FETI

In mathematics, in particular numerical analysis, the FETI method (finite element tearing and interconnect) is an iterative substructuring method for solving systems of linear equations from the finite element method for the solution of elliptic partial differential equations, in particular in computational mechanics[1] In each iteration, FETI requires the solution of a Neumann problem in each substructure and the solution of a coarse problem. The simplest version of FETI with no preconditioner (or only a diagonal preconditioner) in the substructure is scalable with the number of substructures[2] but the condition number grows polynomially with the number of elements per substructure. FETI with a (more expensive) preconditioner consisting of the solution of a Dirichlet problem in each substructure is scalable with the number of substructures and its condition number grows only polylogarithmically with the number of elements per substructure.[3] The coarse space in FETI consists of the nullspace on each substructure.

See also
  • Balancing domain decomposition
  • FETI-DP

References


  1. C. Farhat and F. X. Roux, A method of finite element tearing and interconnecting and its parallel solution algorithm, Internat. J. Numer. Meths. Engrg. 32, 1205-1227 (1991)
  2. Charbel Farhat, Jan Mandel, and François-Xavier Roux, Optimal convergence properties of the FETI domain decomposition method, Comput. Meth. Appl. Mech. Engrg. 115(1994)365-385
  3. J. Mandel and R. Tezaur, On the Convergence of a Substructuring Method with Lagrange multipliers, Numerische Mathematik 73 (1996) 473-487


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