Domain decomposition solution schemes for large-scale IGA problems

Abstract

Isogeometric Analysis (IGA) [5] is a promising concept that establishes a close link between the technologies of CAD (computer aided design) and numerical simulation via finite element analysis (FEA). In the IGA framework, the same function spaces, which are used for the geometric representation of the computational domain, are used for the approximation of the problem unknowns. There are several computational geometry technologies that could serve as a basis for IGA with Non-Uniform Rational B-Splines (NURBS) being the most widely adopted due to their popularity in CAD software. In contrast with FEA where there is a very broad spectrum of solution techniques for the fast and efficient solution of the linear or linearized systems that occur [1-4], IGA solution schemes are still an open issue. With respect to domain decomposition techniques, the Isogeometric Tearing and Interconnecting (IETI) [8] method combines the advanced solver design of dual domain decomposition methods with the exact geometry representation of IGA, relying on patches for the subdivision of the domain. In this work, an innovative solution scheme is presented, showcasing greatly enhanced performance when compared to the established and tested solution schemes for IGA and its numerical performance is exhibited in numerical examples.