Details
| Originalsprache | Englisch |
|---|---|
| Aufsatznummer | 100027 |
| Fachzeitschrift | Examples and Counterexamples |
| Jahrgang | 1 |
| Frühes Online-Datum | 30 Okt. 2021 |
| Publikationsstatus | Veröffentlicht - Nov. 2021 |
Abstract
In this work, we consider the design of a geometric multigrid method with multiplicative Schwarz smoothers for the eddy-current problem and the time-harmonic Maxwell equations. The main purpose is to show numerically that a straightforward application works for the former problem, but not for the latter. The well-known key is a special decomposition of the function spaces within the multigrid algorithm. The failures and performance are shown with the help of a numerical test, implemented in the modern finite element library deal.II, including a github link to the eddy-current implementation.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Computational Mathematics
- Mathematik (insg.)
- Angewandte Mathematik
- Mathematik (insg.)
- Mathematik (sonstige)
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in: Examples and Counterexamples, Jahrgang 1, 100027, 11.2021.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Geometric multigrid with multiplicative Schwarz smoothers for eddy-current and Maxwell’s equations in deal.II
AU - Kinnewig, Sebastian
AU - Roth, Julian
AU - Wick, Thomas
PY - 2021/11
Y1 - 2021/11
N2 - In this work, we consider the design of a geometric multigrid method with multiplicative Schwarz smoothers for the eddy-current problem and the time-harmonic Maxwell equations. The main purpose is to show numerically that a straightforward application works for the former problem, but not for the latter. The well-known key is a special decomposition of the function spaces within the multigrid algorithm. The failures and performance are shown with the help of a numerical test, implemented in the modern finite element library deal.II, including a github link to the eddy-current implementation.
AB - In this work, we consider the design of a geometric multigrid method with multiplicative Schwarz smoothers for the eddy-current problem and the time-harmonic Maxwell equations. The main purpose is to show numerically that a straightforward application works for the former problem, but not for the latter. The well-known key is a special decomposition of the function spaces within the multigrid algorithm. The failures and performance are shown with the help of a numerical test, implemented in the modern finite element library deal.II, including a github link to the eddy-current implementation.
KW - Eddy-current problem
KW - Finite elements
KW - Geometric multigrid
KW - Multiplicative Schwarz smoother
KW - Time-harmonic Maxwell
UR - http://www.scopus.com/inward/record.url?scp=85163927133&partnerID=8YFLogxK
U2 - 10.1016/j.exco.2021.100027
DO - 10.1016/j.exco.2021.100027
M3 - Article
VL - 1
JO - Examples and Counterexamples
JF - Examples and Counterexamples
M1 - 100027
ER -