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

Konstantin Pieper (), Bao Quoc Tang (), Philip Trautmann () and Daniel Walter ()
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Konstantin Pieper: Florida State University
Bao Quoc Tang: University of Graz
Philip Trautmann: University of Graz
Daniel Walter: Technical University of Munich Center for Mathematical Sciences, M17

Computational Optimization and Applications, 2020, vol. 77, issue 1, No 8, 213-249

Abstract: 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.

Keywords: Inverse source location; Sparsity; Helmholtz equation; PDE-constrained optimization; 35R30; 35Q93; 49J20; 90C46 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10589-020-00205-y

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