Details
| Original language | English |
|---|---|
| Article number | 100027 |
| Journal | Examples and Counterexamples |
| Volume | 1 |
| Early online date | 30 Oct 2021 |
| Publication status | Published - 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.
Keywords
- Eddy-current problem, Finite elements, Geometric multigrid, Multiplicative Schwarz smoother, Time-harmonic Maxwell
ASJC Scopus subject areas
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
- Mathematics(all)
- Mathematics (miscellaneous)
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Examples and Counterexamples, Vol. 1, 100027, 11.2021.
Research output: Contribution to journal › Article › Research › 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 -