2024/02/19 by Mengjie Zhao, Zhao, Mengjie, Suliang Si +3
Engineering · Mathematics · #35P25 #35Q30 #45Q05 #78A46 #Analysis of PDEs (math.AP) #FOS: Mathematics #Microwave Imaging and Scattering Analysis #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Ultrasonics and Acoustic Wave Propagation
paper · pdf · doi:10.48550/arxiv.2402.12088
openalex publication_date 2024/02/19 · openalex created_date 2024/02/21 · openalex updated_date 2026/07/28
This paper is concerned with an inverse wavenumber/frequency-dependent source problem for the Helmholtz equation. In two and three dimensions, the unknown source term is supposed to be compactly supported in spatial variables but independent on one spatial variable. The dependence of the source function on wavenumber/frequency is supposed to be unknown. Based on the Dirichlet-Laplacian and Fourier-Transform methods, we develop two effcient non-iterative numerical algorithms to recover the wavenumber-dependent source. Uniqueness proof and increasing stability analysis are carried out in terms of the boundary measurement data of Dirichlet kind. Numerical experiments are conducted to illustrate the effectiveness and efficiency of the proposed methods.