Factorization of the Green’s function of high-frequency acoustic half-space impedance problems
Open Access
- 6 May 2026
- journal article
- research article
- Published by Springer Nature in Zeitschrift für angewandte Mathematik und Physik
- Vol. 77 (5) , 155
Abstract
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 three 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.Keywords
Funding Information
- Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (200020_196995)
- Austrian Science Fund (SFB F65 “Taming complexity in PDE systems”)
This publication has 28 references indexed in Scilit:
- An Explicit Factorization of the Green's Function for an Acoustic Half‐Space Problem with Impedance Boundary Conditions into an Oscillatory Exponential and a Slowly Varying FunctionMathematical Methods in the Applied Sciences, 2025
- A priori error estimates for a time‐dependent boundary element method for the acoustic wave equation in a half‐spaceMathematical Methods in the Applied Sciences, 2014
- Boundary Element Methods2010
- An Atlas of Functions2009
- The Helmholtz Equation in a Locally Perturbed Half-Space with Non-Absorbing BoundaryArchive for Rational Mechanics and Analysis, 2008
- Finite Element Analysis of Acoustic Scattering1998
- A uniformly valid far field asymptotic expansion of the green function for two-dimensional propagation above a homogeneous impedance planeJournal of Sound and Vibration, 1995
- Diagonal Forms of Translation Operators for the Helmholtz Equation in Three DimensionsApplied and Computational Harmonic Analysis, 1993
- Short-Wavelength Diffraction Theory1991
- Bessel Polynomials1978