Linearly convergent nonoverlapping domain decomposition methods for quasilinear parabolic equations
(2023)- Abstract
- We prove linear convergence for a new family of modified Dirichlet–Neumann methods applied to quasilinear parabolic equations, as well as the convergence of the Robin–Robin method. Such nonoverlapping domain decomposition methods are commonly employed for the parallelization of partial differential equation solvers. Convergence has been extensively studied for elliptic equations, but in the case of parabolic equations there are hardly any convergence results that are not relying on strong regularity assumptions. Hence, we construct a new framework for analyzing domain decomposition methods applied to quasilinear parabolic problems, based on fractional time derivatives and time-dependent Steklov–Poincaré operators. The convergence analysis... (More)
- We prove linear convergence for a new family of modified Dirichlet–Neumann methods applied to quasilinear parabolic equations, as well as the convergence of the Robin–Robin method. Such nonoverlapping domain decomposition methods are commonly employed for the parallelization of partial differential equation solvers. Convergence has been extensively studied for elliptic equations, but in the case of parabolic equations there are hardly any convergence results that are not relying on strong regularity assumptions. Hence, we construct a new framework for analyzing domain decomposition methods applied to quasilinear parabolic problems, based on fractional time derivatives and time-dependent Steklov–Poincaré operators. The convergence analysis is conducted without assuming restrictive regularity assumptions on the solutions or the numerical iterates. We also prove that these continuous convergence results extend to the discrete case obtained when combining domain decompositions with space-time finite elements. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/afeeb801-fd2b-456e-b781-ac0dc861b396
- author
- Hansen, Eskil LU and Engström, Emil LU
- organization
- publishing date
- 2023
- type
- Working paper/Preprint
- publication status
- published
- subject
- pages
- 31 pages
- publisher
- arXiv.org
- DOI
- 10.48550/arXiv.2308.15314
- project
- Next generation numerical partitioning schemes for time dependent PDEs
- language
- English
- LU publication?
- yes
- id
- afeeb801-fd2b-456e-b781-ac0dc861b396
- date added to LUP
- 2023-12-06 16:04:20
- date last changed
- 2024-01-18 10:10:53
@misc{afeeb801-fd2b-456e-b781-ac0dc861b396, abstract = {{We prove linear convergence for a new family of modified Dirichlet–Neumann methods applied to quasilinear parabolic equations, as well as the convergence of the Robin–Robin method. Such nonoverlapping domain decomposition methods are commonly employed for the parallelization of partial differential equation solvers. Convergence has been extensively studied for elliptic equations, but in the case of parabolic equations there are hardly any convergence results that are not relying on strong regularity assumptions. Hence, we construct a new framework for analyzing domain decomposition methods applied to quasilinear parabolic problems, based on fractional time derivatives and time-dependent Steklov–Poincaré operators. The convergence analysis is conducted without assuming restrictive regularity assumptions on the solutions or the numerical iterates. We also prove that these continuous convergence results extend to the discrete case obtained when combining domain decompositions with space-time finite elements.}}, author = {{Hansen, Eskil and Engström, Emil}}, language = {{eng}}, note = {{Preprint}}, publisher = {{arXiv.org}}, title = {{Linearly convergent nonoverlapping domain decomposition methods for quasilinear parabolic equations}}, url = {{http://dx.doi.org/10.48550/arXiv.2308.15314}}, doi = {{10.48550/arXiv.2308.15314}}, year = {{2023}}, }