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中波数依赖/频率依赖的反源问题。在d维空间（d=2,3）中，未知源项被假设为空间变量紧支撑且与x_d无关，源函数对波数的依赖关系未知。基于Dirichlet-Laplacian方法与Fourier-Transform方法，我们发展了两种高效的非迭代数值算法来恢复波数依赖源。证明了唯一性分析与递增稳定性，并通过数值实验验证了所提方法的有效性与高效性。