FETI-DP

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The FETI-DP method is a domain decomposition method by Charbel Farhat and others, ^[1] which 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 ^[2]. The method was further improved by enforcing the equality of averages across the edges or faces on subdomain interfaces^[3]^[4] 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.^[5]

[edit] References

^ 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.
^ J. Mandel and R. Tezaur, On the convergence of a dual-primal substructuring method, Numerische Mathematik, 88 (2001), pp. 543--558.
^ 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.
^ 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.