The One-Dimensional Inverse Problem in Photoacoustics. Numerical Testing

D. Langemann, A. S. Mikhaylov, V. S. Mikhaylov

Research output

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.

Original languageEnglish
Pages (from-to)726–733
JournalJournal of Mathematical Sciences (United States)
Volume243
Issue number5
Early online date8 Nov 2019
DOIs
Publication statusPublished - 1 Dec 2019

Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Applied Mathematics

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