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Inverse point source location with the Helmholtz equation on a bounded domain

Author

Listed:
  • Konstantin Pieper

    (Florida State University
    Oak Ridge National Laboratory)

  • Bao Quoc Tang

    (University of Graz)

  • Philip Trautmann

    (University of Graz)

  • Daniel Walter

    (Technical University of Munich Center for Mathematical Sciences, M17)

Abstract

The problem of recovering acoustic sources, more specifically monopoles, from point-wise measurements of the corresponding acoustic pressure at a limited number of frequencies is addressed. To this purpose, a family of sparse optimization problems in measure space in combination with the Helmholtz equation on a bounded domain is considered. A weighted norm with unbounded weight near the observation points is incorporated into the formulation. Optimality conditions and conditions for recovery in the small noise case are discussed, which motivates concrete choices of the weight. The numerical realization is based on an accelerated conditional gradient method in measure space and a finite element discretization.

Suggested Citation

  • Konstantin Pieper & Bao Quoc Tang & Philip Trautmann & Daniel Walter, 2020. "Inverse point source location with the Helmholtz equation on a bounded domain," Computational Optimization and Applications, Springer, vol. 77(1), pages 213-249, September.
    • Handle: RePEc:spr:coopap:v:77:y:2020:i:1:d:10.1007_s10589-020-00205-y
    DOI: 10.1007/s10589-020-00205-y
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    Cited by:

    1. Dimitrios S. Lazaridis & Nikolaos L. Tsitsas, 2023. "Detecting Line Sources inside Cylinders by Analytical Algorithms," Mathematics, MDPI, vol. 11(13), pages 1-14, June.

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