Ftouhi I, Zuazua Iriondo E (2023)
Publication Language: English
Publication Status: Accepted
Publication Type: Journal article, Original article
Future Publication Type: Journal article
Publication year: 2023
Publisher: Journal of Geometric Analysis (JGEA)
Book Volume: 33
Journal Issue: 253
URI: https://link.springer.com/article/10.1007/s12220-023-01301-1
DOI: 10.1007/s12220-023-01301-1
Open Access Link: https://link.springer.com/article/10.1007/s12220-023-01301-1
We consider a convex set Ω and look for the optimal convex sensor ω ⊂ Ω of a given measure that minimizes the maximal distance to the points of Ω. This problem can be written as follows
inf{dH(ω,Ω) | |ω|= c and ω ⊂ Ω},
where c ∈ (0, |Ω|), dH being the Hausdorff distance.
We show that the parametrization via the support functions allows us to formulate the geometric optimal shape design problem as an analytic one. By proving a judicious equivalence result, the shape optimization problem is approximated by a simpler minimization of a quadratic function under linear constraints. We then present some numerical results and qualitative properties of the optimal sensors and exhibit an unexpected symmetry breaking phenomenon.
APA:
Ftouhi, I., & Zuazua Iriondo, E. (2023). Optimal design of sensors via geometric criteria. Journal of Geometric Analysis, 33(253). https://doi.org/10.1007/s12220-023-01301-1
MLA:
Ftouhi, Ilias, and Enrique Zuazua Iriondo. "Optimal design of sensors via geometric criteria." Journal of Geometric Analysis 33.253 (2023).
BibTeX: Download