Optimal control (motion planning) of the free interface in classical two-phase Stefan problems is considered. The evolution of the free interface is modeled by a level set function. The first-order optimality system is derived on a formal basis. It provides gradient information based on the adjoint temperature and adjoint level set function. Suitable discretization schemes for the forward and adjoint systems are described. Numerical examples verify the correctness and flexibility of the proposed scheme.:1 Introduction
2 Model Equations
3 The Optimal Control Problem and Optimality Conditions
4 Discretization of the Forward and Adjoint Systems
5 Numerical Results
6 Discussion and Conclusion
A Formal Derivation of the Optimality Conditions
B Transport Theorems and Shape Calculus
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:19398 |
| Date | January 2010 |
| Creators | Bernauer, Martin K., Herzog, Roland |
| Publisher | Technische Universität Chemnitz |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:preprint, info:eu-repo/semantics/preprint, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
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