Certified Reduced Basis Method for Affinely Parametric Isogeometric Analysis NURBS Approximation
For researchers in computational mechanics and scientific computing, this work combines IGA and RB methods with certification, though it is incremental as it applies existing techniques to a specific class of problems.
This work integrates reduced basis methods with isogeometric analysis (IGA) using NURBS for parametric PDEs, demonstrating a certified greedy RB approach for affinely parametrized geometries. The pipeline from CAD to certified reduced basis solution is shown, but no concrete numerical results are provided.
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 scientific 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. This work wants to demonstrate that it is also possible for some class of problems to deal with affine 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. In this work we show a certification of accuracy and a complete integration between IGA formulation and parametric certified greedy RB formulation.