Uniqueness, stability and algorithm for an inverse wave-number-dependent source problems
CoRR(2024)
摘要
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.
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