SISSA Preprints

Reduced basis method and domain decomposition for elliptic problems in networks and complex parametrized geometries

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dc.contributor.advisor
dc.contributor.author Iapichino, Laura
dc.contributor.author Quarteroni, Alfio
dc.contributor.author Rozza, Gianluigi
dc.date.accessioned 2015-11-09T14:58:00Z
dc.date.available 2015-11-09T14:58:00Z
dc.date.issued 2015
dc.identifier.uri http://preprints.sissa.it/xmlui/handle/1963/34964
dc.description.abstract 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. en_US
dc.language.iso en en_US
dc.subject reduced basis methods en_US
dc.subject interfaces en_US
dc.subject parametrized networks en_US
dc.subject elliptic coercive operators en_US
dc.subject educed basis element method en_US
dc.title Reduced basis method and domain decomposition for elliptic problems in networks and complex parametrized geometries en_US
dc.type Preprint en_US
dc.subject.miur MAT/08 en_US
dc.miur.area 1 en_US
dc.contributor.area Mathematics en_US


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