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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. [Copyright &y& Elsevier]

Abstract: While isogeometric analysis has the potential to close the gap between computer aided design and finite element methods, the underlying structure of NURBS (non-uniform rational B-splines) is a weakness when it comes to local refinement. We propose a hybrid method that combines a globally C 1-continuous, piecewise polynomial finite element basis with rational NURBS-mappings in such a way that an isoparametric setting and exact geometry representation are preserved. We define this basis over T-meshes with a hierarchical structure that allows locally restricted refinement. Combined with a state-of-the-art a posteriori error estimator, we present an adaptive refinement procedure. This concept is successfully demonstrated with the Laplace equation, advection–diffusion problems and linear elasticity problems. [Copyright &y& Elsevier]