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PDE実解析研究会
過去の記録 ～03/19｜次回の予定｜今後の予定 03/20～
| 開催情報 | 火曜日 10:30～11:30 数理科学研究科棟(駒場) 056号室 |
|---|---|
| 担当者 | 儀我美一、石毛和弘、三竹大寿、米田剛 |
| セミナーURL | https://www.math.sci.hokudai.ac.jp/coe/sympo/pde_ra/ |
| 目的 | 首都圏の偏微分方程式、実解析の研究をさらに活発にするために本研究会を東大で開催いたします。 偏微分方程式研究者と実解析研究者の討論がより日常的になることを目指しています。 そのため、講演がその分野の概観をもわかるような形になるよう配慮いたします。 また講演者との1対1の討論がしやすいように講演は火曜の午前とし、午後に討論用の場所を用意いたします。 この研究会を通して皆様に気楽に東大を訪問していただければ幸いです。 北海道大学のHPには、第1回(2004年9月29日)～第38回(2008年10月15日)の情報が掲載されております。 |
2019年11月26日(火)
10:30-11:30 数理科学研究科棟(駒場) 056号室
Dan Tiba 氏 (Institute of Mathematics of the Romanian Academy / Academy of Romanian Scientists)
A Hamiltonian approach with penalization in shape and topology optimization (English)
Dan Tiba 氏 (Institute of Mathematics of the Romanian Academy / Academy of Romanian Scientists)
A Hamiltonian approach with penalization in shape and topology optimization (English)
[ 講演概要 ]
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.
