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

被引：9

作者：

Pieper, Konstantin ^{[1
,2
]}

Bao Quoc Tang ^{[3
]}

Trautmann, Philip ^{[3
]}

Walter, Daniel ^{[4
]}

机构：

[1] Florida State Univ, Dept Sci Comp, 400 Dirac Sci Lib, Tallahassee, FL 32306 USA

[2] Oak Ridge Natl Lab, Comp Sci & Math Div, One Bethel Valley Rd,POB 2008,MS-6211, Oak Ridge, TN 37831 USA

[3] Karl Franzens Univ Graz, Inst Math & Sci Comp, Heinrichstr 36, A-8010 Graz, Austria

[4] Tech Univ Munich, Ctr Math Sci, Ctr Math, M17,Boltzmannstr 3, D-85748 Munich, Germany

来源：

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS | 2020年 / 77卷 / 01期

基金：

奥地利科学基金会; 欧盟地平线“2020”;

关键词：

Inverse source location; Sparsity; Helmholtz equation; PDE-constrained optimization; DIRECTIONAL SPARSITY; SOURCE LOCALIZATION; CONVERGENCE-RATES; SPACES;

D O I：

10.1007/s10589-020-00205-y

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

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.

引用

页码：213 / 249

页数：37

共 40 条

[1]

[Anonymous], SERIES APPL MATH

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