Intelligent Block Iterative Methods

                                  J. Mandel
                     Center for Computational Mathematics
                       University of Colorado at Denver
                            Denver, CO 80217-3364

                                   Abstract

We present several preconditioned conjugate gradient methods for the iterative
solution of the linear, symmetric systems of equations arising from the finite
element method in displacement form, both for the h-version and the p-version.
The preconditioners are based on a decomposition of the solution spaces into
overlapping subspaces and solving separately on each subspace.  A judicious
choice of the subspaces gives good convergence for a uniform mesh.  Local
adaptive techniques are employed to modify the subspaces for real-world
problems with distorted meshes and thin 3D elements.  Computational results on
workstations are presented for solid and shell aircraft structures and up to
over 1,000,000 degrees of freedom and 4GB stiffness matrix.