TY - JOUR
T1 - Reduced basis method and domain decomposition for elliptic problems in networks and complex parametrized geometries
JF - Computers and Mathematics with Applications
Y1 - 2016
A1 - Laura Iapichino
A1 - Alfio Quarteroni
A1 - Gianluigi Rozza
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.
PB - Elsevier
VL - 71
IS - 1
U1 - 35187
U2 - Mathematics
U4 - 1
U5 - MAT/08
ER -
TY - JOUR
T1 - An improvement on geometrical parameterizations by transfinite maps
JF - Comptes Rendus Mathematique
Y1 - 2014
A1 - Jäggli, C.
A1 - Laura Iapichino
A1 - Gianluigi Rozza
AB - 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.
VL - 352
ER -
TY - CONF
T1 - Reduced basis method for the Stokes equations in decomposable domains using greedy optimization
T2 - ECMI 2014 proceedings
Y1 - 2014
A1 - Laura Iapichino
A1 - Alfio Quarteroni
A1 - Gianluigi Rozza
A1 - Volkwein, Stefan
JF - ECMI 2014 proceedings
ER -