| Abstract: |
| In this talk, we show two novel approaches for solving the inverse source problem of the acoustic wave equation in three dimensions. By injecting a small high-contrast droplet into the medium, we exploit the resulting wave field perturbation measured at a single external point over time. First, we derive an asymptotic expansion of the wave field after the droplet injection, using the eigensystem of the Newtonian operator, with error analysis for the spectral truncation. Then two novel numerical methods for reconstructing the source via the expansion and mollification-based numerical differentiation. Our methods require only single-point measurements, overcoming traditional spatial data limitations. Several numerical experiments are presented to demonstrate the performance of the proposed methods. |
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