A scalable substructuring method by Lagrange multipliers for plate bending problems. (English) Zbl 0956.74059

Mandel, Jan; Tezaur, Radek; Farhat, Charbel

SIAM J. Numer. Anal. 36, No. 5, 1370-1391 (1999).

The authors present a Lagrange multiplier-based method for solving iteratively systems of equations arising from finite element discretizations of plate bending problems. The main idea is to apply the nonoverlapping domain decomposition methodology, and to enforce the continuity of the approximate solution at the subdomain cross-points through the iterations by adding the corresponding Lagrange multipliers to the coarse problem. Thus the new method can be considered as an extension of the FETI method to the nonoverlapping case. Computational results presented for bending of square plates confirm theoretically established convergence properties.

Reviewer: Oleg Titow (Berlin)

MSC:

74S05	Finite element methods applied to problems in solid mechanics
74K20	Plates
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N55	Multigrid methods; domain decomposition for boundary value problems involving PDEs
65F10	Iterative numerical methods for linear systems

Keywords:

biharmonic equation; parallel computing; substructuring; duality; iterative solver; plate bending; nonoverlapping domain decomposition; Lagrange multipliers; FETI method; square plates; convergence