Modified Neumann-Neumann methods for semi- and quasilinear elliptic equations
(2023) p.1-22- Abstract
- The Neumann--Neumann method is a commonly employed domain decomposition method for linear elliptic equations. However, the method exhibits slow convergence when applied to semilinear equations and does not seem to converge at all for certain quasilinear equations. We therefore propose two modified Neumann--Neumann methods that have better convergence properties and require less computations. We provide numerical results that show the advantages of these methods when applied to both semilinear and quasilinear equations. We also prove linear convergence with mesh-independent error reduction under certain assumptions on the equation. The analysis is carried out on general Lipschitz domains and relies on the theory of nonlinear... (More)
- The Neumann--Neumann method is a commonly employed domain decomposition method for linear elliptic equations. However, the method exhibits slow convergence when applied to semilinear equations and does not seem to converge at all for certain quasilinear equations. We therefore propose two modified Neumann--Neumann methods that have better convergence properties and require less computations. We provide numerical results that show the advantages of these methods when applied to both semilinear and quasilinear equations. We also prove linear convergence with mesh-independent error reduction under certain assumptions on the equation. The analysis is carried out on general Lipschitz domains and relies on the theory of nonlinear Steklov--Poincaré operators. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/71f203be-93b0-4849-aae5-7b7f3ae95c49
- author
- Engström, Emil LU and Hansen, Eskil LU
- organization
- publishing date
- 2023-12-19
- type
- Working paper/Preprint
- publication status
- published
- subject
- keywords
- Nonoverlapping domain decomposition, Neumann–Neumann method, linear convergence, semi- and quasilinear elliptic equations
- pages
- 22 pages
- publisher
- arXiv.org
- DOI
- 10.48550/arXiv.2312.11177
- project
- Next generation numerical partitioning schemes for time dependent PDEs
- language
- English
- LU publication?
- yes
- id
- 71f203be-93b0-4849-aae5-7b7f3ae95c49
- date added to LUP
- 2023-12-19 08:47:44
- date last changed
- 2024-01-18 15:42:17
@misc{71f203be-93b0-4849-aae5-7b7f3ae95c49, abstract = {{The Neumann--Neumann method is a commonly employed domain decomposition method for linear elliptic equations. However, the method exhibits slow convergence when applied to semilinear equations and does not seem to converge at all for certain quasilinear equations. We therefore propose two modified Neumann--Neumann methods that have better convergence properties and require less computations. We provide numerical results that show the advantages of these methods when applied to both semilinear and quasilinear equations. We also prove linear convergence with mesh-independent error reduction under certain assumptions on the equation. The analysis is carried out on general Lipschitz domains and relies on the theory of nonlinear Steklov--Poincaré operators.}}, author = {{Engström, Emil and Hansen, Eskil}}, keywords = {{Nonoverlapping domain decomposition; Neumann–Neumann method; linear convergence; semi- and quasilinear elliptic equations}}, language = {{eng}}, month = {{12}}, note = {{Preprint}}, pages = {{1--22}}, publisher = {{arXiv.org}}, title = {{Modified Neumann-Neumann methods for semi- and quasilinear elliptic equations}}, url = {{http://dx.doi.org/10.48550/arXiv.2312.11177}}, doi = {{10.48550/arXiv.2312.11177}}, year = {{2023}}, }