Abstract: An iterative substructuring method for the system of
linear elasticity in three dimensions is introduced and
analyzed. The pure displacement formulation for compressible
materials is discretized with the spectral element method. The
resulting stiffness matrix is symmetric and positive definite.
The method proposed provides a domain decomposition
preconditioner constructed from local solvers for the interior
of each element, and for each face of the elements and a coarse,
global solver related to the wire basket of the elements. As in
the scalar case, the condition number of the preconditioned
operator is independent of the number of spectral elements and
grows as the square of the logarithm of the spectral degree.