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I'm learning about the level set method in shape optimization I've only read very introductory texts on the method. However, the texts have spoken only about that the level set method (or specifically the level set function) "evolves" through different shapes,

what I've not been able to find out is,

  • How is level set method used to find optimality?
mavavilj
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  • In my experience "level set method' refers to a technique where a profile is identified as a level set of some function and then evolves. We then track the evolution of the profile by instead tracking the evolution of the function. – Ian Aug 12 '16 at 13:59
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    Anyway, ultimately the level set method is a way of numerically describing some given dynamics of a shape. It does not decide what those dynamics are, nor is it the only way to track the dynamics in the first place. (The main reason why it is well-liked is because it handles topological changes, like a loop splitting into two loops, very easily.) So you're not going to find how it works its way towards an optimal configuration by reading level set method literature. You need to figure out what dynamics you want to use and then figure out how that can be implemented into a level set method. – Ian Aug 12 '16 at 14:10
  • @Winther https://en.wikipedia.org/wiki/Level_set_method – mavavilj Aug 12 '16 at 14:18
  • @Ian I'm looking for a general description on how to use the level set method in the context of (shape) optimization. I've only seen descriptions of the level set method, but not how it's used in the context of optimization, e.g. how does it find the optimum. And for example, what's the objective function like when using level set method. – mavavilj Aug 15 '16 at 08:39
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    I understand what you're asking for. What I'm saying is that your question is not well-defined, because the level set method is not actually an optimization technique. It is a way of numerically resolving the dynamics of shapes. So in shape optimization, you need to choose some dynamics that you expect to flow to your optimum shape, and then simulate those dynamics using the level set method. – Ian Aug 15 '16 at 13:18
  • @Ian Is this better? – mavavilj Aug 17 '16 at 06:48

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