| Issue |
ESAIM: M2AN
Volume 54, Number 3, May-June 2020
|
|
|---|---|---|
| Page(s) | 845 - 878 | |
| DOI | https://doi.org/10.1051/m2an/2019079 | |
| Published online | 01 April 2020 | |
Construction and analysis of fourth order, energy consistent, family of explicit time discretizations for dissipative linear wave equations
1
Project-Team Magique 3D, Inria, E2S UPPA, CNRS 200 Avenue de la Vieille Tour, 33405 Talence Cedex or Avenue de l’Université, 64013 Pau Cedex, France
2
Inria – LMS, Ecole Polytechnique, CNRS – Institut Polytechnique de Paris, 1 Rue Honoré d’Estienne d’Orves, 91120 Palaiseau, France
* Corresponding author: sebastien.imperiale@inria.fr
Received:
3
August
2018
Accepted:
6
November
2019
This paper deals with the construction of a family of fourth order, energy consistent, explicit time discretizations for dissipative linear wave equations. The schemes are obtained by replacing the inversion of a matrix, that comes naturally after using the technique of the Modified Equation on the second order Leap Frog scheme applied to dissipative linear wave equations, by explicit approximations of its inverse. The stability of the schemes are studied using an energy analysis and a convergence analysis is carried out. Numerical results in 1D illustrate the space/time convergence properties of the schemes and their efficiency is compared to more classical time discretizations.
Mathematics Subject Classification: 00A71 / 35L05 / 85A20 / 33C55 / 65M60
Key words: Dissipative linear wave equation / high order time discretisation / energy analysis
© EDP Sciences, SMAI 2020
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