PDE Real Analysis Seminar

Seminar information archive ~12/10Next seminarFuture seminars 12/11~

Date, time & place Tuesday 10:30 - 11:30 056Room #056 (Graduate School of Math. Sci. Bldg.)


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)
[ 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.