A second-order method for structural shape optimization with the level-set method

Abstract eng:
In topology optimization, there are two formalisms for computing derivatives : one where the variations of the shape are given by a transformation by a diffeomorphism, and another one where they are described by the flow of a regular vector field. In the level-set approach, a shape is represented by the negative domain of a scalar function, and its variations are performed trough a transport equation, namely the Hamilton-Jacobi equation. The present work focuses on computing derivatives in that context. The knowledge of the second order shape derivatives gives also different indications on numerical aspects, that we illustrate with a few examples at the end.

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