FETI
Encyclopedia
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
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 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. The coarse space in FETI consists of the nullspace on each substructure.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, in particular numerical analysis
Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical 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
Finite element method
The finite element method is a numerical technique for finding approximate solutions of partial differential equations as well as integral equations...
for the solution of elliptic partial differential equations, in particular in computational mechanics
Computational mechanics
Computational mechanics is the discipline concerned with the use of computational methods to study phenomena governed by the principles of mechanics. Before the emergence of computational science as a "third way" besides theoretical and experimental sciences, computational mechanics was widely...
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 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
Dirichlet problem
In mathematics, a Dirichlet problem is the problem of finding a function which solves a specified partial differential equation in the interior of a given region that takes prescribed values on the boundary of the region....
in each substructure is scalable with the number of substructures and its condition number grows only polylogarithmically with the number of elements per substructure. The coarse space in FETI consists of the nullspace on each substructure.