IETI - Isogeometric Tearing and Interconnecting

Dipl.-Ing. Stefan Kleiss

Jan. 24, 2012, 1:45 p.m. S2 416

Finite Element Tearing and Interconnecting (FETI) methods are a power-
ful 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 decom-
position 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.