01905nas a2200157 4500008004100000245012000041210006900161260002200230300000800252490000700260520128900267100002101556700002201577700002101599856012701620 2016 en d00aReduced basis method and domain decomposition for elliptic problems in networks and complex parametrized geometries0 aReduced basis method and domain decomposition for elliptic probl bElsevierc01/2016 a4300 v713 aThe 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.1 aIapichino, Laura1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/reduced-basis-method-and-domain-decomposition-elliptic-problems-networks-and-complex01082nas a2200145 4500008004100000245007200041210006900113300001400182490000800196520057300204100001600777700002100793700002100814856010100835 2014 eng d00aAn improvement on geometrical parameterizations by transfinite maps0 aimprovement on geometrical parameterizations by transfinite maps a263–2680 v3523 aWe 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.1 aJäggli, C.1 aIapichino, Laura1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/improvement-geometrical-parameterizations-transfinite-maps00566nas a2200133 4500008004100000245010000041210006900141300001000210100002100220700002200241700002100263700002100284856012700305 2014 eng d00aReduced basis method for the Stokes equations in decomposable domains using greedy optimization0 aReduced basis method for the Stokes equations in decomposable do a1–71 aIapichino, Laura1 aQuarteroni, Alfio1 aRozza, Gianluigi1 aVolkwein, Stefan uhttps://www.math.sissa.it/publication/reduced-basis-method-stokes-equations-decomposable-domains-using-greedy-optimization