%0 Book Section %B Spectral and High Order Methods for Partial Differential Equations %D 2017 %T Certified Reduced Basis Method for Affinely Parametric Isogeometric Analysis NURBS Approximation %A Denis Devaud %A Gianluigi Rozza %X
In this work we apply reduced basis methods for parametric PDEs to an isogeometric formulation based on
NURBS. The motivation for this work is an integrated and complete work pipeline from CAD to parametrization
of domain geometry, then from full order to certified reduced basis solution. IsoGeometric Analysis
(IGA) is a growing research theme in scientic computing and computational mechanics, as well as reduced
basis methods for parametric PDEs. Their combination enhances the solution of some class of problems,
especially the ones characterized by parametrized geometries we introduced in this work. For a general
overview on Reduced Basis (RB) methods we recall [7, 15] and on IGA [3]. This work wants to demonstrate
that it is also possible for some class of problems to deal with ane geometrical parametrization combined
with a NURBS IGA formulation. This is what this work brings as original ingredients with respect to other
works dealing with reduced order methods and IGA (set in a non-affine formulation, and using a POD [2]
sampling without certication: see for example for potential flows [12] and for Stokes flows [17]). In this work
we show a certication of accuracy and a complete integration between IGA formulation and parametric
certified greedy RB formulation. Section 2 recalls the abstract setting for parametrized PDEs, Section 3
recalls IGA setting, Section 4 deals with RB formulation, and Section 5 illustrates two numerical examples in heat transfer with different parametrization.
%B Spectral and High Order Methods for Partial Differential Equations %7 Bittencourt, Dumont, Hesthaven. (Eds). %I Springer %C Heildeberg %V 119 %@ 978-3-319-65869-8 %G eng