×

zbMATH — the first resource for mathematics

Iterative and range test methods for an inverse source problem for acoustic waves. (English) Zbl 1170.65087
From the authors’ abstract: 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 by 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.

MSC:
65N21 Numerical methods for inverse problems for boundary value problems involving PDEs
35R30 Inverse problems for PDEs
35J25 Boundary value problems for second-order elliptic equations
65H10 Numerical computation of solutions to systems of equations
PDF BibTeX XML Cite
Full Text: DOI Link