Geodesic
Generalized wave propagation problems and discrete exterior calculus
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 3, pp. 1195-1218

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We introduce a general class of second-order boundary value problems unifying application areas such as acoustics, electromagnetism, elastodynamics, quantum mechanics, and so on, into a single framework. This also enables us to solve wave propagation problems very efficiently with a single software system. The solution method precisely follows the conservation laws in finite-dimensional systems, whereas the constitutive relations are imposed approximately. We employ discrete exterior calculus for the spatial discretization, use natural crystal structures for three-dimensional meshing, and derive a “discrete Hodge” adapted to harmonic wave. The numerical experiments indicate that the cumulative pollution error can be practically eliminated in the case of harmonic wave problems. The restrictions following from the CFL condition can be bypassed with a local time-stepping scheme. The computational savings are at least one order of magnitude.

Reçu le :
Accepté le :
DOI : 10.1051/m2an/2018017
Classification : 35L65, 58A10, 58A14, 58J32, 58J90, 65M06, 65M12, 65M22
Keywords: Differential geometry, exterior algebra, boundary value problems, acoustics, electromagnetism, elasticity, quantum mechanics, finite difference, discrete exterior calculus

Räbinä, Jukka 1 ; Kettunen, Lauri 1 ; Mönkölä, Sanna 1 ; Rossi, Tuomo 1

1 
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     title = {Generalized wave propagation problems and discrete exterior calculus},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1195--1218},
     publisher = {EDP-Sciences},
     volume = {52},
     number = {3},
     year = {2018},
     doi = {10.1051/m2an/2018017},
     zbl = {1404.35288},
     mrnumber = {3865563},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2018017/}
}
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Räbinä, Jukka; Kettunen, Lauri; Mönkölä, Sanna; Rossi, Tuomo. Generalized wave propagation problems and discrete exterior calculus. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 3, pp. 1195-1218. doi: 10.1051/m2an/2018017

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