IETI

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.


References in zbMATH (referenced in 28 articles )

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  1. Chan, C. L.; Anitescu, C.; Rabczuk, T.: Isogeometric analysis with strong multipatch $C^1$-coupling (2018)
  2. Hofer, Christoph: Analysis of discontinuous Galerkin dual-primal isogeometric tearing and interconnecting methods (2018)
  3. Pavarino, L. F.; Scacchi, S.; Widlund, O. B.; Zampini, S.: Isogeometric BDDC deluxe preconditioners for linear elasticity (2018)
  4. 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)
  5. Beirão da Veiga, L.; Pavarino, L. F.; Scacchi, S.; Widlund, O. B.; Zampini, S.: Parallel sum primal spaces for isogeometric deluxe BDDC preconditioners (2017)
  6. Donatelli, Marco; Garoni, Carlo; Manni, Carla; Serra-Capizzano, Stefano; Speleers, Hendrik: Symbol-based multigrid methods for Galerkin B-spline isogeometric analysis (2017)
  7. Hofer, Christoph: Parallelization of continuous and discontinuous Galerkin dual-primal isogeometric tearing and interconnecting methods (2017)
  8. Hofreither, Clemens; Takacs, Stefan: Robust multigrid for isogeometric analysis based on stable splittings of spline spaces (2017)
  9. Jüttler, Bert; Kleiss, Stefan K.: Coupling adaptively refined multi-patch spline discretizations via boundary compatibility (2017)
  10. Kapl, Mario; Vitrih, Vito: Space of $C^2$-smooth geometrically continuous isogeometric functions on two-patch geometries (2017)
  11. Beirão da Veiga, L.; Buffa, A.; Sangalli, G.; Vázquez, R.: An introduction to the numerical analysis of isogeometric methods (2016)
  12. Beirão da Veiga, Lourenço; Buffa, Annalisa; Sangalli, Giancarlo; Vázquez, Rafael: An introduction to the numerical analysis of isogeometric methods (2016)
  13. Beirão da Veiga, Lourenço; Pavarino, Luca F.; Scacchi, Simone; Widlund, O. B.; Zampini, Stefano: BDDC deluxe for isogeometric analysis (2016)
  14. Hofer, Christoph; Langer, Ulrich; Toulopoulos, Ioannis: Discontinuous Galerkin isogeometric analysis of elliptic diffusion problems on segmentations with gaps (2016)
  15. Hofreither, Clemens; Zulehner, Walter: On full multigrid schemes for isogeometric analysis (2016)
  16. Langer, Ulrich; Moore, Stephen E.: Discontinuous Galerkin isogeometric analysis of elliptic PDEs on surfaces (2016)
  17. Sangalli, Giancarlo; Tani, Mattia: Isogeometric preconditioners based on fast solvers for the Sylvester equation (2016)
  18. Vázquez, R.: A new design for the implementation of isogeometric analysis in Octave and Matlab: GeoPDEs 3.0 (2016)
  19. Zore, Urška; Jüttler, Bert; Kosinka, Jiří: On the linear independence of truncated hierarchical generating systems (2016)
  20. Kunoth, Angela: Multilevel preconditioning for variational problems (2015)

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