Carlos Alves et al 2009 Inverse Problems 25 055005 doi:10.1088/0266-5611/25/5/055005
Carlos Alves1, Rainer Kress2 and Pedro Serranho3
Show affiliationsWe propose two methods for solving an inverse source problem for time-harmonic acoustic waves. Based on the reciprocity gap principle a nonlinear equation is presented for the locations and intensities of the point sources that can be solved via Newton iterations. To provide an initial guess for this iteration we suggest a range test algorithm for approximating the source locations. We give a mathematical foundation for the range test and exhibit its feasibility in connection with the iteration method by some numerical examples.
43.25.Jh Reflection, refraction, interference, scattering, and diffraction of intense sound waves
02.60.Gf Algorithms for functional approximation
02.60.Lj Ordinary and partial differential equations; boundary value problems
35R30 Inverse problems (undetermined coefficients, etc.) for PDE
78A46 Inverse scattering problems
35J05 Laplace equation, reduced wave equation (Helmholtz), Poisson equation (See also 31Axx, 31Bxx)
Issue 5 (May 2009)
Received 11 December 2008, in final form 13 February 2009
Published 5 March 2009
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