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PDE Real Analysis Seminar
Seminar information archive ～04/17｜Next seminar｜Future seminars 04/18～
| Date, time & place | Tuesday 10:30 - 11:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
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2019/11/26
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Dan Tiba (Institute of Mathematics of the Romanian Academy / Academy of Romanian Scientists)
A Hamiltonian approach with penalization in shape and topology optimization (English)
Dan Tiba (Institute of Mathematics of the Romanian Academy / Academy of Romanian Scientists)
A Hamiltonian approach with penalization in shape and topology optimization (English)
[ Abstract ]
General geometric optimization problems involve boundary and topology variations. This research area has already almost fifty years of history and very rich applications in computer aided industrial design. Recently, a new representation of manifolds, using iterated Hamiltonian systems, has been introduced in arbitrary dimension and co-dimension. Combining this technique with a penalization procedure for the boundary conditions, a comprehensive approximation method for optimal design problems associated to elliptic equations, is obtained. It reduces shape and topology optimization problems to optimal control problems, in a general setting. It enters the category of fixed domain methods in variable/unknown domain problems and it has consistent advantages at the computational level. It allows "free" changes of the boundary and/or the topology, during the iterations. This methodology, based on iterated Hamiltonian systems and implicit parametrizations, was also applied to nonlinear programming problems in arbitrary dimension.
General geometric optimization problems involve boundary and topology variations. This research area has already almost fifty years of history and very rich applications in computer aided industrial design. Recently, a new representation of manifolds, using iterated Hamiltonian systems, has been introduced in arbitrary dimension and co-dimension. Combining this technique with a penalization procedure for the boundary conditions, a comprehensive approximation method for optimal design problems associated to elliptic equations, is obtained. It reduces shape and topology optimization problems to optimal control problems, in a general setting. It enters the category of fixed domain methods in variable/unknown domain problems and it has consistent advantages at the computational level. It allows "free" changes of the boundary and/or the topology, during the iterations. This methodology, based on iterated Hamiltonian systems and implicit parametrizations, was also applied to nonlinear programming problems in arbitrary dimension.
