Iterative and Range Test Methods for an Inverse Source Problem for Acoustic Waves
Alves, Carlos J. S.; Kress, Rainer; Serranho, Pedro
Inverse Problems, 25(5) (2009), 055005
We 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.