Pontryagin approximations for optimal design
2006 (English)Licentiate thesis, comprehensive summary (Other scientific)
This thesis concerns the approximation of optimally controlled partial differential equations for applications in optimal design and reconstruction. Such optimal control problems are often ill-posed and need to be regularized to obtain good approximations. We here use the theory of the corresponding Hamilton-Jacobi-Bellman equations to construct regularizations and derive error estimates for optimal design problems. The constructed Pontryagin method is a simple and general method where the first, analytical, step is to regularize the Hamiltonian. Next its stationary Hamiltonian system, a nonlinear partial differential equation, is computed efficiently with the Newton method using a sparse Jacobian. An error estimate for the difference between exact and approximate objective functions is derived, depending only on the difference of the Hamiltonian and its finite dimensional regularization along the solution path and its L2 projection, i.e. not on the difference of the exact and approximate solutions to the Hamiltonian systems. In the thesis we present solutions to applications such as optimal design and reconstruction of conducting materials and elastic structures.
Place, publisher, year, edition, pages
Stockholm: KTH , 2006. , 16 p.
Trita-CSC-A, ISSN 1653-5723 ; 2006:11
Topology Optimization, Inverse Problems, Hamilton-Jacobi, Regularization, Error Estimates, Impedance Tomography
IdentifiersURN: urn:nbn:se:kth:diva-4089ISBN: 91-7178-417-9OAI: oai:DiVA.org:kth-4089DiVA: diva2:10677
2006-09-08, D41, Huvudbyggnaden, Lindstedtsvägen 17 1tr, Stockholm, 10:00
QC 201011102006-08-292006-08-292010-11-10Bibliographically approved
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