This paper is concerned with an inverse wave-number-dependent/frequency-dependent source problem for the Helmholtz equation. In d-dimensions (d = 2,3), the unknown source term is supposed to be compactly supported in spatial variables but independent on x_d. The dependance of the source function on k is supposed to be unknown. Based on the Dirichlet-Laplacian method and the Fourier-Transform method, we develop two effcient non-iterative numerical algorithms to recover the wave-number-dependent source. Uniqueness and increasing stability analysis are proved. Numerical experiments are conducted to illustrate the effctiveness and effciency of the proposed method.

翻译：本文研究亥姆霍兹方程的逆波数/频率相关源问题。在d维空间（d=2,3）中，未知源项被假设在空间变量上具有紧支撑，且不依赖于x_d方向。源函数对波数k的依赖性被假定为未知。基于Dirichlet-Laplacian方法和Fourier变换方法，我们开发了两种高效的非迭代数值算法来恢复波数相关源。我们证明了唯一性和递增稳定性分析。通过数值实验验证了所提方法的有效性和高效性。