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A variational approach to splitting schemes, with applications to domain decomposition integrators

Eisenmann, Monika and Hansen, Eskil LU (2019) In Mathematics of Computation
Abstract
Nonlinear parabolic equations are frequently encountered in applications and
approximating their solutions require large scale computations. In order to
obtain efficient numerical approximations, it is crucial to design and analyze
schemes that can be implemented on parallel and distributed hardware. To this
end, we introduce a general framework of non-autonomous, inhomogeneous
evolution equations in a variational setting, and show convergence of the sum
operator splitting scheme. We exemplify the usage to a p-Laplacian type
problem with a possibly time depending domain decomposition.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
submitted
keywords
Nonlinear evolution problem, monotone operator, operator splitting, convergence, domain decomposition
in
Mathematics of Computation
publisher
American Mathematical Society (AMS)
ISSN
1088-6842
language
English
LU publication?
yes
id
2f8cce91-4d80-48aa-83ab-820cbc6d3ed2
alternative location
http://arxiv.org/abs/1902.10023
date added to LUP
2019-02-27 09:56:17
date last changed
2019-05-24 19:34:30
@article{2f8cce91-4d80-48aa-83ab-820cbc6d3ed2,
  abstract     = {Nonlinear parabolic equations are frequently encountered in applications and<br/>approximating their solutions require large scale computations. In order to<br/>obtain efficient numerical approximations, it is crucial to design and analyze<br/>schemes that can be implemented on parallel and distributed hardware. To this<br/>end, we introduce a general framework of non-autonomous, inhomogeneous<br/>evolution equations in a variational setting, and show convergence of the sum<br/>operator splitting scheme. We exemplify the usage to a p-Laplacian type<br/>problem with a possibly time depending domain decomposition.},
  author       = {Eisenmann, Monika and Hansen, Eskil},
  issn         = {1088-6842},
  language     = {eng},
  month        = {02},
  publisher    = {American Mathematical Society (AMS)},
  series       = {Mathematics of Computation},
  title        = {A variational approach to splitting schemes, with applications to domain decomposition integrators},
  url          = {http://arxiv.org/abs/1902.10023},
  year         = {2019},
}