Abstract
In this paper, we consider the geodesic tube characterization using a Galerkin-Level Set strategy. The first section is devoted to the analysis of a geodesic tube construction between two sets through the definition of the shape metric. In the second section, we define the Galerkin-Level Set strategy in shape analysis. This new variational formulation associated to a Hilbert space metric for shape identification problem consists in parameterizing the level set function in a finite dimensional subspace spanned by linear independent functions. Consequently, this method is more focused on topological changes than on high accuracy for the boundary evaluation as in a traditional level set formulation. In the third section, we use the Galerkin-Level Set formulation applied to a geodesic tube construction between two sets, through the calculus of the shape derivative of the normal speed. Finally, this geodesic tube construction is validated by a numerical experiment.
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Blanchard, L., Zolésio, JP. (2009). Galerkin Strategy for Level Set Shape Analysis: Application to Geodesic Tube. In: Korytowski, A., Malanowski, K., Mitkowski, W., Szymkat, M. (eds) System Modeling and Optimization. CSMO 2007. IFIP Advances in Information and Communication Technology, vol 312. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04802-9_8
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DOI: https://doi.org/10.1007/978-3-642-04802-9_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04801-2
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