Substructuring by Lagrange multipliers for solids and plates

Jan Mandel and Radek Tezaur*
Center for Computational Mathematics
University of Colorado at Denver
Denver CO 80217-3364

Charbel Farhat
Center for Aerospace Structures
University of Colorado at Boulder
Boulder, CO 80309-0429

We present principles and theoreretical foundation of
a substructuring method for large structural problems. The algorithm
is preconditioned conjugate gradients on a subspace for the dual
problem. The preconditioning is proved asymptotically optimal and the
method is shown to be parallel scalable, i.e., the condition
number is bounded independently of the number of substructures.

For plate problems, a special modification is needed that retains
continuity of the displacement solution at substructure crosspoints,
resulting in an asymptically optimal method.

The results are confirmed by numerical experiments.