Additive domain decomposition operator splittings – convergence analyses in a dissipative framework
(2017) In IMA Journal of Numerical Analysis 37(3). p.1496-1519- Abstract
- We analyze temporal approximation schemes based on overlapping domain decompositions. As such schemes enable computations on parallel and distributed hardware, they are commonly used when integrating large-scale parabolic systems. Our analysis is conducted by first casting the domain decomposition procedure into a variational framework based on weighted Sobolev spaces. The time integration of a parabolic system can then be interpreted as an operator splitting scheme applied to an abstract evolution equation governed by a maximal dissipative vector field. By utilizing this abstract setting, we derive an optimal temporal error analysis for the two most common choices of domain decomposition based integrators. Namely, alternating direction... (More)
- We analyze temporal approximation schemes based on overlapping domain decompositions. As such schemes enable computations on parallel and distributed hardware, they are commonly used when integrating large-scale parabolic systems. Our analysis is conducted by first casting the domain decomposition procedure into a variational framework based on weighted Sobolev spaces. The time integration of a parabolic system can then be interpreted as an operator splitting scheme applied to an abstract evolution equation governed by a maximal dissipative vector field. By utilizing this abstract setting, we derive an optimal temporal error analysis for the two most common choices of domain decomposition based integrators. Namely, alternating direction implicit schemes and additive splitting schemes of first and second order. For the standard first-order additive splitting scheme we also extend the error analysis to semilinear evolution equations, which may only have mild solutions. The theoretical results are finally illustrated by numerical experiments. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1a867584-b898-4d44-aa15-c45f9acf9b79
- author
- Hansen, Eskil LU and Henningsson, Erik LU
- organization
- publishing date
- 2017
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- domain decomposition, convergence order, additive splitting schemes, alternating direction implicit schemes, parabolic equations, semilinear evolution equations
- in
- IMA Journal of Numerical Analysis
- volume
- 37
- issue
- 3
- pages
- 24 pages
- publisher
- Oxford University Press
- external identifiers
-
- wos:000405416900016
- scopus:85019518727
- ISSN
- 1464-3642
- DOI
- 10.1093/imanum/drw043
- language
- English
- LU publication?
- yes
- id
- 1a867584-b898-4d44-aa15-c45f9acf9b79
- alternative location
- http://www.maths.lth.se/na/staff/eskil/dataEskil/articles/Domsplit.pdf
- date added to LUP
- 2016-08-02 16:14:53
- date last changed
- 2022-02-14 04:18:59
@article{1a867584-b898-4d44-aa15-c45f9acf9b79,
abstract = {{We analyze temporal approximation schemes based on overlapping domain decompositions. As such schemes enable computations on parallel and distributed hardware, they are commonly used when integrating large-scale parabolic systems. Our analysis is conducted by first casting the domain decomposition procedure into a variational framework based on weighted Sobolev spaces. The time integration of a parabolic system can then be interpreted as an operator splitting scheme applied to an abstract evolution equation governed by a maximal dissipative vector field. By utilizing this abstract setting, we derive an optimal temporal error analysis for the two most common choices of domain decomposition based integrators. Namely, alternating direction implicit schemes and additive splitting schemes of first and second order. For the standard first-order additive splitting scheme we also extend the error analysis to semilinear evolution equations, which may only have mild solutions. The theoretical results are finally illustrated by numerical experiments.}},
author = {{Hansen, Eskil and Henningsson, Erik}},
issn = {{1464-3642}},
keywords = {{domain decomposition; convergence order; additive splitting schemes; alternating direction implicit schemes; parabolic equations; semilinear evolution equations}},
language = {{eng}},
number = {{3}},
pages = {{1496--1519}},
publisher = {{Oxford University Press}},
series = {{IMA Journal of Numerical Analysis}},
title = {{Additive domain decomposition operator splittings – convergence analyses in a dissipative framework}},
url = {{http://dx.doi.org/10.1093/imanum/drw043}},
doi = {{10.1093/imanum/drw043}},
volume = {{37}},
year = {{2017}},
}