%0 Journal Article
%J Computers and Mathematics with Applications
%D 2016
%T Reduced basis method and domain decomposition for elliptic problems in networks and complex parametrized geometries
%A Laura Iapichino
%A Alfio Quarteroni
%A Gianluigi Rozza
%X The aim of this work is to solve parametrized partial differential equations in computational domains represented by networks of repetitive geometries by combining reduced basis and domain decomposition techniques. The main idea behind this approach is to compute once, locally and for few reference shapes, some representative finite element solutions for different values of the parameters and with a set of different suitable boundary conditions on the boundaries: these functions will represent the basis of a reduced space where the global solution is sought for. The continuity of the latter is assured by a classical domain decomposition approach. Test results on Poisson problem show the flexibility of the proposed method in which accuracy and computational time may be tuned by varying the number of reduced basis functions employed, or the set of boundary conditions used for defining locally the basis functions. The proposed approach simplifies the pre-computation of the reduced basis space by splitting the global problem into smaller local subproblems. Thanks to this feature, it allows dealing with arbitrarily complex network and features more flexibility than a classical global reduced basis approximation where the topology of the geometry is fixed.
%B Computers and Mathematics with Applications
%I Elsevier
%V 71
%P 430
%8 01/2016
%G en
%N 1
%1 35187
%2 Mathematics
%4 1
%# MAT/08
%$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2015-11-05T14:59:46Z
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%& 408
%0 Journal Article
%J Comptes Rendus Mathematique
%D 2014
%T An improvement on geometrical parameterizations by transfinite maps
%A Jäggli, C.
%A Laura Iapichino
%A Gianluigi Rozza
%X We present a method to generate a non-affine transfinite map from a given reference domain to a family of deformed domains. The map is a generalization of the Gordon-Hall transfinite interpolation approach. It is defined globally over the reference domain. Once we have computed some functions over the reference domain, the map can be generated by knowing the parametric expressions of the boundaries of the deformed domain. Being able to define a suitable map from a reference domain to a desired deformation is useful for the management of parameterized geometries.
%B Comptes Rendus Mathematique
%V 352
%P 263–268
%G eng
%R 10.1016/j.crma.2013.12.017
%0 Conference Paper
%B ECMI 2014 proceedings
%D 2014
%T Reduced basis method for the Stokes equations in decomposable domains using greedy optimization
%A Laura Iapichino
%A Alfio Quarteroni
%A Gianluigi Rozza
%A Volkwein, Stefan
%B ECMI 2014 proceedings
%P 1–7
%G eng