|Appears in Collections:||Computing Science and Mathematics Journal Articles|
|Peer Review Status:||Refereed|
|Title:||Construction of Artificial Point Sources for a Linear Wave Equation in Unknown Medium|
|Keywords:||Focusing of waves|
|Citation:||Kirpichnikova A, Korpela J, Lassas M & Oksanen L (2021) Construction of Artificial Point Sources for a Linear Wave Equation in Unknown Medium. SIAM Journal on Control and Optimization, 59 (5), pp. 3737-3761. https://doi.org/10.1137/20M136904X|
|Abstract:||We study the wave equation on a bounded domain of $\mathbb R^m$ and on a compact Riemannian manifold $M$ with boundary. We assume that the coefficients of the wave equation are unknown but that we are given the hyperbolic Neumann-to-Dirichlet map $\Lambda$ that corresponds to the physical measurements on the boundary. Using the knowledge of $\Lambda$ we construct a sequence of Neumann boundary values so that at a time $T$ the corresponding waves converge to zero while the time derivative of the waves converge to a delta distribution. The limit of such waves can be considered as a wave produced by an artificial point source. The convergence of the wave takes place in the function spaces naturally related to the energy of the wave. We apply the results for inverse problems and demonstrate the focusing of the waves numerically in the 1-dimensional case.|
|Rights:||Publisher policy allows this work to be made available in this repository. Published in SIAM Journal on Control and Optimization by the Society for Industrial and Applied Mathematics. The original publication will be available at: https://www.siam.org/publications/journals/siam-journal-on-control-and-optimization-sicon|
|Artificial_point_sources_latest_August_2021.pdf||Fulltext - Accepted Version||955.72 kB||Adobe PDF||View/Open|
This item is protected by original copyright
Items in the Repository are protected by copyright, with all rights reserved, unless otherwise indicated.
The metadata of the records in the Repository are available under the CC0 public domain dedication: No Rights Reserved https://creativecommons.org/publicdomain/zero/1.0/
If you believe that any material held in STORRE infringes copyright, please contact firstname.lastname@example.org providing details and we will remove the Work from public display in STORRE and investigate your claim.