A unified discrete-continuous sensitivity analysis method for shape optimization
2010 (English)In: Applied and numerical PDEs: scientific computing in simulation, optimization and control and its multiphysics applications / [ed] W. Fitzgibbon, Y.A. Kuznetsov, P. Neittaanmäki, J. Periaux, O. Pironneau, Springer, 2010, 25-39 p.Conference paper (Refereed)
Boundary shape optimization problems for systems governed by partial differential equations involve a calculus of variation with respect to boundary modifications. As typically presented in the literature, the first-order necessary conditions of optimality are derived in a quite different manner for the problems before and after discretization, and the final directional-derivative expressions look very different. However, a systematic use of the material-derivative concept allows a unified treatment of the cases before and after discretization. The final expression when performing such a derivation includes the classical before-discretization (“continuous”) expression, which contains objects solely restricted to the design boundary, plus a number of “correction” terms that involve field variables inside the domain. Some or all of the correction terms vanish when the associated state and adjoint variables are smooth enough.
Place, publisher, year, edition, pages
Springer, 2010. 25-39 p.
, Computational methods in applied sciences, ISSN 1871-3033 ; 15
Computer and Information Science
IdentifiersURN: urn:nbn:se:umu:diva-40316DOI: 10.1007/978-90-481-3239-3_4ISBN: 978-90-481-3238-6OAI: oai:DiVA.org:umu-40316DiVA: diva2:399283
Conference on Scientific Computing in Simulation, Optimization and Control and its Multidisciplinary Applications