02450nas a2200169 4500008004100000020002200041024003400063245010200097210006900199250004300268260002500311490000900336520177800345100001802123700002102141856011802162 2017 eng d a978-3-319-65869-8 aDOI 10.1007/978-3-319-65870-400aCerti fied Reduced Basis Method for Affinely Parametric Isogeometric Analysis NURBS Approximation0 aCerti fied Reduced Basis Method for Affinely Parametric Isogeome aBittencourt, Dumont, Hesthaven. (Eds). aHeildebergbSpringer0 v 1193 a

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.

1 aDevaud, Denis1 aRozza, Gianluigi uhttps://math.sissa.it/publication/certi-fied-reduced-basis-method-affinely-parametric-isogeometric-analysis-nurbs