Iterative substructuring methods for spectral element discretizations of elliptic systems - I: Compressible linear elasticity

An iterative substructuring method for the system of linear elasticity in t hree dimensions is introduced and analyzed. The pure displacement formulati on for compressible materials is discretized with the spectral element meth od. The resulting stiffness matrix is symmetric and positive definite. The proposed method provides a domain decomposition preconditioner constructed from local solvers for the interior of each element and for each face of th e elements and a coarse, global solver related to the wire basket of the el ements. As in the scalar case, the condition number of the preconditioned o perator is independent of the number of spectral elements and grows as the square of the logarithm of the spectral degree.