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A unified discrete-continuous sensitivity analysis method for shape optimization
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. (UMIT)ORCID-id: 0000-0003-0473-3263
2010 (Engelska)Ingår i: Applied and Numerical Partial Differential Equations: Scientific Computing in Simulation, Optimization and Control in a Multidisciplinary Context / [ed] W. Fitzgibbon, Y.A. Kuznetsov, P. Neittaanmäki, J. Periaux, O. Pironneau, Springer, 2010, s. 25-39Konferensbidrag, Publicerat paper (Refereegranskat)
Abstract [en]

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.

Ort, förlag, år, upplaga, sidor
Springer, 2010. s. 25-39
Serie
Computational methods in applied sciences, ISSN 1871-3033 ; 15
Nationell ämneskategori
Data- och informationsvetenskap
Identifikatorer
URN: urn:nbn:se:umu:diva-40316DOI: 10.1007/978-90-481-3239-3_4ISBN: 978-90-481-3238-6 (tryckt)ISBN: 978-90-481-3239-3 (digital)OAI: oai:DiVA.org:umu-40316DiVA, id: diva2:399283
Konferens
Conference on Scientific Computing in Simulation, Optimization and Control and its Multidisciplinary Applications
Tillgänglig från: 2011-02-21 Skapad: 2011-02-21 Senast uppdaterad: 2019-04-16Bibliografiskt granskad

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Berggren, Martin

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