A Software Framework for Reduced Basis Methods Using DUNE-RB and
RBMATLAB
M. Drohmann, B. Haasdonk, and M. Ohlberger. Advances in DUNE: Proceedings of the DUNE User Meeting, Held in October
6th-8th 2010 in Stuttgart, Germany, Springer, (April 2012)
Abstract
Many applications from science and engineering are based on parametrized
evolution equations and depend on time-consuming parameter studies
or need to ensure critical constraints on the simulation time. For
both settings, model order reduction by the reduced basis approach
is a suitable means to reduce computational time. The method is based
on a projection of an underlying high dimensional nu- merical scheme
onto a low dimensional function space. In this contribution, a new
software framework is introduced that allows fast development of
reduced schemes for a large class of discretizations of evolution
equations implemented in DUNE. The approach provides a strict separation
of low-dimensional and high-dimensional computations, each implemented
by its own software package RBMATLAB, respectively DUNE-RB. The functionality
of the framework is exemplified for a finite volume approximation
of an instationary linear convection-diffusion problem.
%0 Book Section
%1 drohmann2012software
%A Drohmann, Martin
%A Haasdonk, Bernard
%A Ohlberger, Mario
%B Advances in DUNE: Proceedings of the DUNE User Meeting, Held in October
6th-8th 2010 in Stuttgart, Germany
%D 2012
%E Dedner, Andreas
%E Flemisch, Bernd
%E Klöfkorn, Robert
%I Springer
%K from:mhartmann ians imported vorlaeufig
%T A Software Framework for Reduced Basis Methods Using DUNE-RB and
RBMATLAB
%U http://www.springer.com/engineering/computational+intelligence+and+complexity/book/978-3-642-28588-2
%X Many applications from science and engineering are based on parametrized
evolution equations and depend on time-consuming parameter studies
or need to ensure critical constraints on the simulation time. For
both settings, model order reduction by the reduced basis approach
is a suitable means to reduce computational time. The method is based
on a projection of an underlying high dimensional nu- merical scheme
onto a low dimensional function space. In this contribution, a new
software framework is introduced that allows fast development of
reduced schemes for a large class of discretizations of evolution
equations implemented in DUNE. The approach provides a strict separation
of low-dimensional and high-dimensional computations, each implemented
by its own software package RBMATLAB, respectively DUNE-RB. The functionality
of the framework is exemplified for a finite volume approximation
of an instationary linear convection-diffusion problem.
%@ 978-3-642-28589-9
@incollection{drohmann2012software,
abstract = {Many applications from science and engineering are based on parametrized
evolution equations and depend on time-consuming parameter studies
or need to ensure critical constraints on the simulation time. For
both settings, model order reduction by the reduced basis approach
is a suitable means to reduce computational time. The method is based
on a projection of an underlying high dimensional nu- merical scheme
onto a low dimensional function space. In this contribution, a new
software framework is introduced that allows fast development of
reduced schemes for a large class of discretizations of evolution
equations implemented in DUNE. The approach provides a strict separation
of low-dimensional and high-dimensional computations, each implemented
by its own software package RBMATLAB, respectively DUNE-RB. The functionality
of the framework is exemplified for a finite volume approximation
of an instationary linear convection-diffusion problem.},
added-at = {2018-07-20T10:54:52.000+0200},
author = {Drohmann, Martin and Haasdonk, Bernard and Ohlberger, Mario},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/23d7fc70ef23b1d186938f43daaf9a8da/mathematik},
booktitle = {Advances in DUNE: Proceedings of the DUNE User Meeting, Held in October
6th-8th 2010 in Stuttgart, Germany},
date-added = {2012-10-24T14:53:21GMT},
date-modified = {2014-06-03T08:54:33GMT},
editor = {Dedner, Andreas and Flemisch, Bernd and Kl{\"o}fkorn, Robert},
interhash = {69fc1b0b66363058ed42912aa2fdfead},
intrahash = {3d7fc70ef23b1d186938f43daaf9a8da},
isbn = {978-3-642-28589-9},
keywords = {from:mhartmann ians imported vorlaeufig},
month = apr,
owner = {kaulmann},
publisher = {Springer},
rating = {0},
read = {Yes},
timestamp = {2019-12-18T14:37:55.000+0100},
title = {{A Software Framework for Reduced Basis Methods Using DUNE-RB and
RBMATLAB}},
url = {http://www.springer.com/engineering/computational+intelligence+and+complexity/book/978-3-642-28588-2},
year = 2012
}
