Obstacle identification using the TRAC algorithm with a second-order ABC

Tomer Levin, Eli Turkel, Dan Givoli

Research output: Contribution to journalArticlepeer-review


We consider obstacle identification using wave propagation. In such problems, one wants to find the location, shape, and size of an unknown obstacle from given measurements. We propose an algorithm for the identification task based on a time-reversed absorbing condition (TRAC) technique. Here, we apply the TRAC method to time-dependent linear acoustics, although our methodology can be applied to other wave-related problems as well, such as elastodynamics. There are two main contributions of our identification algorithm. The first contribution is the development of a robust and effective method for obstacle identification. While the original paper presented criteria for accepting or rejecting regions that enclose the obstacle, we use these criteria to develop an algorithm that automatically identifies the location of the obstacle. The second contribution is the utilization of an improved absorbing boundary condition (ABC) for the identification. We use the second-order Engquist-Majda ABC, and we implement it with a finite element scheme. To our knowledge, this is the first time that the second-order Engquist-Majda ABC is employed with the finite element method, as this boundary condition does not naturally fit in finite element schemes in its original form. Numerical experiments for the algorithms are presented.

Original languageEnglish
Pages (from-to)61-92
Number of pages32
JournalInternational Journal for Numerical Methods in Engineering
Issue number2
StatePublished - 13 Apr 2019


  • TRAC
  • absorbing boundary conditions
  • finite element method
  • inverse problems
  • obstacle identification
  • time reversal

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics


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