Institutional Repository
Technical University of Crete
Technical University of Crete
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| URI | http://purl.tuc.gr/dl/dias/CE246EDE-494C-4EEC-AACD-F2C861FC874C | - |
| Identifier | http://www.sciencedirect.com/science/article/pii/S0168927411000882 | - |
| Identifier | https://doi.org/10.1016/j.apnum.2011.05.005 | - |
| Language | en | - |
| Extent | 15 pages | en |
| Title | A finite element discretization of the standard parabolic equation in generalized boundary fitting coordinates | en |
| Creator | Kampanis, Nikolaos A | en |
| Creator | Delis Anargyros | en |
| Creator | Δελης Αναργυρος | el |
| Creator | Antonopoulou D.C. | en |
| Creator | Kozyrakis G. | en |
| Publisher | Elsevier | en |
| Content Summary | A simplified, but quantitatively reliable approximation of atmospheric sound propagation is given by the standard parabolic equation. The waveguide is a cylindrically symmetric, unbounded, domain with an irregular lower boundary. The associated initial-boundary value problem uses a mixed-type boundary condition along the lower boundary and a nonlocal, absorbing boundary condition of the DtN (or NtD) type, applied on an artificial upper boundary. Exterior wave fields of a constant index of refraction and a linear, when squared (as function of height) one, are considered. The physical, complex waveguide reduces to an orthogonal computational domain by the means of a numerical transformation to generalized coordinates, fitting the lower, irregular boundary. The technique presented is of practical interest for its proper handling of complex ground topographies; it is interfaced with a mesh generator and processes the topographic data retrieved from a geographic information system, hence the transformation of coordinates is computed numerically. The transformed initial-boundary value problem (on the orthogonal computational domain) is discretized by the Crank–Nicolson in time and a continuous, piecewise linear finite element method in space. The propagation of cylindrically symmetric sound waves over a complex terrain, emitted to the atmosphere by a harmonic source, has been studied. The effectiveness of the numerical method introduced, is exploited on several test cases. | en |
| Type of Item | Peer-Reviewed Journal Publication | en |
| Type of Item | Δημοσίευση σε Περιοδικό με Κριτές | el |
| License | http://creativecommons.org/licenses/by/4.0/ | en |
| Date of Item | 2015-10-26 | - |
| Date of Publication | 2013 | - |
| Subject | Atmospheric acoustics | en |
| Subject | Standard parabolic approximation | en |
| Subject | Irregular ground topography | en |
| Subject | Generalized boundary fitting coordinates | en |
| Subject | Finite element formulation | en |
| Subject | Nonlocal boundary conditions | en |
| Bibliographic Citation | N. A. Kampanis, A. I. Delis, D. C. Antonopoulou and G. Kozyrakis, "A finite element discretization of the standard parabolic equation in generalized boundary fitting coordinates," Appl. Num. Math., vol. 67, pp. 152-166, May 2013. doi:10.1016/j.apnum.2011.05.005 | en |
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