Details
| Originalsprache | Englisch |
|---|---|
| Aufsatznummer | 22 |
| Seitenumfang | 29 |
| Fachzeitschrift | ACM Transactions on Mathematical Software |
| Jahrgang | 51 |
| Ausgabenummer | 4 |
| Frühes Online-Datum | 10 Sept. 2025 |
| Publikationsstatus | Veröffentlicht - 13 Dez. 2025 |
Abstract
In this work, restricted additive Schwarz (RAS) and optimized restricted additive Schwarz (ORAS) preconditioners from the Trilinos package FROSch (Fast and Robust Overlapping Schwarz) are employed to solve model problems implemented using deal.II (differential equations analysis library). Therefore, a Tpetra-based interface for coupling deal.II and FROSch is implemented. While RAS preconditioners have been available before, ORAS preconditioners have been newly added to FROSch. The deal.II–FROSch interface works for both Lagrange-based and Nédélec finite elements. Here, as model problems, nonstationary, nonlinear, variational-monolithic fluid-structure interaction and the indefinite time-harmonic Maxwell’s equations are considered. Several numerical experiments in two and three spatial dimensions confirm the performance of the preconditioners as well as the FROSch-deal.II interface. In conclusion, the overall software interface is straightforward and easy to use while giving satisfactory solver performances for challenging PDE systems.
ASJC Scopus Sachgebiete
- Informatik (insg.)
- Software
- Mathematik (insg.)
- Angewandte Mathematik
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in: ACM Transactions on Mathematical Software, Jahrgang 51, Nr. 4, 22, 13.12.2025.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Coupling deal.II and FROSch
T2 - A Sustainable and Accessible (O)RAS Preconditioner
AU - Kinnewig, Sebastian
AU - Heinlein, Alexander
AU - Wick, Thomas
N1 - Publisher Copyright: © 2025 Copyright held by the owner/author(s).
PY - 2025/12/13
Y1 - 2025/12/13
N2 - In this work, restricted additive Schwarz (RAS) and optimized restricted additive Schwarz (ORAS) preconditioners from the Trilinos package FROSch (Fast and Robust Overlapping Schwarz) are employed to solve model problems implemented using deal.II (differential equations analysis library). Therefore, a Tpetra-based interface for coupling deal.II and FROSch is implemented. While RAS preconditioners have been available before, ORAS preconditioners have been newly added to FROSch. The deal.II–FROSch interface works for both Lagrange-based and Nédélec finite elements. Here, as model problems, nonstationary, nonlinear, variational-monolithic fluid-structure interaction and the indefinite time-harmonic Maxwell’s equations are considered. Several numerical experiments in two and three spatial dimensions confirm the performance of the preconditioners as well as the FROSch-deal.II interface. In conclusion, the overall software interface is straightforward and easy to use while giving satisfactory solver performances for challenging PDE systems.
AB - In this work, restricted additive Schwarz (RAS) and optimized restricted additive Schwarz (ORAS) preconditioners from the Trilinos package FROSch (Fast and Robust Overlapping Schwarz) are employed to solve model problems implemented using deal.II (differential equations analysis library). Therefore, a Tpetra-based interface for coupling deal.II and FROSch is implemented. While RAS preconditioners have been available before, ORAS preconditioners have been newly added to FROSch. The deal.II–FROSch interface works for both Lagrange-based and Nédélec finite elements. Here, as model problems, nonstationary, nonlinear, variational-monolithic fluid-structure interaction and the indefinite time-harmonic Maxwell’s equations are considered. Several numerical experiments in two and three spatial dimensions confirm the performance of the preconditioners as well as the FROSch-deal.II interface. In conclusion, the overall software interface is straightforward and easy to use while giving satisfactory solver performances for challenging PDE systems.
KW - domain decomposition
KW - Finite element method
KW - fluid-structure interaction
KW - optimized Schwarz method
KW - Schwarz method
KW - time-harmonic Maxwell’s equations
UR - http://www.scopus.com/inward/record.url?scp=105025957137&partnerID=8YFLogxK
U2 - 10.1145/3766906
DO - 10.1145/3766906
M3 - Article
AN - SCOPUS:105025957137
VL - 51
JO - ACM Transactions on Mathematical Software
JF - ACM Transactions on Mathematical Software
SN - 0098-3500
IS - 4
M1 - 22
ER -