Certified Reduced Basis Method for Affinely Parametric Isogeometric Analysis NURBS Approximation

TL;DR

This paper develops a certified reduced basis method integrated with isogeometric analysis using NURBS for parametrized PDEs, enabling efficient and accurate solutions for geometrically parametrized problems.

Contribution

It introduces a novel combination of affine NURBS-based IGA with reduced basis methods, providing a complete pipeline from CAD to certified reduced order solutions.

Findings

Successful certification of accuracy for parametric PDEs using NURBS IGA

Integration of IGA formulation with greedy reduced basis algorithms

Demonstrated efficiency for geometrically parametrized problems

Abstract

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.