This work deals with an inverse source problem for the biharmonic wave equation. A two-stage numerical method is proposed to identify the unknown source from the multi-frequency phaseless data. In the first stage, we introduce some artificially 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 multi-frequency data. The proposed method is easy-to-implement and there is no forward solver involved in the reconstruction. Numerical experiments are conducted to verify the performance of the proposed method.

翻译：本文研究双调和波动方程的反源问题。提出了一种两阶段数值方法，用于从多频率无相位数据中识别未知源。在第一阶段，我们向反源系统引入若干人工辅助点源，并建立相位恢复公式。理论上，我们指出相位可唯一确定，并估计了该相位恢复方法的稳定性。一旦相位信息恢复，便采用傅里叶方法从含相位的多频率数据重建源函数。所提方法易于实现，且重建过程中无需正向求解器。通过数值实验验证了所提方法的性能。