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

Konstantin Pieper; Bao Quoc Tang; Philip Trautmann; Daniel Walter

doi:10.1007/s10589-020-00205-y

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

Konstantin Pieper, Bao Quoc Tang, Philip Trautmann, Daniel Walter

Data Analysis and Machine Learning

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

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.

Original language	English
Pages (from-to)	213-249
Number of pages	37
Journal	Computational Optimization and Applications
Volume	77
Issue number	1
DOIs	https://doi.org/10.1007/s10589-020-00205-y
State	Published - Sep 1 2020

Bibliographical note

Publisher Copyright:
© 2020, This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply.

Keywords

Helmholtz equation
Inverse source location
PDE-constrained optimization
Sparsity

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10.1007/s10589-020-00205-y

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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.",

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AU - Trautmann, Philip

AU - Walter, Daniel

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AB - 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.

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KW - Sparsity

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

Abstract

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Keywords

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