Sensor placement via large deviations in the Eikonal equation

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dc.contributor.authorFtouhi, Ilias
dc.contributor.authorZuazua, Enrique
dc.date.accessioned2026-08-19T06:11:18Z
dc.date.available2026-08-19T06:11:18Z
dc.date.issued2026-03-11
dc.date.updated2026-08-19T06:11:18Z
dc.description.abstractIn this work, we address the problem of optimally placing a finite number of sensors within a given region so as to minimize the mean or maximal distance to the points of the domain. To tackle this natural geometric performance criterion, formulated in terms of distance functions, we combine tools from geometric analysis with a classical result of Varadhan (Commun Pure Appl Math 20:431–455, 1967), which provides an efficient approximation of the distance function via the solution of a simple elliptic PDE. The effectiveness of the proposed approach is demonstrated through illustrative numerical simulations.en
dc.description.sponsorshipThe work of I. Ftouhi was supported by the Alexander von Humboldt Foundation via a Postdoctoral fellowship and also partially supported by the French National Research Agency under the France 2030 program, grant ANR-23-EXES-0005 (project Gardener/MASRA), and by the Occitanie Region. The work of E. Zuazua was funded by the Alexander von Humboldt-Professorship program, the ERC Advanced Grant CoDeFeL, the Grants PID2020-112617GB-C22 KiLearn and TED2021-131390B-I00-DasEl of INECO and PID2023-146872OB-I00-DyCMaMod of MICIU (Spain), the European Union’s Horizon Europe MSCA project ModConFlex, the Transregio 154 Project “Mathematical Modelling, Simulation and Optimization Using the Example of Gas Networks” of the DFG, the AFOSR 24IOE027 project, and the Madrid Government - UAM Agreement for the Excellence of the University Research Staff in the context of the V PRICIT (Regional Programme of Research and Technological Innovation)en
dc.identifier.citationFtouhi, I., & Zuazua, E. (2026). Sensor placement via large deviations in the Eikonal equation. Arabian Journal of Mathematics, 15(2), 1137-1148. https://doi.org/10.1007/S40065-026-00628-1
dc.identifier.doi10.1007/S40065-026-00628-1
dc.identifier.eissn2193-5351
dc.identifier.issn2193-5343
dc.identifier.urihttps://hdl.handle.net/20.500.14454/6510
dc.language.isoeng
dc.publisherSpringer Science and Business Media Deutschland GmbH
dc.rights© The Author(s) 2026
dc.titleSensor placement via large deviations in the Eikonal equationen
dc.typejournal article
dcterms.accessRightsopen access
oaire.citation.endPage1148
oaire.citation.issue2
oaire.citation.startPage1137
oaire.citation.titleArabian Journal of Mathematics
oaire.citation.volume15
oaire.licenseConditionhttps://creativecommons.org/licenses/by/4.0/
oaire.versionVoR
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