# 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

## References

- 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)
- 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
- J. Mandel and R. Tezaur, On the Convergence of a Substructuring Method with Lagrange multipliers, Numerische Mathematik 73 (1996) 473-487