Many applications in numerical acoustics occur in exterior domains. The advantage of benchmark problems is a closed form solution (e.g. circumferentially harmonic radiation from an infinite cylinder or radiation from a portion of the infinite cylinder). Different models such as perfectly matched layers (PML) and absorbing boundary conditions ABCs (like Enquist Majda, Bayliss Turkel) are used in the finite element method to approximate Sommerfelds radiation condition. I am interested in a publication, where these approaches are compared.
These links may help you
https://www.researchgate.net/publication/267945103_A_comparison_between_PML_infinite_elements_and_an_iterative_BEM_as_mesh_truncation_methods_for_HP_self-adaptive_procedures_in_electromagnetics
https://www.researchgate.net/publication/307175531_Perfectly_matched_layers_for_time_harmonic_acoustics
https://www.publish.csiro.au/eg/EG15068
These links may help you
https://www.researchgate.net/publication/267945103_A_comparison_between_PML_infinite_elements_and_an_iterative_BEM_as_mesh_truncation_methods_for_HP_self-adaptive_procedures_in_electromagnetics
https://www.researchgate.net/publication/307175531_Perfectly_matched_layers_for_time_harmonic_acoustics
https://www.publish.csiro.au/eg/EG15068
one concise comparison is the review paper
X. Antoine, A. Arnold, C. Besse, M. Ehrhardt and A. Schädle,
A Review of Transparent and Artificial Boundary Conditions Techniques for Linear and Nonlinear Schrödinger Equations,
Commun. Comput. Phys. Vol. 4, Number 4, (2008), 729-796.
It is open access and , yes, it is dealing with the schroedinger equation, i.e. the "parabolic equation" in acoustics.
Hi Nils
The book "Formulas of Acoustics" by Mechel et al contains loads of analytically solved cases in acoustics. https://www.amazon.co.uk/Formulas-Acoustics-F-P-Mechel/dp/3540768327/ref=sr_1_1?s=books&ie=UTF8&qid=1537819520&sr=1-1&keywords=mechel+formulas+acoustics
As open space is the simplest boundary condition when doing analytical work, you should be be able to find a bunch of good cases with analytical solutions for QA work.
There exists a whole section of analytical solutions for various 2D shapes where it is shown that the real part (radiation) of the radiated acoustic power is only weakly affected by shape while the imaginary part (mass load) is greatly affected.
To recover these findings, I think, would be a good way to show that numerically implemented infinite boundary elements behave as expected. It is a good reference case also for simplified analysis of 'wetted' modes where the mass loading is of primary interest.
Last, the simple acoustic monopole has a basic solution, one that never can be captured with FE, as the mass load grows exponentially in the vicinity of the mathematical point source, while the FE mesh has a finite resolution due to its shape functions. In this situation, BE invariably beats FE when response is evaluated close to the source, where 'close', of course, refers to distance from the source in relation to the wavelength.
Sincerely
Claes
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