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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)


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Laurain, Antoine
Total Authors: 1
Document type: Journal article
Source: SIAM JOURNAL ON MATHEMATICAL ANALYSIS; v. 50, n. 4, p. 4327-4370, 2018.
Web of Science Citations: 0

In the standard level set method, the evolution of the level set function is determined by solving the Hamilton-Jacobi equation, which is derived by considering smooth boundary perturbations of the zero level set. The converse approach is to consider smooth perturbations of the level set function and to find the corresponding perturbations of the zero level set. In this paper, we show how the latter approach allows us to analyze not only smooth perturbations of the level set, but also singular perturbations in the form of topological changes. In particular, it is an appropriate framework for analyzing splitting and merging of components. In this way, we establish a link between the Gateaux derivative with respect to the level set function and the shape and topological derivatives. In the smooth case, we determine a transformation of the zero level set, defined as the flow of a vector field, which corresponds to the perturbation of the level set function. For topological changes, we study the cases of splitting or merging and creation of an island or a hole, and provide asymptotic expansions of volume and boundary integrals. (AU)

FAPESP's process: 16/24776-6 - Shape optimization and free boundary problems
Grantee:Antoine Laurain
Support type: Regular Research Grants