2012 Fiscal Year Final Research Report
Regularization solutions to shape and topology optimization problems of domains for elliptic boundary value problems
| Project/Area Number |
20540113
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Nagoya University |
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Principal Investigator |
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| Project Period (FY) |
2008 – 2012
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| Keywords | 応用数学 / 関数解析学 / 数理工学 / 設計工学 / 境界値問題 / 最適化 |
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| Research Abstract |
Optimization problem of shape of domain in which an elastic body or a flow field is defined is called the shape optimization problem. Here, a deformation field of an elastic body for example is given as a solution of a boundary value problem of a partial differential equation (main problem). Cost functions are defined as functionals of the domain in which the main problem is defined and the solution of the main problem. In the present research, an admissible set of a design variable representing domain variation was defined. Based on the definition, an evaluation method of the shape derivatives of cost functions and a gradient method (H1 gradient method) for reshaping were presented. Moreover, it was confirmed that the domain sequence obtained by the method remains in the admissible set.
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