Convergent algorithm based on Carleman estimates for the recovery of a potential in the wave equation.

Abstract : This article develops the numerical and theoretical study of the reconstruction algorithm of a potential in a wave equation from boundary measurements, using a cost functional built on weighted energy terms coming from a Carleman estimate. More precisely, this inverse problem for the wave equation consists in the determination of an unknown time-independent potential from a single measurement of the Neumann derivative of the solution on a part of the boundary. While its uniqueness and stability properties are already well known and studied, a constructive and globally convergent algorithm based on Carleman estimates for the wave operator was recently proposed in [BdBE13]. However, the numerical implementation of this strategy still presents several challenges, that we propose to address here.
Document type :
Journal articles
Complete list of metadatas

Cited literature [24 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01352772
Contributor : Maya de Buhan <>
Submitted on : Tuesday, August 9, 2016 - 3:38:23 PM
Last modification on : Tuesday, January 28, 2020 - 8:42:08 PM
Long-term archiving on: Thursday, November 10, 2016 - 10:21:06 AM

File

LBMdBSE.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01352772, version 1

Citation

Lucie Baudouin, Maya de Buhan, Sylvain Ervedoza. Convergent algorithm based on Carleman estimates for the recovery of a potential in the wave equation.. SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2017, 55 (4), pp.1578-1613. ⟨hal-01352772⟩

Share

Metrics

Record views

452

Files downloads

304