in the context of shape optimization problems analyzed by the Finite Element Method. A suitable and very general technique for the parametrization of the optimization problem using B-splines to define the boundary is first presented. Then, mesh generation using the advancing front method, the estimation of error and the mesh refinement criterion are studied in the context of shape optimization problems. In particular, the sensitivities of the different ingredients ruling the problem (B-splines, finite element mesh, flow behavior, and error estimator) are studied in detail. The sensitivities of the finite element mesh and the error estimator allow their projection from one design to the next, thus leading to an “a priori knowledge” of the error distribution on the new design without the need of any additional analysis. This information allows to build up a finite element mesh for the new design with a specified and controlled level error. The robustness and reliability of the proposed methodology is checked out with some 2D application examples.