%0 Conference Paper %1 drohmann2012software %A Drohmann, Martin %A Haasdonk, Bernard %A Ohlberger, Mario %B Advances in DUNE : proceedings of the DUNE User Meeting %C Berlin %D 2012 %E Dedner, Andreas %E Flemisch, Bernd %E Klöfkorn, Robert %I Springer %K %P 7-88 %T A Software Framework for Reduced Basis Methods Using DUNE-RB and RBMATLAB %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 and 978-3-642-28588-2

@inproceedings{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 = {2023-08-31T16:40:03.000+0200}, address = {Berlin}, author = {Drohmann, Martin and Haasdonk, Bernard and Ohlberger, Mario}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2419b1c72908b4e7051a60dcda2daed26/puma-wartung}, booktitle = {Advances in DUNE : proceedings of the DUNE User Meeting}, editor = {Dedner, Andreas and Flemisch, Bernd and Klöfkorn, Robert}, eventdate = {2010-10-06/2010-10-08}, eventtitle = {DUNE User Meeting}, interhash = {69fc1b0b66363058ed42912aa2fdfead}, intrahash = {419b1c72908b4e7051a60dcda2daed26}, isbn = {{978-3-642-28589-9} and {978-3-642-28588-2}}, keywords = {}, language = {eng}, pages = {7-88}, publisher = {Springer}, timestamp = {2023-08-31T14:40:03.000+0200}, title = {A Software Framework for Reduced Basis Methods Using DUNE-RB and RBMATLAB}, venue = {Stuttgart}, year = 2012 }