Special Session 20: Stochastic analysis, inverse problems and related topics

Solving the phaseless inverse source problem of the biharmonic equation

Yukun Guo
Harbin Institute of Technology
Peoples Rep of China
Co-Author(s):    Yan Chang, Yue Zhao
Abstract:
This talk concerns an inverse source problem for the biharmonic wave equation. A two-stage numerical method is proposed to identify the unknown source from the multifrequency phaseless data. In the first stage, we introduce some artificial auxiliary point sources to the inverse source system and establish a phase retrieval formula. Theoretically, we point out that the phase can be uniquely determined and estimate the stability of this phase retrieval approach. Once the phase information is retrieved, the Fourier method is adopted to reconstruct the source function from the phased multifrequency data. Numerical examples will be presented to verify the performance of the proposed method.