Sensor placement via large deviations in the eikonal equation

Ftouhi I, Zuazua Iriondo E (2026)

Publication Language: English

Publication Status: Published

Publication Type: Journal article, Original article

Future Publication Type: Journal article

Publication year: 2026

Journal

Arabian Journal of Mathematics SpringerOpen

Publisher: Arabian Journal of Mathematics

DOI: 10.1007/s40065-026-00628-1

Open Access Link: https://doi.org/10.48550/arXiv.2508.21469

Abstract

In 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.

Authors with CRIS profile

Ilias Ftouhi Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur) Enrique Zuazua Iriondo Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

How to cite

APA:

Ftouhi, I., & Zuazua Iriondo, E. (2026). Sensor placement via large deviations in the eikonal equation. Arabian Journal of Mathematics. https://doi.org/10.1007/s40065-026-00628-1

MLA:

Ftouhi, Ilias, and Enrique Zuazua Iriondo. "Sensor placement via large deviations in the eikonal equation." Arabian Journal of Mathematics (2026).

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