Albrecht, Felix; Haasdonk, Bernard; Kaulmann, Sven; Ohlberger, Mario The localized reduced basis multiscale method. (English) Zbl 1278.65172 Handlovičová, Angela (ed.) et al., Algoritmy 2012. 19th conference on scientific computing, Vysoké Tatry, Podbanské, Slovakia, September 9–14, 2012. Proceedings of contributed papers and posters. Bratislava: Slovak University of Technology, Faculty of Civil Engineering, Department of Mathematics and Descriptive Geometry (ISBN 978-80-227-3742-5/pbk). 393-403 (2012). Summary: We introduce the Localized Reduced Basis Multiscale (LRBMS) method for parameter dependent heterogeneous elliptic multiscale problems. The LRBMS method brings together ideas from both reduced basis methods to efficiently solve parametrized problems and from multiscale methods in order to deal with complex heterogeneities and large domains. Experiments on 2D and real world 3D data demonstrate the performance of the approach.For the entire collection see [Zbl 1260.00028]. Cited in 1 ReviewCited in 25 Documents MSC: 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35J20 Variational methods for second-order elliptic equations 35B27 Homogenization in context of PDEs; PDEs in media with periodic structure Keywords:heterogeneous elliptic multiscale problems; numerical multiscale schemes; reduced basis methods; model order reduction; flow in porous media PDFBibTeX XMLCite \textit{F. Albrecht} et al., in: Algoritmy 2012. 19th conference on scientific computing, Vysoké Tatry, Podbanské, Slovakia, September 9--14, 2012. Proceedings of contributed papers and posters. Bratislava: Slovak University of Technology, Faculty of Civil Engineering, Department of Mathematics and Descriptive Geometry. 393--403 (2012; Zbl 1278.65172)