SIAM Journal of Scientific Computing, volume 44, issue 3, pages A1254-A1289
Explicit Time Stepping for the Wave Equation using CutFEM with Discrete Extension
Publication type: Journal Article
Publication date: 2022-05-12
Journal:
SIAM Journal of Scientific Computing
Q1
Q1
SJR: 1.803
CiteScore: 5.5
Impact factor: 3
ISSN: 10648275, 10957197
Computational Mathematics
Applied Mathematics
Abstract
In this note we develop a fully explicit cut finite element method for the wave equation. The method is based on using a standard leap frog scheme combined with an extension operator that defines the nodal values outside of the domain in terms of the nodal values inside the domain. We show that the mass matrix associated with the extended finite element space can be lumped leading to a fully explicit scheme. We derive stability estimates for the method and provide optimal order a priori error estimates. Finally, we present some illustrating numerical examples.
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Burman E., Hansbo P., Larson M. G. Explicit Time Stepping for the Wave Equation using CutFEM with Discrete Extension // SIAM Journal of Scientific Computing. 2022. Vol. 44. No. 3. p. A1254-A1289.
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Burman E., Hansbo P., Larson M. G. Explicit Time Stepping for the Wave Equation using CutFEM with Discrete Extension // SIAM Journal of Scientific Computing. 2022. Vol. 44. No. 3. p. A1254-A1289.
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TY - JOUR
DO - 10.1137/20m137937x
UR - https://doi.org/10.1137/20m137937x
TI - Explicit Time Stepping for the Wave Equation using CutFEM with Discrete Extension
T2 - SIAM Journal of Scientific Computing
AU - Burman, Erik
AU - Hansbo, Peter
AU - Larson, Mats G.
PY - 2022
DA - 2022/05/12
PB - Society for Industrial and Applied Mathematics (SIAM)
SP - A1254-A1289
IS - 3
VL - 44
SN - 1064-8275
SN - 1095-7197
ER -
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BibTex (up to 50 authors)
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@article{2022_Burman,
author = {Erik Burman and Peter Hansbo and Mats G. Larson},
title = {Explicit Time Stepping for the Wave Equation using CutFEM with Discrete Extension},
journal = {SIAM Journal of Scientific Computing},
year = {2022},
volume = {44},
publisher = {Society for Industrial and Applied Mathematics (SIAM)},
month = {may},
url = {https://doi.org/10.1137/20m137937x},
number = {3},
pages = {A1254--A1289},
doi = {10.1137/20m137937x}
}
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Burman, Erik, et al. “Explicit Time Stepping for the Wave Equation using CutFEM with Discrete Extension.” SIAM Journal of Scientific Computing, vol. 44, no. 3, May. 2022, pp. A1254-A1289. https://doi.org/10.1137/20m137937x.