IETI - Isogeometric tearing and interconnecting. 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.

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  1. Schneckenleitner, Rainer; Takacs, Stefan: Convergence theory for IETI-DP solvers for discontinuous Galerkin isogeometric analysis that is explicit in (h) and (p) (2022)
  2. Schneckenleitner, Rainer; Takacs, Stefan: IETI-DP methods for discontinuous Galerkin multi-patch isogeometric analysis with T-junctions (2022)
  3. Antolin, Pablo; Buffa, Annalisa; Puppi, Riccardo; Wei, Xiaodong: Overlapping multipatch isogeometric method with minimal stabilization (2021)
  4. Bucelli, Michele; Salvador, Matteo; Dede’, Luca; Quarteroni, Alfio: Multipatch isogeometric analysis for electrophysiology: simulation in a human heart (2021)
  5. Cho, D.; Pavarino, L. F.; Scacchi, S.: Overlapping additive Schwarz preconditioners for isogeometric collocation discretizations of linear elasticity (2021)
  6. Widlund, O. B.; Zampini, S.; Scacchi, S.; Pavarino, L. F.: Block FETI-DP/BDDC preconditioners for mixed isogeometric discretizations of three-dimensional almost incompressible elasticity (2021)
  7. Bosy, Michał; Montardini, Monica; Sangalli, Giancarlo; Tani, Mattia: A domain decomposition method for isogeometric multi-patch problems with inexact local solvers (2020)
  8. Cho, Durkbin: Overlapping Schwarz methods for isogeometric analysis based on generalized B-splines (2020)
  9. Cho, Durkbin: Optimal multilevel preconditioners for isogeometric collocation methods (2020)
  10. Gervasio, Paola; Marini, Federico: The INTERNODES method for the treatment of non-conforming multipatch geometries in isogeometric analysis (2020)
  11. Schneckenleitner, Rainer; Takacs, Stefan: Condition number bounds for IETI-DP methods that are explicit in (h) and (p) (2020)
  12. Takacs, Stefan: Fast multigrid solvers for conforming and non-conforming multi-patch isogeometric analysis (2020)
  13. Anitescu, Cosmin; Nguyen, Chuong; Rabczuk, Timon; Zhuang, Xiaoying: Isogeometric analysis for explicit elastodynamics using a dual-basis diagonal mass formulation (2019)
  14. De La Riva, Alvaro Pe; Rodrigo, Carmen; Gaspar, Francisco J.: A robust multigrid solver for isogeometric analysis based on multiplicative Schwarz smoothers (2019)
  15. de Prenter, F.; Verhoosel, C. V.; van Brummelen, E. H.: Preconditioning immersed isogeometric finite element methods with application to flow problems (2019)
  16. Hirschler, T.; Bouclier, R.; Duval, A.; Elguedj, T.; Morlier, J.: The embedded isogeometric Kirchhoff-Love shell: from design to shape optimization of non-conforming stiffened multipatch structures (2019)
  17. Hofer, Christoph; Langer, Ulrich: Dual-primal isogeometric tearing and interconnecting methods (2019)
  18. Hofer, Christoph; Langer, Ulrich; Toulopoulos, Ioannis: Isogeometric analysis on non-matching segmentation: discontinuous Galerkin techniques and efficient solvers (2019)
  19. Kargaran, S.; Jüttler, B.; Kleiss, S. K.; Mantzaflaris, A.; Takacs, T.: Overlapping multi-patch structures in isogeometric analysis (2019)
  20. Mantzaflaris, Angelos; Scholz, Felix; Toulopoulos, Ioannis: Low-rank space-time decoupled isogeometric analysis for parabolic problems with varying coefficients (2019)

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