The FETI-DP method is a
domain decomposition method
In mathematics, numerical analysis, and numerical partial differential equations, domain decomposition methods solve a boundary value problem by splitting it into smaller boundary value problems on subdomains and iterating to coordinate the solu ...
[C. Farhat, M. Lesoinne, P. LeTallec, K. Pierson, and D. Rixen, ''FETI-DP: a dual-primal unified FETI method. I. A faster alternative to the two-level FETI method'', Internat. J. Numer. Methods Engrg., 50 (2001), pp. 1523--1544.
] that enforces equality of the solution at subdomain interfaces by
Lagrange multipliers
In mathematical optimization, the method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function subject to equality constraints (i.e., subject to the condition that one or more equations have to be satisfied ex ...
except at subdomain corners, which remain primal variables. The first mathematical analysis of the method was provided by Mandel and Tezaur.
[J. Mandel and R. Tezaur, ''On the convergence of a dual-primal substructuring method'', Numerische Mathematik, 88 (2001), pp. 543--558.] The method was further improved by enforcing the equality of averages across the edges or faces on subdomain interfaces
[C. Farhat, M. Lesoinne, and K. Pierson, ''A scalable dual-primal domain decomposition method'', Numer. Linear Algebra Appl., 7 (2000), pp. 687--714. Preconditioning techniques for large sparse matrix problems in industrial applications (Minneapolis, MN, 1999).
][A. Klawonn, O. B. Widlund, and M. Dryja, ''Dual-primal FETI methods for three-dimensional elliptic problems with heterogeneous coefficients'', SIAM J. Numer. Anal., 40 (2002), pp. 159--179.
] 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 In numerical analysis, BDDC (balancing domain decomposition by constraints) 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 prec ...
, except for the eigenvalue equal to one, and so the performance of FETI-DP and BDDC is essentially same.
[J. Mandel, C. R. Dohrmann, and R. Tezaur, ''An algebraic theory for primal and dual substructuring methods by constraints'', Appl. Numer. Math., 54 (2005), pp. 167--193.
]
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 prize in 2002.
[Manoj Bhardwaj, Kendall H. Pierson, Garth Reese, Tim Walsh, David Day, Ken Alvin, James Peery, Charbel Farhat, and Michel Lesoinne. ''Salinas: A scalable software for high performance structural and mechanics simulation. In ACM/IEEE Proceedings of SC02: High Performance Networking and Computing. Gordon Bell Award'', pages 1–19, 2002.
]
A recent FETI-DP method has scaled to more than 65000 processor cores of the JUGENE supercomputer solving a model problem.
[.]
See also
*
BDDC In numerical analysis, BDDC (balancing domain decomposition by constraints) 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 prec ...
*
FETI
References
Domain decomposition methods
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