TY - JOUR
T1 - Reduced basis method and domain decomposition for elliptic problems in networks and complex parametrized geometries
AU - Iapichino, Laura
AU - Quarteroni, Alfio
AU - Rozza, Gianluigi
PY - 2016
Y1 - 2016
N2 - 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.
AB - 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.
KW - Domain decomposition
KW - Parametrized domains and networks
KW - Parametrized PDEs
KW - Reduced basis method
UR - http://www.scopus.com/inward/record.url?scp=84953897347&partnerID=8YFLogxK
U2 - 10.1016/j.camwa.2015.12.001
DO - 10.1016/j.camwa.2015.12.001
M3 - Article
AN - SCOPUS:84953897347
SN - 0898-1221
VL - 71
SP - 408
EP - 430
JO - Computers & Mathematics with Applications
JF - Computers & Mathematics with Applications
IS - 1
ER -