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. Gervasio, Paola; Marini, Federico: The INTERNODES method for the treatment of non-conforming multipatch geometries in isogeometric analysis (2020)
  2. Anitescu, Cosmin; Nguyen, Chuong; Rabczuk, Timon; Zhuang, Xiaoying: Isogeometric analysis for explicit elastodynamics using a dual-basis diagonal mass formulation (2019)
  3. De La Riva, Alvaro Pe; Rodrigo, Carmen; Gaspar, Francisco J.: A robust multigrid solver for isogeometric analysis based on multiplicative Schwarz smoothers (2019)
  4. de Prenter, F.; Verhoosel, C. V.; van Brummelen, E. H.: Preconditioning immersed isogeometric finite element methods with application to flow problems (2019)
  5. 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)
  6. Hofer, Christoph; Langer, Ulrich: Dual-primal isogeometric tearing and interconnecting methods (2019)
  7. Hofer, Christoph; Langer, Ulrich; Toulopoulos, Ioannis: Isogeometric analysis on non-matching segmentation: discontinuous Galerkin techniques and efficient solvers (2019)
  8. Kargaran, S.; Jüttler, B.; Kleiss, S. K.; Mantzaflaris, A.; Takacs, T.: Overlapping multi-patch structures in isogeometric analysis (2019)
  9. Mantzaflaris, Angelos; Scholz, Felix; Toulopoulos, Ioannis: Low-rank space-time decoupled isogeometric analysis for parabolic problems with varying coefficients (2019)
  10. Chan, C. L.; Anitescu, C.; Rabczuk, T.: Isogeometric analysis with strong multipatch (C^1)-coupling (2018)
  11. Hofer, Christoph: Analysis of discontinuous Galerkin dual-primal isogeometric tearing and interconnecting methods (2018)
  12. Mi, Yongzhen; Zheng, Hui: An interpolation method for coupling non-conforming patches in isogeometric analysis of vibro-acoustic systems (2018)
  13. Pavarino, L. F.; Scacchi, S.; Widlund, O. B.; Zampini, S.: Isogeometric BDDC deluxe preconditioners for linear elasticity (2018)
  14. Stavroulakis, George; Tsapetis, Dimitris; Papadrakakis, Manolis: Non-overlapping domain decomposition solution schemes for structural mechanics isogeometric analysis (2018)
  15. Takacs, Stefan: Robust approximation error estimates and multigrid solvers for isogeometric multi-patch discretizations (2018)
  16. Beirão da Veiga, L.; Pavarino, L. F.; Scacchi, S.; Widlund, O. B.; Zampini, S.: Parallel sum primal spaces for isogeometric deluxe BDDC preconditioners (2017)
  17. Beirão da Veiga, L.; Pavarino, L. F.; Scacchi, S.; Widlund, O. B.; Zampini, S.: Adaptive selection of primal constraints for isogeometric BDDC deluxe preconditioners (2017)
  18. Charawi, Lara Antonella: Isogeometric overlapping Schwarz preconditioners for the bidomain reaction-diffusion system (2017)
  19. Coox, Laurens; Greco, Francesco; Atak, Onur; Vandepitte, Dirk; Desmet, Wim: A robust patch coupling method for NURBS-based isogeometric analysis of non-conforming multipatch surfaces (2017)
  20. Coox, Laurens; Maurin, Florian; Greco, Francesco; Deckers, Elke; Vandepitte, Dirk; Desmet, Wim: A flexible approach for coupling NURBS patches in rotationless isogeometric analysis of Kirchhoff-Love shells (2017)

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