Lin, C., Melenk, J. M., & Sauter, S. (2024). The Green`s function for an acoustic, half-space impedance problem Part II: Analysis of the slowly varying and the plane wave component. arXiv. https://doi.org/10.48550/arXiv.2408.03587
We show that the acoustic Green’s function for a half-space impedance problem in arbitrary spatial dimension d can be written as a sum of two terms, each of which is the product of an exponential function with the eikonal in the argument and a slowly varying function. We introduce the notion of families of slowly varying functions to formulate this statement as a theorem and present its proof.
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Research Areas:
Mathematical and Algorithmic Foundations: 80% Modeling and Simulation: 20%
