FETI-DP
Encyclopedia
The FETI-DP method is a domain decomposition method
that enforces equality of the solution at subdomain interfaces by Lagrange multipliers
except at subdomain corners, which remain primal variables.The first mathematical analysis of the method was provided by Mandel and Tezaur. The method was further improved by enforcing the equality of averages across the edges or faces on subdomain interfaces which is important for parallel scalability for 3D problems. FETI-DP is a simplification and a better performing version of FETI
. The eigenvalues of FETI-DP are same as those of BDDC
, except for the eigenvalue equal to one, and so the performance of FETI-DP and BDDC is essentially same.
FETI-DP methods are very suitable for high performance parallel computing. A structural simulation using a FETI-DP algorithm and running on 3783 processors of the ASCI White supercomputer was awarded a Gordon Bell price in 2002.
A recent FETI-DP method has scaled to more than 65000 processor cores of the JUGENE supercomputer solving a model problem.
Domain decomposition method
In mathematics, the additive Schwarz method, named after Hermann Schwarz, solves a boundary value problem for a partial differential equation approximately by splitting it into boundary value problems on smaller domains and adding the results.- Overview :...
that enforces equality of the solution at subdomain interfaces by Lagrange multipliers
Lagrange multipliers
In mathematical optimization, the method of Lagrange multipliers provides a strategy for finding the maxima and minima of a function subject to constraints.For instance , consider the optimization problem...
except at subdomain corners, which remain primal variables.The first mathematical analysis of the method was provided by Mandel and Tezaur. The method was further improved by enforcing the equality of averages across the edges or faces on subdomain interfaces which is important for parallel scalability for 3D problems. FETI-DP is a simplification and a better performing version of FETI
FETI
In mathematics, in particular numerical analysis, the FETI method 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,...
. The eigenvalues of FETI-DP are same as those of BDDC
BDDC
In numerical analysis, BDDC is a domain decomposition method for solving large symmetric, positive definite systems of linear equations that arise from the finite element method. BDDC is used as a preconditioner to the conjugate gradient method...
, except for the eigenvalue equal to one, and so the performance of FETI-DP and BDDC is essentially same.
FETI-DP methods are very suitable for high performance parallel computing. A structural simulation using a FETI-DP algorithm and running on 3783 processors of the ASCI White supercomputer was awarded a Gordon Bell price in 2002.
A recent FETI-DP method has scaled to more than 65000 processor cores of the JUGENE supercomputer solving a model problem.