Email this article The One-Dimensional Inverse Problem in Photoacoustics. Numerical Testing
- Authors: Langemann D.1, Mikhaylov A.S.2, Mikhaylov V.S.2
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Affiliations:
- Technische Universität Braunschweig, Inst. Computational Mathematics, AG PDE
- St. Petersburg Department of the V. A. Steklov Institute of Mathematics, the Russian Academy of Sciences, St. Petersburg State University
- Issue: Vol 243, No 5 (2019)
- Pages: 726-733
- Section: Article
- URL: https://ogarev-online.ru/1072-3374/article/view/243149
- DOI: https://doi.org/10.1007/s10958-019-04574-6
- ID: 243149
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Abstract
The problem of reconstruction of the Cauchy data for the wave equation in ℝ1 from the measurements of its solution on the boundary of a finite interval is considered. This is a one-dimensional model for the multidimensional problem of photoacoustics, which was studied previously. The method was adapted and simplified for the one-dimensional situation. The results of numerical testing to see the rate of convergence and the stability of the procedure are given. Some hints are also given on how the procedure of reconstruction can be simplified in the 2d and 3d cases.
About the authors
D. Langemann
Technische Universität Braunschweig, Inst. Computational Mathematics, AG PDE
Author for correspondence.
Email: d.langemann@tu-bs.de
Germany, Braunschweig
A. S. Mikhaylov
St. Petersburg Department of the V. A. Steklov Institute of Mathematics, the Russian Academy of Sciences, St. Petersburg State University
Email: d.langemann@tu-bs.de
Russian Federation, St. Petersburg
V. S. Mikhaylov
St. Petersburg Department of the V. A. Steklov Institute of Mathematics, the Russian Academy of Sciences, St. Petersburg State University
Email: d.langemann@tu-bs.de
Russian Federation, St. Petersburg
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