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.
Accepté le :
DOI : 10.1051/m2an/2018017
Mots clés : Differential geometry, exterior algebra, boundary value problems, acoustics, electromagnetism, elasticity, quantum mechanics, finite difference, discrete exterior calculus
@article{M2AN_2018__52_3_1195_0,
author = {R\"abin\"a, Jukka and Kettunen, Lauri and M\"onk\"ol\"a, Sanna and Rossi, Tuomo},
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://www.numdam.org/articles/10.1051/m2an/2018017/}
}
TY - JOUR AU - Räbinä, Jukka AU - Kettunen, Lauri AU - Mönkölä, Sanna AU - Rossi, Tuomo TI - Generalized wave propagation problems and discrete exterior calculus JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2018 SP - 1195 EP - 1218 VL - 52 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2018017/ DO - 10.1051/m2an/2018017 LA - en ID - M2AN_2018__52_3_1195_0 ER -
%0 Journal Article %A Räbinä, Jukka %A Kettunen, Lauri %A Mönkölä, Sanna %A Rossi, Tuomo %T Generalized wave propagation problems and discrete exterior calculus %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2018 %P 1195-1218 %V 52 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2018017/ %R 10.1051/m2an/2018017 %G en %F M2AN_2018__52_3_1195_0
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. http://www.numdam.org/articles/10.1051/m2an/2018017/
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