| 講演要旨： |
We first give an overview on topological optimization. We will show that in topological optimization, unknown domains are defined implicitly by a level set function:
- The level set function is the material density (up to an additive constant) for the topological optimization via the homogenization theory (N. Kikuchi, M. Bendsoe, G. Allaire, …)
- The built-in level set function for the level set method (Osher, Santosa, Sethian, Allaire, …)
- The topological gradient itself is a level set function when topological gradient method is considered.
The last method has, in addition, a fundamental property: at convergence, the positiveness of the topological gradient is a necessary and sufficient local optimality condition.
We will focus this talk on the basic concepts of topological gradient, the related algorithms, and its applications in shape optimal design and inverse problems.
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