FETI‐DP: a dual–primal unified FETI method—part I: A faster alternative to the two‐level FETI method

@article{Farhat2001FETIDPAD,
  title={FETI‐DP: a dual–primal unified FETI method—part I: A faster alternative to the two‐level FETI method},
  author={Charbel Farhat and Michel Lesoinne and P. Letallec and Kendall H. Pierson and Daniel Jean Rixen},
  journal={International Journal for Numerical Methods in Engineering},
  year={2001},
  volume={50}
}
  • C. Farhat, M. Lesoinne, D. Rixen
  • Published 10 March 2001
  • Computer Science, Mathematics
  • International Journal for Numerical Methods in Engineering
The FETI method and its two‐level extension (FETI‐2) are two numerically scalable domain decomposition methods with Lagrange multipliers for the iterative solution of second‐order solid mechanics and fourth‐order beam, plate and shell structural problems, respectively.The FETI‐2 method distinguishes itself from the basic or one‐level FETI method by a second set of Lagrange multipliers that are introduced at the subdomain cross‐points to enforce at each iteration the exact continuity of a subset… 
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Optimal convergence properties of the FETI domain decomposition method
A scalable Lagrange multiplier based domain decomposition method for time‐dependent problems
TLDR
It is proved that in the limit for large time steps, the new method converges toward the FETI algorithm for time-independent problems, and it is shown that this new domain decomposition method outperforms the popular direct skyline solver.
DOMAIN DECOMPOSITION METHODS FOR PARALLEL SOLUTION OF SHAPE SENSITIVITY ANALYSIS PROBLEMS
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A two-level iterative method is proposed particularly tailored to solve re-analysis type of problems, where the dual domain decomposition method is incorporated in the preconditioning step of a subdomain global PCG implementation.
Scalable Substructuring by Lagrange Multipliers in Theory and Practice
TLDR
A formulation of the FETI substructuring method as a matrix preconditioning algorithm is presented and it is proved mathematically that solving this coarse problem accomplishes a global exchange of information between the subdomains and results in a method which, for elasticity problems, has a condition number that grows only polylogarithmically.
Analysis Of Lagrange Multiplier Based Domain Decomposition
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The convergence of a substructuring iterative method with Lagrange multipliers known as Finite Element Tearing and Interconnecting (FETI) method is analyzed in this thesis, showing optimal properties hold for numerous plate bending elements that are used in practice including the HCT, DKT, and a class of non-locking elements for the Reissner-Mindlin plate models.
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Summary. We present a Lagrange multiplier based two-level domain decomposition method for solving iteratively large-scale systems of equations arising from the finite element discretization of
A scalable dual-primal domain decomposition method
We blend dual and primal domain decomposition approaches to construct a fast iterative method for the solution of large-scale systems of equations arising from the finite element discretization of
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