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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.

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
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