title: IETI - Isogeometric Tearing and Interconnecting.
abstract: Finite Element Tearing and Interconnecting (FETI) methods are a powerful approach to designing solvers for large-scale problems in computational mechanics. The numerical simulation problem is subdivided into a number of independent sub-problems, which are then coupled in appropriate ways. NURBS- (Non-Uniform Rational B-spline) based isogeometric analysis (IGA) applied to complex geometries requires to represent the computational domain as a collection of several NURBS geometries. Since there is a natural decomposition of the computational domain into several subdomains, NURBS-based IGA is particularly well suited for using FETI methods. This paper proposes the new IsogEometric Tearing and Interconnecting (IETI) method, which combines the advanced solver design of FETI with the exact geometry representation of IGA. We describe the IETI framework for two classes of simple model problems (Poisson and linearized elasticity) and discuss the coupling of the subdomains along interfaces (both for matching interfaces and for interfaces with T-joints, i.e. hanging nodes). Special attention is paid to the construction of a suitable preconditioner for the iterative linear solver used for the interface problem. We report several computational experiments to demonstrate the performance of the proposed IETI method.
authors: Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenberger Straße 69, A-4040 Linz, Austria.
authors: Stefan K
authors: SK
authors: Kleiss
authors: Institute of Computational Mathematics, Johannes Kepler University Linz, Altenberger Straße 69, A-4040 Linz, Austria.
authors: Clemens
authors: C
authors: Pechstein
authors: Institute of Applied Geometry, Johannes Kepler University Linz, Altenberger Straße 69, A-4040 Linz, Austria.
authors: Bert
authors: B
authors: Jüttler
authors: Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenberger Straße 69, A-4040 Linz, Austria.
authors: Satyendra
authors: S
authors: Tomar
keywords: Domain decomposition; FETI; IETI; Isogeometric analysis; NURBS