Two-level additive Schwarz preconditioners with GDSW coarse spaces for high-order discretizations in 2D
Abstract
Two-level overlapping Schwarz preconditioners with Generalized Dryja-Smith-Widlund (GDSW) and Reduced GDSW (RGDSW) coarse spaces for high-order finite element methods (FEM) and virtual element methods (VEM) are investigated and applied to the Poisson problem in 2D. The GDSW coarse space is a well-established robust choice for preconditioners in domain decomposition, while the RGDSW coarse space offers a competitive alternative by reducing the coarse problem dimension while maintaining robustness. On the theoretical side, a condition number bound for both preconditioners is proved for conforming ℙk and ℚk finite element spaces with explicit dependence on the polynomial degree k. Through numerical experiments on structured triangular and quadrilateral meshes for FEM and on polygonal meshes for VEM, it is demonstrated that both GDSW and RGDSW maintain scalability properties across polynomial orders up to k=9 for selected degrees. The RGDSW approach achieves a reduction in the coarse problem dimension by a factor of approximately three compared to GDSW while maintaining competitive iteration counts.
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BibTeX
@misc{bevilacqua2026twolevel,
title = {{Two-level additive Schwarz preconditioners with GDSW coarse spaces for high-order discretizations in 2D}},
author = {Tommaso Bevilacqua and Axel Klawonn and Martin Lanser and Adam Wasiak},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18502},
eprint = {2610.18502},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18502},
}
RIS
TY - UNPB
TI - Two-level additive Schwarz preconditioners with GDSW coarse spaces for high-order discretizations in 2D
AU - Tommaso Bevilacqua
AU - Axel Klawonn
AU - Martin Lanser
AU - Adam Wasiak
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18502
UR - https://arxiv.org/abs/2610.18502
AB - Two-level overlapping Schwarz preconditioners with Generalized Dryja-Smith-Widlund (GDSW) and Reduced GDSW (RGDSW) coarse spaces for high-order finite element methods (FEM) and virtual element methods (VEM) are investigated and applied to the Poisson problem in 2D. The GDSW coarse space is a well-established robust choice for preconditioners in domain decomposition, while the RGDSW coarse space offers a competitive alternative by reducing the coarse problem dimension while maintaining robustness. On the theoretical side, a condition number bound for both preconditioners is proved for conforming ℙ_k and ℚ_k finite element spaces with explicit dependence on the polynomial degree k. Through numerical experiments on structured triangular and quadrilateral meshes for FEM and on polygonal meshes for VEM, it is demonstrated that both GDSW and RGDSW maintain scalability properties across polynomial orders up to k=9 for selected degrees. The RGDSW approach achieves a reduction in the coarse problem dimension by a factor of approximately three compared to GDSW while maintaining competitive iteration counts.
ER -